<?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>nsmr_to_aK1.out</source>

<heading><![CDATA[
Prover9 (64) version 2022-12A (+ restricted para), January 2023.
Process 113672 was started by veroff on b146-16,
Sat Mar 14 13:51:58 2026
The command was "prover9 -f nsmr_to_aK1.in".
]]></heading>

<proof number="1" length="19393" max_count="61">

<comments><![CDATA[
% Proof 1 at 5496.39 (+ 318.26) seconds: "aK1".
% Length of proof: 19393 (0 new hints)
% Level of proof: 869
% Maximum clause weight: 61.000
% Given clauses in run: 20278
% Given clauses in proof: 19376 (0 new hints)
]]></comments>

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

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

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

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

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

  <clause id="6" type="goal">
    <literal><![CDATA[
      a(K(x,y),z,u) = 1
    ]]></literal>
    <attribute><![CDATA[
      label("aK1")
    ]]></attribute>
    <attribute><![CDATA[
      label(non_clause)
    ]]></attribute>
    <attribute><![CDATA[
      label(goal)
    ]]></attribute>
    <justification jstring="[goal].">
      <j1 rule="goal"/>
    </justification>
  </clause>

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

  <clause id="8" type="assumption">
    <literal><![CDATA[
      x * 1 = x
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="9" type="assumption">
    <literal><![CDATA[
      x \ (x * y) = y
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

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

  <clause id="11" type="assumption">
    <literal><![CDATA[
      (x * y) / y = x
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

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

  <clause id="13" 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="14">
    <literal><![CDATA[
      a(x,y,z) = (x * (y * z)) \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[copy(13),flip(a)].">
      <j1 rule="copy" parents="13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15" 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="16">
    <literal><![CDATA[
      K(x,y) = (y * x) \ (x * y)
    ]]></literal>
    <justification jstring="[copy(15),flip(a)].">
      <j1 rule="copy" parents="15"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17" type="assumption">
    <literal><![CDATA[
      (x * y) \ (x * (y * z)) = L(z,y,x)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="18">
    <literal><![CDATA[
      L(x,y,z) = (z * y) \ (z * (y * x))
    ]]></literal>
    <justification jstring="[copy(17),flip(a)].">
      <j1 rule="copy" parents="17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

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

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

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

  <clause id="22">
    <literal><![CDATA[
      T(x,y) = y \ (x * 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[
      T(T(x,y),z) = T(T(x,z),y)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="24" 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="25">
    <literal><![CDATA[
      L(T(x,y),z,u) = T(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[copy(24),flip(a)].">
      <j1 rule="copy" parents="24"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26" 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="27">
    <literal><![CDATA[
      R(T(x,y),z,u) = T(R(x,z,u),y)
    ]]></literal>
    <justification jstring="[copy(26),flip(a)].">
      <j1 rule="copy" parents="26"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28" 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="29">
    <literal><![CDATA[
      R(L(x,y,z),u,w) = L(R(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[copy(28),flip(a)].">
      <j1 rule="copy" parents="28"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30" 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="31" 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="32" type="assumption">
    <literal><![CDATA[
      (x * (y * y)) * z = x * ((y * y) * z)
    ]]></literal>
    <attribute><![CDATA[
      label("NucSq_m")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="33" type="assumption">
    <literal><![CDATA[
      (x * y) * (z * z) = x * (y * (z * z))
    ]]></literal>
    <attribute><![CDATA[
      label("NucSq_r")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="34" 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="35" 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="36" 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="37" 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="38" 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="39" 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="40" 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="41" 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="42" 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="43" 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="44" 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="45" 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="46" 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="47" 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="48" 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="49" 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="50" 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="51" 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="52" type="clausify">
    <literal><![CDATA[
      a(x,y,z) != 1
    ]]></literal>
    <literal><![CDATA[
      L(z,y,x) = z
    ]]></literal>
    <justification jstring="[clausify(1)].">
      <j1 rule="clausify" parents="1"/>
    </justification>
  </clause>

  <clause id="53" type="clausify">
    <literal><![CDATA[
      L(x,y,z) != x
    ]]></literal>
    <literal><![CDATA[
      a(z,y,x) = 1
    ]]></literal>
    <justification jstring="[clausify(2)].">
      <j1 rule="clausify" parents="2"/>
    </justification>
  </clause>

  <clause id="54" type="clausify">
    <literal><![CDATA[
      T(x,y) != x
    ]]></literal>
    <literal><![CDATA[
      T(y,x) = y
    ]]></literal>
    <justification jstring="[clausify(3)].">
      <j1 rule="clausify" parents="3"/>
    </justification>
  </clause>

  <clause id="55" type="clausify">
    <literal><![CDATA[
      T(x,y) != x
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = 1
    ]]></literal>
    <justification jstring="[clausify(4)].">
      <j1 rule="clausify" parents="4"/>
    </justification>
  </clause>

  <clause id="56" type="clausify">
    <literal><![CDATA[
      K(x,y) != 1
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = x
    ]]></literal>
    <justification jstring="[clausify(5)].">
      <j1 rule="clausify" parents="5"/>
    </justification>
  </clause>

  <clause id="57" 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="58" 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="59" 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="61" 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="62" 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="63" 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="64" type="deny">
    <literal><![CDATA[
      a(K(c1,c2),c3,c4) != 1
    ]]></literal>
    <attribute><![CDATA[
      label("aK1")
    ]]></attribute>
    <attribute><![CDATA[
      answer("aK1")
    ]]></attribute>
    <justification jstring="[deny(6)].">
      <j1 rule="deny" parents="6"/>
    </justification>
  </clause>

  <clause id="65">
    <literal><![CDATA[
      1 \ x = x
    ]]></literal>
    <justification jstring="[para(7(a,1),9(a,1,2))].">
      <j1 rule="para" parents="7 9"/>
    </justification>
  </clause>

  <clause id="66">
    <literal><![CDATA[
      x \ x = 1
    ]]></literal>
    <justification jstring="[para(8(a,1),9(a,1,2))].">
      <j1 rule="para" parents="8 9"/>
    </justification>
  </clause>

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

  <clause id="68">
    <literal><![CDATA[
      (x * (x \ 1)) * y = y
    ]]></literal>
    <justification jstring="[para(10(a,2),7(a,1,1))].">
      <j1 rule="para" parents="10 7"/>
    </justification>
  </clause>

  <clause id="69">
    <literal><![CDATA[
      x * (y * (y \ 1)) = x
    ]]></literal>
    <justification jstring="[para(10(a,2),8(a,1,2))].">
      <j1 rule="para" parents="10 8"/>
    </justification>
  </clause>

  <clause id="70">
    <literal><![CDATA[
      x \ (y * (y \ (x * z))) = z
    ]]></literal>
    <justification jstring="[para(10(a,2),9(a,1,2))].">
      <j1 rule="para" parents="10 9"/>
    </justification>
  </clause>

  <clause id="71">
    <literal><![CDATA[
      x * (y \ (y * (x \ z))) = z
    ]]></literal>
    <justification jstring="[para(9(a,2),10(a,1,2))].">
      <j1 rule="para" parents="9 10"/>
    </justification>
  </clause>

  <clause id="72">
    <literal><![CDATA[
      x * (y * (y \ (x \ z))) = z
    ]]></literal>
    <justification jstring="[para(10(a,2),10(a,1,2))].">
      <j1 rule="para" parents="10 10"/>
    </justification>
  </clause>

  <clause id="73">
    <literal><![CDATA[
      x / x = 1
    ]]></literal>
    <justification jstring="[para(7(a,1),11(a,1,1))].">
      <j1 rule="para" parents="7 11"/>
    </justification>
  </clause>

  <clause id="74">
    <literal><![CDATA[
      x / 1 = x
    ]]></literal>
    <justification jstring="[para(8(a,1),11(a,1,1))].">
      <j1 rule="para" parents="8 11"/>
    </justification>
  </clause>

  <clause id="75">
    <literal><![CDATA[
      x * (((x \ y) * z) / z) = y
    ]]></literal>
    <justification jstring="[para(11(a,2),10(a,1,2))].">
      <j1 rule="para" parents="11 10"/>
    </justification>
  </clause>

  <clause id="76">
    <literal><![CDATA[
      x / (y \ x) = y
    ]]></literal>
    <justification jstring="[para(10(a,1),11(a,1,1))].">
      <j1 rule="para" parents="10 11"/>
    </justification>
  </clause>

  <clause id="77">
    <literal><![CDATA[
      ((1 / x) * x) * y = y
    ]]></literal>
    <justification jstring="[para(12(a,2),7(a,1,1))].">
      <j1 rule="para" parents="12 7"/>
    </justification>
  </clause>

  <clause id="78">
    <literal><![CDATA[
      x * ((1 / y) * y) = x
    ]]></literal>
    <justification jstring="[para(12(a,2),8(a,1,2))].">
      <j1 rule="para" parents="12 8"/>
    </justification>
  </clause>

  <clause id="79">
    <literal><![CDATA[
      (x / y) \ x = y
    ]]></literal>
    <justification jstring="[para(12(a,1),9(a,1,2))].">
      <j1 rule="para" parents="12 9"/>
    </justification>
  </clause>

  <clause id="80">
    <literal><![CDATA[
      (x \ (x * (y / z))) * z = y
    ]]></literal>
    <justification jstring="[para(9(a,2),12(a,1,1))].">
      <j1 rule="para" parents="9 12"/>
    </justification>
  </clause>

  <clause id="81">
    <literal><![CDATA[
      ((x * (x \ y)) / z) * z = y
    ]]></literal>
    <justification jstring="[para(12(a,2),10(a,1))].">
      <j1 rule="para" parents="12 10"/>
    </justification>
  </clause>

  <clause id="82">
    <literal><![CDATA[
      (((x * y) / z) * z) / y = x
    ]]></literal>
    <justification jstring="[para(12(a,2),11(a,1,1))].">
      <j1 rule="para" parents="12 11"/>
    </justification>
  </clause>

  <clause id="83">
    <literal><![CDATA[
      (((x / y) / z) * z) * y = x
    ]]></literal>
    <justification jstring="[para(12(a,2),12(a,1,1))].">
      <j1 rule="para" parents="12 12"/>
    </justification>
  </clause>

  <clause id="84">
    <literal><![CDATA[
      (x * (y * z)) * a(x,y,z) = (x * y) * z
    ]]></literal>
    <justification jstring="[para(14(a,2),10(a,1,2))].">
      <j1 rule="para" parents="14 10"/>
    </justification>
  </clause>

  <clause id="85">
    <literal><![CDATA[
      (x * ((x \ y) * z)) \ (y * z) = a(x,x \ y,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),14(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="86">
    <literal><![CDATA[
      (x * y) \ ((x * (y / z)) * z) = a(x,y / z,z)
    ]]></literal>
    <justification jstring="[para(12(a,1),14(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="12 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="87">
    <literal><![CDATA[
      ((x / y) * (y * z)) \ (x * z) = a(x / y,y,z)
    ]]></literal>
    <justification jstring="[para(12(a,1),14(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="12 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="88">
    <literal><![CDATA[
      (x * y) * K(y,x) = y * x
    ]]></literal>
    <justification jstring="[para(16(a,2),10(a,1,2))].">
      <j1 rule="para" parents="16 10"/>
    </justification>
  </clause>

  <clause id="89">
    <literal><![CDATA[
      x \ ((y \ x) * y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),16(a,2,1)),flip(a)].">
      <j1 rule="para" parents="10 16"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="90">
    <literal><![CDATA[
      ((x \ y) * x) \ y = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),16(a,2,2)),flip(a)].">
      <j1 rule="para" parents="10 16"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="91">
    <literal><![CDATA[
      x \ (y * (x / y)) = K(y,x / y)
    ]]></literal>
    <justification jstring="[para(12(a,1),16(a,2,1)),flip(a)].">
      <j1 rule="para" parents="12 16"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="92">
    <literal><![CDATA[
      (x * (y / x)) \ y = K(y / x,x)
    ]]></literal>
    <justification jstring="[para(12(a,1),16(a,2,2)),flip(a)].">
      <j1 rule="para" parents="12 16"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="93">
    <literal><![CDATA[
      K(x * x,x) = a(x,x,x)
    ]]></literal>
    <justification jstring="[para(16(a,2),14(a,2)),flip(a)].">
      <j1 rule="para" parents="16 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="94">
    <literal><![CDATA[
      x \ (1 * (x * y)) = L(y,x,1)
    ]]></literal>
    <justification jstring="[para(7(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="7 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="95">
    <literal><![CDATA[
      (x * 1) \ (x * y) = L(y,1,x)
    ]]></literal>
    <justification jstring="[para(7(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="7 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="96">
    <literal><![CDATA[
      (x * y) \ (x * y) = L(1,y,x)
    ]]></literal>
    <justification jstring="[para(8(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="8 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="97">
    <literal><![CDATA[
      (x * y) * L(z,y,x) = x * (y * z)
    ]]></literal>
    <justification jstring="[para(18(a,2),10(a,1,2))].">
      <j1 rule="para" parents="18 10"/>
    </justification>
  </clause>

  <clause id="98">
    <literal><![CDATA[
      x \ (y * ((y \ x) * z)) = L(z,y \ x,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="10 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="99">
    <literal><![CDATA[
      L(x \ y,x,z) = (z * x) \ (z * y)
    ]]></literal>
    <justification jstring="[para(10(a,1),18(a,2,2,2))].">
      <j1 rule="para" parents="10 18"/>
    </justification>
  </clause>

  <clause id="100">
    <literal><![CDATA[
      x \ ((x / y) * (y * z)) = L(z,y,x / y)
    ]]></literal>
    <justification jstring="[para(12(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="12 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="101">
    <literal><![CDATA[
      L(x,y / x,z) = (z * (y / x)) \ (z * y)
    ]]></literal>
    <justification jstring="[para(12(a,1),18(a,2,2,2))].">
      <j1 rule="para" parents="12 18"/>
    </justification>
  </clause>

  <clause id="102">
    <literal><![CDATA[
      L(x,y,z / (y * x)) = ((z / (y * x)) * y) \ z
    ]]></literal>
    <justification jstring="[para(12(a,1),18(a,2,2))].">
      <j1 rule="para" parents="12 18"/>
    </justification>
  </clause>

  <clause id="103">
    <literal><![CDATA[
      (x * y) / (x * y) = R(1,x,y)
    ]]></literal>
    <justification jstring="[para(7(a,1),20(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="7 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="104">
    <literal><![CDATA[
      R(x,x \ y,z) = (y * z) / ((x \ y) * z)
    ]]></literal>
    <justification jstring="[para(10(a,1),20(a,2,1,1))].">
      <j1 rule="para" parents="10 20"/>
    </justification>
  </clause>

  <clause id="105">
    <literal><![CDATA[
      R(x,y,(x * y) \ z) = z / (y * ((x * y) \ z))
    ]]></literal>
    <justification jstring="[para(10(a,1),20(a,2,1))].">
      <j1 rule="para" parents="10 20"/>
    </justification>
  </clause>

  <clause id="106">
    <literal><![CDATA[
      ((x * y) * (y \ z)) / z = R(x,y,y \ z)
    ]]></literal>
    <justification jstring="[para(10(a,1),20(a,2,2)),flip(a)].">
      <j1 rule="para" parents="10 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="107">
    <literal><![CDATA[
      R(x,y,z) * (y * z) = (x * y) * z
    ]]></literal>
    <justification jstring="[para(20(a,2),12(a,1,1))].">
      <j1 rule="para" parents="20 12"/>
    </justification>
  </clause>

  <clause id="108">
    <literal><![CDATA[
      R(x / y,y,z) = (x * z) / (y * z)
    ]]></literal>
    <justification jstring="[para(12(a,1),20(a,2,1,1))].">
      <j1 rule="para" parents="12 20"/>
    </justification>
  </clause>

  <clause id="109">
    <literal><![CDATA[
      ((x * (y / z)) * z) / y = R(x,y / z,z)
    ]]></literal>
    <justification jstring="[para(12(a,1),20(a,2,2)),flip(a)].">
      <j1 rule="para" parents="12 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="110">
    <literal><![CDATA[
      T(x,x) = x
    ]]></literal>
    <justification jstring="[para(22(a,2),9(a,1))].">
      <j1 rule="para" parents="22 9"/>
    </justification>
  </clause>

  <clause id="111">
    <literal><![CDATA[
      x * T(y,x) = y * x
    ]]></literal>
    <justification jstring="[para(22(a,2),10(a,1,2))].">
      <j1 rule="para" parents="22 10"/>
    </justification>
  </clause>

  <clause id="112">
    <literal><![CDATA[
      T(x,x \ y) = (x \ y) \ y
    ]]></literal>
    <justification jstring="[para(10(a,1),22(a,2,2))].">
      <j1 rule="para" parents="10 22"/>
    </justification>
  </clause>

  <clause id="113">
    <literal><![CDATA[
      T(x / y,y) = y \ x
    ]]></literal>
    <justification jstring="[para(12(a,1),22(a,2,2))].">
      <j1 rule="para" parents="12 22"/>
    </justification>
  </clause>

  <clause id="114">
    <literal><![CDATA[
      T(x,x * x) = L(x,x,x)
    ]]></literal>
    <justification jstring="[para(22(a,2),18(a,2)),flip(a)].">
      <j1 rule="para" parents="22 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="115">
    <literal><![CDATA[
      x \ (T(y,z) * x) = T(T(y,x),z)
    ]]></literal>
    <justification jstring="[para(23(a,1),22(a,1)),flip(a)].">
      <j1 rule="para" parents="23 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="116">
    <literal><![CDATA[
      T(T(T(x,y),z),u) = T(T(T(x,u),y),z)
    ]]></literal>
    <justification jstring="[para(23(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="23 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="117">
    <literal><![CDATA[
      T(T(R(x,y,z),u),w) = T(R(T(x,w),y,z),u)
    ]]></literal>
    <justification jstring="[para(27(a,2),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="27 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="118">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      1 * z != y
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(7(a,1),34(a,1))].">
      <j1 rule="para" parents="7 34"/>
    </justification>
  </clause>

  <clause id="119">
    <literal><![CDATA[
      1 * x != y
    ]]></literal>
    <literal><![CDATA[
      z != y
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(7(a,1),34(b,1))].">
      <j1 rule="para" parents="7 34"/>
    </justification>
  </clause>

  <clause id="120">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      x * z != y
    ]]></literal>
    <literal><![CDATA[
      1 = z
    ]]></literal>
    <justification jstring="[para(8(a,1),34(a,1))].">
      <j1 rule="para" parents="8 34"/>
    </justification>
  </clause>

  <clause id="121">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z * u != y
    ]]></literal>
    <literal><![CDATA[
      z \ x = u
    ]]></literal>
    <justification jstring="[para(10(a,1),34(a,1))].">
      <j1 rule="para" parents="10 34"/>
    </justification>
  </clause>

  <clause id="122">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z * x != y
    ]]></literal>
    <literal><![CDATA[
      1 = z
    ]]></literal>
    <justification jstring="[para(7(a,1),35(a,1))].">
      <j1 rule="para" parents="7 35"/>
    </justification>
  </clause>

  <clause id="123">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z * u != y
    ]]></literal>
    <literal><![CDATA[
      x / u = z
    ]]></literal>
    <justification jstring="[para(12(a,1),35(a,1))].">
      <j1 rule="para" parents="12 35"/>
    </justification>
  </clause>

  <clause id="124">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      (x * z) / u != y
    ]]></literal>
    <literal><![CDATA[
      z = u
    ]]></literal>
    <justification jstring="[para(11(a,1),36(a,1))].">
      <j1 rule="para" parents="11 36"/>
    </justification>
  </clause>

  <clause id="125">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z / u != y
    ]]></literal>
    <literal><![CDATA[
      x * u = z
    ]]></literal>
    <justification jstring="[para(11(a,1),37(a,1))].">
      <j1 rule="para" parents="11 37"/>
    </justification>
  </clause>

  <clause id="126">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z \ u != y
    ]]></literal>
    <literal><![CDATA[
      z * x = u
    ]]></literal>
    <justification jstring="[para(9(a,1),38(a,1))].">
      <j1 rule="para" parents="9 38"/>
    </justification>
  </clause>

  <clause id="127">
    <literal><![CDATA[
      1 * x != y
    ]]></literal>
    <literal><![CDATA[
      x = y
    ]]></literal>
    <justification jstring="[para(7(a,1),43(a,2))].">
      <j1 rule="para" parents="7 43"/>
    </justification>
  </clause>

  <clause id="128">
    <literal><![CDATA[
      x * y != x
    ]]></literal>
    <literal><![CDATA[
      1 = y
    ]]></literal>
    <justification jstring="[para(8(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="8 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="129">
    <literal><![CDATA[
      x * y != z
    ]]></literal>
    <literal><![CDATA[
      x \ z = y
    ]]></literal>
    <justification jstring="[para(10(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="10 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="130">
    <literal><![CDATA[
      x * (x \ (y * z)) != y * u
    ]]></literal>
    <literal><![CDATA[
      u = z
    ]]></literal>
    <justification jstring="[para(10(a,2),43(a,2)),flip(a)].">
      <j1 rule="para" parents="10 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="131">
    <literal><![CDATA[
      (x / y) * z != x
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(12(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="12 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="132">
    <literal><![CDATA[
      ((x * y) / z) * z != x * u
    ]]></literal>
    <literal><![CDATA[
      y = u
    ]]></literal>
    <justification jstring="[para(12(a,2),43(a,1))].">
      <j1 rule="para" parents="12 43"/>
    </justification>
  </clause>

  <clause id="134">
    <literal><![CDATA[
      x * 1 != y
    ]]></literal>
    <literal><![CDATA[
      y = x
    ]]></literal>
    <justification jstring="[para(8(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="8 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="135">
    <literal><![CDATA[
      x * 1 != y
    ]]></literal>
    <literal><![CDATA[
      x = y
    ]]></literal>
    <justification jstring="[para(8(a,1),44(a,2))].">
      <j1 rule="para" parents="8 44"/>
    </justification>
  </clause>

  <clause id="136">
    <literal><![CDATA[
      x \ (x * (y * z)) != u * z
    ]]></literal>
    <literal><![CDATA[
      y = u
    ]]></literal>
    <justification jstring="[para(9(a,2),44(a,1))].">
      <j1 rule="para" parents="9 44"/>
    </justification>
  </clause>

  <clause id="137">
    <literal><![CDATA[
      x * (y \ z) != z
    ]]></literal>
    <literal><![CDATA[
      x = y
    ]]></literal>
    <justification jstring="[para(10(a,1),44(a,2))].">
      <j1 rule="para" parents="10 44"/>
    </justification>
  </clause>

  <clause id="138">
    <literal><![CDATA[
      x * y != z
    ]]></literal>
    <literal><![CDATA[
      z / y = x
    ]]></literal>
    <justification jstring="[para(12(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="12 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="139">
    <literal><![CDATA[
      (x * y) / z != x
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(11(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="11 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="140">
    <literal><![CDATA[
      x / y != z
    ]]></literal>
    <literal><![CDATA[
      z * y = x
    ]]></literal>
    <justification jstring="[para(11(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="11 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="141">
    <literal><![CDATA[
      R(x,y,z) != u / (y * z)
    ]]></literal>
    <literal><![CDATA[
      (x * y) * z = u
    ]]></literal>
    <justification jstring="[para(20(a,2),46(a,1))].">
      <j1 rule="para" parents="20 46"/>
    </justification>
  </clause>

  <clause id="142">
    <literal><![CDATA[
      x \ y != z
    ]]></literal>
    <literal><![CDATA[
      x * z = y
    ]]></literal>
    <justification jstring="[para(9(a,1),47(a,1)),flip(a)].">
      <j1 rule="para" parents="9 47"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="143">
    <literal><![CDATA[
      T(x,y) != y \ z
    ]]></literal>
    <literal><![CDATA[
      x * y = z
    ]]></literal>
    <justification jstring="[para(22(a,2),47(a,1))].">
      <j1 rule="para" parents="22 47"/>
    </justification>
  </clause>

  <clause id="144">
    <literal><![CDATA[
      x \ (y * z) != z
    ]]></literal>
    <literal><![CDATA[
      y = x
    ]]></literal>
    <justification jstring="[para(9(a,1),48(a,1)),flip(a)].">
      <j1 rule="para" parents="9 48"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="145">
    <literal><![CDATA[
      x \ ((y * z) * u) != a(y,z,u)
    ]]></literal>
    <literal><![CDATA[
      y * (z * u) = x
    ]]></literal>
    <justification jstring="[para(14(a,2),48(a,1)),flip(a)].">
      <j1 rule="para" parents="14 48"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="147">
    <literal><![CDATA[
      T(T(x,y),z) != T(u,y)
    ]]></literal>
    <literal><![CDATA[
      T(x,z) = u
    ]]></literal>
    <justification jstring="[para(23(a,1),49(a,1))].">
      <j1 rule="para" parents="23 49"/>
    </justification>
  </clause>

  <clause id="148">
    <literal><![CDATA[
      T(x,y) != L(T(z,y),u,w)
    ]]></literal>
    <literal><![CDATA[
      L(z,u,w) = x
    ]]></literal>
    <justification jstring="[para(25(a,2),49(a,1)),flip(a)].">
      <j1 rule="para" parents="25 49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="149">
    <literal><![CDATA[
      T(x,y) != R(T(z,y),u,w)
    ]]></literal>
    <literal><![CDATA[
      R(z,u,w) = x
    ]]></literal>
    <justification jstring="[para(27(a,2),49(a,1)),flip(a)].">
      <j1 rule="para" parents="27 49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="150">
    <literal><![CDATA[
      T(L(x,y,z),u) != L(w,y,z)
    ]]></literal>
    <literal><![CDATA[
      T(x,u) = w
    ]]></literal>
    <justification jstring="[para(25(a,1),50(a,1))].">
      <j1 rule="para" parents="25 50"/>
    </justification>
  </clause>

  <clause id="151">
    <literal><![CDATA[
      T(R(x,y,z),u) != R(w,y,z)
    ]]></literal>
    <literal><![CDATA[
      T(x,u) = w
    ]]></literal>
    <justification jstring="[para(27(a,1),51(a,1))].">
      <j1 rule="para" parents="27 51"/>
    </justification>
  </clause>

  <clause id="152">
    <literal><![CDATA[
      ((x / y) * y) * z = x * z
    ]]></literal>
    <justification jstring="[hyper(57,a,12,a)].">
      <j1 rule="hyper" parents="57 12"/>
    </justification>
  </clause>

  <clause id="153">
    <literal><![CDATA[
      (x * (x \ y)) * z = y * z
    ]]></literal>
    <justification jstring="[hyper(57,a,10,a)].">
      <j1 rule="hyper" parents="57 10"/>
    </justification>
  </clause>

  <clause id="154">
    <literal><![CDATA[
      x * (y * (y \ z)) = x * z
    ]]></literal>
    <justification jstring="[hyper(58,a,10,a)].">
      <j1 rule="hyper" parents="58 10"/>
    </justification>
  </clause>

  <clause id="155">
    <literal><![CDATA[
      x * (y \ (y * z)) = x * z
    ]]></literal>
    <justification jstring="[hyper(58,a,9,a)].">
      <j1 rule="hyper" parents="58 9"/>
    </justification>
  </clause>

  <clause id="156">
    <literal><![CDATA[
      ((x / y) * y) / z = x / z
    ]]></literal>
    <justification jstring="[hyper(59,a,12,a)].">
      <j1 rule="hyper" parents="59 12"/>
    </justification>
  </clause>

  <clause id="157">
    <literal><![CDATA[
      (1 * x) / y = x / y
    ]]></literal>
    <justification jstring="[hyper(59,a,7,a)].">
      <j1 rule="hyper" parents="59 7"/>
    </justification>
  </clause>

  <clause id="158">
    <literal><![CDATA[
      (x * (x \ y)) \ z = y \ z
    ]]></literal>
    <justification jstring="[hyper(61,a,10,a)].">
      <j1 rule="hyper" parents="61 10"/>
    </justification>
  </clause>

  <clause id="159">
    <literal><![CDATA[
      (x * y) / y = (x / z) * z
    ]]></literal>
    <justification jstring="[hyper(63,a,12,a,b,11,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="63 12 11"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="160">
    <literal><![CDATA[
      (x / y) * y = x * 1
    ]]></literal>
    <justification jstring="[hyper(63,a,12,a,b,8,a(flip))].">
      <j1 rule="hyper" parents="63 12 8"/>
    </justification>
  </clause>

  <clause id="161">
    <literal><![CDATA[
      (x / y) * y = 1 * x
    ]]></literal>
    <justification jstring="[hyper(63,a,12,a,b,7,a(flip))].">
      <j1 rule="hyper" parents="63 12 7"/>
    </justification>
  </clause>

  <clause id="162">
    <literal><![CDATA[
      (x * y) / y = x * 1
    ]]></literal>
    <justification jstring="[hyper(63,a,11,a,b,8,a(flip))].">
      <j1 rule="hyper" parents="63 11 8"/>
    </justification>
  </clause>

  <clause id="163">
    <literal><![CDATA[
      x \ (x * y) = z * (z \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,10,a,b,9,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="63 10 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="164">
    <literal><![CDATA[
      x * (x \ y) = y * 1
    ]]></literal>
    <justification jstring="[hyper(63,a,10,a,b,8,a(flip))].">
      <j1 rule="hyper" parents="63 10 8"/>
    </justification>
  </clause>

  <clause id="165">
    <literal><![CDATA[
      1 \ (x * 1) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,65,a,b,8,a)].">
      <j1 rule="hyper" parents="63 65 8"/>
    </justification>
  </clause>

  <clause id="166">
    <literal><![CDATA[
      (x * (x \ 1)) \ y = y
    ]]></literal>
    <justification jstring="[para(10(a,2),65(a,1,1))].">
      <j1 rule="para" parents="10 65"/>
    </justification>
  </clause>

  <clause id="167">
    <literal><![CDATA[
      ((1 / x) * x) \ y = y
    ]]></literal>
    <justification jstring="[para(12(a,2),65(a,1,1))].">
      <j1 rule="para" parents="12 65"/>
    </justification>
  </clause>

  <clause id="168">
    <literal><![CDATA[
      1 \ x != y
    ]]></literal>
    <literal><![CDATA[
      y = x
    ]]></literal>
    <justification jstring="[para(65(a,1),47(a,1)),flip(a)].">
      <j1 rule="para" parents="65 47"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="169">
    <literal><![CDATA[
      1 \ x != y
    ]]></literal>
    <literal><![CDATA[
      x = y
    ]]></literal>
    <justification jstring="[para(65(a,1),47(a,2))].">
      <j1 rule="para" parents="65 47"/>
    </justification>
  </clause>

  <clause id="170">
    <literal><![CDATA[
      x \ y != y
    ]]></literal>
    <literal><![CDATA[
      1 = x
    ]]></literal>
    <justification jstring="[para(65(a,1),48(a,1)),flip(a)].">
      <j1 rule="para" parents="65 48"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="171">
    <literal><![CDATA[
      K(x,x) = 1
    ]]></literal>
    <justification jstring="[hyper(63,a,16,a,b,66,a)].">
      <j1 rule="hyper" parents="63 16 66"/>
    </justification>
  </clause>

  <clause id="172">
    <literal><![CDATA[
      (x \ x) * y = y
    ]]></literal>
    <justification jstring="[para(66(a,2),7(a,1,1))].">
      <j1 rule="para" parents="66 7"/>
    </justification>
  </clause>

  <clause id="173">
    <literal><![CDATA[
      x * (y \ y) = x
    ]]></literal>
    <justification jstring="[para(66(a,2),8(a,1,2))].">
      <j1 rule="para" parents="66 8"/>
    </justification>
  </clause>

  <clause id="174">
    <literal><![CDATA[
      (x / x) * y = y
    ]]></literal>
    <justification jstring="[para(73(a,2),7(a,1,1))].">
      <j1 rule="para" parents="73 7"/>
    </justification>
  </clause>

  <clause id="175">
    <literal><![CDATA[
      x / 1 != y
    ]]></literal>
    <literal><![CDATA[
      y = x
    ]]></literal>
    <justification jstring="[para(74(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="74 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="176">
    <literal><![CDATA[
      x / 1 != y
    ]]></literal>
    <literal><![CDATA[
      x = y
    ]]></literal>
    <justification jstring="[para(74(a,1),46(a,2))].">
      <j1 rule="para" parents="74 46"/>
    </justification>
  </clause>

  <clause id="177">
    <literal><![CDATA[
      T(x,R(x,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(42,a,27,a,b,110,a(flip))].">
      <j1 rule="hyper" parents="42 27 110"/>
    </justification>
  </clause>

  <clause id="178">
    <literal><![CDATA[
      T(x,L(x,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(41,a,25,a,b,110,a(flip))].">
      <j1 rule="hyper" parents="41 25 110"/>
    </justification>
  </clause>

  <clause id="179">
    <literal><![CDATA[
      T(T(x,y),x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(110(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="110 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="180">
    <literal><![CDATA[
      T(L(x,y,z),x) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(110(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="110 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="181">
    <literal><![CDATA[
      T(x,y) != y
    ]]></literal>
    <literal><![CDATA[
      y = x
    ]]></literal>
    <justification jstring="[para(110(a,1),49(a,1)),flip(a)].">
      <j1 rule="para" parents="110 49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="182">
    <literal><![CDATA[
      x * K(y,y) = x
    ]]></literal>
    <justification jstring="[para(171(a,2),8(a,1,2))].">
      <j1 rule="para" parents="171 8"/>
    </justification>
  </clause>

  <clause id="183">
    <literal><![CDATA[
      x / (y \ x) = z / (y \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,76,a,b,76,a(flip))].">
      <j1 rule="hyper" parents="63 76 76"/>
    </justification>
  </clause>

  <clause id="184">
    <literal><![CDATA[
      (x * y) / y = z / (x \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,76,a,b,11,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="63 76 11"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="185">
    <literal><![CDATA[
      x / (y \ x) = z * (z \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,76,a,b,10,a(flip))].">
      <j1 rule="hyper" parents="63 76 10"/>
    </justification>
  </clause>

  <clause id="186">
    <literal><![CDATA[
      (x / (y \ x)) * z = y * z
    ]]></literal>
    <justification jstring="[hyper(57,a,76,a)].">
      <j1 rule="hyper" parents="57 76"/>
    </justification>
  </clause>

  <clause id="187">
    <literal><![CDATA[
      R(x,y,z) \ ((x * y) * z) = y * z
    ]]></literal>
    <justification jstring="[hyper(36,a,20,a(flip),b,76,a),flip(a)].">
      <j1 rule="hyper" parents="36 20 76"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="189">
    <literal><![CDATA[
      (x * y) / K(x,y) = y * x
    ]]></literal>
    <justification jstring="[para(16(a,2),76(a,1,2))].">
      <j1 rule="para" parents="16 76"/>
    </justification>
  </clause>

  <clause id="190">
    <literal><![CDATA[
      (x * (y * z)) / L(z,y,x) = x * y
    ]]></literal>
    <justification jstring="[para(18(a,2),76(a,1,2))].">
      <j1 rule="para" parents="18 76"/>
    </justification>
  </clause>

  <clause id="191">
    <literal><![CDATA[
      (x * y) / T(x,y) = y
    ]]></literal>
    <justification jstring="[para(22(a,2),76(a,1,2))].">
      <j1 rule="para" parents="22 76"/>
    </justification>
  </clause>

  <clause id="192">
    <literal><![CDATA[
      x / y != z
    ]]></literal>
    <literal><![CDATA[
      z \ x = y
    ]]></literal>
    <justification jstring="[para(76(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="76 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="193">
    <literal><![CDATA[
      x / (y / ((z \ x) \ y)) = z
    ]]></literal>
    <justification jstring="[para(76(a,2),76(a,1,2))].">
      <j1 rule="para" parents="76 76"/>
    </justification>
  </clause>

  <clause id="194">
    <literal><![CDATA[
      (x / y) \ x = z * (z \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,79,a,b,10,a(flip))].">
      <j1 rule="hyper" parents="63 79 10"/>
    </justification>
  </clause>

  <clause id="195">
    <literal><![CDATA[
      ((x / y) \ x) * z = y * z
    ]]></literal>
    <justification jstring="[hyper(57,a,79,a)].">
      <j1 rule="hyper" parents="57 79"/>
    </justification>
  </clause>

  <clause id="197">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z \ u != y
    ]]></literal>
    <literal><![CDATA[
      u / x = z
    ]]></literal>
    <justification jstring="[para(79(a,1),39(a,1))].">
      <j1 rule="para" parents="79 39"/>
    </justification>
  </clause>

  <clause id="198">
    <literal><![CDATA[
      x \ y != z
    ]]></literal>
    <literal><![CDATA[
      y / z = x
    ]]></literal>
    <justification jstring="[para(79(a,1),48(a,1)),flip(a)].">
      <j1 rule="para" parents="79 48"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="199">
    <literal><![CDATA[
      T(x,1) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,22,a,b,165,a)].">
      <j1 rule="hyper" parents="63 22 165"/>
    </justification>
  </clause>

  <clause id="200">
    <literal><![CDATA[
      K(x,1) = 1
    ]]></literal>
    <justification jstring="[hyper(55,a,199,a)].">
      <j1 rule="hyper" parents="55 199"/>
    </justification>
  </clause>

  <clause id="201">
    <literal><![CDATA[
      T(1,x) = 1
    ]]></literal>
    <justification jstring="[hyper(54,a,199,a)].">
      <j1 rule="hyper" parents="54 199"/>
    </justification>
  </clause>

  <clause id="202">
    <literal><![CDATA[
      T(x,y * (y \ 1)) = x
    ]]></literal>
    <justification jstring="[para(10(a,2),199(a,1,2))].">
      <j1 rule="para" parents="10 199"/>
    </justification>
  </clause>

  <clause id="203">
    <literal><![CDATA[
      T(x,1) != y
    ]]></literal>
    <literal><![CDATA[
      y = x
    ]]></literal>
    <justification jstring="[para(199(a,1),49(a,1)),flip(a)].">
      <j1 rule="para" parents="199 49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="204">
    <literal><![CDATA[
      T(x,y \ y) = x
    ]]></literal>
    <justification jstring="[para(66(a,2),199(a,1,2))].">
      <j1 rule="para" parents="66 199"/>
    </justification>
  </clause>

  <clause id="206">
    <literal><![CDATA[
      K(1,x) = 1
    ]]></literal>
    <justification jstring="[hyper(55,a,201,a)].">
      <j1 rule="hyper" parents="55 201"/>
    </justification>
  </clause>

  <clause id="207">
    <literal><![CDATA[
      L(x,y,z) != (u \ u) * L(w,y,z)
    ]]></literal>
    <literal><![CDATA[
      w = x
    ]]></literal>
    <justification jstring="[para(172(a,2),50(a,1)),flip(a)].">
      <j1 rule="para" parents="172 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="208">
    <literal><![CDATA[
      R(x,y,z) != (u \ u) * R(w,y,z)
    ]]></literal>
    <literal><![CDATA[
      w = x
    ]]></literal>
    <justification jstring="[para(172(a,2),51(a,1)),flip(a)].">
      <j1 rule="para" parents="172 51"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="209">
    <literal><![CDATA[
      x * (y \ y) != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(173(a,1),44(a,2))].">
      <j1 rule="para" parents="173 44"/>
    </justification>
  </clause>

  <clause id="210">
    <literal><![CDATA[
      T(x,y \ y) != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(204(a,1),49(a,2))].">
      <j1 rule="para" parents="204 49"/>
    </justification>
  </clause>

  <clause id="211">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      1 \ x = y
    ]]></literal>
    <justification jstring="[para(10(a,1),127(a,1))].">
      <j1 rule="para" parents="10 127"/>
    </justification>
  </clause>

  <clause id="212">
    <literal><![CDATA[
      (x * (x \ 1)) * y != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(10(a,2),127(a,1,1))].">
      <j1 rule="para" parents="10 127"/>
    </justification>
  </clause>

  <clause id="213">
    <literal><![CDATA[
      ((1 / x) * x) * y != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(12(a,2),127(a,1,1))].">
      <j1 rule="para" parents="12 127"/>
    </justification>
  </clause>

  <clause id="214">
    <literal><![CDATA[
      K(x,1) * y != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(200(a,2),127(a,1,1))].">
      <j1 rule="para" parents="200 127"/>
    </justification>
  </clause>

  <clause id="215">
    <literal><![CDATA[
      x \ x != y
    ]]></literal>
    <literal><![CDATA[
      1 = y
    ]]></literal>
    <justification jstring="[para(172(a,1),128(a,1)),flip(a)].">
      <j1 rule="para" parents="172 128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="216">
    <literal><![CDATA[
      x / x != y
    ]]></literal>
    <literal><![CDATA[
      1 = y
    ]]></literal>
    <justification jstring="[para(174(a,1),128(a,1)),flip(a)].">
      <j1 rule="para" parents="174 128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="217">
    <literal><![CDATA[
      ((1 / x) * x) \ y != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(12(a,2),169(a,1,1))].">
      <j1 rule="para" parents="12 169"/>
    </justification>
  </clause>

  <clause id="218">
    <literal><![CDATA[
      x / (y * (y \ 1)) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(10(a,2),175(a,1,2))].">
      <j1 rule="para" parents="10 175"/>
    </justification>
  </clause>

  <clause id="219">
    <literal><![CDATA[
      T(x,R(T(x,y),z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(40,a,23,a,b,177,a(flip))].">
      <j1 rule="hyper" parents="40 23 177"/>
    </justification>
  </clause>

  <clause id="220">
    <literal><![CDATA[
      K(x,L(x,y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(55,a,178,a)].">
      <j1 rule="hyper" parents="55 178"/>
    </justification>
  </clause>

  <clause id="221">
    <literal><![CDATA[
      T(x,L(L(x,y,z),u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(41,a,25,a,b,178,a(flip))].">
      <j1 rule="hyper" parents="41 25 178"/>
    </justification>
  </clause>

  <clause id="222">
    <literal><![CDATA[
      T(x,L(T(x,y),z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(40,a,23,a,b,178,a(flip))].">
      <j1 rule="hyper" parents="40 23 178"/>
    </justification>
  </clause>

  <clause id="223">
    <literal><![CDATA[
      (x \ 1) * (x * x) = x
    ]]></literal>
    <justification jstring="[hyper(34,a,33,a(flip),b,68,a(flip))].">
      <j1 rule="hyper" parents="34 33 68"/>
    </justification>
  </clause>

  <clause id="224">
    <literal><![CDATA[
      (x * ((x \ 1) * y)) \ y = a(x,x \ 1,y)
    ]]></literal>
    <justification jstring="[para(68(a,1),14(a,2,2)),flip(a)].">
      <j1 rule="para" parents="68 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="225">
    <literal><![CDATA[
      R(x,x \ 1,y) = y / ((x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(68(a,1),20(a,2,1))].">
      <j1 rule="para" parents="68 20"/>
    </justification>
  </clause>

  <clause id="226">
    <literal><![CDATA[
      x \ ((x * y) * (y \ 1)) = a(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(69(a,1),14(a,2,1)),flip(a)].">
      <j1 rule="para" parents="69 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="227">
    <literal><![CDATA[
      L(x \ 1,x,y) = (y * x) \ y
    ]]></literal>
    <justification jstring="[para(69(a,1),18(a,2,2))].">
      <j1 rule="para" parents="69 18"/>
    </justification>
  </clause>

  <clause id="228">
    <literal><![CDATA[
      x * ((1 / x) * (1 / x)) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(34,a,33,a(flip),b,77,a(flip))].">
      <j1 rule="hyper" parents="34 33 77"/>
    </justification>
  </clause>

  <clause id="229">
    <literal><![CDATA[
      ((1 / x) * (x * y)) \ y = a(1 / x,x,y)
    ]]></literal>
    <justification jstring="[para(77(a,1),14(a,2,2)),flip(a)].">
      <j1 rule="para" parents="77 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="230">
    <literal><![CDATA[
      R(1 / x,x,y) = y / (x * y)
    ]]></literal>
    <justification jstring="[para(77(a,1),20(a,2,1))].">
      <j1 rule="para" parents="77 20"/>
    </justification>
  </clause>

  <clause id="232">
    <literal><![CDATA[
      L(x,1 / x,y) = (y * (1 / x)) \ y
    ]]></literal>
    <justification jstring="[para(78(a,1),18(a,2,2))].">
      <j1 rule="para" parents="78 18"/>
    </justification>
  </clause>

  <clause id="233">
    <literal><![CDATA[
      x * T(y / x,x) = y
    ]]></literal>
    <justification jstring="[hyper(63,a,111,a,b,12,a)].">
      <j1 rule="hyper" parents="63 111 12"/>
    </justification>
  </clause>

  <clause id="234">
    <literal><![CDATA[
      (x \ y) * T(x,x \ y) = y
    ]]></literal>
    <justification jstring="[hyper(63,a,111,a,b,10,a)].">
      <j1 rule="hyper" parents="63 111 10"/>
    </justification>
  </clause>

  <clause id="235">
    <literal><![CDATA[
      x * (y * T(z,y)) = x * (z * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,111,a)].">
      <j1 rule="hyper" parents="58 111"/>
    </justification>
  </clause>

  <clause id="236">
    <literal><![CDATA[
      (x * T(y,x)) * z = (y * x) * z
    ]]></literal>
    <justification jstring="[hyper(57,a,111,a)].">
      <j1 rule="hyper" parents="57 111"/>
    </justification>
  </clause>

  <clause id="237">
    <literal><![CDATA[
      T(x * (y * y),x) = (y * y) * x
    ]]></literal>
    <justification jstring="[hyper(34,a,32,a(flip),b,111,a),flip(a)].">
      <j1 rule="hyper" parents="34 32 111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="238">
    <literal><![CDATA[
      T((x * y) / x,x) = y
    ]]></literal>
    <justification jstring="[hyper(34,a,12,a(flip),b,111,a),flip(a)].">
      <j1 rule="hyper" parents="34 12 111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="239">
    <literal><![CDATA[
      (x * T(y,x)) / x = y
    ]]></literal>
    <justification jstring="[hyper(35,a,12,a,b,111,a(flip))].">
      <j1 rule="hyper" parents="35 12 111"/>
    </justification>
  </clause>

  <clause id="240">
    <literal><![CDATA[
      x \ (y * T(x,y)) = y
    ]]></literal>
    <justification jstring="[hyper(34,a,10,a,b,111,a(flip))].">
      <j1 rule="hyper" parents="34 10 111"/>
    </justification>
  </clause>

  <clause id="241">
    <literal><![CDATA[
      x * (y * (y \ T(z,x))) = z * x
    ]]></literal>
    <justification jstring="[para(10(a,2),111(a,1,2))].">
      <j1 rule="para" parents="10 111"/>
    </justification>
  </clause>

  <clause id="243">
    <literal><![CDATA[
      (x * (T(y,x) * z)) \ ((y * x) * z) = a(x,T(y,x),z)
    ]]></literal>
    <justification jstring="[para(111(a,1),14(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="111 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="244">
    <literal><![CDATA[
      (x * y) \ (T(x,y) * y) = K(T(x,y),y)
    ]]></literal>
    <justification jstring="[para(111(a,1),16(a,2,1)),flip(a)].">
      <j1 rule="para" parents="111 16"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="245">
    <literal><![CDATA[
      (x * y) \ (y * (T(x,y) * z)) = L(z,T(x,y),y)
    ]]></literal>
    <justification jstring="[para(111(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="111 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="246">
    <literal><![CDATA[
      (x * y) \ (x * (z * y)) = L(T(z,y),y,x)
    ]]></literal>
    <justification jstring="[para(111(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="111 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="247">
    <literal><![CDATA[
      ((x * y) * z) / (T(x,y) * z) = R(y,T(x,y),z)
    ]]></literal>
    <justification jstring="[para(111(a,1),20(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="111 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="248">
    <literal><![CDATA[
      (x * (y * z)) / (z * T(x,y * z)) = R(y,z,T(x,y * z))
    ]]></literal>
    <justification jstring="[para(111(a,1),20(a,2,1)),flip(a)].">
      <j1 rule="para" parents="111 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="249">
    <literal><![CDATA[
      T(x,y) \ (x * y) = T(y,T(x,y))
    ]]></literal>
    <justification jstring="[para(111(a,1),22(a,2,2)),flip(a)].">
      <j1 rule="para" parents="111 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="250">
    <literal><![CDATA[
      x * T(T(y,x),z) = T(y,z) * x
    ]]></literal>
    <justification jstring="[para(23(a,1),111(a,1,2))].">
      <j1 rule="para" parents="23 111"/>
    </justification>
  </clause>

  <clause id="251">
    <literal><![CDATA[
      x * L(T(y,x),z,u) = L(y,z,u) * x
    ]]></literal>
    <justification jstring="[para(25(a,2),111(a,1,2))].">
      <j1 rule="para" parents="25 111"/>
    </justification>
  </clause>

  <clause id="252">
    <literal><![CDATA[
      x * R(T(y,x),z,u) = R(y,z,u) * x
    ]]></literal>
    <justification jstring="[para(27(a,2),111(a,1,2))].">
      <j1 rule="para" parents="27 111"/>
    </justification>
  </clause>

  <clause id="253">
    <literal><![CDATA[
      x * y != z
    ]]></literal>
    <literal><![CDATA[
      y * u != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = u
    ]]></literal>
    <justification jstring="[para(111(a,1),34(a,1))].">
      <j1 rule="para" parents="111 34"/>
    </justification>
  </clause>

  <clause id="254">
    <literal><![CDATA[
      x * y != z * x
    ]]></literal>
    <literal><![CDATA[
      T(z,x) = y
    ]]></literal>
    <justification jstring="[para(111(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="111 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="256">
    <literal><![CDATA[
      x * T(y,x) != z * x
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(111(a,2),44(a,1))].">
      <j1 rule="para" parents="111 44"/>
    </justification>
  </clause>

  <clause id="257">
    <literal><![CDATA[
      x * T(y,x) != z * x
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(111(a,2),44(a,2)),flip(a)].">
      <j1 rule="para" parents="111 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="258">
    <literal><![CDATA[
      T(x / (x / y),x / y) = y
    ]]></literal>
    <justification jstring="[hyper(63,a,113,a,b,79,a)].">
      <j1 rule="hyper" parents="63 113 79"/>
    </justification>
  </clause>

  <clause id="259">
    <literal><![CDATA[
      T(T(x / y,z),y) = T(y \ x,z)
    ]]></literal>
    <justification jstring="[para(113(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="113 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="260">
    <literal><![CDATA[
      T(L(x / y,z,u),y) = L(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(113(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="113 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="261">
    <literal><![CDATA[
      T(R(x / y,z,u),y) = R(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(113(a,1),27(a,1,1)),flip(a)].">
      <j1 rule="para" parents="113 27"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="262">
    <literal><![CDATA[
      T(x,y) != y \ z
    ]]></literal>
    <literal><![CDATA[
      z / y = x
    ]]></literal>
    <justification jstring="[para(113(a,1),49(a,1)),flip(a)].">
      <j1 rule="para" parents="113 49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="263">
    <literal><![CDATA[
      x * 1 != y * z
    ]]></literal>
    <literal><![CDATA[
      x / z = y
    ]]></literal>
    <justification jstring="[para(160(a,1),44(a,1))].">
      <j1 rule="para" parents="160 44"/>
    </justification>
  </clause>

  <clause id="264">
    <literal><![CDATA[
      (x / y) * y != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(160(a,2),134(a,1))].">
      <j1 rule="para" parents="160 134"/>
    </justification>
  </clause>

  <clause id="265">
    <literal><![CDATA[
      (x / y) * y != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(160(a,2),135(a,1))].">
      <j1 rule="para" parents="160 135"/>
    </justification>
  </clause>

  <clause id="266">
    <literal><![CDATA[
      1 * x != y * z
    ]]></literal>
    <literal><![CDATA[
      x / z = y
    ]]></literal>
    <justification jstring="[para(161(a,1),44(a,1))].">
      <j1 rule="para" parents="161 44"/>
    </justification>
  </clause>

  <clause id="267">
    <literal><![CDATA[
      x / y != z * 1
    ]]></literal>
    <literal><![CDATA[
      z * y = x
    ]]></literal>
    <justification jstring="[para(162(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="162 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="268">
    <literal><![CDATA[
      (x * y) / y != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(162(a,2),134(a,1))].">
      <j1 rule="para" parents="162 134"/>
    </justification>
  </clause>

  <clause id="269">
    <literal><![CDATA[
      (x * y) / y != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(162(a,2),135(a,1))].">
      <j1 rule="para" parents="162 135"/>
    </justification>
  </clause>

  <clause id="271">
    <literal><![CDATA[
      x * 1 != y * z
    ]]></literal>
    <literal><![CDATA[
      y \ x = z
    ]]></literal>
    <justification jstring="[para(164(a,1),43(a,1))].">
      <j1 rule="para" parents="164 43"/>
    </justification>
  </clause>

  <clause id="272">
    <literal><![CDATA[
      x * (x \ y) != y * z
    ]]></literal>
    <literal><![CDATA[
      1 = z
    ]]></literal>
    <justification jstring="[para(164(a,2),43(a,1))].">
      <j1 rule="para" parents="164 43"/>
    </justification>
  </clause>

  <clause id="273">
    <literal><![CDATA[
      x * (x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(164(a,2),134(a,1))].">
      <j1 rule="para" parents="164 134"/>
    </justification>
  </clause>

  <clause id="274">
    <literal><![CDATA[
      x * (x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(164(a,2),135(a,1))].">
      <j1 rule="para" parents="164 135"/>
    </justification>
  </clause>

  <clause id="275">
    <literal><![CDATA[
      x * ((x \ 1) * y) = L(y,x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,18,a,b,166,a),flip(a)].">
      <j1 rule="hyper" parents="63 18 166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="276">
    <literal><![CDATA[
      K(x \ 1,x) = (x \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(63,a,16,a,b,166,a)].">
      <j1 rule="hyper" parents="63 16 166"/>
    </justification>
  </clause>

  <clause id="277">
    <literal><![CDATA[
      (1 / x) * (x * y) = L(y,x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(63,a,18,a,b,167,a),flip(a)].">
      <j1 rule="hyper" parents="63 18 167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="278">
    <literal><![CDATA[
      K(x,1 / x) = x * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(63,a,16,a,b,167,a)].">
      <j1 rule="hyper" parents="63 16 167"/>
    </justification>
  </clause>

  <clause id="279">
    <literal><![CDATA[
      K(T(x,y),x) = 1
    ]]></literal>
    <justification jstring="[hyper(55,a,179,a)].">
      <j1 rule="hyper" parents="55 179"/>
    </justification>
  </clause>

  <clause id="280">
    <literal><![CDATA[
      T(x,y) * x = x * T(x,y)
    ]]></literal>
    <justification jstring="[para(179(a,1),111(a,1,2)),flip(a)].">
      <j1 rule="para" parents="179 111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="281">
    <literal><![CDATA[
      x / T(y,y \ x) = y \ x
    ]]></literal>
    <justification jstring="[para(10(a,1),191(a,1,1))].">
      <j1 rule="para" parents="10 191"/>
    </justification>
  </clause>

  <clause id="282">
    <literal><![CDATA[
      (T(x,y) * z) / T(T(x,z),y) = z
    ]]></literal>
    <justification jstring="[para(23(a,1),191(a,1,2))].">
      <j1 rule="para" parents="23 191"/>
    </justification>
  </clause>

  <clause id="283">
    <literal><![CDATA[
      (x * y) / z != y
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(191(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="191 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="284">
    <literal><![CDATA[
      x / (x * x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(35,a,12,a,b,223,a)].">
      <j1 rule="hyper" parents="35 12 223"/>
    </justification>
  </clause>

  <clause id="285">
    <literal><![CDATA[
      (x \ 1) \ x = x * x
    ]]></literal>
    <justification jstring="[hyper(34,a,10,a,b,223,a)].">
      <j1 rule="hyper" parents="34 10 223"/>
    </justification>
  </clause>

  <clause id="286">
    <literal><![CDATA[
      x * y != z
    ]]></literal>
    <literal><![CDATA[
      T(z / x,x) = y
    ]]></literal>
    <justification jstring="[para(233(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="233 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="287">
    <literal><![CDATA[
      (x * T(T(y,x),z)) / x = T(y,z)
    ]]></literal>
    <justification jstring="[hyper(40,a,23,a,b,238,a),flip(a)].">
      <j1 rule="hyper" parents="40 23 238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="288">
    <literal><![CDATA[
      T(T((x * y) / x,z),x) = T(y,z)
    ]]></literal>
    <justification jstring="[para(238(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="238 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="289">
    <literal><![CDATA[
      T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      (y * z) / y = x
    ]]></literal>
    <justification jstring="[para(238(a,1),49(a,1)),flip(a)].">
      <j1 rule="para" parents="238 49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="290">
    <literal><![CDATA[
      K(x,(y * x) / y) = 1
    ]]></literal>
    <justification jstring="[para(238(a,1),279(a,1,1))].">
      <j1 rule="para" parents="238 279"/>
    </justification>
  </clause>

  <clause id="291">
    <literal><![CDATA[
      x / y != z
    ]]></literal>
    <literal><![CDATA[
      y * T(z,y) = x
    ]]></literal>
    <justification jstring="[para(239(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="239 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="292">
    <literal><![CDATA[
      L(x,y,z) \ (u * L(T(x,u),y,z)) = u
    ]]></literal>
    <justification jstring="[para(25(a,2),240(a,1,2,2))].">
      <j1 rule="para" parents="25 240"/>
    </justification>
  </clause>

  <clause id="293">
    <literal><![CDATA[
      (1 / x) * (1 / x) = x \ (1 / x)
    ]]></literal>
    <justification jstring="[para(79(a,1),285(a,1,1)),flip(a)].">
      <j1 rule="para" parents="79 285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="294">
    <literal><![CDATA[
      T(x,(y * x) / y) = x
    ]]></literal>
    <justification jstring="[hyper(56,a,290,a)].">
      <j1 rule="hyper" parents="56 290"/>
    </justification>
  </clause>

  <clause id="295">
    <literal><![CDATA[
      T(x \ y,y / x) = x \ y
    ]]></literal>
    <justification jstring="[para(10(a,1),294(a,1,2,1))].">
      <j1 rule="para" parents="10 294"/>
    </justification>
  </clause>

  <clause id="296">
    <literal><![CDATA[
      x * y != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = y \ z
    ]]></literal>
    <justification jstring="[para(111(a,1),129(a,1)),flip(b)].">
      <j1 rule="para" parents="111 129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="297">
    <literal><![CDATA[
      x * y != x * z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(11(a,1),131(a,1,1))].">
      <j1 rule="para" parents="11 131"/>
    </justification>
  </clause>

  <clause id="299">
    <literal><![CDATA[
      R(x,y,z) * (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      (x * y) * z = u
    ]]></literal>
    <justification jstring="[para(20(a,2),264(a,1,1)),flip(b)].">
      <j1 rule="para" parents="20 264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="300">
    <literal><![CDATA[
      x * T(y,x) != z
    ]]></literal>
    <literal><![CDATA[
      y * x = z
    ]]></literal>
    <justification jstring="[para(191(a,1),264(a,1,1)),flip(b)].">
      <j1 rule="para" parents="191 264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="301">
    <literal><![CDATA[
      x / (y \ x) != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(10(a,1),268(a,1,1))].">
      <j1 rule="para" parents="10 268"/>
    </justification>
  </clause>

  <clause id="302">
    <literal><![CDATA[
      (x * T(y,x)) / x != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(111(a,2),268(a,1,1))].">
      <j1 rule="para" parents="111 268"/>
    </justification>
  </clause>

  <clause id="303">
    <literal><![CDATA[
      (1 * x) / y != z
    ]]></literal>
    <literal><![CDATA[
      x / y = z
    ]]></literal>
    <justification jstring="[para(161(a,1),268(a,1,1)),flip(b)].">
      <j1 rule="para" parents="161 268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="304">
    <literal><![CDATA[
      x / (y \ x) != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(10(a,1),269(a,1,1))].">
      <j1 rule="para" parents="10 269"/>
    </justification>
  </clause>

  <clause id="305">
    <literal><![CDATA[
      (x * T(y,x)) / x != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(111(a,2),269(a,1,1))].">
      <j1 rule="para" parents="111 269"/>
    </justification>
  </clause>

  <clause id="306">
    <literal><![CDATA[
      (x * y) * L(z,y,x) != u
    ]]></literal>
    <literal><![CDATA[
      x * (y * z) = u
    ]]></literal>
    <justification jstring="[para(18(a,2),273(a,1,2)),flip(b)].">
      <j1 rule="para" parents="18 273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="307">
    <literal><![CDATA[
      x * (y \ (y * (x \ z))) != u
    ]]></literal>
    <literal><![CDATA[
      z = u
    ]]></literal>
    <justification jstring="[para(9(a,2),274(a,1,2))].">
      <j1 rule="para" parents="9 274"/>
    </justification>
  </clause>

  <clause id="308">
    <literal><![CDATA[
      x * (y * (y \ (x \ z))) != u
    ]]></literal>
    <literal><![CDATA[
      z = u
    ]]></literal>
    <justification jstring="[para(10(a,2),274(a,1,2))].">
      <j1 rule="para" parents="10 274"/>
    </justification>
  </clause>

  <clause id="309">
    <literal><![CDATA[
      (x / y) \ (z * (z \ x)) = y
    ]]></literal>
    <justification jstring="[para(12(a,1),70(a,1,2,2,2))].">
      <j1 rule="para" parents="12 70"/>
    </justification>
  </clause>

  <clause id="310">
    <literal><![CDATA[
      x \ ((x * y) * L(z,y,x)) = y * z
    ]]></literal>
    <justification jstring="[para(18(a,2),70(a,1,2,2))].">
      <j1 rule="para" parents="18 70"/>
    </justification>
  </clause>

  <clause id="311">
    <literal><![CDATA[
      L(x \ (y \ z),x,y) = (y * x) \ z
    ]]></literal>
    <justification jstring="[para(72(a,1),18(a,2,2))].">
      <j1 rule="para" parents="72 18"/>
    </justification>
  </clause>

  <clause id="312">
    <literal><![CDATA[
      ((x * (x \ y)) / z) \ y = z
    ]]></literal>
    <justification jstring="[hyper(129,a,81,a)].">
      <j1 rule="hyper" parents="129 81"/>
    </justification>
  </clause>

  <clause id="313">
    <literal><![CDATA[
      (R(x,y,z) * (y * z)) / z = x * y
    ]]></literal>
    <justification jstring="[para(20(a,2),82(a,1,1,1))].">
      <j1 rule="para" parents="20 82"/>
    </justification>
  </clause>

  <clause id="314">
    <literal><![CDATA[
      R((x / y) / z,z,y) = x / (z * y)
    ]]></literal>
    <justification jstring="[para(83(a,1),20(a,2,1))].">
      <j1 rule="para" parents="83 20"/>
    </justification>
  </clause>

  <clause id="315">
    <literal><![CDATA[
      ((x / y) * y) * (x \ z) = z
    ]]></literal>
    <justification jstring="[para(76(a,1),83(a,1,1,1,1))].">
      <j1 rule="para" parents="76 83"/>
    </justification>
  </clause>

  <clause id="316">
    <literal><![CDATA[
      ((x \ y) * x) * K(x,x \ y) = y
    ]]></literal>
    <justification jstring="[hyper(63,a,88,a,b,10,a)].">
      <j1 rule="hyper" parents="63 88 10"/>
    </justification>
  </clause>

  <clause id="317">
    <literal><![CDATA[
      x * K(y \ x,y) = (y \ x) * y
    ]]></literal>
    <justification jstring="[para(10(a,1),88(a,1,1))].">
      <j1 rule="para" parents="10 88"/>
    </justification>
  </clause>

  <clause id="318">
    <literal><![CDATA[
      x * K(y,x / y) = y * (x / y)
    ]]></literal>
    <justification jstring="[para(12(a,1),88(a,1,1))].">
      <j1 rule="para" parents="12 88"/>
    </justification>
  </clause>

  <clause id="319">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (z * y)) = L(K(z,y),y * z,x)
    ]]></literal>
    <justification jstring="[para(88(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="88 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="320">
    <literal><![CDATA[
      (x * y) / (x * K(x,y)) = R(y,x,K(x,y))
    ]]></literal>
    <justification jstring="[para(88(a,1),20(a,2,1)),flip(a)].">
      <j1 rule="para" parents="88 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="321">
    <literal><![CDATA[
      T(x * y,K(y,x)) = K(y,x) \ (y * x)
    ]]></literal>
    <justification jstring="[para(88(a,1),22(a,2,2))].">
      <j1 rule="para" parents="88 22"/>
    </justification>
  </clause>

  <clause id="322">
    <literal><![CDATA[
      (x * y) * z != y * x
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(88(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="88 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="323">
    <literal><![CDATA[
      R(T(x,R(x,y,z) \ u),y,z) = (R(x,y,z) \ u) \ u
    ]]></literal>
    <justification jstring="[hyper(63,a,27,a,b,112,a)].">
      <j1 rule="hyper" parents="63 27 112"/>
    </justification>
  </clause>

  <clause id="324">
    <literal><![CDATA[
      (x \ y) \ y = z * (z \ T(x,x \ y))
    ]]></literal>
    <justification jstring="[hyper(63,a,10,a,b,112,a),flip(a)].">
      <j1 rule="hyper" parents="63 10 112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="325">
    <literal><![CDATA[
      x \ T(y,y \ z) = x \ ((y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(62,a,112,a)].">
      <j1 rule="hyper" parents="62 112"/>
    </justification>
  </clause>

  <clause id="326">
    <literal><![CDATA[
      T(x,x \ y) \ z = ((x \ y) \ y) \ z
    ]]></literal>
    <justification jstring="[hyper(61,a,112,a)].">
      <j1 rule="hyper" parents="61 112"/>
    </justification>
  </clause>

  <clause id="328">
    <literal><![CDATA[
      x * T(y,y \ z) = x * ((y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,112,a)].">
      <j1 rule="hyper" parents="58 112"/>
    </justification>
  </clause>

  <clause id="329">
    <literal><![CDATA[
      T(x,x \ y) * z = ((x \ y) \ y) * z
    ]]></literal>
    <justification jstring="[hyper(57,a,112,a)].">
      <j1 rule="hyper" parents="57 112"/>
    </justification>
  </clause>

  <clause id="330">
    <literal><![CDATA[
      T(T(x,y),x \ z) = T((x \ z) \ z,y)
    ]]></literal>
    <justification jstring="[para(112(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="112 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="331">
    <literal><![CDATA[
      T(L(x,y,z),x \ u) = L((x \ u) \ u,y,z)
    ]]></literal>
    <justification jstring="[para(112(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="112 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="332">
    <literal><![CDATA[
      T(x / y,(x / y) \ x) = y \ x
    ]]></literal>
    <justification jstring="[para(79(a,1),112(a,2,1))].">
      <j1 rule="para" parents="79 112"/>
    </justification>
  </clause>

  <clause id="333">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z != y
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(7(a,1),118(b,1))].">
      <j1 rule="para" parents="7 118"/>
    </justification>
  </clause>

  <clause id="334">
    <literal><![CDATA[
      ((x / y) * y) * z != u
    ]]></literal>
    <literal><![CDATA[
      x \ u = z
    ]]></literal>
    <justification jstring="[para(152(a,2),129(a,1))].">
      <j1 rule="para" parents="152 129"/>
    </justification>
  </clause>

  <clause id="335">
    <literal><![CDATA[
      (x / (y * (y \ z))) * z = x
    ]]></literal>
    <justification jstring="[hyper(265,a,154,a),flip(a)].">
      <j1 rule="hyper" parents="265 154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="336">
    <literal><![CDATA[
      x / (y \ ((x / z) * z)) = y
    ]]></literal>
    <justification jstring="[hyper(304,a,156,a),flip(a)].">
      <j1 rule="hyper" parents="304 156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="338">
    <literal><![CDATA[
      x / y != (z / u) * u
    ]]></literal>
    <literal><![CDATA[
      z * y = x
    ]]></literal>
    <justification jstring="[para(159(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="159 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="339">
    <literal><![CDATA[
      ((x / y) * y) * z != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(159(a,1),264(a,1,1)),flip(b)].">
      <j1 rule="para" parents="159 264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="340">
    <literal><![CDATA[
      x \ (x * y) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ y = u
    ]]></literal>
    <justification jstring="[para(163(a,2),43(a,1))].">
      <j1 rule="para" parents="163 43"/>
    </justification>
  </clause>

  <clause id="341">
    <literal><![CDATA[
      x \ y != z * (z \ u)
    ]]></literal>
    <literal><![CDATA[
      x * u = y
    ]]></literal>
    <justification jstring="[para(163(a,1),47(a,1)),flip(a)].">
      <j1 rule="para" parents="163 47"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="342">
    <literal><![CDATA[
      x \ (x * y) != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(163(a,2),209(a,1))].">
      <j1 rule="para" parents="163 209"/>
    </justification>
  </clause>

  <clause id="343">
    <literal><![CDATA[
      x * (y * (y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(163(a,1),273(a,1,2)),flip(b)].">
      <j1 rule="para" parents="163 273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="344">
    <literal><![CDATA[
      x \ (x * y) != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(163(a,2),273(a,1))].">
      <j1 rule="para" parents="163 273"/>
    </justification>
  </clause>

  <clause id="345">
    <literal><![CDATA[
      (x / y) \ x != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(12(a,1),342(a,1,2))].">
      <j1 rule="para" parents="12 342"/>
    </justification>
  </clause>

  <clause id="346">
    <literal><![CDATA[
      T(x,x) != y
    ]]></literal>
    <literal><![CDATA[
      x = y
    ]]></literal>
    <justification jstring="[para(22(a,2),342(a,1))].">
      <j1 rule="para" parents="22 342"/>
    </justification>
  </clause>

  <clause id="347">
    <literal><![CDATA[
      x \ (y * x) != z
    ]]></literal>
    <literal><![CDATA[
      T(y,x) = z
    ]]></literal>
    <justification jstring="[para(111(a,1),342(a,1,2))].">
      <j1 rule="para" parents="111 342"/>
    </justification>
  </clause>

  <clause id="348">
    <literal><![CDATA[
      x \ (y * 1) != z
    ]]></literal>
    <literal><![CDATA[
      x \ y = z
    ]]></literal>
    <justification jstring="[para(164(a,1),342(a,1,2))].">
      <j1 rule="para" parents="164 342"/>
    </justification>
  </clause>

  <clause id="349">
    <literal><![CDATA[
      (x * y) \ (y * x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(88(a,1),342(a,1,2))].">
      <j1 rule="para" parents="88 342"/>
    </justification>
  </clause>

  <clause id="350">
    <literal><![CDATA[
      T((x * y) / x,x) != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(113(a,2),344(a,1))].">
      <j1 rule="para" parents="113 344"/>
    </justification>
  </clause>

  <clause id="351">
    <literal><![CDATA[
      (x / (y \ x)) * z != u
    ]]></literal>
    <literal><![CDATA[
      y * z = u
    ]]></literal>
    <justification jstring="[para(184(a,1),264(a,1,1)),flip(b)].">
      <j1 rule="para" parents="184 264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="352">
    <literal><![CDATA[
      x / y != z * (z \ u)
    ]]></literal>
    <literal><![CDATA[
      u \ x = y
    ]]></literal>
    <justification jstring="[para(185(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="185 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="353">
    <literal><![CDATA[
      (x * (x \ y)) \ z != u
    ]]></literal>
    <literal><![CDATA[
      y \ z = u
    ]]></literal>
    <justification jstring="[para(185(a,1),345(a,1,1))].">
      <j1 rule="para" parents="185 345"/>
    </justification>
  </clause>

  <clause id="354">
    <literal><![CDATA[
      x \ y != z * (z \ u)
    ]]></literal>
    <literal><![CDATA[
      y / u = x
    ]]></literal>
    <justification jstring="[para(194(a,1),48(a,1)),flip(a)].">
      <j1 rule="para" parents="194 48"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="355">
    <literal><![CDATA[
      ((x / y) \ x) * z != u
    ]]></literal>
    <literal><![CDATA[
      y \ u = z
    ]]></literal>
    <justification jstring="[para(195(a,2),129(a,1))].">
      <j1 rule="para" parents="195 129"/>
    </justification>
  </clause>

  <clause id="356">
    <literal><![CDATA[
      (x \ y) * z != y
    ]]></literal>
    <literal><![CDATA[
      T(x,x \ y) = z
    ]]></literal>
    <justification jstring="[para(234(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="234 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="357">
    <literal><![CDATA[
      T(x / (x / y),(z / (x / y)) \ z) = y
    ]]></literal>
    <justification jstring="[para(79(a,2),258(a,1,2))].">
      <j1 rule="para" parents="79 258"/>
    </justification>
  </clause>

  <clause id="358">
    <literal><![CDATA[
      x * T(x \ 1,x) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,111,a,b,276,a)].">
      <j1 rule="hyper" parents="333 111 276"/>
    </justification>
  </clause>

  <clause id="359">
    <literal><![CDATA[
      (x \ 1) \ K(x \ 1,x) = x
    ]]></literal>
    <justification jstring="[hyper(129,a,276,a(flip))].">
      <j1 rule="hyper" parents="129 276"/>
    </justification>
  </clause>

  <clause id="360">
    <literal><![CDATA[
      x \ K(x \ 1,x) = T(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(276(a,2),22(a,2,2)),flip(a)].">
      <j1 rule="para" parents="276 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="362">
    <literal><![CDATA[
      x * (x \ y) != z * u
    ]]></literal>
    <literal><![CDATA[
      y / u = z
    ]]></literal>
    <justification jstring="[para(309(a,1),137(a,1,2)),flip(a),flip(b)].">
      <j1 rule="para" parents="309 137"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="363">
    <literal><![CDATA[
      (x * (x \ y)) / z != u
    ]]></literal>
    <literal><![CDATA[
      y / z = u
    ]]></literal>
    <justification jstring="[para(309(a,1),301(a,1,2)),flip(b)].">
      <j1 rule="para" parents="309 301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="364">
    <literal><![CDATA[
      R(x,y,(x * y) \ z) \ z = y * ((x * y) \ z)
    ]]></literal>
    <justification jstring="[para(20(a,2),312(a,1,1))].">
      <j1 rule="para" parents="20 312"/>
    </justification>
  </clause>

  <clause id="365">
    <literal><![CDATA[
      R(x / y,y,x \ z) = z / (y * (x \ z))
    ]]></literal>
    <justification jstring="[para(315(a,1),20(a,2,1))].">
      <j1 rule="para" parents="315 20"/>
    </justification>
  </clause>

  <clause id="366">
    <literal><![CDATA[
      x / y != (z / u) * u
    ]]></literal>
    <literal><![CDATA[
      z \ x = y
    ]]></literal>
    <justification jstring="[para(315(a,1),139(a,1,1))].">
      <j1 rule="para" parents="315 139"/>
    </justification>
  </clause>

  <clause id="367">
    <literal><![CDATA[
      R(x,y,y \ z) * z = (x * y) * (y \ z)
    ]]></literal>
    <justification jstring="[para(20(a,2),335(a,1,1))].">
      <j1 rule="para" parents="20 335"/>
    </justification>
  </clause>

  <clause id="368">
    <literal><![CDATA[
      x / L(y,z,x / (z * y)) = (x / (z * y)) * z
    ]]></literal>
    <justification jstring="[para(18(a,2),336(a,1,2))].">
      <j1 rule="para" parents="18 336"/>
    </justification>
  </clause>

  <clause id="370">
    <literal><![CDATA[
      x \ (x * y) = L(y,x,1)
    ]]></literal>
    <justification jstring="[para(7(a,1),94(a,1,2))].">
      <j1 rule="para" parents="7 94"/>
    </justification>
  </clause>

  <clause id="371">
    <literal><![CDATA[
      L(x,y,1) = x
    ]]></literal>
    <justification jstring="[hyper(344,a,370,a)].">
      <j1 rule="hyper" parents="344 370"/>
    </justification>
  </clause>

  <clause id="372">
    <literal><![CDATA[
      L(x,y,1) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(370(a,1),344(a,1))].">
      <j1 rule="para" parents="370 344"/>
    </justification>
  </clause>

  <clause id="374">
    <literal><![CDATA[
      x \ (x * y) = L(y,1,x)
    ]]></literal>
    <justification jstring="[para(8(a,1),95(a,1,1))].">
      <j1 rule="para" parents="8 95"/>
    </justification>
  </clause>

  <clause id="375">
    <literal><![CDATA[
      L(x,1,y) = x
    ]]></literal>
    <justification jstring="[hyper(344,a,374,a)].">
      <j1 rule="hyper" parents="344 374"/>
    </justification>
  </clause>

  <clause id="376">
    <literal><![CDATA[
      L(x,1,y) = z \ (z * x)
    ]]></literal>
    <justification jstring="[hyper(333,a,9,a,b,375,a),flip(a)].">
      <j1 rule="hyper" parents="333 9 375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="377">
    <literal><![CDATA[
      L(x,1,y) != z \ (z * u)
    ]]></literal>
    <literal><![CDATA[
      u = x
    ]]></literal>
    <justification jstring="[para(376(a,1),50(a,1)),flip(a)].">
      <j1 rule="para" parents="376 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="378">
    <literal><![CDATA[
      L(1,x,y) = 1
    ]]></literal>
    <justification jstring="[hyper(215,a,96,a),flip(a)].">
      <j1 rule="hyper" parents="215 96"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="380">
    <literal><![CDATA[
      a(x,y,1) = 1
    ]]></literal>
    <justification jstring="[hyper(53,a,378,a)].">
      <j1 rule="hyper" parents="53 378"/>
    </justification>
  </clause>

  <clause id="381">
    <literal><![CDATA[
      a(x,y,K(1,z)) = 1
    ]]></literal>
    <justification jstring="[para(206(a,2),380(a,1,3))].">
      <j1 rule="para" parents="206 380"/>
    </justification>
  </clause>

  <clause id="382">
    <literal><![CDATA[
      R(1,x,y) = 1
    ]]></literal>
    <justification jstring="[hyper(216,a,103,a),flip(a)].">
      <j1 rule="hyper" parents="216 103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="384">
    <literal><![CDATA[
      K(x,1 / x) != y
    ]]></literal>
    <literal><![CDATA[
      x * (1 / x) = y
    ]]></literal>
    <justification jstring="[para(16(a,2),217(a,1))].">
      <j1 rule="para" parents="16 217"/>
    </justification>
  </clause>

  <clause id="385">
    <literal><![CDATA[
      (x * y) * (y \ 1) = R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(218,a,20,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="218 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="386">
    <literal><![CDATA[
      R(x,y,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      (x * y) * (y \ 1) = z
    ]]></literal>
    <justification jstring="[para(20(a,2),218(a,1)),flip(b)].">
      <j1 rule="para" parents="20 218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="387">
    <literal><![CDATA[
      L(x \ 1,x,1 / x) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(333,a,167,a(flip),b,227,a),flip(a)].">
      <j1 rule="hyper" parents="333 167 227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="388">
    <literal><![CDATA[
      L((x \ y) \ 1,x \ y,x) = y \ x
    ]]></literal>
    <justification jstring="[hyper(333,a,158,a(flip),b,227,a),flip(a)].">
      <j1 rule="hyper" parents="333 158 227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="389">
    <literal><![CDATA[
      L(x \ 1,x,y) \ z = ((y * x) \ y) \ z
    ]]></literal>
    <justification jstring="[hyper(61,a,227,a)].">
      <j1 rule="hyper" parents="61 227"/>
    </justification>
  </clause>

  <clause id="390">
    <literal><![CDATA[
      x * L(y \ 1,y,z) = x * ((z * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,227,a)].">
      <j1 rule="hyper" parents="58 227"/>
    </justification>
  </clause>

  <clause id="391">
    <literal><![CDATA[
      x / L(y \ 1,y,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(198,a,227,a(flip))].">
      <j1 rule="hyper" parents="198 227"/>
    </justification>
  </clause>

  <clause id="392">
    <literal><![CDATA[
      (x * y) * L(y \ 1,y,x) = x
    ]]></literal>
    <justification jstring="[hyper(142,a,227,a(flip))].">
      <j1 rule="hyper" parents="142 227"/>
    </justification>
  </clause>

  <clause id="393">
    <literal><![CDATA[
      L(x \ 1,x,y / x) = y \ (y / x)
    ]]></literal>
    <justification jstring="[para(12(a,1),227(a,2,1))].">
      <j1 rule="para" parents="12 227"/>
    </justification>
  </clause>

  <clause id="394">
    <literal><![CDATA[
      T((x * y) \ x,z) = L(T(y \ 1,z),y,x)
    ]]></literal>
    <justification jstring="[para(227(a,1),25(a,2,1)),flip(a)].">
      <j1 rule="para" parents="227 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="395">
    <literal><![CDATA[
      L(L(x \ 1,y,z),x,u) = L((u * x) \ u,y,z)
    ]]></literal>
    <justification jstring="[para(227(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="227 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="396">
    <literal><![CDATA[
      L(T(x,x \ 1),x \ 1,y) = (y * (x \ 1)) \ y
    ]]></literal>
    <justification jstring="[para(112(a,2),227(a,1,1))].">
      <j1 rule="para" parents="112 227"/>
    </justification>
  </clause>

  <clause id="397">
    <literal><![CDATA[
      x * R(1 / y,y,z) = x * (z / (y * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,230,a)].">
      <j1 rule="hyper" parents="58 230"/>
    </justification>
  </clause>

  <clause id="398">
    <literal><![CDATA[
      R(1 / x,x,y) \ y = x * y
    ]]></literal>
    <justification jstring="[hyper(192,a,230,a(flip))].">
      <j1 rule="hyper" parents="192 230"/>
    </justification>
  </clause>

  <clause id="399">
    <literal><![CDATA[
      R(1 / x,x,x \ y) = (x \ y) / y
    ]]></literal>
    <justification jstring="[para(10(a,1),230(a,2,2))].">
      <j1 rule="para" parents="10 230"/>
    </justification>
  </clause>

  <clause id="400">
    <literal><![CDATA[
      R(1 / (x / y),x / y,y) = y / x
    ]]></literal>
    <justification jstring="[para(12(a,1),230(a,2,2))].">
      <j1 rule="para" parents="12 230"/>
    </justification>
  </clause>

  <clause id="401">
    <literal><![CDATA[
      T(x / (y * x),z) = R(T(1 / y,z),y,x)
    ]]></literal>
    <justification jstring="[para(230(a,1),27(a,2,1)),flip(a)].">
      <j1 rule="para" parents="230 27"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="402">
    <literal><![CDATA[
      R(R(1 / x,y,z),x,u) = R(u / (x * u),y,z)
    ]]></literal>
    <justification jstring="[para(230(a,1),31(a,1,1)),flip(a)].">
      <j1 rule="para" parents="230 31"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="405">
    <literal><![CDATA[
      (x * y) * K(y,x) != x * z
    ]]></literal>
    <literal><![CDATA[
      T(y,x) = z
    ]]></literal>
    <justification jstring="[para(88(a,2),254(a,2)),flip(a)].">
      <j1 rule="para" parents="88 254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="407">
    <literal><![CDATA[
      x * T(T(y,x),z) != u * x
    ]]></literal>
    <literal><![CDATA[
      T(y,z) = u
    ]]></literal>
    <justification jstring="[para(23(a,1),256(a,1,2))].">
      <j1 rule="para" parents="23 256"/>
    </justification>
  </clause>

  <clause id="410">
    <literal><![CDATA[
      (x / y) * y != z * u
    ]]></literal>
    <literal><![CDATA[
      x / u = z
    ]]></literal>
    <justification jstring="[para(160(a,2),263(a,1))].">
      <j1 rule="para" parents="160 263"/>
    </justification>
  </clause>

  <clause id="411">
    <literal><![CDATA[
      ((1 / x) * x) * y != z * u
    ]]></literal>
    <literal><![CDATA[
      y / u = z
    ]]></literal>
    <justification jstring="[para(12(a,2),266(a,1,1))].">
      <j1 rule="para" parents="12 266"/>
    </justification>
  </clause>

  <clause id="412">
    <literal><![CDATA[
      x * (y * (y \ 1)) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ x = u
    ]]></literal>
    <justification jstring="[para(10(a,2),271(a,1,2))].">
      <j1 rule="para" parents="10 271"/>
    </justification>
  </clause>

  <clause id="413">
    <literal><![CDATA[
      x * (y \ y) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ x = u
    ]]></literal>
    <justification jstring="[para(66(a,2),271(a,1,2))].">
      <j1 rule="para" parents="66 271"/>
    </justification>
  </clause>

  <clause id="414">
    <literal><![CDATA[
      (x / y) * y != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ x = u
    ]]></literal>
    <justification jstring="[para(160(a,2),271(a,1))].">
      <j1 rule="para" parents="160 271"/>
    </justification>
  </clause>

  <clause id="415">
    <literal><![CDATA[
      (x * y) / y != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ x = u
    ]]></literal>
    <justification jstring="[para(162(a,2),271(a,1))].">
      <j1 rule="para" parents="162 271"/>
    </justification>
  </clause>

  <clause id="416">
    <literal><![CDATA[
      x * (x \ y) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ y = u
    ]]></literal>
    <justification jstring="[para(164(a,2),271(a,1))].">
      <j1 rule="para" parents="164 271"/>
    </justification>
  </clause>

  <clause id="417">
    <literal><![CDATA[
      x * (y \ (y * (x \ z))) != z * u
    ]]></literal>
    <literal><![CDATA[
      1 = u
    ]]></literal>
    <justification jstring="[para(9(a,2),272(a,1,2))].">
      <j1 rule="para" parents="9 272"/>
    </justification>
  </clause>

  <clause id="418">
    <literal><![CDATA[
      x * (y * (y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z) = z \ u
    ]]></literal>
    <justification jstring="[para(154(a,2),296(a,1))].">
      <j1 rule="para" parents="154 296"/>
    </justification>
  </clause>

  <clause id="419">
    <literal><![CDATA[
      x * T(T(y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) * x = u
    ]]></literal>
    <justification jstring="[para(23(a,1),300(a,1,2))].">
      <j1 rule="para" parents="23 300"/>
    </justification>
  </clause>

  <clause id="420">
    <literal><![CDATA[
      x * L(T(y,x),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(y,z,u) * x = w
    ]]></literal>
    <justification jstring="[para(25(a,2),300(a,1,2))].">
      <j1 rule="para" parents="25 300"/>
    </justification>
  </clause>

  <clause id="421">
    <literal><![CDATA[
      x * R(T(y,x),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      R(y,z,u) * x = w
    ]]></literal>
    <justification jstring="[para(27(a,2),300(a,1,2))].">
      <j1 rule="para" parents="27 300"/>
    </justification>
  </clause>

  <clause id="422">
    <literal><![CDATA[
      ((x / y) * y) / z != u
    ]]></literal>
    <literal><![CDATA[
      x / z = u
    ]]></literal>
    <justification jstring="[para(161(a,2),303(a,1,1))].">
      <j1 rule="para" parents="161 303"/>
    </justification>
  </clause>

  <clause id="423">
    <literal><![CDATA[
      T(x / y,y) != z
    ]]></literal>
    <literal><![CDATA[
      y \ x = z
    ]]></literal>
    <justification jstring="[para(10(a,1),350(a,1,1,1)),flip(b)].">
      <j1 rule="para" parents="10 350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="424">
    <literal><![CDATA[
      x / y != x * z
    ]]></literal>
    <literal><![CDATA[
      L(z \ 1,z,x) = y
    ]]></literal>
    <justification jstring="[para(391(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="391 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="426">
    <literal><![CDATA[
      (x * y) \ x != z
    ]]></literal>
    <literal><![CDATA[
      L(y \ 1,y,x) = z
    ]]></literal>
    <justification jstring="[para(391(a,1),345(a,1,1))].">
      <j1 rule="para" parents="391 345"/>
    </justification>
  </clause>

  <clause id="427">
    <literal><![CDATA[
      x \ (L(y \ 1,y,x) * (x * y)) = K(L(y \ 1,y,x),x * y)
    ]]></literal>
    <justification jstring="[para(392(a,1),16(a,2,1)),flip(a)].">
      <j1 rule="para" parents="392 16"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="428">
    <literal><![CDATA[
      L(L(x \ 1,x,y),y * x,z) = (z * (y * x)) \ (z * y)
    ]]></literal>
    <justification jstring="[para(392(a,1),18(a,2,2,2))].">
      <j1 rule="para" parents="392 18"/>
    </justification>
  </clause>

  <clause id="430">
    <literal><![CDATA[
      R(x,x \ 1,y) \ y = (x \ 1) * y
    ]]></literal>
    <justification jstring="[para(76(a,1),398(a,1,1,1))].">
      <j1 rule="para" parents="76 398"/>
    </justification>
  </clause>

  <clause id="431">
    <literal><![CDATA[
      x / (y * x) != z
    ]]></literal>
    <literal><![CDATA[
      R(1 / y,y,x) = z
    ]]></literal>
    <justification jstring="[para(398(a,1),301(a,1,2)),flip(b)].">
      <j1 rule="para" parents="398 301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="432">
    <literal><![CDATA[
      T(x,x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ y) \ y = z
    ]]></literal>
    <justification jstring="[para(76(a,1),423(a,1,1))].">
      <j1 rule="para" parents="76 423"/>
    </justification>
  </clause>

  <clause id="433">
    <literal><![CDATA[
      K(x,y) = (y * x) \ ((y \ (y * x)) * y)
    ]]></literal>
    <justification jstring="[para(9(a,1),89(a,2,1)),flip(a)].">
      <j1 rule="para" parents="9 89"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="434">
    <literal><![CDATA[
      x \ (y * T(y \ x,y)) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[para(111(a,2),89(a,1,2))].">
      <j1 rule="para" parents="111 89"/>
    </justification>
  </clause>

  <clause id="435">
    <literal><![CDATA[
      K(x \ 1,x) \ 1 = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(276(a,2),90(a,1,1))].">
      <j1 rule="para" parents="276 90"/>
    </justification>
  </clause>

  <clause id="436">
    <literal><![CDATA[
      K(x,1 / x) \ 1 = K(1 / x,x)
    ]]></literal>
    <justification jstring="[para(278(a,2),92(a,1,1))].">
      <j1 rule="para" parents="278 92"/>
    </justification>
  </clause>

  <clause id="437">
    <literal><![CDATA[
      T(T(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(T(x,z),y) = u
    ]]></literal>
    <justification jstring="[para(115(a,1),347(a,1))].">
      <j1 rule="para" parents="115 347"/>
    </justification>
  </clause>

  <clause id="438">
    <literal><![CDATA[
      (1 / x) \ L(y,x,1 / x) = x * y
    ]]></literal>
    <justification jstring="[hyper(121,a,18,a,b,167,a(flip))].">
      <j1 rule="hyper" parents="121 18 167"/>
    </justification>
  </clause>

  <clause id="439">
    <literal><![CDATA[
      x \ L(y,x \ 1,x) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(121,a,18,a,b,166,a(flip))].">
      <j1 rule="hyper" parents="121 18 166"/>
    </justification>
  </clause>

  <clause id="440">
    <literal><![CDATA[
      (x / (y * y)) \ z = (y * y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(121,a,315,a(flip),b,32,a(flip))].">
      <j1 rule="hyper" parents="121 315 32"/>
    </justification>
  </clause>

  <clause id="441">
    <literal><![CDATA[
      x \ (y * (z * z)) = (x \ y) * (z * z)
    ]]></literal>
    <justification jstring="[hyper(121,a,153,a(flip),b,33,a(flip))].">
      <j1 rule="hyper" parents="121 153 33"/>
    </justification>
  </clause>

  <clause id="442">
    <literal><![CDATA[
      (x * (y * y)) \ z = (y * y) \ (x \ z)
    ]]></literal>
    <justification jstring="[hyper(121,a,72,a(flip),b,32,a)].">
      <j1 rule="hyper" parents="121 72 32"/>
    </justification>
  </clause>

  <clause id="443">
    <literal><![CDATA[
      (x \ 1) * (y * y) = x \ (y * y)
    ]]></literal>
    <justification jstring="[hyper(121,a,68,a(flip),b,33,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="121 68 33"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="444">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z * u != y
    ]]></literal>
    <literal><![CDATA[
      T(z,u) = u \ x
    ]]></literal>
    <justification jstring="[para(111(a,1),121(b,1)),flip(c)].">
      <j1 rule="para" parents="111 121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="445">
    <literal><![CDATA[
      L(x,y,1 / y) / (y * x) = 1 / y
    ]]></literal>
    <justification jstring="[hyper(123,a,18,a,b,167,a(flip))].">
      <j1 rule="hyper" parents="123 18 167"/>
    </justification>
  </clause>

  <clause id="446">
    <literal><![CDATA[
      L(x,y \ 1,y) / ((y \ 1) * x) = y
    ]]></literal>
    <justification jstring="[hyper(123,a,18,a,b,166,a(flip))].">
      <j1 rule="hyper" parents="123 18 166"/>
    </justification>
  </clause>

  <clause id="447">
    <literal><![CDATA[
      (x / y) / (z * z) = x / ((z * z) * y)
    ]]></literal>
    <justification jstring="[hyper(123,a,83,a(flip),b,32,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="123 83 32"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="448">
    <literal><![CDATA[
      x / ((y * y) \ 1) = x * (y * y)
    ]]></literal>
    <justification jstring="[hyper(123,a,69,a(flip),b,32,a)].">
      <j1 rule="hyper" parents="123 69 32"/>
    </justification>
  </clause>

  <clause id="449">
    <literal><![CDATA[
      ((x \ y) \ y) \ (T(x,x \ y) * z) = z
    ]]></literal>
    <justification jstring="[hyper(124,a,112,a,b,76,a),flip(a)].">
      <j1 rule="hyper" parents="124 112 76"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="450">
    <literal><![CDATA[
      T(x,x \ y) \ (((x \ y) \ y) * z) = z
    ]]></literal>
    <justification jstring="[hyper(124,a,112,a(flip),b,76,a),flip(a)].">
      <j1 rule="hyper" parents="124 112 76"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="451">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z != y
    ]]></literal>
    <literal><![CDATA[
      T(x,z) = z
    ]]></literal>
    <justification jstring="[para(191(a,1),124(b,1)),flip(c)].">
      <j1 rule="para" parents="191 124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="453">
    <literal><![CDATA[
      R(R(x,y,z),u,w) * (y * z) = (R(x,u,w) * y) * z
    ]]></literal>
    <justification jstring="[hyper(125,a,31,a,b,20,a(flip))].">
      <j1 rule="hyper" parents="125 31 20"/>
    </justification>
  </clause>

  <clause id="456">
    <literal><![CDATA[
      ((x \ y) \ y) * (T(x,x \ y) \ z) = z
    ]]></literal>
    <justification jstring="[hyper(125,a,112,a(flip),b,76,a)].">
      <j1 rule="hyper" parents="125 112 76"/>
    </justification>
  </clause>

  <clause id="457">
    <literal><![CDATA[
      L(R(x,y,z),u,w) * (y * z) = (L(x,u,w) * y) * z
    ]]></literal>
    <justification jstring="[hyper(125,a,29,a(flip),b,20,a(flip))].">
      <j1 rule="hyper" parents="125 29 20"/>
    </justification>
  </clause>

  <clause id="458">
    <literal><![CDATA[
      T(R(x,y,z),u) * (y * z) = (T(x,u) * y) * z
    ]]></literal>
    <justification jstring="[hyper(125,a,27,a(flip),b,20,a(flip))].">
      <j1 rule="hyper" parents="125 27 20"/>
    </justification>
  </clause>

  <clause id="459">
    <literal><![CDATA[
      (x / y) * ((z / y) \ z) = x
    ]]></literal>
    <justification jstring="[hyper(126,a,194,a,b,194,a)].">
      <j1 rule="hyper" parents="126 194 194"/>
    </justification>
  </clause>

  <clause id="460">
    <literal><![CDATA[
      (x / ((y \ z) \ z)) * T(y,y \ z) = x
    ]]></literal>
    <justification jstring="[hyper(126,a,112,a,b,79,a)].">
      <j1 rule="hyper" parents="126 112 79"/>
    </justification>
  </clause>

  <clause id="461">
    <literal><![CDATA[
      (x * y) * L(L(z,y,x),u,w) = x * (y * L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(126,a,30,a,b,18,a(flip))].">
      <j1 rule="hyper" parents="126 30 18"/>
    </justification>
  </clause>

  <clause id="462">
    <literal><![CDATA[
      (x * y) * R(L(z,y,x),u,w) = x * (y * R(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(126,a,29,a,b,18,a(flip))].">
      <j1 rule="hyper" parents="126 29 18"/>
    </justification>
  </clause>

  <clause id="463">
    <literal><![CDATA[
      x * L(y,z \ x,z) = z * ((z \ x) * y)
    ]]></literal>
    <justification jstring="[hyper(126,a,18,a,b,158,a(flip))].">
      <j1 rule="hyper" parents="126 18 158"/>
    </justification>
  </clause>

  <clause id="464">
    <literal><![CDATA[
      (x / T(y,y \ z)) * ((y \ z) \ z) = x
    ]]></literal>
    <justification jstring="[hyper(126,a,112,a(flip),b,79,a)].">
      <j1 rule="hyper" parents="126 112 79"/>
    </justification>
  </clause>

  <clause id="465">
    <literal><![CDATA[
      (x * y) * T(L(z,y,x),u) = x * (y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(126,a,25,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="126 25 18"/>
    </justification>
  </clause>

  <clause id="466">
    <literal><![CDATA[
      x * ((y / z) \ y) != u
    ]]></literal>
    <literal><![CDATA[
      u / z = x
    ]]></literal>
    <justification jstring="[para(459(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="459 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="467">
    <literal><![CDATA[
      (x / y) \ x != z \ u
    ]]></literal>
    <literal><![CDATA[
      u / y = z
    ]]></literal>
    <justification jstring="[para(459(a,1),144(a,1,2)),flip(a)].">
      <j1 rule="para" parents="459 144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="468">
    <literal><![CDATA[
      L(x \ T(y,z),x,z) = (z * x) \ (y * z)
    ]]></literal>
    <justification jstring="[para(241(a,1),18(a,2,2))].">
      <j1 rule="para" parents="241 18"/>
    </justification>
  </clause>

  <clause id="470">
    <literal><![CDATA[
      x * T(T(T(y,x),z),u) = T(T(y,z),u) * x
    ]]></literal>
    <justification jstring="[para(23(a,1),250(a,1,2,1))].">
      <j1 rule="para" parents="23 250"/>
    </justification>
  </clause>

  <clause id="471">
    <literal><![CDATA[
      T(x / y,z) * y = y * T(y \ x,z)
    ]]></literal>
    <justification jstring="[para(113(a,1),250(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="113 250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="472">
    <literal><![CDATA[
      T((x * y) / x,z) * x = x * T(y,z)
    ]]></literal>
    <justification jstring="[para(238(a,1),250(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="238 250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="473">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ y,z) = T(x,z) * (x \ y)
    ]]></literal>
    <justification jstring="[para(112(a,1),250(a,1,2,1))].">
      <j1 rule="para" parents="112 250"/>
    </justification>
  </clause>

  <clause id="474">
    <literal><![CDATA[
      (x * T(x \ y,z)) / x = T(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(289,a,259,a)].">
      <j1 rule="hyper" parents="289 259"/>
    </justification>
  </clause>

  <clause id="475">
    <literal><![CDATA[
      (x * T(x \ y,z)) / x != u
    ]]></literal>
    <literal><![CDATA[
      T(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(259(a,1),302(a,1,1,2)),flip(b)].">
      <j1 rule="para" parents="259 302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="476">
    <literal><![CDATA[
      (x * T(y,z)) / x = T((x * y) / x,z)
    ]]></literal>
    <justification jstring="[para(238(a,1),287(a,1,1,2,1))].">
      <j1 rule="para" parents="238 287"/>
    </justification>
  </clause>

  <clause id="477">
    <literal><![CDATA[
      ((x / y) * T(y,z)) / (x / y) = T(x / (x / y),z)
    ]]></literal>
    <justification jstring="[para(258(a,1),287(a,1,1,2,1))].">
      <j1 rule="para" parents="258 287"/>
    </justification>
  </clause>

  <clause id="478">
    <literal><![CDATA[
      T(x,y) != T(z,u)
    ]]></literal>
    <literal><![CDATA[
      T((y * z) / y,u) = x
    ]]></literal>
    <justification jstring="[para(288(a,1),49(a,2)),flip(b)].">
      <j1 rule="para" parents="288 49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="479">
    <literal><![CDATA[
      (x * T(y,z)) / x != u
    ]]></literal>
    <literal><![CDATA[
      T((x * y) / x,z) = u
    ]]></literal>
    <justification jstring="[para(288(a,1),302(a,1,1,2)),flip(b)].">
      <j1 rule="para" parents="288 302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="480">
    <literal><![CDATA[
      (x * y) \ (x * ((z \ y) * z)) = L(K(z \ y,z),y,x)
    ]]></literal>
    <justification jstring="[para(317(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="317 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="481">
    <literal><![CDATA[
      (x \ y) * x != y * z
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,x) = z
    ]]></literal>
    <justification jstring="[para(317(a,1),43(a,1))].">
      <j1 rule="para" parents="317 43"/>
    </justification>
  </clause>

  <clause id="482">
    <literal><![CDATA[
      K(x \ y,x) * z != (x \ y) * x
    ]]></literal>
    <literal><![CDATA[
      T(y,K(x \ y,x)) = z
    ]]></literal>
    <justification jstring="[para(317(a,1),254(a,2))].">
      <j1 rule="para" parents="317 254"/>
    </justification>
  </clause>

  <clause id="483">
    <literal><![CDATA[
      x \ (y * (x / y)) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x / y) = z
    ]]></literal>
    <justification jstring="[para(318(a,1),342(a,1,2))].">
      <j1 rule="para" parents="318 342"/>
    </justification>
  </clause>

  <clause id="486">
    <literal><![CDATA[
      L(x,y,z) \ (z * (y * x)) = T(z * y,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(296,a,97,a),flip(a)].">
      <j1 rule="hyper" parents="296 97"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="487">
    <literal><![CDATA[
      (x * (y * z)) / L(T(y,z),z,x) = x * z
    ]]></literal>
    <justification jstring="[hyper(123,a,235,a(flip),b,97,a)].">
      <j1 rule="hyper" parents="123 235 97"/>
    </justification>
  </clause>

  <clause id="488">
    <literal><![CDATA[
      (x * y) / L(z \ y,z,x) = x * z
    ]]></literal>
    <justification jstring="[hyper(123,a,154,a(flip),b,97,a)].">
      <j1 rule="hyper" parents="123 154 97"/>
    </justification>
  </clause>

  <clause id="489">
    <literal><![CDATA[
      (x * y) * L(z,T(x,y),y) = y * (T(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,236,a(flip),b,97,a)].">
      <j1 rule="hyper" parents="63 236 97"/>
    </justification>
  </clause>

  <clause id="490">
    <literal><![CDATA[
      x * L(y,z,x / z) = (x / z) * (z * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,152,a(flip),b,97,a)].">
      <j1 rule="hyper" parents="63 152 97"/>
    </justification>
  </clause>

  <clause id="491">
    <literal><![CDATA[
      L(x,y * y,z) = x
    ]]></literal>
    <justification jstring="[hyper(34,a,32,a,b,97,a),flip(a)].">
      <j1 rule="hyper" parents="34 32 97"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="492">
    <literal><![CDATA[
      L(x \ T(y * x,y),x,y) = y
    ]]></literal>
    <justification jstring="[hyper(34,a,241,a(flip),b,97,a),flip(a)].">
      <j1 rule="hyper" parents="34 241 97"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="493">
    <literal><![CDATA[
      (x * (y * z)) * K(L(z,y,x),x * y) = L(z,y,x) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(125,a,97,a(flip),b,189,a)].">
      <j1 rule="hyper" parents="125 97 189"/>
    </justification>
  </clause>

  <clause id="495">
    <literal><![CDATA[
      x \ (y * L(z,x \ y,x)) = (x \ y) * z
    ]]></literal>
    <justification jstring="[hyper(121,a,153,a(flip),b,97,a(flip))].">
      <j1 rule="hyper" parents="121 153 97"/>
    </justification>
  </clause>

  <clause id="496">
    <literal><![CDATA[
      (x * (y * (z * u))) \ ((x * (y * z)) * L(u,z,y)) = a(x,y * z,L(u,z,y))
    ]]></literal>
    <justification jstring="[para(97(a,1),14(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="97 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="497">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * (L(z,y,x) * u)) = L(u,L(z,y,x),x * y)
    ]]></literal>
    <justification jstring="[para(97(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="97 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="498">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (y * (z * u))) = L(L(u,z,y),y * z,x)
    ]]></literal>
    <justification jstring="[para(97(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="97 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="499">
    <literal><![CDATA[
      ((x * (y * z)) * u) / (L(z,y,x) * u) = R(x * y,L(z,y,x),u)
    ]]></literal>
    <justification jstring="[para(97(a,1),20(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="97 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="500">
    <literal><![CDATA[
      (x * (y * z)) / (y * L(z,y,x)) = R(x,y,L(z,y,x))
    ]]></literal>
    <justification jstring="[para(97(a,1),20(a,2,1)),flip(a)].">
      <j1 rule="para" parents="97 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="501">
    <literal><![CDATA[
      (x * y) * z != x * (y * u)
    ]]></literal>
    <literal><![CDATA[
      L(u,y,x) = z
    ]]></literal>
    <justification jstring="[para(97(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="97 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="502">
    <literal><![CDATA[
      (x * y) * L(z,y,x) != x * u
    ]]></literal>
    <literal><![CDATA[
      y * z = u
    ]]></literal>
    <justification jstring="[para(97(a,2),43(a,1))].">
      <j1 rule="para" parents="97 43"/>
    </justification>
  </clause>

  <clause id="504">
    <literal><![CDATA[
      (x * y) \ (x * (y * z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(z,y,x) = u
    ]]></literal>
    <justification jstring="[para(97(a,1),342(a,1,2))].">
      <j1 rule="para" parents="97 342"/>
    </justification>
  </clause>

  <clause id="505">
    <literal><![CDATA[
      x * ((x \ 1) * y) != z
    ]]></literal>
    <literal><![CDATA[
      L(y,x \ 1,x) = z
    ]]></literal>
    <justification jstring="[para(97(a,1),212(a,1))].">
      <j1 rule="para" parents="97 212"/>
    </justification>
  </clause>

  <clause id="507">
    <literal><![CDATA[
      x * (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x * y,L(z,y,x)) = L(z,y,x) \ u
    ]]></literal>
    <justification jstring="[para(97(a,1),296(a,1))].">
      <j1 rule="para" parents="97 296"/>
    </justification>
  </clause>

  <clause id="508">
    <literal><![CDATA[
      a(x,y * y,z) = 1
    ]]></literal>
    <justification jstring="[hyper(53,a,491,a)].">
      <j1 rule="hyper" parents="53 491"/>
    </justification>
  </clause>

  <clause id="509">
    <literal><![CDATA[
      L(x,y * y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(491(a,1),50(a,2))].">
      <j1 rule="para" parents="491 50"/>
    </justification>
  </clause>

  <clause id="510">
    <literal><![CDATA[
      L(x,y \ (1 / y),z) = x
    ]]></literal>
    <justification jstring="[para(293(a,1),491(a,1,2))].">
      <j1 rule="para" parents="293 491"/>
    </justification>
  </clause>

  <clause id="511">
    <literal><![CDATA[
      L(x,y,z) != z
    ]]></literal>
    <literal><![CDATA[
      y \ T(z * y,z) = x
    ]]></literal>
    <justification jstring="[para(492(a,1),50(a,1)),flip(a)].">
      <j1 rule="para" parents="492 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="512">
    <literal><![CDATA[
      L(x \ (y * x),x,y) = T(y,y * x)
    ]]></literal>
    <justification jstring="[hyper(333,a,22,a,b,99,a),flip(a)].">
      <j1 rule="hyper" parents="333 22 99"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="513">
    <literal><![CDATA[
      L(x \ y,x,1 / x) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(333,a,167,a(flip),b,99,a),flip(a)].">
      <j1 rule="hyper" parents="333 167 99"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="514">
    <literal><![CDATA[
      L((x \ 1) \ y,x \ 1,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(333,a,166,a(flip),b,99,a),flip(a)].">
      <j1 rule="hyper" parents="333 166 99"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="515">
    <literal><![CDATA[
      L((x \ y) \ z,x \ y,x) = y \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(333,a,158,a(flip),b,99,a),flip(a)].">
      <j1 rule="hyper" parents="333 158 99"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="516">
    <literal><![CDATA[
      L(x \ ((y * x) / y),x,y) = K(y,(y * x) / y)
    ]]></literal>
    <justification jstring="[hyper(333,a,91,a(flip),b,99,a),flip(a)].">
      <j1 rule="hyper" parents="333 91 99"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="517">
    <literal><![CDATA[
      L(x \ y,x,z / x) = z \ ((z / x) * y)
    ]]></literal>
    <justification jstring="[para(12(a,1),99(a,2,1))].">
      <j1 rule="para" parents="12 99"/>
    </justification>
  </clause>

  <clause id="518">
    <literal><![CDATA[
      L(x \ y,x,z / y) = ((z / y) * x) \ z
    ]]></literal>
    <justification jstring="[para(12(a,1),99(a,2,2))].">
      <j1 rule="para" parents="12 99"/>
    </justification>
  </clause>

  <clause id="519">
    <literal><![CDATA[
      (x * (y * (z * u))) \ (x * ((y * z) * u)) = L(a(y,z,u),y * (z * u),x)
    ]]></literal>
    <justification jstring="[para(14(a,2),99(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14 99"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="520">
    <literal><![CDATA[
      L(T(x,y) \ z,T(x,y),y) = (x * y) \ (y * z)
    ]]></literal>
    <justification jstring="[para(111(a,1),99(a,2,1))].">
      <j1 rule="para" parents="111 99"/>
    </justification>
  </clause>

  <clause id="522">
    <literal><![CDATA[
      L(x \ (1 / y),x,y) = (y * x) \ K(y,1 / y)
    ]]></literal>
    <justification jstring="[para(278(a,2),99(a,2,2))].">
      <j1 rule="para" parents="278 99"/>
    </justification>
  </clause>

  <clause id="523">
    <literal><![CDATA[
      L(x \ 1,x,y) != z
    ]]></literal>
    <literal><![CDATA[
      (y * x) \ y = z
    ]]></literal>
    <justification jstring="[para(99(a,2),348(a,1))].">
      <j1 rule="para" parents="99 348"/>
    </justification>
  </clause>

  <clause id="524">
    <literal><![CDATA[
      L(L(x,y,z) \ u,L(x,y,z),z * y) = (z * (y * x)) \ ((z * y) * u)
    ]]></literal>
    <justification jstring="[para(97(a,1),99(a,2,1))].">
      <j1 rule="para" parents="97 99"/>
    </justification>
  </clause>

  <clause id="525">
    <literal><![CDATA[
      L(x \ L(y,z,u),x,u * z) = ((u * z) * x) \ (u * (z * y))
    ]]></literal>
    <justification jstring="[para(97(a,1),99(a,2,2))].">
      <j1 rule="para" parents="97 99"/>
    </justification>
  </clause>

  <clause id="526">
    <literal><![CDATA[
      L(L(x \ y,x,z),z * x,u) = (u * (z * x)) \ (u * (z * y))
    ]]></literal>
    <justification jstring="[para(99(a,2),99(a,1,1))].">
      <j1 rule="para" parents="99 99"/>
    </justification>
  </clause>

  <clause id="527">
    <literal><![CDATA[
      R(x / y,y,x \ z) \ z = y * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(121,a,315,a(flip),b,107,a)].">
      <j1 rule="hyper" parents="121 315 107"/>
    </justification>
  </clause>

  <clause id="528">
    <literal><![CDATA[
      R(x,T(y,x),z) \ ((y * x) * z) = T(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(121,a,236,a(flip),b,107,a)].">
      <j1 rule="hyper" parents="121 236 107"/>
    </justification>
  </clause>

  <clause id="529">
    <literal><![CDATA[
      R(x,x \ y,z) \ (y * z) = (x \ y) * z
    ]]></literal>
    <justification jstring="[hyper(121,a,153,a(flip),b,107,a)].">
      <j1 rule="hyper" parents="121 153 107"/>
    </justification>
  </clause>

  <clause id="530">
    <literal><![CDATA[
      R(x / y,y,z) \ (x * z) = y * z
    ]]></literal>
    <justification jstring="[hyper(121,a,152,a(flip),b,107,a)].">
      <j1 rule="hyper" parents="121 152 107"/>
    </justification>
  </clause>

  <clause id="531">
    <literal><![CDATA[
      R(x,y,T(z,x * y)) \ (z * (x * y)) = y * T(z,x * y)
    ]]></literal>
    <justification jstring="[hyper(121,a,111,a(flip),b,107,a)].">
      <j1 rule="hyper" parents="121 111 107"/>
    </justification>
  </clause>

  <clause id="532">
    <literal><![CDATA[
      R(x,y,T(z,y)) * (z * y) = (x * y) * T(z,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,235,a(flip),b,107,a)].">
      <j1 rule="hyper" parents="63 235 107"/>
    </justification>
  </clause>

  <clause id="533">
    <literal><![CDATA[
      (x * (1 / y)) * y = R(x,1 / y,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,78,a(flip),b,107,a),flip(a)].">
      <j1 rule="hyper" parents="63 78 107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="534">
    <literal><![CDATA[
      R(x,y,z * z) = x
    ]]></literal>
    <justification jstring="[hyper(35,a,33,a(flip),b,107,a),flip(a)].">
      <j1 rule="hyper" parents="35 33 107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="535">
    <literal><![CDATA[
      R(x,y * y,z) = x
    ]]></literal>
    <justification jstring="[hyper(35,a,32,a(flip),b,107,a),flip(a)].">
      <j1 rule="hyper" parents="35 32 107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="536">
    <literal><![CDATA[
      R(x,1 / y,y) / y = x * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(123,a,78,a(flip),b,107,a(flip))].">
      <j1 rule="hyper" parents="123 78 107"/>
    </justification>
  </clause>

  <clause id="537">
    <literal><![CDATA[
      R(x,y,y \ 1) / (y \ 1) = x * y
    ]]></literal>
    <justification jstring="[hyper(123,a,69,a(flip),b,107,a(flip))].">
      <j1 rule="hyper" parents="123 69 107"/>
    </justification>
  </clause>

  <clause id="538">
    <literal><![CDATA[
      (x * y) \ R(x,y,y \ 1) = y \ 1
    ]]></literal>
    <justification jstring="[hyper(121,a,69,a(flip),b,107,a(flip))].">
      <j1 rule="hyper" parents="121 69 107"/>
    </justification>
  </clause>

  <clause id="539">
    <literal><![CDATA[
      (R(x,y,z) * y) \ ((x * y) * z) = L(z,y,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(121,a,107,a(flip),b,97,a)].">
      <j1 rule="hyper" parents="121 107 97"/>
    </justification>
  </clause>

  <clause id="540">
    <literal><![CDATA[
      R(x,y / z,z) * y = (x * (y / z)) * z
    ]]></literal>
    <justification jstring="[para(12(a,1),107(a,1,2))].">
      <j1 rule="para" parents="12 107"/>
    </justification>
  </clause>

  <clause id="541">
    <literal><![CDATA[
      (((x * y) * z) * u) / ((y * z) * u) = R(R(x,y,z),y * z,u)
    ]]></literal>
    <justification jstring="[para(107(a,1),20(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="107 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="542">
    <literal><![CDATA[
      ((x * R(y,z,u)) * (z * u)) / ((y * z) * u) = R(x,R(y,z,u),z * u)
    ]]></literal>
    <justification jstring="[para(107(a,1),20(a,2,2)),flip(a)].">
      <j1 rule="para" parents="107 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="543">
    <literal><![CDATA[
      (x * y) * z != u * (y * z)
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(107(a,1),44(a,1))].">
      <j1 rule="para" parents="107 44"/>
    </justification>
  </clause>

  <clause id="544">
    <literal><![CDATA[
      ((x * y) * z) / (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(107(a,1),268(a,1,1)),flip(b)].">
      <j1 rule="para" parents="107 268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="545">
    <literal><![CDATA[
      R(x,y * z,K(z,y)) * (z * y) = (x * (y * z)) * K(z,y)
    ]]></literal>
    <justification jstring="[para(88(a,1),107(a,1,2))].">
      <j1 rule="para" parents="88 107"/>
    </justification>
  </clause>

  <clause id="546">
    <literal><![CDATA[
      R(x,R(y,z,u),z * u) * ((y * z) * u) = (x * R(y,z,u)) * (z * u)
    ]]></literal>
    <justification jstring="[para(107(a,1),107(a,1,2))].">
      <j1 rule="para" parents="107 107"/>
    </justification>
  </clause>

  <clause id="547">
    <literal><![CDATA[
      R(x,y,z * z) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(534(a,1),51(a,2))].">
      <j1 rule="para" parents="534 51"/>
    </justification>
  </clause>

  <clause id="548">
    <literal><![CDATA[
      R(x,y,z \ (1 / z)) = x
    ]]></literal>
    <justification jstring="[para(293(a,1),534(a,1,3))].">
      <j1 rule="para" parents="293 534"/>
    </justification>
  </clause>

  <clause id="549">
    <literal><![CDATA[
      R(x,1,y) = x
    ]]></literal>
    <justification jstring="[para(7(a,1),535(a,1,2))].">
      <j1 rule="para" parents="7 535"/>
    </justification>
  </clause>

  <clause id="550">
    <literal><![CDATA[
      R(x,y * y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(535(a,1),51(a,2))].">
      <j1 rule="para" parents="535 51"/>
    </justification>
  </clause>

  <clause id="551">
    <literal><![CDATA[
      R(x,y \ (1 / y),z) = x
    ]]></literal>
    <justification jstring="[para(293(a,1),535(a,1,2))].">
      <j1 rule="para" parents="293 535"/>
    </justification>
  </clause>

  <clause id="552">
    <literal><![CDATA[
      R(x,1,y) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(549(a,1),51(a,1)),flip(a)].">
      <j1 rule="para" parents="549 51"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="553">
    <literal><![CDATA[
      (x * y) * (z \ (1 / z)) = x * (y * (z \ (1 / z)))
    ]]></literal>
    <justification jstring="[hyper(125,a,548,a(flip),b,20,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="125 548 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="554">
    <literal><![CDATA[
      R(x / y,y,y \ 1) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(218,a,108,a(flip))].">
      <j1 rule="hyper" parents="218 108"/>
    </justification>
  </clause>

  <clause id="555">
    <literal><![CDATA[
      R(x / y,y,y \ z) = (x * (y \ z)) / z
    ]]></literal>
    <justification jstring="[para(10(a,1),108(a,2,2))].">
      <j1 rule="para" parents="10 108"/>
    </justification>
  </clause>

  <clause id="556">
    <literal><![CDATA[
      R(x / (y / z),y / z,z) = (x * z) / y
    ]]></literal>
    <justification jstring="[para(12(a,1),108(a,2,2))].">
      <j1 rule="para" parents="12 108"/>
    </justification>
  </clause>

  <clause id="557">
    <literal><![CDATA[
      T((x * y) / (z * y),u) = R(T(x / z,u),z,y)
    ]]></literal>
    <justification jstring="[para(108(a,1),27(a,2,1)),flip(a)].">
      <j1 rule="para" parents="108 27"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="558">
    <literal><![CDATA[
      R(x / T(y,z),T(y,z),y) = (x * y) / (y * T(y,z))
    ]]></literal>
    <justification jstring="[para(280(a,1),108(a,2,2))].">
      <j1 rule="para" parents="280 108"/>
    </justification>
  </clause>

  <clause id="559">
    <literal><![CDATA[
      R(x / y,y,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      x * (y \ 1) = z
    ]]></literal>
    <justification jstring="[para(108(a,2),218(a,1)),flip(b)].">
      <j1 rule="para" parents="108 218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="560">
    <literal><![CDATA[
      R(1 / x,x,y) != z
    ]]></literal>
    <literal><![CDATA[
      y / (x * y) = z
    ]]></literal>
    <justification jstring="[para(108(a,2),303(a,1))].">
      <j1 rule="para" parents="108 303"/>
    </justification>
  </clause>

  <clause id="561">
    <literal><![CDATA[
      R(R(x,y,z) / u,u,y * z) = ((x * y) * z) / (u * (y * z))
    ]]></literal>
    <justification jstring="[para(107(a,1),108(a,2,1))].">
      <j1 rule="para" parents="107 108"/>
    </justification>
  </clause>

  <clause id="562">
    <literal><![CDATA[
      R(x / R(y,z,u),R(y,z,u),z * u) = (x * (z * u)) / ((y * z) * u)
    ]]></literal>
    <justification jstring="[para(107(a,1),108(a,2,2))].">
      <j1 rule="para" parents="107 108"/>
    </justification>
  </clause>

  <clause id="563">
    <literal><![CDATA[
      R(R(x / y,y,z),y * z,u) = ((x * z) * u) / ((y * z) * u)
    ]]></literal>
    <justification jstring="[para(108(a,2),108(a,1,1))].">
      <j1 rule="para" parents="108 108"/>
    </justification>
  </clause>

  <clause id="564">
    <literal><![CDATA[
      x * y != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ (x * y) = u
    ]]></literal>
    <justification jstring="[para(70(a,1),130(a,1,2)),flip(b)].">
      <j1 rule="para" parents="70 130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="565">
    <literal><![CDATA[
      x \ (x * y) != z * u
    ]]></literal>
    <literal><![CDATA[
      y / u = z
    ]]></literal>
    <justification jstring="[para(12(a,1),136(a,1,2,2))].">
      <j1 rule="para" parents="12 136"/>
    </justification>
  </clause>

  <clause id="566">
    <literal><![CDATA[
      R(x * y,K(y,x),z) \ ((y * x) * z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[para(88(a,1),187(a,1,2,1))].">
      <j1 rule="para" parents="88 187"/>
    </justification>
  </clause>

  <clause id="567">
    <literal><![CDATA[
      R(x,K(y \ x,y),z) \ (((y \ x) * y) * z) = K(y \ x,y) * z
    ]]></literal>
    <justification jstring="[para(317(a,1),187(a,1,2,1))].">
      <j1 rule="para" parents="317 187"/>
    </justification>
  </clause>

  <clause id="568">
    <literal><![CDATA[
      R(x * y,L(z,y,x),u) \ ((x * (y * z)) * u) = L(z,y,x) * u
    ]]></literal>
    <justification jstring="[para(97(a,1),187(a,1,2,1))].">
      <j1 rule="para" parents="97 187"/>
    </justification>
  </clause>

  <clause id="569">
    <literal><![CDATA[
      (x * y) / L(z,y / z,x) = x * (y / z)
    ]]></literal>
    <justification jstring="[para(12(a,1),190(a,1,1,2))].">
      <j1 rule="para" parents="12 190"/>
    </justification>
  </clause>

  <clause id="570">
    <literal><![CDATA[
      x \ T(L(y,x \ 1,x),z) = (x \ 1) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(121,a,25,a(flip),b,275,a)].">
      <j1 rule="hyper" parents="121 25 275"/>
    </justification>
  </clause>

  <clause id="571">
    <literal><![CDATA[
      L(T(x,y \ 1),y \ 1,y) = y * (x * (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,235,a(flip),b,275,a),flip(a)].">
      <j1 rule="hyper" parents="63 235 275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="572">
    <literal><![CDATA[
      L(x,y \ 1,y) != y * z
    ]]></literal>
    <literal><![CDATA[
      (y \ 1) * x = z
    ]]></literal>
    <justification jstring="[para(275(a,1),43(a,1))].">
      <j1 rule="para" parents="275 43"/>
    </justification>
  </clause>

  <clause id="573">
    <literal><![CDATA[
      (1 / x) \ L(L(y,x,1 / x),z,u) = x * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(121,a,30,a,b,277,a)].">
      <j1 rule="hyper" parents="121 30 277"/>
    </justification>
  </clause>

  <clause id="574">
    <literal><![CDATA[
      L(T(x,y),y,1 / y) = (1 / y) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,235,a(flip),b,277,a),flip(a)].">
      <j1 rule="hyper" parents="63 235 277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="575">
    <literal><![CDATA[
      x * (y \ (y * z)) != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(9(a,1),307(a,1,2,2,2))].">
      <j1 rule="para" parents="9 307"/>
    </justification>
  </clause>

  <clause id="576">
    <literal><![CDATA[
      L(T(x \ (y \ z),u),x,y) = T((y * x) \ z,u)
    ]]></literal>
    <justification jstring="[para(311(a,1),25(a,2,1))].">
      <j1 rule="para" parents="311 25"/>
    </justification>
  </clause>

  <clause id="577">
    <literal><![CDATA[
      L(L(x \ (y \ z),u,w),x,y) = L((y * x) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(311(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="311 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="578">
    <literal><![CDATA[
      L(x,y,z) != (z * y) \ u
    ]]></literal>
    <literal><![CDATA[
      y \ (z \ u) = x
    ]]></literal>
    <justification jstring="[para(311(a,1),50(a,1)),flip(a)].">
      <j1 rule="para" parents="311 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="579">
    <literal><![CDATA[
      x / y != z * T(u,z)
    ]]></literal>
    <literal><![CDATA[
      (u * z) * y = x
    ]]></literal>
    <justification jstring="[para(191(a,1),338(a,2,1))].">
      <j1 rule="para" parents="191 338"/>
    </justification>
  </clause>

  <clause id="580">
    <literal><![CDATA[
      x / y != (z * u) * K(u,z)
    ]]></literal>
    <literal><![CDATA[
      (u * z) * y = x
    ]]></literal>
    <justification jstring="[para(189(a,1),338(a,2,1))].">
      <j1 rule="para" parents="189 338"/>
    </justification>
  </clause>

  <clause id="582">
    <literal><![CDATA[
      (x * (x \ y)) * z != u
    ]]></literal>
    <literal><![CDATA[
      y * z = u
    ]]></literal>
    <justification jstring="[para(76(a,1),339(a,1,1,1))].">
      <j1 rule="para" parents="76 339"/>
    </justification>
  </clause>

  <clause id="583">
    <literal><![CDATA[
      (x * T(y,x)) * z != u
    ]]></literal>
    <literal><![CDATA[
      (y * x) * z = u
    ]]></literal>
    <justification jstring="[para(191(a,1),339(a,1,1,1))].">
      <j1 rule="para" parents="191 339"/>
    </justification>
  </clause>

  <clause id="585">
    <literal><![CDATA[
      x \ (y * (y \ x)) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ 1 = u
    ]]></literal>
    <justification jstring="[para(164(a,2),340(a,1,2))].">
      <j1 rule="para" parents="164 340"/>
    </justification>
  </clause>

  <clause id="591">
    <literal><![CDATA[
      x \ y != (z / u) * u
    ]]></literal>
    <literal><![CDATA[
      x * z = y
    ]]></literal>
    <justification jstring="[para(79(a,1),341(a,2,2))].">
      <j1 rule="para" parents="79 341"/>
    </justification>
  </clause>

  <clause id="592">
    <literal><![CDATA[
      x \ (x * y) != z \ u
    ]]></literal>
    <literal><![CDATA[
      z * y = u
    ]]></literal>
    <justification jstring="[para(163(a,2),341(a,2)),flip(a)].">
      <j1 rule="para" parents="163 341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="593">
    <literal><![CDATA[
      (x / y) \ x != z \ u
    ]]></literal>
    <literal><![CDATA[
      z * y = u
    ]]></literal>
    <justification jstring="[para(194(a,2),341(a,2)),flip(a)].">
      <j1 rule="para" parents="194 341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="594">
    <literal><![CDATA[
      x \ y != z * T(z \ 1,z)
    ]]></literal>
    <literal><![CDATA[
      x * K(z \ 1,z) = y
    ]]></literal>
    <justification jstring="[para(360(a,1),341(a,2,2))].">
      <j1 rule="para" parents="360 341"/>
    </justification>
  </clause>

  <clause id="595">
    <literal><![CDATA[
      x * (y * T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      x * (z * y) = u
    ]]></literal>
    <justification jstring="[para(22(a,2),343(a,1,2,2))].">
      <j1 rule="para" parents="22 343"/>
    </justification>
  </clause>

  <clause id="596">
    <literal><![CDATA[
      x * ((y / z) \ y) != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(194(a,2),343(a,1,2))].">
      <j1 rule="para" parents="194 343"/>
    </justification>
  </clause>

  <clause id="597">
    <literal><![CDATA[
      L((x \ y) \ z,x \ y,x) != u
    ]]></literal>
    <literal><![CDATA[
      y \ (x * z) = u
    ]]></literal>
    <justification jstring="[para(99(a,2),353(a,1))].">
      <j1 rule="para" parents="99 353"/>
    </justification>
  </clause>

  <clause id="598">
    <literal><![CDATA[
      x \ y != z * (u * (u \ (z \ w)))
    ]]></literal>
    <literal><![CDATA[
      y / w = x
    ]]></literal>
    <justification jstring="[para(10(a,2),354(a,2,2))].">
      <j1 rule="para" parents="10 354"/>
    </justification>
  </clause>

  <clause id="599">
    <literal><![CDATA[
      x \ y != (z / u) * u
    ]]></literal>
    <literal><![CDATA[
      y / z = x
    ]]></literal>
    <justification jstring="[para(79(a,1),354(a,2,2))].">
      <j1 rule="para" parents="79 354"/>
    </justification>
  </clause>

  <clause id="600">
    <literal><![CDATA[
      x \ y != (z \ 1) * z
    ]]></literal>
    <literal><![CDATA[
      y / K(z \ 1,z) = x
    ]]></literal>
    <justification jstring="[para(359(a,1),354(a,2,2))].">
      <j1 rule="para" parents="359 354"/>
    </justification>
  </clause>

  <clause id="601">
    <literal><![CDATA[
      x \ y != R(z,u,w) * (u * w)
    ]]></literal>
    <literal><![CDATA[
      y / ((z * u) * w) = x
    ]]></literal>
    <justification jstring="[para(187(a,1),354(a,2,2))].">
      <j1 rule="para" parents="187 354"/>
    </justification>
  </clause>

  <clause id="602">
    <literal><![CDATA[
      x * y != z * u
    ]]></literal>
    <literal><![CDATA[
      (x * y) / u = z
    ]]></literal>
    <justification jstring="[para(9(a,1),362(a,1,2))].">
      <j1 rule="para" parents="9 362"/>
    </justification>
  </clause>

  <clause id="603">
    <literal><![CDATA[
      x * (y \ (y * (x \ z))) != u * w
    ]]></literal>
    <literal><![CDATA[
      z / w = u
    ]]></literal>
    <justification jstring="[para(9(a,2),362(a,1,2))].">
      <j1 rule="para" parents="9 362"/>
    </justification>
  </clause>

  <clause id="607">
    <literal><![CDATA[
      x * (y * (y \ z)) != u * w
    ]]></literal>
    <literal><![CDATA[
      (x * z) / w = u
    ]]></literal>
    <justification jstring="[para(163(a,1),362(a,1,2))].">
      <j1 rule="para" parents="163 362"/>
    </justification>
  </clause>

  <clause id="609">
    <literal><![CDATA[
      (x \ 1) \ R(y,x,x \ 1) = T(y * x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(296,a,385,a),flip(a)].">
      <j1 rule="hyper" parents="296 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="610">
    <literal><![CDATA[
      L(R(x,y,y \ 1),z,u) / (y \ 1) = L(x,z,u) * y
    ]]></literal>
    <justification jstring="[hyper(123,a,29,a(flip),b,385,a)].">
      <j1 rule="hyper" parents="123 29 385"/>
    </justification>
  </clause>

  <clause id="611">
    <literal><![CDATA[
      T(R(x,y,y \ 1),z) / (y \ 1) = T(x,z) * y
    ]]></literal>
    <justification jstring="[hyper(123,a,27,a(flip),b,385,a)].">
      <j1 rule="hyper" parents="123 27 385"/>
    </justification>
  </clause>

  <clause id="612">
    <literal><![CDATA[
      R(x,y,y \ 1) / (y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      x * y = z
    ]]></literal>
    <justification jstring="[para(385(a,1),268(a,1,1)),flip(b)].">
      <j1 rule="para" parents="385 268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="613">
    <literal><![CDATA[
      R(R(x,y,z),y * z,(y * z) \ 1) = ((x * y) * z) * ((y * z) \ 1)
    ]]></literal>
    <justification jstring="[para(107(a,1),385(a,1,1)),flip(a)].">
      <j1 rule="para" parents="107 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="614">
    <literal><![CDATA[
      T((x \ y) \ 1,y \ x) = (x \ y) \ 1
    ]]></literal>
    <justification jstring="[para(388(a,1),178(a,1,2))].">
      <j1 rule="para" parents="388 178"/>
    </justification>
  </clause>

  <clause id="615">
    <literal><![CDATA[
      K((x \ y) \ 1,y \ x) = 1
    ]]></literal>
    <justification jstring="[para(388(a,1),220(a,1,2))].">
      <j1 rule="para" parents="388 220"/>
    </justification>
  </clause>

  <clause id="616">
    <literal><![CDATA[
      K(((x * y) \ x) \ 1,y) = 1
    ]]></literal>
    <justification jstring="[para(9(a,1),615(a,1,2))].">
      <j1 rule="para" parents="9 615"/>
    </justification>
  </clause>

  <clause id="617">
    <literal><![CDATA[
      T((x \ y) / y,z) = R(T(1 / x,z),x,x \ y)
    ]]></literal>
    <justification jstring="[para(399(a,1),27(a,2,1)),flip(a)].">
      <j1 rule="para" parents="399 27"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="618">
    <literal><![CDATA[
      R(R(1 / x,x,x \ y),y,z) = ((x \ y) * z) / (y * z)
    ]]></literal>
    <justification jstring="[para(399(a,2),108(a,1,1))].">
      <j1 rule="para" parents="399 108"/>
    </justification>
  </clause>

  <clause id="619">
    <literal><![CDATA[
      T(1 / (x / y),y / x) = 1 / (x / y)
    ]]></literal>
    <justification jstring="[para(400(a,1),177(a,1,2))].">
      <j1 rule="para" parents="400 177"/>
    </justification>
  </clause>

  <clause id="620">
    <literal><![CDATA[
      (((x / y) / z) * z) * y != u * w
    ]]></literal>
    <literal><![CDATA[
      x / w = u
    ]]></literal>
    <justification jstring="[para(12(a,2),410(a,1,1))].">
      <j1 rule="para" parents="12 410"/>
    </justification>
  </clause>

  <clause id="621">
    <literal><![CDATA[
      ((x / y) * y) * z != u * w
    ]]></literal>
    <literal><![CDATA[
      (x * z) / w = u
    ]]></literal>
    <justification jstring="[para(159(a,1),410(a,1,1))].">
      <j1 rule="para" parents="159 410"/>
    </justification>
  </clause>

  <clause id="622">
    <literal><![CDATA[
      R(x,y,z) * (y * z) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ ((x * y) * z) = w
    ]]></literal>
    <justification jstring="[para(20(a,2),414(a,1,1))].">
      <j1 rule="para" parents="20 414"/>
    </justification>
  </clause>

  <clause id="623">
    <literal><![CDATA[
      x * T(y,x) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ (y * x) = u
    ]]></literal>
    <justification jstring="[para(191(a,1),414(a,1,1))].">
      <j1 rule="para" parents="191 414"/>
    </justification>
  </clause>

  <clause id="625">
    <literal><![CDATA[
      ((x / y) * y) * z != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (x * z) = w
    ]]></literal>
    <justification jstring="[para(159(a,1),414(a,1,1))].">
      <j1 rule="para" parents="159 414"/>
    </justification>
  </clause>

  <clause id="626">
    <literal><![CDATA[
      (x * y) * L(z,y,x) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (x * (y * z)) = w
    ]]></literal>
    <justification jstring="[para(190(a,1),414(a,1,1))].">
      <j1 rule="para" parents="190 414"/>
    </justification>
  </clause>

  <clause id="627">
    <literal><![CDATA[
      (x * T(y,x)) / x != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ y = u
    ]]></literal>
    <justification jstring="[para(111(a,2),415(a,1,1))].">
      <j1 rule="para" parents="111 415"/>
    </justification>
  </clause>

  <clause id="629">
    <literal><![CDATA[
      x * (y * (y \ (x \ z))) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ z = w
    ]]></literal>
    <justification jstring="[para(10(a,2),416(a,1,2))].">
      <j1 rule="para" parents="10 416"/>
    </justification>
  </clause>

  <clause id="631">
    <literal><![CDATA[
      x * (y * (y \ z)) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (x * z) = w
    ]]></literal>
    <justification jstring="[para(163(a,1),416(a,1,2))].">
      <j1 rule="para" parents="163 416"/>
    </justification>
  </clause>

  <clause id="632">
    <literal><![CDATA[
      R((x / y) / z,z,y) != u
    ]]></literal>
    <literal><![CDATA[
      x / (z * y) = u
    ]]></literal>
    <justification jstring="[para(108(a,2),422(a,1))].">
      <j1 rule="para" parents="108 422"/>
    </justification>
  </clause>

  <clause id="633">
    <literal><![CDATA[
      (x * y) \ (x * z) != u
    ]]></literal>
    <literal><![CDATA[
      L(y \ z,y,x) = u
    ]]></literal>
    <justification jstring="[para(488(a,1),345(a,1,1))].">
      <j1 rule="para" parents="488 345"/>
    </justification>
  </clause>

  <clause id="634">
    <literal><![CDATA[
      L(T(x,y),y,x) = T(x,x * y)
    ]]></literal>
    <justification jstring="[para(22(a,2),512(a,1,1))].">
      <j1 rule="para" parents="22 512"/>
    </justification>
  </clause>

  <clause id="635">
    <literal><![CDATA[
      T(L(x,y,x),y) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,25,a(flip),b,634,a)].">
      <j1 rule="hyper" parents="63 25 634"/>
    </justification>
  </clause>

  <clause id="636">
    <literal><![CDATA[
      L(T(T(x,y),z),y,x) = T(T(x,x * y),z)
    ]]></literal>
    <justification jstring="[para(634(a,1),25(a,2,1))].">
      <j1 rule="para" parents="634 25"/>
    </justification>
  </clause>

  <clause id="637">
    <literal><![CDATA[
      L(R(T(x,y),z,u),y,x) = R(T(x,x * y),z,u)
    ]]></literal>
    <justification jstring="[para(634(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="634 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="638">
    <literal><![CDATA[
      (x * T(y,y * x)) / x = L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(289,a,635,a)].">
      <j1 rule="hyper" parents="289 635"/>
    </justification>
  </clause>

  <clause id="639">
    <literal><![CDATA[
      T((x * y) / x,y * x) = L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(40,a,288,a,b,635,a)].">
      <j1 rule="hyper" parents="40 288 635"/>
    </justification>
  </clause>

  <clause id="640">
    <literal><![CDATA[
      x * T(y,y * x) = L(y,x,y) * x
    ]]></literal>
    <justification jstring="[hyper(126,a,635,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="126 635 22"/>
    </justification>
  </clause>

  <clause id="641">
    <literal><![CDATA[
      T(L(L(x,y,x),z,u),y) = L(T(x,x * y),z,u)
    ]]></literal>
    <justification jstring="[para(635(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="635 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="643">
    <literal><![CDATA[
      L(T((x \ 1) \ y,z),x \ 1,x) = T(x * y,z)
    ]]></literal>
    <justification jstring="[para(514(a,1),25(a,2,1))].">
      <j1 rule="para" parents="514 25"/>
    </justification>
  </clause>

  <clause id="644">
    <literal><![CDATA[
      (x * y) / (z * y) != u
    ]]></literal>
    <literal><![CDATA[
      R(x / z,z,y) = u
    ]]></literal>
    <justification jstring="[para(530(a,1),301(a,1,2)),flip(b)].">
      <j1 rule="para" parents="530 301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="645">
    <literal><![CDATA[
      R(x / (1 / y),1 / y,y) = x * y
    ]]></literal>
    <justification jstring="[hyper(339,a,533,a),flip(a)].">
      <j1 rule="hyper" parents="339 533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="646">
    <literal><![CDATA[
      R(T(x / y,z),y,y \ 1) = T(x * (y \ 1),z)
    ]]></literal>
    <justification jstring="[para(554(a,1),27(a,2,1))].">
      <j1 rule="para" parents="554 27"/>
    </justification>
  </clause>

  <clause id="647">
    <literal><![CDATA[
      R(R(x / y,z,u),y,y \ 1) = R(x * (y \ 1),z,u)
    ]]></literal>
    <justification jstring="[para(554(a,1),31(a,1,1)),flip(a)].">
      <j1 rule="para" parents="554 31"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="648">
    <literal><![CDATA[
      (x * (x \ y)) * z != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (y * z) = w
    ]]></literal>
    <justification jstring="[para(153(a,2),564(a,1))].">
      <j1 rule="para" parents="153 564"/>
    </justification>
  </clause>

  <clause id="649">
    <literal><![CDATA[
      x * (y \ (y * z)) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (x * z) = w
    ]]></literal>
    <justification jstring="[para(155(a,2),564(a,1))].">
      <j1 rule="para" parents="155 564"/>
    </justification>
  </clause>

  <clause id="650">
    <literal><![CDATA[
      x * (y * T(z,y)) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (x * (z * y)) = w
    ]]></literal>
    <justification jstring="[para(235(a,2),564(a,1))].">
      <j1 rule="para" parents="235 564"/>
    </justification>
  </clause>

  <clause id="652">
    <literal><![CDATA[
      (x * y) \ x != z * u
    ]]></literal>
    <literal><![CDATA[
      L(y \ 1,y,x) / u = z
    ]]></literal>
    <justification jstring="[para(392(a,1),565(a,1,2))].">
      <j1 rule="para" parents="392 565"/>
    </justification>
  </clause>

  <clause id="653">
    <literal><![CDATA[
      x * ((y \ z) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      x * T(y,y \ z) = u
    ]]></literal>
    <justification jstring="[para(234(a,1),575(a,1,2,2))].">
      <j1 rule="para" parents="234 575"/>
    </justification>
  </clause>

  <clause id="654">
    <literal><![CDATA[
      ((x / y) \ x) * z != u
    ]]></literal>
    <literal><![CDATA[
      y * z = u
    ]]></literal>
    <justification jstring="[para(194(a,2),582(a,1,1))].">
      <j1 rule="para" parents="194 582"/>
    </justification>
  </clause>

  <clause id="656">
    <literal><![CDATA[
      (x * y) \ x != z \ u
    ]]></literal>
    <literal><![CDATA[
      z * L(y \ 1,y,x) = u
    ]]></literal>
    <justification jstring="[para(392(a,1),592(a,1,2))].">
      <j1 rule="para" parents="392 592"/>
    </justification>
  </clause>

  <clause id="657">
    <literal><![CDATA[
      x \ y != (z * u) / u
    ]]></literal>
    <literal><![CDATA[
      y / z = x
    ]]></literal>
    <justification jstring="[para(159(a,2),599(a,2))].">
      <j1 rule="para" parents="159 599"/>
    </justification>
  </clause>

  <clause id="658">
    <literal><![CDATA[
      x * (y \ (y * z)) != u * w
    ]]></literal>
    <literal><![CDATA[
      (x * z) / w = u
    ]]></literal>
    <justification jstring="[para(155(a,2),602(a,1))].">
      <j1 rule="para" parents="155 602"/>
    </justification>
  </clause>

  <clause id="659">
    <literal><![CDATA[
      T(((x \ y) * x) / (x \ y),y) = L(x,x \ y,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),639(a,1,2))].">
      <j1 rule="para" parents="10 639"/>
    </justification>
  </clause>

  <clause id="660">
    <literal><![CDATA[
      T(T((x * y) / x,z),y * x) = T(L(y,x,y),z)
    ]]></literal>
    <justification jstring="[para(639(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="639 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="662">
    <literal><![CDATA[
      L(x,T(y,x),x) * T(y,x) = T(y,x) * T(x,y * x)
    ]]></literal>
    <justification jstring="[para(111(a,1),640(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="111 640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="663">
    <literal><![CDATA[
      R(T(x / (1 / y),z),1 / y,y) = T(x * y,z)
    ]]></literal>
    <justification jstring="[para(645(a,1),27(a,2,1))].">
      <j1 rule="para" parents="645 27"/>
    </justification>
  </clause>

  <clause id="664">
    <literal><![CDATA[
      x * (y * T(z,x * y)) = L(z,y,x) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,97,a(flip),b,251,a)].">
      <j1 rule="hyper" parents="63 97 251"/>
    </justification>
  </clause>

  <clause id="665">
    <literal><![CDATA[
      x \ (L(y,z,x) * (x * z)) = z * T(y,x * z)
    ]]></literal>
    <justification jstring="[hyper(121,a,251,a(flip),b,97,a(flip))].">
      <j1 rule="hyper" parents="121 251 97"/>
    </justification>
  </clause>

  <clause id="666">
    <literal><![CDATA[
      x * L(x \ (y * x),z,u) = L(y,z,u) * x
    ]]></literal>
    <justification jstring="[para(22(a,1),251(a,1,2,1))].">
      <j1 rule="para" parents="22 251"/>
    </justification>
  </clause>

  <clause id="667">
    <literal><![CDATA[
      x * L(R(T(y,x),z,u),w,v5) = L(R(y,z,u),w,v5) * x
    ]]></literal>
    <justification jstring="[para(27(a,2),251(a,1,2,1))].">
      <j1 rule="para" parents="27 251"/>
    </justification>
  </clause>

  <clause id="668">
    <literal><![CDATA[
      L(x / y,z,u) * y = y * L(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(113(a,1),251(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="113 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="669">
    <literal><![CDATA[
      L((x * y) / x,z,u) * x = x * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(238(a,1),251(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="238 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="670">
    <literal><![CDATA[
      (x \ y) * L((x \ y) \ y,z,u) = L(x,z,u) * (x \ y)
    ]]></literal>
    <justification jstring="[para(112(a,1),251(a,1,2,1))].">
      <j1 rule="para" parents="112 251"/>
    </justification>
  </clause>

  <clause id="671">
    <literal><![CDATA[
      x * L(T(y,y * x),z,u) = L(L(y,x,y),z,u) * x
    ]]></literal>
    <justification jstring="[para(635(a,1),251(a,1,2,1))].">
      <j1 rule="para" parents="635 251"/>
    </justification>
  </clause>

  <clause id="673">
    <literal><![CDATA[
      (x * y) * R(T(z,x * y),x,y) = (z * x) * y
    ]]></literal>
    <justification jstring="[hyper(333,a,107,a(flip),b,252,a),flip(a)].">
      <j1 rule="hyper" parents="333 107 252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="674">
    <literal><![CDATA[
      (x * y) \ ((z * x) * y) = R(T(z,x * y),x,y)
    ]]></literal>
    <justification jstring="[hyper(121,a,107,a(flip),b,252,a)].">
      <j1 rule="hyper" parents="121 107 252"/>
    </justification>
  </clause>

  <clause id="675">
    <literal><![CDATA[
      R(x / y,z,u) * y = y * R(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(113(a,1),252(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="113 252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="676">
    <literal><![CDATA[
      (x \ y) * R((x \ y) \ y,z,u) = R(x,z,u) * (x \ y)
    ]]></literal>
    <justification jstring="[para(112(a,1),252(a,1,2,1))].">
      <j1 rule="para" parents="112 252"/>
    </justification>
  </clause>

  <clause id="679">
    <literal><![CDATA[
      T(x * (x \ y),z) = T(y,z)
    ]]></literal>
    <justification jstring="[hyper(253,a,153,a,b,111,a)].">
      <j1 rule="hyper" parents="253 153 111"/>
    </justification>
  </clause>

  <clause id="680">
    <literal><![CDATA[
      ((x * x) \ y) * (x * x) = T(y,x * x)
    ]]></literal>
    <justification jstring="[hyper(253,a,153,a(flip),b,33,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="253 153 33"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="681">
    <literal><![CDATA[
      T((x * y) / x,x * y) = L(y,x,(x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(253,a,97,a(flip),b,152,a(flip))].">
      <j1 rule="hyper" parents="253 97 152"/>
    </justification>
  </clause>

  <clause id="682">
    <literal><![CDATA[
      (x * x) \ (y \ (z * (y * (x * x)))) = T(z,y * (x * x))
    ]]></literal>
    <justification jstring="[hyper(253,a,72,a(flip),b,32,a),flip(a)].">
      <j1 rule="hyper" parents="253 72 32"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="683">
    <literal><![CDATA[
      (x * L(x \ y,z,u)) / x = L(y / x,z,u)
    ]]></literal>
    <justification jstring="[hyper(289,a,260,a)].">
      <j1 rule="hyper" parents="289 260"/>
    </justification>
  </clause>

  <clause id="685">
    <literal><![CDATA[
      (x * R(x \ y,z,u)) / x = R(y / x,z,u)
    ]]></literal>
    <justification jstring="[hyper(289,a,261,a)].">
      <j1 rule="hyper" parents="289 261"/>
    </justification>
  </clause>

  <clause id="686">
    <literal><![CDATA[
      T(x / (y * x),y) = R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(230(a,1),261(a,1,1))].">
      <j1 rule="para" parents="230 261"/>
    </justification>
  </clause>

  <clause id="687">
    <literal><![CDATA[
      x * R(x \ y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      R(y / x,z,u) * x = w
    ]]></literal>
    <justification jstring="[para(261(a,1),300(a,1,2))].">
      <j1 rule="para" parents="261 300"/>
    </justification>
  </clause>

  <clause id="688">
    <literal><![CDATA[
      T((x * y) / (z * y),z) = R(z \ x,z,y)
    ]]></literal>
    <justification jstring="[para(108(a,1),261(a,1,1))].">
      <j1 rule="para" parents="108 261"/>
    </justification>
  </clause>

  <clause id="689">
    <literal><![CDATA[
      R(x \ (y / z),x,z) = T(y / (x * z),x)
    ]]></literal>
    <justification jstring="[para(314(a,1),261(a,1,1)),flip(a)].">
      <j1 rule="para" parents="314 261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="690">
    <literal><![CDATA[
      R((x / y) \ 1,x / y,y) = T(y / x,x / y)
    ]]></literal>
    <justification jstring="[para(400(a,1),261(a,1,1)),flip(a)].">
      <j1 rule="para" parents="400 261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="691">
    <literal><![CDATA[
      R(x \ y,x,x \ 1) = T(y * (x \ 1),x)
    ]]></literal>
    <justification jstring="[para(554(a,1),261(a,1,1)),flip(a)].">
      <j1 rule="para" parents="554 261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="692">
    <literal><![CDATA[
      (x / (y * x)) * y = y * R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(126,a,686,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="126 686 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="693">
    <literal><![CDATA[
      x \ ((y \ z) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      x \ T(y,y \ z) = u
    ]]></literal>
    <justification jstring="[para(324(a,2),342(a,1,2))].">
      <j1 rule="para" parents="324 342"/>
    </justification>
  </clause>

  <clause id="694">
    <literal><![CDATA[
      T(T(x,x \ y),z) = T((x \ y) \ y,z)
    ]]></literal>
    <justification jstring="[para(324(a,2),679(a,1,1)),flip(a)].">
      <j1 rule="para" parents="324 679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="695">
    <literal><![CDATA[
      T(x \ T(y,y \ z),x \ ((y \ z) \ z)) = x \ ((y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(451,a,325,a,b,xx)].">
      <j1 rule="hyper" parents="451 325"/>
    </justification>
  </clause>

  <clause id="696">
    <literal><![CDATA[
      x \ ((y \ z) \ z) != x \ u
    ]]></literal>
    <literal><![CDATA[
      T(y,y \ z) = u
    ]]></literal>
    <justification jstring="[para(325(a,1),47(a,1))].">
      <j1 rule="para" parents="325 47"/>
    </justification>
  </clause>

  <clause id="697">
    <literal><![CDATA[
      ((x \ y) \ y) \ (z * T(x,x \ y)) = T(z,T(x,x \ y))
    ]]></literal>
    <justification jstring="[hyper(347,a,326,a),flip(a)].">
      <j1 rule="hyper" parents="347 326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="699">
    <literal><![CDATA[
      (T(x,x \ y) * z) \ (((x \ y) \ y) * (z * u)) = L(u,z,T(x,x \ y))
    ]]></literal>
    <justification jstring="[hyper(121,a,329,a(flip),b,97,a)].">
      <j1 rule="hyper" parents="121 329 97"/>
    </justification>
  </clause>

  <clause id="700">
    <literal><![CDATA[
      (T(x,x \ y) * z) \ (((x \ y) \ y) * (z * u)) = L(u,z,(x \ y) \ y)
    ]]></literal>
    <justification jstring="[para(329(a,2),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="329 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="701">
    <literal><![CDATA[
      (x \ y) * L(T((x \ y) \ y,z),u,w) = L(T(x,z),u,w) * (x \ y)
    ]]></literal>
    <justification jstring="[para(330(a,1),251(a,1,2,1))].">
      <j1 rule="para" parents="330 251"/>
    </justification>
  </clause>

  <clause id="703">
    <literal><![CDATA[
      T(x,y) / (x * y) != z
    ]]></literal>
    <literal><![CDATA[
      R(1 / y,y,T(x,y)) = z
    ]]></literal>
    <justification jstring="[para(111(a,1),431(a,1,2))].">
      <j1 rule="para" parents="111 431"/>
    </justification>
  </clause>

  <clause id="704">
    <literal><![CDATA[
      K(x \ (x * y),x) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,89,a(flip),b,433,a)].">
      <j1 rule="hyper" parents="333 89 433"/>
    </justification>
  </clause>

  <clause id="705">
    <literal><![CDATA[
      K(x \ (x * y),z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(67(a,1),704(a,1,1)),flip(a)].">
      <j1 rule="para" parents="67 704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="706">
    <literal><![CDATA[
      K((x / y) \ x,z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(12(a,1),705(a,1,1,2))].">
      <j1 rule="para" parents="12 705"/>
    </justification>
  </clause>

  <clause id="707">
    <literal><![CDATA[
      (x / (y * y)) * z = x * ((y * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(126,a,71,a(flip),b,440,a)].">
      <j1 rule="hyper" parents="126 71 440"/>
    </justification>
  </clause>

  <clause id="708">
    <literal><![CDATA[
      (x * x) * (x \ y) = (x \ 1) \ y
    ]]></literal>
    <justification jstring="[para(284(a,1),440(a,1,1)),flip(a)].">
      <j1 rule="para" parents="284 440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="709">
    <literal><![CDATA[
      (x \ 1) \ (x * y) = (x * x) * y
    ]]></literal>
    <justification jstring="[hyper(575,a,708,a),flip(a)].">
      <j1 rule="hyper" parents="575 708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="710">
    <literal><![CDATA[
      (x * x) \ ((x \ 1) \ y) = x \ y
    ]]></literal>
    <justification jstring="[hyper(129,a,708,a)].">
      <j1 rule="hyper" parents="129 708"/>
    </justification>
  </clause>

  <clause id="711">
    <literal><![CDATA[
      (x * x) \ 1 = x \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(121,a,66,a(flip),b,708,a)].">
      <j1 rule="hyper" parents="121 66 708"/>
    </justification>
  </clause>

  <clause id="712">
    <literal><![CDATA[
      x \ ((x \ 1) * y) = (x * x) \ y
    ]]></literal>
    <justification jstring="[hyper(121,a,9,a(flip),b,708,a),flip(a)].">
      <j1 rule="hyper" parents="121 9 708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="713">
    <literal><![CDATA[
      x * ((x * x) \ y) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(126,a,71,a(flip),b,708,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="126 71 708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="714">
    <literal><![CDATA[
      x / (y \ (y \ 1)) = x * (y * y)
    ]]></literal>
    <justification jstring="[para(711(a,1),448(a,1,2))].">
      <j1 rule="para" parents="711 448"/>
    </justification>
  </clause>

  <clause id="715">
    <literal><![CDATA[
      (x \ 1) * (x * (x * y)) = x * L(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(126,a,97,a(flip),b,709,a)].">
      <j1 rule="hyper" parents="126 97 709"/>
    </justification>
  </clause>

  <clause id="716">
    <literal><![CDATA[
      T(x \ 1,x) = (x * x) \ x
    ]]></literal>
    <justification jstring="[hyper(121,a,240,a(flip),b,709,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="121 240 709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="719">
    <literal><![CDATA[
      ((x * y) * ((y * y) \ z)) / ((y \ 1) * z) = R(x,y,(y * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(197,a,713,a(flip),b,187,a)].">
      <j1 rule="hyper" parents="197 713 187"/>
    </justification>
  </clause>

  <clause id="720">
    <literal><![CDATA[
      (x * ((y \ 1) * z)) \ ((x * y) * ((y * y) \ z)) = a(x,y,(y * y) \ z)
    ]]></literal>
    <justification jstring="[para(713(a,1),14(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="713 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="721">
    <literal><![CDATA[
      x \ ((x \ 1) * y) != z
    ]]></literal>
    <literal><![CDATA[
      (x * x) \ y = z
    ]]></literal>
    <justification jstring="[para(713(a,1),342(a,1,2))].">
      <j1 rule="para" parents="713 342"/>
    </justification>
  </clause>

  <clause id="722">
    <literal><![CDATA[
      x * (y \ (y \ 1)) = x / (y * y)
    ]]></literal>
    <justification jstring="[hyper(338,a,714,a)].">
      <j1 rule="hyper" parents="338 714"/>
    </justification>
  </clause>

  <clause id="723">
    <literal><![CDATA[
      T(x,y * y) / (y * y) = (y * y) \ x
    ]]></literal>
    <justification jstring="[hyper(123,a,22,a,b,441,a(flip))].">
      <j1 rule="hyper" parents="123 22 441"/>
    </justification>
  </clause>

  <clause id="724">
    <literal><![CDATA[
      (x \ (y / (z * z))) * (z * z) = x \ y
    ]]></literal>
    <justification jstring="[para(12(a,1),441(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12 441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="725">
    <literal><![CDATA[
      x \ (y * (z * (u * u))) = (x \ (y * z)) * (u * u)
    ]]></literal>
    <justification jstring="[para(33(a,1),441(a,1,2))].">
      <j1 rule="para" parents="33 441"/>
    </justification>
  </clause>

  <clause id="726">
    <literal><![CDATA[
      ((x * x) \ 1) * y = (x * x) \ y
    ]]></literal>
    <justification jstring="[hyper(38,a,712,a,b,442,a(flip))].">
      <j1 rule="hyper" parents="38 712 442"/>
    </justification>
  </clause>

  <clause id="727">
    <literal><![CDATA[
      (x * (y * (z * z))) \ u = (z * z) \ ((x * y) \ u)
    ]]></literal>
    <justification jstring="[para(33(a,1),442(a,1,1))].">
      <j1 rule="para" parents="33 442"/>
    </justification>
  </clause>

  <clause id="728">
    <literal><![CDATA[
      (x \ (x \ 1)) * y = (x * x) \ y
    ]]></literal>
    <justification jstring="[para(711(a,1),726(a,1,1))].">
      <j1 rule="para" parents="711 726"/>
    </justification>
  </clause>

  <clause id="729">
    <literal><![CDATA[
      (x * x) * (y * (x \ (x \ 1))) = T(y,x \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(253,a,9,a(flip),b,728,a),flip(a)].">
      <j1 rule="hyper" parents="253 9 728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="730">
    <literal><![CDATA[
      ((x * x) \ y) / y = x \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(138,a,728,a)].">
      <j1 rule="hyper" parents="138 728"/>
    </justification>
  </clause>

  <clause id="732">
    <literal><![CDATA[
      ((x * (y \ (y \ 1))) * z) / ((y * y) \ z) = R(x,y \ (y \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(197,a,728,a(flip),b,187,a)].">
      <j1 rule="hyper" parents="197 728 187"/>
    </justification>
  </clause>

  <clause id="733">
    <literal><![CDATA[
      ((1 / x) * (1 / x)) \ y = ((1 / x) \ x) * y
    ]]></literal>
    <justification jstring="[para(79(a,1),728(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="79 728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="735">
    <literal><![CDATA[
      (x \ (x \ 1)) * y != z
    ]]></literal>
    <literal><![CDATA[
      (x * x) \ y = z
    ]]></literal>
    <justification jstring="[para(730(a,1),264(a,1,1)),flip(b)].">
      <j1 rule="para" parents="730 264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="736">
    <literal><![CDATA[
      T(x,x \ y) * z != u
    ]]></literal>
    <literal><![CDATA[
      ((x \ y) \ y) * z = u
    ]]></literal>
    <justification jstring="[para(450(a,1),273(a,1,2)),flip(b)].">
      <j1 rule="para" parents="450 273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="738">
    <literal><![CDATA[
      R(T(x / (1 / y),z),1 / y,y) / y = (1 / y) * T((1 / y) \ x,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,536,a,b,471,a)].">
      <j1 rule="hyper" parents="63 536 471"/>
    </justification>
  </clause>

  <clause id="739">
    <literal><![CDATA[
      T(x / y,z) * y != u
    ]]></literal>
    <literal><![CDATA[
      y * T(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(474(a,1),264(a,1,1)),flip(b)].">
      <j1 rule="para" parents="474 264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="740">
    <literal><![CDATA[
      T(T(x / y,z),y) != u
    ]]></literal>
    <literal><![CDATA[
      T(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(474(a,1),350(a,1,1)),flip(b)].">
      <j1 rule="para" parents="474 350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="741">
    <literal><![CDATA[
      T((x * (y / z)) / x,z) = (x * (z \ y)) / x
    ]]></literal>
    <justification jstring="[para(113(a,1),476(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="113 476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="742">
    <literal><![CDATA[
      T(T((x * y) / x,z),x) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) = u
    ]]></literal>
    <justification jstring="[para(476(a,1),350(a,1,1)),flip(b)].">
      <j1 rule="para" parents="476 350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="744">
    <literal><![CDATA[
      (x \ ((x \ 1) * y)) * (x * x) = T(y,x * x)
    ]]></literal>
    <justification jstring="[para(712(a,2),680(a,1,1))].">
      <j1 rule="para" parents="712 680"/>
    </justification>
  </clause>

  <clause id="745">
    <literal><![CDATA[
      (x * y) * ((y * y) \ z) = R(x / y,y,y) * z
    ]]></literal>
    <justification jstring="[para(108(a,2),707(a,1,1)),flip(a)].">
      <j1 rule="para" parents="108 707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="746">
    <literal><![CDATA[
      (x \ y) / (z * z) != u
    ]]></literal>
    <literal><![CDATA[
      x \ (y / (z * z)) = u
    ]]></literal>
    <justification jstring="[para(724(a,1),268(a,1,1)),flip(b)].">
      <j1 rule="para" parents="724 268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="747">
    <literal><![CDATA[
      (x * y) / a(z,z \ x,y) = z * ((z \ x) * y)
    ]]></literal>
    <justification jstring="[hyper(123,a,153,a(flip),b,84,a)].">
      <j1 rule="hyper" parents="123 153 84"/>
    </justification>
  </clause>

  <clause id="748">
    <literal><![CDATA[
      (x * y) / a(x / z,z,y) = (x / z) * (z * y)
    ]]></literal>
    <justification jstring="[hyper(123,a,152,a(flip),b,84,a)].">
      <j1 rule="hyper" parents="123 152 84"/>
    </justification>
  </clause>

  <clause id="749">
    <literal><![CDATA[
      (x * y) * a(x,z,z \ y) = (x * z) * (z \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),84(a,1,1,2))].">
      <j1 rule="para" parents="10 84"/>
    </justification>
  </clause>

  <clause id="750">
    <literal><![CDATA[
      x * a(x,y,y \ 1) = (x * y) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(69(a,1),84(a,1,1))].">
      <j1 rule="para" parents="69 84"/>
    </justification>
  </clause>

  <clause id="751">
    <literal><![CDATA[
      (x * (y * z)) * a(x,z,T(y,z)) = (x * z) * T(y,z)
    ]]></literal>
    <justification jstring="[para(111(a,1),84(a,1,1,2))].">
      <j1 rule="para" parents="111 84"/>
    </justification>
  </clause>

  <clause id="752">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(84(a,1),342(a,1,2))].">
      <j1 rule="para" parents="84 342"/>
    </justification>
  </clause>

  <clause id="753">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * z) != u \ w
    ]]></literal>
    <literal><![CDATA[
      u * a(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(84(a,1),592(a,1,2))].">
      <j1 rule="para" parents="84 592"/>
    </justification>
  </clause>

  <clause id="754">
    <literal><![CDATA[
      L(T(x,y \ z),y \ z,y) = z \ (y * (x * (y \ z)))
    ]]></literal>
    <justification jstring="[para(111(a,1),98(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="111 98"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="755">
    <literal><![CDATA[
      x \ ((x * y) * (L(y \ 1,y,x) * z)) = L(z,(x * y) \ x,x * y)
    ]]></literal>
    <justification jstring="[para(227(a,2),98(a,1,2,2,1))].">
      <j1 rule="para" parents="227 98"/>
    </justification>
  </clause>

  <clause id="756">
    <literal><![CDATA[
      x * L(y,z,x / z) != u
    ]]></literal>
    <literal><![CDATA[
      (x / z) * (z * y) = u
    ]]></literal>
    <justification jstring="[para(100(a,1),273(a,1,2)),flip(b)].">
      <j1 rule="para" parents="100 273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="757">
    <literal><![CDATA[
      L(L(x,y,z),z * y,u / (z * y)) = u \ ((u / (z * y)) * (z * (y * x)))
    ]]></literal>
    <justification jstring="[para(97(a,1),100(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="97 100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="758">
    <literal><![CDATA[
      R(x,x \ y,(x \ y) \ z) = (y * ((x \ y) \ z)) / z
    ]]></literal>
    <justification jstring="[para(10(a,1),104(a,2,2))].">
      <j1 rule="para" parents="10 104"/>
    </justification>
  </clause>

  <clause id="759">
    <literal><![CDATA[
      R(x,x \ y,y \ z) \ z = (x \ y) * (y \ z)
    ]]></literal>
    <justification jstring="[para(104(a,2),312(a,1,1))].">
      <j1 rule="para" parents="104 312"/>
    </justification>
  </clause>

  <clause id="760">
    <literal><![CDATA[
      L(R(x,y,y \ z),u,w) * z = (L(x,u,w) * y) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(125,a,29,a(flip),b,106,a)].">
      <j1 rule="hyper" parents="125 29 106"/>
    </justification>
  </clause>

  <clause id="761">
    <literal><![CDATA[
      R(x,y,y \ z) * z != u
    ]]></literal>
    <literal><![CDATA[
      (x * y) * (y \ z) = u
    ]]></literal>
    <justification jstring="[para(106(a,1),264(a,1,1)),flip(b)].">
      <j1 rule="para" parents="106 264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="762">
    <literal><![CDATA[
      R(x,x,x \ y) = ((x \ 1) \ y) / y
    ]]></literal>
    <justification jstring="[para(708(a,1),106(a,1,1)),flip(a)].">
      <j1 rule="para" parents="708 106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="763">
    <literal><![CDATA[
      (x \ 1) \ (1 / x) = x * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(125,a,548,a(flip),b,762,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="125 548 762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="765">
    <literal><![CDATA[
      (x \ 1) \ (1 / x) = K(x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(333,a,278,a,b,763,a),flip(a)].">
      <j1 rule="hyper" parents="333 278 763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="766">
    <literal><![CDATA[
      L(x,y \ 1,y) \ x = a(y,y \ 1,x)
    ]]></literal>
    <justification jstring="[para(275(a,1),224(a,1,1))].">
      <j1 rule="para" parents="275 224"/>
    </justification>
  </clause>

  <clause id="767">
    <literal><![CDATA[
      x \ R(x,y,y \ 1) = a(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(385(a,1),226(a,1,2))].">
      <j1 rule="para" parents="385 226"/>
    </justification>
  </clause>

  <clause id="768">
    <literal><![CDATA[
      x * a(x,y,y \ 1) = R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(142,a,767,a)].">
      <j1 rule="hyper" parents="142 767"/>
    </justification>
  </clause>

  <clause id="769">
    <literal><![CDATA[
      L(x \ a(y,z,z \ 1),x,y) = (y * x) \ R(y,z,z \ 1)
    ]]></literal>
    <justification jstring="[para(767(a,1),311(a,1,1,2))].">
      <j1 rule="para" parents="767 311"/>
    </justification>
  </clause>

  <clause id="771">
    <literal><![CDATA[
      x \ R(x,y,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      a(x,y,y \ 1) = z
    ]]></literal>
    <justification jstring="[para(768(a,1),342(a,1,2))].">
      <j1 rule="para" parents="768 342"/>
    </justification>
  </clause>

  <clause id="774">
    <literal><![CDATA[
      (x * y) \ (x * (z * y)) = T(L(z,y,x),y)
    ]]></literal>
    <justification jstring="[hyper(333,a,25,a(flip),b,246,a),flip(a)].">
      <j1 rule="hyper" parents="333 25 246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="775">
    <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(320(a,1),471(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="320 471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="776">
    <literal><![CDATA[
      x * R(T(y,x),z,z \ x) = (y * z) * (z \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,252,a,b,367,a)].">
      <j1 rule="hyper" parents="63 252 367"/>
    </justification>
  </clause>

  <clause id="777">
    <literal><![CDATA[
      L(x \ 1,x,y) \ (z * ((y * x) \ y)) = T(z,(y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(333,a,22,a,b,389,a),flip(a)].">
      <j1 rule="hyper" parents="333 22 389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="778">
    <literal><![CDATA[
      (x * y) * T((x * y) \ x,z) = x * (y * T(y \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(126,a,394,a,b,18,a(flip))].">
      <j1 rule="hyper" parents="126 394 18"/>
    </justification>
  </clause>

  <clause id="779">
    <literal><![CDATA[
      R(T(1 / x,x * y),x,y) = (x * y) \ y
    ]]></literal>
    <justification jstring="[hyper(423,a,401,a),flip(a)].">
      <j1 rule="hyper" parents="423 401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="780">
    <literal><![CDATA[
      x * ((T(y,x) \ z) \ z) != u * x
    ]]></literal>
    <literal><![CDATA[
      T(y,T(y,x) \ z) = u
    ]]></literal>
    <justification jstring="[para(112(a,1),407(a,1,2))].">
      <j1 rule="para" parents="112 407"/>
    </justification>
  </clause>

  <clause id="781">
    <literal><![CDATA[
      x * T(x \ (y * x),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) * x = u
    ]]></literal>
    <justification jstring="[para(22(a,1),419(a,1,2,1))].">
      <j1 rule="para" parents="22 419"/>
    </justification>
  </clause>

  <clause id="782">
    <literal><![CDATA[
      x * ((x \ y) * T(z,y)) = L(z,x \ y,x) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,251,a(flip),b,463,a),flip(a)].">
      <j1 rule="hyper" parents="63 251 463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="783">
    <literal><![CDATA[
      x * ((x \ y) * z) != y * u
    ]]></literal>
    <literal><![CDATA[
      L(z,x \ y,x) = u
    ]]></literal>
    <justification jstring="[para(463(a,1),43(a,1))].">
      <j1 rule="para" parents="463 43"/>
    </justification>
  </clause>

  <clause id="784">
    <literal><![CDATA[
      x \ (y * ((y \ x) * z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(z,y \ x,y) = u
    ]]></literal>
    <justification jstring="[para(463(a,1),342(a,1,2))].">
      <j1 rule="para" parents="463 342"/>
    </justification>
  </clause>

  <clause id="785">
    <literal><![CDATA[
      K(x,y) = L(x \ T(x,y),x,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,16,a,b,468,a)].">
      <j1 rule="hyper" parents="333 16 468"/>
    </justification>
  </clause>

  <clause id="786">
    <literal><![CDATA[
      L(T(x \ T(y,z),u),x,z) = T((z * x) \ (y * z),u)
    ]]></literal>
    <justification jstring="[para(468(a,1),25(a,2,1))].">
      <j1 rule="para" parents="468 25"/>
    </justification>
  </clause>

  <clause id="787">
    <literal><![CDATA[
      (x * y) \ (x * (z * y)) != u
    ]]></literal>
    <literal><![CDATA[
      L(T(z,y),y,x) = u
    ]]></literal>
    <justification jstring="[para(487(a,1),345(a,1,1))].">
      <j1 rule="para" parents="487 345"/>
    </justification>
  </clause>

  <clause id="788">
    <literal><![CDATA[
      L(x \ y,x,y / x) = T(y / x,y)
    ]]></literal>
    <justification jstring="[hyper(253,a,154,a(flip),b,490,a),flip(a)].">
      <j1 rule="hyper" parents="253 154 490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="789">
    <literal><![CDATA[
      (x / y) * (y * T(z,x)) = L(z,y,x / y) * x
    ]]></literal>
    <justification jstring="[hyper(63,a,251,a(flip),b,490,a),flip(a)].">
      <j1 rule="hyper" parents="63 251 490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="790">
    <literal><![CDATA[
      (x / y) \ (L(z,y,x / y) * x) = y * T(z,x)
    ]]></literal>
    <justification jstring="[hyper(121,a,251,a(flip),b,490,a(flip))].">
      <j1 rule="hyper" parents="121 251 490"/>
    </justification>
  </clause>

  <clause id="791">
    <literal><![CDATA[
      L(T((x \ y) \ z,u),x \ y,x) = T(y \ (x * z),u)
    ]]></literal>
    <justification jstring="[para(515(a,1),25(a,2,1))].">
      <j1 rule="para" parents="515 25"/>
    </justification>
  </clause>

  <clause id="792">
    <literal><![CDATA[
      L(R((x \ y) \ z,u,w),x \ y,x) = R(y \ (x * z),u,w)
    ]]></literal>
    <justification jstring="[para(515(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="515 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="793">
    <literal><![CDATA[
      L(L((x \ y) \ z,u,w),x \ y,x) = L(y \ (x * z),u,w)
    ]]></literal>
    <justification jstring="[para(515(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="515 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="794">
    <literal><![CDATA[
      x / ((y * y) \ z) = (x / z) * (y * y)
    ]]></literal>
    <justification jstring="[hyper(197,a,491,a(flip),b,518,a(flip))].">
      <j1 rule="hyper" parents="197 491 518"/>
    </justification>
  </clause>

  <clause id="795">
    <literal><![CDATA[
      R((x * y) / z,z,K(y,x)) \ (y * x) = z * ((x * y) \ (y * x))
    ]]></literal>
    <justification jstring="[para(16(a,2),527(a,1,1,3))].">
      <j1 rule="para" parents="16 527"/>
    </justification>
  </clause>

  <clause id="796">
    <literal><![CDATA[
      R(x,T(y,x),(y * x) \ z) \ z = T(y,x) * ((y * x) \ z)
    ]]></literal>
    <justification jstring="[para(191(a,1),527(a,1,1,1))].">
      <j1 rule="para" parents="191 527"/>
    </justification>
  </clause>

  <clause id="797">
    <literal><![CDATA[
      R(x,x \ (y / z),z) \ y = (x \ (y / z)) * z
    ]]></literal>
    <justification jstring="[para(12(a,1),529(a,1,2))].">
      <j1 rule="para" parents="12 529"/>
    </justification>
  </clause>

  <clause id="798">
    <literal><![CDATA[
      (x * y) / ((z \ x) * y) != u
    ]]></literal>
    <literal><![CDATA[
      R(z,z \ x,y) = u
    ]]></literal>
    <justification jstring="[para(529(a,1),301(a,1,2)),flip(b)].">
      <j1 rule="para" parents="529 301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="799">
    <literal><![CDATA[
      ((x * (y / z)) * z) / y != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y / z,z) = u
    ]]></literal>
    <justification jstring="[para(540(a,1),268(a,1,1)),flip(b)].">
      <j1 rule="para" parents="540 268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="800">
    <literal><![CDATA[
      (x / y) * (1 / y) = x * (y \ (1 / y))
    ]]></literal>
    <justification jstring="[hyper(125,a,548,a(flip),b,555,a(flip))].">
      <j1 rule="hyper" parents="125 548 555"/>
    </justification>
  </clause>

  <clause id="801">
    <literal><![CDATA[
      (x * (y * y)) / z = x / (z / (y * y))
    ]]></literal>
    <justification jstring="[hyper(547,a,556,a),flip(a)].">
      <j1 rule="hyper" parents="547 556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="802">
    <literal><![CDATA[
      R(T(x / (y / z),u),y / z,z) = T((x * z) / y,u)
    ]]></literal>
    <justification jstring="[para(556(a,1),27(a,2,1))].">
      <j1 rule="para" parents="556 27"/>
    </justification>
  </clause>

  <clause id="803">
    <literal><![CDATA[
      R(R(x / (y / z),u,w),y / z,z) = R((x * z) / y,u,w)
    ]]></literal>
    <justification jstring="[para(556(a,1),31(a,1,1)),flip(a)].">
      <j1 rule="para" parents="556 31"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="804">
    <literal><![CDATA[
      R(x / R(1 / y,y,z),z / (y * z),y * z) = (x * (y * z)) / z
    ]]></literal>
    <justification jstring="[para(230(a,2),556(a,1,1,2))].">
      <j1 rule="para" parents="230 556"/>
    </justification>
  </clause>

  <clause id="805">
    <literal><![CDATA[
      R(x / (y / (z * y)),R(1 / z,z,y),z * y) = (x * (z * y)) / y
    ]]></literal>
    <justification jstring="[para(230(a,2),556(a,1,2))].">
      <j1 rule="para" parents="230 556"/>
    </justification>
  </clause>

  <clause id="806">
    <literal><![CDATA[
      (x * (y * y)) / z != u
    ]]></literal>
    <literal><![CDATA[
      x / (z / (y * y)) = u
    ]]></literal>
    <justification jstring="[para(556(a,1),547(a,1))].">
      <j1 rule="para" parents="556 547"/>
    </justification>
  </clause>

  <clause id="807">
    <literal><![CDATA[
      R((x / y) \ z,x / y,y) = T((z * y) / x,x / y)
    ]]></literal>
    <justification jstring="[para(556(a,1),261(a,1,1)),flip(a)].">
      <j1 rule="para" parents="556 261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="808">
    <literal><![CDATA[
      (x * y) * (y / (y * y)) = R(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(125,a,313,a(flip),b,801,a(flip))].">
      <j1 rule="hyper" parents="125 313 801"/>
    </justification>
  </clause>

  <clause id="809">
    <literal><![CDATA[
      (x * y) / (z * z) = x * (y / (z * z))
    ]]></literal>
    <justification jstring="[hyper(125,a,82,a(flip),b,801,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="125 82 801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="810">
    <literal><![CDATA[
      (x * y) * (y \ 1) = R(x,y,y)
    ]]></literal>
    <justification jstring="[para(284(a,1),808(a,1,2))].">
      <j1 rule="para" parents="284 808"/>
    </justification>
  </clause>

  <clause id="811">
    <literal><![CDATA[
      (x \ 1) \ R(y,x,x) = T(y * x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(444,a,xx,b,810,a),flip(a)].">
      <j1 rule="hyper" parents="444 810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="812">
    <literal><![CDATA[
      R(x / y,y,y) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(339,a,810,a),flip(a)].">
      <j1 rule="hyper" parents="339 810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="813">
    <literal><![CDATA[
      R(x,y,y) / (y \ 1) = x * y
    ]]></literal>
    <justification jstring="[hyper(138,a,810,a)].">
      <j1 rule="hyper" parents="138 810"/>
    </justification>
  </clause>

  <clause id="814">
    <literal><![CDATA[
      R(x,x,x) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,708,a(flip),b,810,a),flip(a)].">
      <j1 rule="hyper" parents="63 708 810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="815">
    <literal><![CDATA[
      R(x / y,y,y) != z
    ]]></literal>
    <literal><![CDATA[
      x * (y \ 1) = z
    ]]></literal>
    <justification jstring="[para(810(a,1),339(a,1))].">
      <j1 rule="para" parents="810 339"/>
    </justification>
  </clause>

  <clause id="816">
    <literal><![CDATA[
      R(x,x,x) \ y = ((x \ 1) \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(61,a,814,a)].">
      <j1 rule="hyper" parents="61 814"/>
    </justification>
  </clause>

  <clause id="817">
    <literal><![CDATA[
      T((x \ 1) \ 1,y) = R(T(x,y),x,x)
    ]]></literal>
    <justification jstring="[para(814(a,1),27(a,2,1)),flip(a)].">
      <j1 rule="para" parents="814 27"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="818">
    <literal><![CDATA[
      (x / y) * (y \ 1) = x / (y * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,314,a(flip),b,812,a),flip(a)].">
      <j1 rule="hyper" parents="63 314 812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="819">
    <literal><![CDATA[
      R(T(x / y,z),y,y) = T(x * (y \ 1),z)
    ]]></literal>
    <justification jstring="[para(812(a,1),27(a,2,1))].">
      <j1 rule="para" parents="812 27"/>
    </justification>
  </clause>

  <clause id="820">
    <literal><![CDATA[
      (1 / x) * (x \ 1) = x \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,722,a,b,818,a),flip(a)].">
      <j1 rule="hyper" parents="119 722 818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="821">
    <literal><![CDATA[
      (x \ 1) \ (y / (x * x)) != z
    ]]></literal>
    <literal><![CDATA[
      T(y / x,x \ 1) = z
    ]]></literal>
    <justification jstring="[para(818(a,1),347(a,1,2))].">
      <j1 rule="para" parents="818 347"/>
    </justification>
  </clause>

  <clause id="822">
    <literal><![CDATA[
      (x * y) * (z \ (z \ 1)) = x * (y / (z * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,722,a,b,809,a)].">
      <j1 rule="hyper" parents="63 722 809"/>
    </justification>
  </clause>

  <clause id="824">
    <literal><![CDATA[
      R(T((x * y) / x,z),x,x) != u
    ]]></literal>
    <literal><![CDATA[
      (x * T(y,z)) * (x \ 1) = u
    ]]></literal>
    <justification jstring="[para(476(a,1),815(a,1,1))].">
      <j1 rule="para" parents="476 815"/>
    </justification>
  </clause>

  <clause id="825">
    <literal><![CDATA[
      T(L(x,y,1 / y),y) = (1 / y) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,25,a(flip),b,574,a)].">
      <j1 rule="hyper" parents="63 25 574"/>
    </justification>
  </clause>

  <clause id="827">
    <literal><![CDATA[
      T(x,y) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ T(x,y) = u
    ]]></literal>
    <justification jstring="[para(287(a,1),627(a,1))].">
      <j1 rule="para" parents="287 627"/>
    </justification>
  </clause>

  <clause id="829">
    <literal><![CDATA[
      (x * y) * T(T(x,x * y),z) = x * (y * T(T(x,y),z))
    ]]></literal>
    <justification jstring="[hyper(126,a,636,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="126 636 18"/>
    </justification>
  </clause>

  <clause id="830">
    <literal><![CDATA[
      R(x,y,z) = T(((y * x) * z) / (y * z),y)
    ]]></literal>
    <justification jstring="[para(9(a,1),688(a,2,1)),flip(a)].">
      <j1 rule="para" parents="9 688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="831">
    <literal><![CDATA[
      T(x / (y * z),y) * (y * z) = ((y \ (x / z)) * y) * z
    ]]></literal>
    <justification jstring="[hyper(125,a,689,a(flip),b,20,a(flip))].">
      <j1 rule="hyper" parents="125 689 20"/>
    </justification>
  </clause>

  <clause id="832">
    <literal><![CDATA[
      ((x \ y) * x) * (x \ 1) = T(y * (x \ 1),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,385,a,b,691,a)].">
      <j1 rule="hyper" parents="63 385 691"/>
    </justification>
  </clause>

  <clause id="833">
    <literal><![CDATA[
      T((x * y) * (x \ 1),x) = R(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[para(9(a,1),691(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="834">
    <literal><![CDATA[
      (x / y) * R((x / y) \ 1,x / y,y) = (y / x) * (x / y)
    ]]></literal>
    <justification jstring="[para(12(a,1),692(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="12 692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="835">
    <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(688(a,1),740(a,1,1))].">
      <j1 rule="para" parents="688 740"/>
    </justification>
  </clause>

  <clause id="836">
    <literal><![CDATA[
      T(T(x,y),x) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(11(a,1),742(a,1,1,1))].">
      <j1 rule="para" parents="11 742"/>
    </justification>
  </clause>

  <clause id="837">
    <literal><![CDATA[
      (x * y) * (y \ 1) != x * z
    ]]></literal>
    <literal><![CDATA[
      a(x,y,y \ 1) = z
    ]]></literal>
    <justification jstring="[para(750(a,1),43(a,1))].">
      <j1 rule="para" parents="750 43"/>
    </justification>
  </clause>

  <clause id="838">
    <literal><![CDATA[
      T(L(x,y \ z,y),y \ z) = z \ (y * (x * (y \ z)))
    ]]></literal>
    <justification jstring="[hyper(353,a,774,a),flip(a)].">
      <j1 rule="hyper" parents="353 774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="840">
    <literal><![CDATA[
      T(L(x,y \ z,y),y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      z \ (y * (x * (y \ z))) = u
    ]]></literal>
    <justification jstring="[para(774(a,1),353(a,1))].">
      <j1 rule="para" parents="774 353"/>
    </justification>
  </clause>

  <clause id="841">
    <literal><![CDATA[
      T((1 / x) * (x * y),x) = (1 / x) * (y * x)
    ]]></literal>
    <justification jstring="[para(277(a,2),825(a,1,1))].">
      <j1 rule="para" parents="277 825"/>
    </justification>
  </clause>

  <clause id="842">
    <literal><![CDATA[
      (((x * y) * z) / (x * z)) * x = x * R(y,x,z)
    ]]></literal>
    <justification jstring="[hyper(126,a,830,a,b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="126 830 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="843">
    <literal><![CDATA[
      T(x,y) != R(z,y,u)
    ]]></literal>
    <literal><![CDATA[
      ((y * z) * u) / (y * u) = x
    ]]></literal>
    <justification jstring="[para(830(a,2),49(a,1)),flip(a)].">
      <j1 rule="para" parents="830 49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="844">
    <literal><![CDATA[
      T(R(x,y,x),y * x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(830(a,2),288(a,1,1))].">
      <j1 rule="para" parents="830 288"/>
    </justification>
  </clause>

  <clause id="845">
    <literal><![CDATA[
      R(T(x,y * x),y,x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,27,a,b,844,a)].">
      <j1 rule="hyper" parents="63 27 844"/>
    </justification>
  </clause>

  <clause id="847">
    <literal><![CDATA[
      L(R(x,y,x),z,u) * (y * x) = (y * x) * L(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(844(a,1),251(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="844 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="848">
    <literal><![CDATA[
      R(R(x,y,x),z,u) * (y * x) = (y * x) * R(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(844(a,1),252(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="844 252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="849">
    <literal><![CDATA[
      R(x,y,z) != T(z,y)
    ]]></literal>
    <literal><![CDATA[
      T(z,y * z) = x
    ]]></literal>
    <justification jstring="[para(844(a,1),151(a,1)),flip(a)].">
      <j1 rule="para" parents="844 151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="850">
    <literal><![CDATA[
      ((x * T(y,x * y)) * y) / (x * y) = y
    ]]></literal>
    <justification jstring="[hyper(40,a,830,a(flip),b,845,a(flip))].">
      <j1 rule="hyper" parents="40 830 845"/>
    </justification>
  </clause>

  <clause id="851">
    <literal><![CDATA[
      R(T(x,y),y / x,x) = T(x,y / x)
    ]]></literal>
    <justification jstring="[para(12(a,1),845(a,1,1,2))].">
      <j1 rule="para" parents="12 845"/>
    </justification>
  </clause>

  <clause id="852">
    <literal><![CDATA[
      R(x,y / z,z) != T(z,y / z)
    ]]></literal>
    <literal><![CDATA[
      T(z,y) = x
    ]]></literal>
    <justification jstring="[para(851(a,1),51(a,1)),flip(a)].">
      <j1 rule="para" parents="851 51"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="853">
    <literal><![CDATA[
      R(x,1 / x,x) = T(x,1 / x)
    ]]></literal>
    <justification jstring="[para(199(a,1),851(a,1,1))].">
      <j1 rule="para" parents="199 851"/>
    </justification>
  </clause>

  <clause id="854">
    <literal><![CDATA[
      T(x,1 / x) / x = x * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(123,a,853,a(flip),b,533,a)].">
      <j1 rule="hyper" parents="123 853 533"/>
    </justification>
  </clause>

  <clause id="855">
    <literal><![CDATA[
      T(x,1 / x) / x = K(x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(333,a,278,a,b,854,a),flip(a)].">
      <j1 rule="hyper" parents="333 278 854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="856">
    <literal><![CDATA[
      T(x * T(y,x * y),y) = x * y
    ]]></literal>
    <justification jstring="[hyper(283,a,850,a)].">
      <j1 rule="hyper" parents="283 850"/>
    </justification>
  </clause>

  <clause id="857">
    <literal><![CDATA[
      (x * (y * x)) / x = y * T(x,y * x)
    ]]></literal>
    <justification jstring="[para(850(a,1),82(a,1,1,1))].">
      <j1 rule="para" parents="850 82"/>
    </justification>
  </clause>

  <clause id="858">
    <literal><![CDATA[
      T((x / y) * T(y,(x / y) * y),y) = x
    ]]></literal>
    <justification jstring="[hyper(333,a,12,a(flip),b,856,a),flip(a)].">
      <j1 rule="hyper" parents="333 12 856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="859">
    <literal><![CDATA[
      x \ ((y * (x * y)) / y) = T(y,x * y)
    ]]></literal>
    <justification jstring="[hyper(121,a,857,a,b,xx)].">
      <j1 rule="hyper" parents="121 857"/>
    </justification>
  </clause>

  <clause id="860">
    <literal><![CDATA[
      T((x / y) * T(y,x),y) = x
    ]]></literal>
    <justification jstring="[para(12(a,1),858(a,1,1,2,2))].">
      <j1 rule="para" parents="12 858"/>
    </justification>
  </clause>

  <clause id="861">
    <literal><![CDATA[
      (x / y) * T(y,x) = (y * x) / y
    ]]></literal>
    <justification jstring="[hyper(289,a,860,a),flip(a)].">
      <j1 rule="hyper" parents="289 860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="862">
    <literal><![CDATA[
      T(x,y) \ ((x * y) / x) = T(y / x,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(444,a,xx,b,861,a),flip(a)].">
      <j1 rule="hyper" parents="444 861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="863">
    <literal><![CDATA[
      ((x \ y) * y) / (x \ y) = x * T(x \ y,y)
    ]]></literal>
    <justification jstring="[hyper(351,a,861,a),flip(a)].">
      <j1 rule="hyper" parents="351 861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="864">
    <literal><![CDATA[
      ((x * y) / x) / T(x,y) = y / x
    ]]></literal>
    <justification jstring="[hyper(138,a,861,a)].">
      <j1 rule="hyper" parents="138 861"/>
    </justification>
  </clause>

  <clause id="865">
    <literal><![CDATA[
      T(x,y) = (y / x) \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(129,a,861,a),flip(a)].">
      <j1 rule="hyper" parents="129 861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="866">
    <literal><![CDATA[
      (x * R(y,x,x \ 1)) / x = (x * y) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(289,a,833,a)].">
      <j1 rule="hyper" parents="289 833"/>
    </justification>
  </clause>

  <clause id="867">
    <literal><![CDATA[
      R(T(T(x,y),z),u,w) = T(T(R(x,u,w),z),y)
    ]]></literal>
    <justification jstring="[hyper(333,a,27,a,b,117,a)].">
      <j1 rule="hyper" parents="333 27 117"/>
    </justification>
  </clause>

  <clause id="871">
    <literal><![CDATA[
      R(x,y,T(z,y)) * (z * y) != u
    ]]></literal>
    <literal><![CDATA[
      (x * y) * T(z,y) = u
    ]]></literal>
    <justification jstring="[para(111(a,1),299(a,1,2))].">
      <j1 rule="para" parents="111 299"/>
    </justification>
  </clause>

  <clause id="872">
    <literal><![CDATA[
      T(x,y) * (y * x) != z
    ]]></literal>
    <literal><![CDATA[
      (T(x,y * x) * y) * x = z
    ]]></literal>
    <justification jstring="[para(845(a,1),299(a,1,1))].">
      <j1 rule="para" parents="845 299"/>
    </justification>
  </clause>

  <clause id="873">
    <literal><![CDATA[
      (x * y) * z != y * (T(x,y) * u)
    ]]></literal>
    <literal><![CDATA[
      L(u,T(x,y),y) = z
    ]]></literal>
    <justification jstring="[para(111(a,1),501(a,1,1))].">
      <j1 rule="para" parents="111 501"/>
    </justification>
  </clause>

  <clause id="874">
    <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(88(a,1),501(a,1,1)),flip(a)].">
      <j1 rule="para" parents="88 501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="875">
    <literal><![CDATA[
      K(x \ 1,x) * y != (x \ 1) * (x * z)
    ]]></literal>
    <literal><![CDATA[
      L(z,x,x \ 1) = y
    ]]></literal>
    <justification jstring="[para(276(a,2),501(a,1,1))].">
      <j1 rule="para" parents="276 501"/>
    </justification>
  </clause>

  <clause id="876">
    <literal><![CDATA[
      (x * y) \ (y * (T(x,y) * z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(z,T(x,y),y) = u
    ]]></literal>
    <justification jstring="[para(111(a,1),504(a,1,1))].">
      <j1 rule="para" parents="111 504"/>
    </justification>
  </clause>

  <clause id="877">
    <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(97(a,1),504(a,1,2,2))].">
      <j1 rule="para" parents="97 504"/>
    </justification>
  </clause>

  <clause id="878">
    <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(84(a,1),504(a,1,2,2))].">
      <j1 rule="para" parents="84 504"/>
    </justification>
  </clause>

  <clause id="881">
    <literal><![CDATA[
      (x * y) * K(z \ y,z) != u * ((z \ y) * z)
    ]]></literal>
    <literal><![CDATA[
      R(x,y,K(z \ y,z)) = u
    ]]></literal>
    <justification jstring="[para(317(a,1),543(a,2,2))].">
      <j1 rule="para" parents="317 543"/>
    </justification>
  </clause>

  <clause id="882">
    <literal><![CDATA[
      x / (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      R((x / z) / y,y,z) = u
    ]]></literal>
    <justification jstring="[para(83(a,1),544(a,1,1))].">
      <j1 rule="para" parents="83 544"/>
    </justification>
  </clause>

  <clause id="883">
    <literal><![CDATA[
      R(x / y,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      (x * z) / (y * z) = u
    ]]></literal>
    <justification jstring="[para(11(a,1),632(a,1,1,1))].">
      <j1 rule="para" parents="11 632"/>
    </justification>
  </clause>

  <clause id="885">
    <literal><![CDATA[
      (x * y) / K(y \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      R(x / (y \ 1),y \ 1,y) = z
    ]]></literal>
    <justification jstring="[para(276(a,2),644(a,1,2))].">
      <j1 rule="para" parents="276 644"/>
    </justification>
  </clause>

  <clause id="886">
    <literal><![CDATA[
      x \ L(L((x \ 1) \ y,z,u),x \ 1,x) = L(y / (x \ 1),z,u) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(333,a,439,a,b,668,a)].">
      <j1 rule="hyper" parents="333 439 668"/>
    </justification>
  </clause>

  <clause id="887">
    <literal><![CDATA[
      (x * ((y * x) \ y)) / x = L(1 / x,x,y)
    ]]></literal>
    <justification jstring="[hyper(123,a,390,a(flip),b,668,a)].">
      <j1 rule="hyper" parents="123 390 668"/>
    </justification>
  </clause>

  <clause id="888">
    <literal><![CDATA[
      R(L(x / (1 / y),z,u),1 / y,y) / y = (1 / y) * L((1 / y) \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,536,a,b,668,a)].">
      <j1 rule="hyper" parents="63 536 668"/>
    </justification>
  </clause>

  <clause id="889">
    <literal><![CDATA[
      L(1 / (x \ y),x \ y,x) * (x \ y) = (x \ y) * (y \ x)
    ]]></literal>
    <justification jstring="[para(388(a,1),668(a,2,2))].">
      <j1 rule="para" parents="388 668"/>
    </justification>
  </clause>

  <clause id="890">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) / (x \ y) = L(1 / (x \ y),x \ y,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),887(a,1,1,2,1))].">
      <j1 rule="para" parents="10 887"/>
    </justification>
  </clause>

  <clause id="891">
    <literal><![CDATA[
      L((x * y) / x,z,u) = (x * L(y,z,u)) / x
    ]]></literal>
    <justification jstring="[hyper(138,a,669,a),flip(a)].">
      <j1 rule="hyper" parents="138 669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="892">
    <literal><![CDATA[
      L(((x * y) * z) / (x * y),y,x) = (x * (y * z)) / (x * y)
    ]]></literal>
    <justification jstring="[hyper(123,a,97,a(flip),b,669,a),flip(a)].">
      <j1 rule="hyper" parents="123 97 669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="893">
    <literal><![CDATA[
      (x * L(y,z,u)) / x != w
    ]]></literal>
    <literal><![CDATA[
      L((x * y) / x,z,u) = w
    ]]></literal>
    <justification jstring="[para(669(a,1),268(a,1,1)),flip(b)].">
      <j1 rule="para" parents="669 268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="894">
    <literal><![CDATA[
      ((x / y) * L(y,z,u)) / (x / y) = L(x / (x / y),z,u)
    ]]></literal>
    <justification jstring="[para(79(a,1),683(a,1,1,2,1))].">
      <j1 rule="para" parents="79 683"/>
    </justification>
  </clause>

  <clause id="895">
    <literal><![CDATA[
      L(x / y,z,u) * y != w
    ]]></literal>
    <literal><![CDATA[
      y * L(y \ x,z,u) = w
    ]]></literal>
    <justification jstring="[para(683(a,1),264(a,1,1)),flip(b)].">
      <j1 rule="para" parents="683 264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="896">
    <literal><![CDATA[
      T(L(x / y,z,u),y) != w
    ]]></literal>
    <literal><![CDATA[
      L(y \ x,z,u) = w
    ]]></literal>
    <justification jstring="[para(683(a,1),350(a,1,1)),flip(b)].">
      <j1 rule="para" parents="683 350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="897">
    <literal><![CDATA[
      (x * ((y * x) \ (y * z))) / x = L(z / x,x,y)
    ]]></literal>
    <justification jstring="[para(99(a,1),683(a,1,1,2))].">
      <j1 rule="para" parents="99 683"/>
    </justification>
  </clause>

  <clause id="898">
    <literal><![CDATA[
      L((x \ y) / z,z,x) = (z * ((x * z) \ y)) / z
    ]]></literal>
    <justification jstring="[para(311(a,1),683(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="311 683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="899">
    <literal><![CDATA[
      (x * ((1 / x) * y)) / x = L(y / x,x,1 / x)
    ]]></literal>
    <justification jstring="[para(513(a,1),683(a,1,1,2))].">
      <j1 rule="para" parents="513 683"/>
    </justification>
  </clause>

  <clause id="900">
    <literal><![CDATA[
      ((x \ 1) * (x * y)) / (x \ 1) = L(y / (x \ 1),x \ 1,x)
    ]]></literal>
    <justification jstring="[para(514(a,1),683(a,1,1,2))].">
      <j1 rule="para" parents="514 683"/>
    </justification>
  </clause>

  <clause id="901">
    <literal><![CDATA[
      L(T(x,y) / x,x,y) = (x * K(x,y)) / x
    ]]></literal>
    <justification jstring="[para(785(a,2),683(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="785 683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="902">
    <literal><![CDATA[
      R((x * y) / x,z,u) = (x * R(y,z,u)) / x
    ]]></literal>
    <justification jstring="[para(9(a,1),685(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="903">
    <literal><![CDATA[
      R(x / y,z,u) * y != w
    ]]></literal>
    <literal><![CDATA[
      y * R(y \ x,z,u) = w
    ]]></literal>
    <justification jstring="[para(685(a,1),264(a,1,1)),flip(b)].">
      <j1 rule="para" parents="685 264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="905">
    <literal><![CDATA[
      (x * ((y * (x \ z)) / y)) / x = (y * (z / x)) / y
    ]]></literal>
    <justification jstring="[hyper(289,a,741,a)].">
      <j1 rule="hyper" parents="289 741"/>
    </justification>
  </clause>

  <clause id="906">
    <literal><![CDATA[
      ((x * (y / z)) / x) * z = z * ((x * (z \ y)) / x)
    ]]></literal>
    <justification jstring="[hyper(126,a,741,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="126 741 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="907">
    <literal><![CDATA[
      T(((x * x) * (y / x)) / (x * x),x) = ((x \ 1) \ y) / (x * x)
    ]]></literal>
    <justification jstring="[para(708(a,1),741(a,2,1))].">
      <j1 rule="para" parents="708 741"/>
    </justification>
  </clause>

  <clause id="908">
    <literal><![CDATA[
      (x / y) \ (x \ 1) = y / (x * x)
    ]]></literal>
    <justification jstring="[hyper(121,a,315,a(flip),b,822,a(flip))].">
      <j1 rule="hyper" parents="121 315 822"/>
    </justification>
  </clause>

  <clause id="909">
    <literal><![CDATA[
      x / (y * (x * x)) = (x \ 1) / y
    ]]></literal>
    <justification jstring="[hyper(657,a,908,a),flip(a)].">
      <j1 rule="hyper" parents="657 908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="910">
    <literal><![CDATA[
      (x * K(y \ x,y)) * (y \ 1) = T(x * (y \ 1),y)
    ]]></literal>
    <justification jstring="[para(317(a,2),832(a,1,1))].">
      <j1 rule="para" parents="317 832"/>
    </justification>
  </clause>

  <clause id="911">
    <literal><![CDATA[
      T(x,y * T(y \ x,x)) = x
    ]]></literal>
    <justification jstring="[para(863(a,1),294(a,1,2))].">
      <j1 rule="para" parents="863 294"/>
    </justification>
  </clause>

  <clause id="912">
    <literal><![CDATA[
      T(T(R(x / y,z,u),w),y) = R(T(y \ x,w),z,u)
    ]]></literal>
    <justification jstring="[para(113(a,1),867(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="113 867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="913">
    <literal><![CDATA[
      R(x,x \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      (y * z) / ((x \ y) * z) = u
    ]]></literal>
    <justification jstring="[para(76(a,1),883(a,1,1))].">
      <j1 rule="para" parents="76 883"/>
    </justification>
  </clause>

  <clause id="914">
    <literal><![CDATA[
      L((x * (y \ (z \ u))) / x,y,z) = (x * ((z * y) \ u)) / x
    ]]></literal>
    <justification jstring="[para(311(a,1),891(a,2,1,2))].">
      <j1 rule="para" parents="311 891"/>
    </justification>
  </clause>

  <clause id="915">
    <literal><![CDATA[
      L((x * (y \ 1)) / x,y,z / y) = (x * (z \ (z / y))) / x
    ]]></literal>
    <justification jstring="[para(393(a,1),891(a,2,1,2))].">
      <j1 rule="para" parents="393 891"/>
    </justification>
  </clause>

  <clause id="916">
    <literal><![CDATA[
      L((x * (y \ z)) / x,y,1 / y) = (x * ((1 / y) * z)) / x
    ]]></literal>
    <justification jstring="[para(513(a,1),891(a,2,1,2))].">
      <j1 rule="para" parents="513 891"/>
    </justification>
  </clause>

  <clause id="917">
    <literal><![CDATA[
      L((x * ((y \ z) \ u)) / x,y \ z,y) = (x * (z \ (y * u))) / x
    ]]></literal>
    <justification jstring="[para(515(a,1),891(a,2,1,2))].">
      <j1 rule="para" parents="515 891"/>
    </justification>
  </clause>

  <clause id="918">
    <literal><![CDATA[
      ((((x * y) * z) / (x * y)) * x) * y = (x * y) * R(z,x,y)
    ]]></literal>
    <justification jstring="[hyper(141,a,902,a)].">
      <j1 rule="hyper" parents="141 902"/>
    </justification>
  </clause>

  <clause id="920">
    <literal><![CDATA[
      (((x * y) / x) * z) * (z \ x) = x * R(y,z,z \ x)
    ]]></literal>
    <justification jstring="[hyper(37,a,106,a,b,902,a(flip))].">
      <j1 rule="hyper" parents="37 106 902"/>
    </justification>
  </clause>

  <clause id="922">
    <literal><![CDATA[
      R((x * (1 / y)) / x,y,z) = (x * (z / (y * z))) / x
    ]]></literal>
    <justification jstring="[para(230(a,1),902(a,2,1,2))].">
      <j1 rule="para" parents="230 902"/>
    </justification>
  </clause>

  <clause id="923">
    <literal><![CDATA[
      R((x * ((y / z) / u)) / x,u,z) = (x * (y / (u * z))) / x
    ]]></literal>
    <justification jstring="[para(314(a,1),902(a,2,1,2))].">
      <j1 rule="para" parents="314 902"/>
    </justification>
  </clause>

  <clause id="924">
    <literal><![CDATA[
      R((x * (y / z)) / x,z,z \ 1) = (x * (y * (z \ 1))) / x
    ]]></literal>
    <justification jstring="[para(554(a,1),902(a,2,1,2))].">
      <j1 rule="para" parents="554 902"/>
    </justification>
  </clause>

  <clause id="925">
    <literal><![CDATA[
      R((x * (y / (1 / z))) / x,1 / z,z) = (x * (y * z)) / x
    ]]></literal>
    <justification jstring="[para(645(a,1),902(a,2,1,2))].">
      <j1 rule="para" parents="645 902"/>
    </justification>
  </clause>

  <clause id="926">
    <literal><![CDATA[
      ((x * R(y,z,u)) / x) * (z * u) != w
    ]]></literal>
    <literal><![CDATA[
      (((x * y) / x) * z) * u = w
    ]]></literal>
    <justification jstring="[para(902(a,1),299(a,1,1))].">
      <j1 rule="para" parents="902 299"/>
    </justification>
  </clause>

  <clause id="927">
    <literal><![CDATA[
      (x * y) / a(x / z,z,y) != u
    ]]></literal>
    <literal><![CDATA[
      (x / z) * (z * y) = u
    ]]></literal>
    <justification jstring="[para(87(a,1),301(a,1,2)),flip(b)].">
      <j1 rule="para" parents="87 301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="928">
    <literal><![CDATA[
      L(L(x \ 1,y * x,z),x,y) = (z * (y * x)) \ (z * y)
    ]]></literal>
    <justification jstring="[hyper(333,a,99,a(flip),b,395,a),flip(a)].">
      <j1 rule="hyper" parents="333 99 395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="929">
    <literal><![CDATA[
      (x * y) * L((x * y) \ x,z,u) = x * (y * L(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[hyper(126,a,395,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="126 395 18"/>
    </justification>
  </clause>

  <clause id="930">
    <literal><![CDATA[
      L((x * y) \ x,y,1 / y) = L(1 / y,y,x)
    ]]></literal>
    <justification jstring="[para(387(a,1),395(a,1,1)),flip(a)].">
      <j1 rule="para" parents="387 395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="931">
    <literal><![CDATA[
      L(x \ y,y \ x,1 / (y \ x)) = L(1 / (y \ x),y \ x,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),930(a,1,1,1))].">
      <j1 rule="para" parents="10 930"/>
    </justification>
  </clause>

  <clause id="932">
    <literal><![CDATA[
      R(x / (y * x),z,u) * (y * x) = (R(1 / y,z,u) * y) * x
    ]]></literal>
    <justification jstring="[hyper(125,a,402,a(flip),b,20,a(flip))].">
      <j1 rule="hyper" parents="125 402 20"/>
    </justification>
  </clause>

  <clause id="935">
    <literal><![CDATA[
      x * L(x \ (y * x),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(y,z,u) * x = w
    ]]></literal>
    <justification jstring="[para(22(a,1),420(a,1,2,1))].">
      <j1 rule="para" parents="22 420"/>
    </justification>
  </clause>

  <clause id="938">
    <literal><![CDATA[
      (T((x / y) / z,u) * z) * y = T(x / (z * y),u) * (z * y)
    ]]></literal>
    <justification jstring="[para(314(a,1),458(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="314 458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="939">
    <literal><![CDATA[
      (x * y) * T((x * y) \ (x * z),u) = x * (y * T(y \ z,u))
    ]]></literal>
    <justification jstring="[para(99(a,1),465(a,1,2,1))].">
      <j1 rule="para" parents="99 465"/>
    </justification>
  </clause>

  <clause id="940">
    <literal><![CDATA[
      (x * y) * T((x * y) \ z,u) = x * (y * T(y \ (x \ z),u))
    ]]></literal>
    <justification jstring="[para(311(a,1),465(a,1,2,1))].">
      <j1 rule="para" parents="311 465"/>
    </justification>
  </clause>

  <clause id="941">
    <literal><![CDATA[
      ((x / y) * y) * T(x \ (x / y),z) = (x / y) * (y * T(y \ 1,z))
    ]]></literal>
    <justification jstring="[para(393(a,1),465(a,1,2,1))].">
      <j1 rule="para" parents="393 465"/>
    </justification>
  </clause>

  <clause id="943">
    <literal><![CDATA[
      L(T(T(x,y) \ z,u),T(x,y),y) = T((x * y) \ (y * z),u)
    ]]></literal>
    <justification jstring="[para(520(a,1),25(a,2,1))].">
      <j1 rule="para" parents="520 25"/>
    </justification>
  </clause>

  <clause id="944">
    <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(520(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="520 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="945">
    <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(520(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="520 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="946">
    <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(111(a,1),528(a,1,2))].">
      <j1 rule="para" parents="111 528"/>
    </justification>
  </clause>

  <clause id="947">
    <literal><![CDATA[
      T(((x * y) * x) / (x * y),y) = R(x,y,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(35,a,472,a,b,532,a)].">
      <j1 rule="hyper" parents="35 472 532"/>
    </justification>
  </clause>

  <clause id="948">
    <literal><![CDATA[
      R(T(x,x * y),y,T(x,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(34,a,252,a,b,532,a(flip))].">
      <j1 rule="hyper" parents="34 252 532"/>
    </justification>
  </clause>

  <clause id="949">
    <literal><![CDATA[
      R(x,y,T(z,y)) != T(z,y)
    ]]></literal>
    <literal><![CDATA[
      T(z,z * y) = x
    ]]></literal>
    <justification jstring="[para(948(a,1),51(a,1)),flip(a)].">
      <j1 rule="para" parents="948 51"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="950">
    <literal><![CDATA[
      (T(x,x * y) * y) * T(x,y) = T(x,y) * (x * y)
    ]]></literal>
    <justification jstring="[para(948(a,1),532(a,1,1)),flip(a)].">
      <j1 rule="para" parents="948 532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="951">
    <literal><![CDATA[
      R(T(x / y,y * z),y,z) = (y * z) \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(423,a,557,a),flip(a)].">
      <j1 rule="hyper" parents="423 557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="952">
    <literal><![CDATA[
      R(T(x / y,y * z),y,z) != u
    ]]></literal>
    <literal><![CDATA[
      (y * z) \ (x * z) = u
    ]]></literal>
    <justification jstring="[para(557(a,1),423(a,1))].">
      <j1 rule="para" parents="557 423"/>
    </justification>
  </clause>

  <clause id="953">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ y,z) = x \ T(x * y,z)
    ]]></literal>
    <justification jstring="[para(514(a,1),570(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="514 570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="954">
    <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(576(a,1),306(a,1,2))].">
      <j1 rule="para" parents="576 306"/>
    </justification>
  </clause>

  <clause id="955">
    <literal><![CDATA[
      T((x \ y) / y,z) * y = (T(1 / x,z) * x) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(125,a,617,a,b,106,a)].">
      <j1 rule="hyper" parents="125 617 106"/>
    </justification>
  </clause>

  <clause id="956">
    <literal><![CDATA[
      R(T(1 / x,y),x,x \ 1) = T(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(74(a,1),617(a,1,1)),flip(a)].">
      <j1 rule="para" parents="74 617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="957">
    <literal><![CDATA[
      T(x \ 1,y) / (x \ 1) = T(1 / x,y) * x
    ]]></literal>
    <justification jstring="[hyper(123,a,956,a(flip),b,385,a)].">
      <j1 rule="hyper" parents="123 956 385"/>
    </justification>
  </clause>

  <clause id="959">
    <literal><![CDATA[
      T(x \ 1,y) / (x \ 1) = x * T(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,471,a(flip),b,957,a),flip(a)].">
      <j1 rule="hyper" parents="333 471 957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="960">
    <literal><![CDATA[
      T(x * T(x \ 1,y),x \ 1) = (x \ 1) \ T(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(959(a,1),113(a,1,1))].">
      <j1 rule="para" parents="959 113"/>
    </justification>
  </clause>

  <clause id="961">
    <literal><![CDATA[
      T(L(L(x,y,x),z,u),y) = T(L(x,z,u),x * y)
    ]]></literal>
    <justification jstring="[hyper(333,a,25,a(flip),b,641,a),flip(a)].">
      <j1 rule="hyper" parents="333 25 641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="962">
    <literal><![CDATA[
      x * (((x \ 1) \ y) * (x \ 1)) = T(x * y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,571,a(flip),b,643,a)].">
      <j1 rule="hyper" parents="63 571 643"/>
    </justification>
  </clause>

  <clause id="963">
    <literal><![CDATA[
      x \ T(x * y,x \ 1) = ((x \ 1) \ y) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(121,a,643,a(flip),b,571,a(flip))].">
      <j1 rule="hyper" parents="121 643 571"/>
    </justification>
  </clause>

  <clause id="964">
    <literal><![CDATA[
      T(T((x * y) / x,z),y * x) = L(T(y,z),x,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,25,a,b,660,a),flip(a)].">
      <j1 rule="hyper" parents="333 25 660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="965">
    <literal><![CDATA[
      T(((1 / x) * y) * x,1 / x) = R(y,1 / x,x)
    ]]></literal>
    <justification jstring="[para(238(a,1),663(a,1,1)),flip(a)].">
      <j1 rule="para" parents="238 663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="966">
    <literal><![CDATA[
      ((x * y) \ x) * (x * y) = x * (y * T(y \ 1,x * y))
    ]]></literal>
    <justification jstring="[para(227(a,1),664(a,2,1)),flip(a)].">
      <j1 rule="para" parents="227 664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="967">
    <literal><![CDATA[
      R(T(x,(y * z) * a(x,y,z)),y * z,a(x,y,z)) = ((y * z) * a(x,y,z)) \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[hyper(121,a,84,a(flip),b,673,a),flip(a)].">
      <j1 rule="hyper" parents="121 84 673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="968">
    <literal><![CDATA[
      (x * y) * T(y,x) = (y * x) * y
    ]]></literal>
    <justification jstring="[para(845(a,1),673(a,1,2))].">
      <j1 rule="para" parents="845 673"/>
    </justification>
  </clause>

  <clause id="969">
    <literal><![CDATA[
      (x * (y / x)) * x = y * T(x,y / x)
    ]]></literal>
    <justification jstring="[hyper(339,a,968,a),flip(a)].">
      <j1 rule="hyper" parents="339 968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="970">
    <literal><![CDATA[
      ((x \ 1) * x) \ x = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(121,a,68,a(flip),b,968,a)].">
      <j1 rule="hyper" parents="121 68 968"/>
    </justification>
  </clause>

  <clause id="971">
    <literal><![CDATA[
      K(x \ 1,x) \ x = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(276(a,2),970(a,1,1))].">
      <j1 rule="para" parents="276 970"/>
    </justification>
  </clause>

  <clause id="972">
    <literal><![CDATA[
      K(x \ 1,x) * ((x \ 1) \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(126,a,112,a(flip),b,971,a)].">
      <j1 rule="hyper" parents="126 112 971"/>
    </justification>
  </clause>

  <clause id="973">
    <literal><![CDATA[
      L(x,y,(y * x) / y) * y = y * T(x,y * x)
    ]]></literal>
    <justification jstring="[hyper(125,a,681,a(flip),b,476,a)].">
      <j1 rule="hyper" parents="125 681 476"/>
    </justification>
  </clause>

  <clause id="975">
    <literal><![CDATA[
      T(x \ 1,y) / (x \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      x * T(x \ 1,y) = z
    ]]></literal>
    <justification jstring="[para(957(a,2),739(a,1))].">
      <j1 rule="para" parents="957 739"/>
    </justification>
  </clause>

  <clause id="976">
    <literal><![CDATA[
      (x * y) * ((y * y) \ z) = (x * (y \ 1)) * z
    ]]></literal>
    <justification jstring="[para(812(a,1),745(a,2,1))].">
      <j1 rule="para" parents="812 745"/>
    </justification>
  </clause>

  <clause id="977">
    <literal><![CDATA[
      T(x * (y \ 1),y * y) = (y * y) \ (x * y)
    ]]></literal>
    <justification jstring="[hyper(444,a,173,a(flip),b,976,a(flip))].">
      <j1 rule="hyper" parents="444 173 976"/>
    </justification>
  </clause>

  <clause id="978">
    <literal><![CDATA[
      (x * y) / a(z,z \ y,T(x,y)) = z * ((z \ y) * T(x,y))
    ]]></literal>
    <justification jstring="[para(111(a,1),747(a,1,1))].">
      <j1 rule="para" parents="111 747"/>
    </justification>
  </clause>

  <clause id="979">
    <literal><![CDATA[
      (x * T(y,(x / z) * z)) / a(x / z,z,T(y,(x / z) * z)) = L(y,z,x / z) * ((x / z) * z)
    ]]></literal>
    <justification jstring="[hyper(333,a,664,a(flip),b,748,a),flip(a)].">
      <j1 rule="hyper" parents="333 664 748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="980">
    <literal><![CDATA[
      ((x * y) * (y \ z)) / T(x * z,a(x,y,y \ z)) = a(x,y,y \ z)
    ]]></literal>
    <justification jstring="[hyper(123,a,749,a(flip),b,111,a)].">
      <j1 rule="hyper" parents="123 749 111"/>
    </justification>
  </clause>

  <clause id="982">
    <literal><![CDATA[
      R(T(x / y,z),y,y \ z) = z \ (x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(121,a,152,a(flip),b,776,a),flip(a)].">
      <j1 rule="hyper" parents="121 152 776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="983">
    <literal><![CDATA[
      (x / y) \ (L(z,y,x / y) * x) != u
    ]]></literal>
    <literal><![CDATA[
      y * T(z,x) = u
    ]]></literal>
    <justification jstring="[para(789(a,1),342(a,1,2))].">
      <j1 rule="para" parents="789 342"/>
    </justification>
  </clause>

  <clause id="984">
    <literal><![CDATA[
      (x \ (1 / x)) * x = x \ 1
    ]]></literal>
    <justification jstring="[para(551(a,1),797(a,1,1)),flip(a)].">
      <j1 rule="para" parents="551 797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="985">
    <literal><![CDATA[
      (x \ 1) / x = x \ (1 / x)
    ]]></literal>
    <justification jstring="[hyper(138,a,984,a)].">
      <j1 rule="hyper" parents="138 984"/>
    </justification>
  </clause>

  <clause id="986">
    <literal><![CDATA[
      (x * (y \ 1)) / L(y,y \ (1 / y),x) = x * (y \ (1 / y))
    ]]></literal>
    <justification jstring="[para(984(a,1),190(a,1,1,2))].">
      <j1 rule="para" parents="984 190"/>
    </justification>
  </clause>

  <clause id="987">
    <literal><![CDATA[
      (x * (y * (z * z))) / u != w
    ]]></literal>
    <literal><![CDATA[
      (x * y) / (u / (z * z)) = w
    ]]></literal>
    <justification jstring="[para(33(a,1),806(a,1,1))].">
      <j1 rule="para" parents="33 806"/>
    </justification>
  </clause>

  <clause id="989">
    <literal><![CDATA[
      (x * (y * (x \ 1))) / x = (x * (y / x)) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(554(a,1),866(a,1,1,2))].">
      <j1 rule="para" parents="554 866"/>
    </justification>
  </clause>

  <clause id="990">
    <literal><![CDATA[
      L((x \ (y * (x * z))) / z,z,x) = (z * T(y,x * z)) / z
    ]]></literal>
    <justification jstring="[para(22(a,2),898(a,2,1,2))].">
      <j1 rule="para" parents="22 898"/>
    </justification>
  </clause>

  <clause id="991">
    <literal><![CDATA[
      L((x \ (T(x,y) * y)) / y,y,x) = (y * K(T(x,y),y)) / y
    ]]></literal>
    <justification jstring="[para(244(a,1),898(a,2,1,2))].">
      <j1 rule="para" parents="244 898"/>
    </justification>
  </clause>

  <clause id="992">
    <literal><![CDATA[
      (x \ (y * (z \ x))) * x = (T(y / z,x) * z) * (z \ x)
    ]]></literal>
    <justification jstring="[hyper(125,a,982,a(flip),b,106,a)].">
      <j1 rule="hyper" parents="125 982 106"/>
    </justification>
  </clause>

  <clause id="993">
    <literal><![CDATA[
      (x * y) \ (x * ((y * z) * (u * u))) = L(z,y,x) * (u * u)
    ]]></literal>
    <justification jstring="[para(18(a,2),725(a,2,1))].">
      <j1 rule="para" parents="18 725"/>
    </justification>
  </clause>

  <clause id="994">
    <literal><![CDATA[
      ((1 / x) * (1 / x)) \ ((y * x) \ z) = (y * (1 / x)) \ z
    ]]></literal>
    <justification jstring="[para(228(a,1),727(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="228 727"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="995">
    <literal><![CDATA[
      (x * x) * (y / (x * x)) = T(y,x \ (x \ 1))
    ]]></literal>
    <justification jstring="[para(722(a,1),729(a,1,2))].">
      <j1 rule="para" parents="722 729"/>
    </justification>
  </clause>

  <clause id="996">
    <literal><![CDATA[
      (x * x) * (y * (z / (x * x))) = T(y * z,x \ (x \ 1))
    ]]></literal>
    <justification jstring="[para(822(a,1),729(a,1,2))].">
      <j1 rule="para" parents="822 729"/>
    </justification>
  </clause>

  <clause id="997">
    <literal><![CDATA[
      T(x,x \ (x \ 1)) = R(x,x,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,808,a(flip),b,995,a),flip(a)].">
      <j1 rule="hyper" parents="63 808 995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="998">
    <literal><![CDATA[
      (x * ((y * z) / y)) / x = (y * ((x * z) / x)) / y
    ]]></literal>
    <justification jstring="[para(9(a,1),905(a,1,1,2,1,2))].">
      <j1 rule="para" parents="9 905"/>
    </justification>
  </clause>

  <clause id="999">
    <literal><![CDATA[
      ((x * (y / z)) / x) * z != u
    ]]></literal>
    <literal><![CDATA[
      z * ((x * (z \ y)) / x) = u
    ]]></literal>
    <justification jstring="[para(905(a,1),264(a,1,1)),flip(b)].">
      <j1 rule="para" parents="905 264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1000">
    <literal><![CDATA[
      T((x * (y / z)) / x,z) != u
    ]]></literal>
    <literal><![CDATA[
      (x * (z \ y)) / x = u
    ]]></literal>
    <justification jstring="[para(905(a,1),350(a,1,1)),flip(b)].">
      <j1 rule="para" parents="905 350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1001">
    <literal><![CDATA[
      R((x * (y / z)) / x,z,z \ 1) / (z \ 1) = z * ((x * (z \ y)) / x)
    ]]></literal>
    <justification jstring="[hyper(63,a,537,a,b,906,a)].">
      <j1 rule="hyper" parents="63 537 906"/>
    </justification>
  </clause>

  <clause id="1002">
    <literal><![CDATA[
      (x \ y) * ((z * ((x \ y) \ y)) / z) = ((z * x) / z) * (x \ y)
    ]]></literal>
    <justification jstring="[para(76(a,1),906(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="76 906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1003">
    <literal><![CDATA[
      ((x * R(y / z,z,u)) / x) * (z * u) = (z * u) * ((x * ((z * u) \ (y * u))) / x)
    ]]></literal>
    <justification jstring="[para(108(a,2),906(a,1,1,1,2))].">
      <j1 rule="para" parents="108 906"/>
    </justification>
  </clause>

  <clause id="1004">
    <literal><![CDATA[
      (x * K(y \ x,y)) * (y \ 1) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ T(x * (y \ 1),y) = u
    ]]></literal>
    <justification jstring="[para(910(a,2),827(a,1))].">
      <j1 rule="para" parents="910 827"/>
    </justification>
  </clause>

  <clause id="1005">
    <literal><![CDATA[
      T(T((x * y) / (z * y),u),z) = R(T(z \ x,u),z,y)
    ]]></literal>
    <justification jstring="[para(108(a,1),912(a,1,1,1))].">
      <j1 rule="para" parents="108 912"/>
    </justification>
  </clause>

  <clause id="1006">
    <literal><![CDATA[
      T(T(x,x * y) * y,T(x,y)) = x * y
    ]]></literal>
    <justification jstring="[hyper(253,a,950,a,b,xx)].">
      <j1 rule="hyper" parents="253 950"/>
    </justification>
  </clause>

  <clause id="1007">
    <literal><![CDATA[
      x \ T(x * (y * (x \ 1)),z) = T(y,z) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(781,a,953,a),flip(a)].">
      <j1 rule="hyper" parents="781 953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1008">
    <literal><![CDATA[
      (1 / x) \ T((1 / x) * y,z) = x * T(((1 / x) \ 1) \ y,z)
    ]]></literal>
    <justification jstring="[hyper(654,a,953,a),flip(a)].">
      <j1 rule="hyper" parents="654 953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1009">
    <literal><![CDATA[
      (x \ 1) \ (x \ T(x * y,z)) = T((x \ 1) \ y,z)
    ]]></literal>
    <justification jstring="[hyper(129,a,953,a)].">
      <j1 rule="hyper" parents="129 953"/>
    </justification>
  </clause>

  <clause id="1010">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ 1,y) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[para(8(a,1),953(a,2,2,1))].">
      <j1 rule="para" parents="8 953"/>
    </justification>
  </clause>

  <clause id="1011">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ (x \ y),z) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),953(a,2,2,1))].">
      <j1 rule="para" parents="10 953"/>
    </justification>
  </clause>

  <clause id="1012">
    <literal><![CDATA[
      T(x,y) * (x \ 1) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,473,a(flip),b,1010,a)].">
      <j1 rule="hyper" parents="63 473 1010"/>
    </justification>
  </clause>

  <clause id="1015">
    <literal><![CDATA[
      (x * y) \ (y * (x \ T(x,y))) = L(x \ 1,T(x,y),y)
    ]]></literal>
    <justification jstring="[para(1012(a,1),245(a,1,2,2))].">
      <j1 rule="para" parents="1012 245"/>
    </justification>
  </clause>

  <clause id="1016">
    <literal><![CDATA[
      (x / y) \ T(x,(x / y) \ 1) = (((x / y) \ 1) \ y) * ((x / y) \ 1)
    ]]></literal>
    <justification jstring="[para(12(a,1),963(a,1,2,1))].">
      <j1 rule="para" parents="12 963"/>
    </justification>
  </clause>

  <clause id="1017">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x \ T(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(1009(a,1),273(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1009 273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1018">
    <literal><![CDATA[
      (x \ T(y,z)) / (x \ 1) = T((x \ y) / (x \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(123,a,1011,a(flip),b,471,a)].">
      <j1 rule="hyper" parents="123 1011 471"/>
    </justification>
  </clause>

  <clause id="1019">
    <literal><![CDATA[
      R((x * y) / (z * y),u,w) * (z * y) = (R(x / z,u,w) * z) * y
    ]]></literal>
    <justification jstring="[para(108(a,1),453(a,1,1,1))].">
      <j1 rule="para" parents="108 453"/>
    </justification>
  </clause>

  <clause id="1020">
    <literal><![CDATA[
      x \ ((L(y,z,x) * x) * z) = z * T(R(y,x,z),x * z)
    ]]></literal>
    <justification jstring="[hyper(121,a,457,a(flip),b,664,a)].">
      <j1 rule="hyper" parents="121 457 664"/>
    </justification>
  </clause>

  <clause id="1021">
    <literal><![CDATA[
      (L(x,y,z) * u) * w != v5 * (u * w)
    ]]></literal>
    <literal><![CDATA[
      L(R(x,u,w),y,z) = v5
    ]]></literal>
    <justification jstring="[para(457(a,1),44(a,1))].">
      <j1 rule="para" parents="457 44"/>
    </justification>
  </clause>

  <clause id="1022">
    <literal><![CDATA[
      (L((x / y) / z,u,w) * z) * y = L(x / (z * y),u,w) * (z * y)
    ]]></literal>
    <justification jstring="[para(314(a,1),457(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="314 457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1024">
    <literal><![CDATA[
      (x * y) * L((x * y) \ z,u,w) = x * (y * L(y \ (x \ z),u,w))
    ]]></literal>
    <justification jstring="[para(311(a,1),461(a,1,2,1))].">
      <j1 rule="para" parents="311 461"/>
    </justification>
  </clause>

  <clause id="1025">
    <literal><![CDATA[
      (x * y) * L(T(x,x * y),z,u) = x * (y * L(T(x,y),z,u))
    ]]></literal>
    <justification jstring="[para(634(a,1),461(a,1,2,1))].">
      <j1 rule="para" parents="634 461"/>
    </justification>
  </clause>

  <clause id="1026">
    <literal><![CDATA[
      (x * y) * R((x * y) \ x,z,u) = x * (y * R(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[para(227(a,1),462(a,1,2,1))].">
      <j1 rule="para" parents="227 462"/>
    </justification>
  </clause>

  <clause id="1027">
    <literal><![CDATA[
      (x * y) * R((x * y) \ (x * z),u,w) = x * (y * R(y \ z,u,w))
    ]]></literal>
    <justification jstring="[para(99(a,1),462(a,1,2,1))].">
      <j1 rule="para" parents="99 462"/>
    </justification>
  </clause>

  <clause id="1028">
    <literal><![CDATA[
      (x * y) * R((x * y) \ z,u,w) = x * (y * R(y \ (x \ z),u,w))
    ]]></literal>
    <justification jstring="[para(311(a,1),462(a,1,2,1))].">
      <j1 rule="para" parents="311 462"/>
    </justification>
  </clause>

  <clause id="1029">
    <literal><![CDATA[
      (x * y) * R(T(x,x * y),z,u) = x * (y * R(y \ (x * y),z,u))
    ]]></literal>
    <justification jstring="[para(512(a,1),462(a,1,2,1))].">
      <j1 rule="para" parents="512 462"/>
    </justification>
  </clause>

  <clause id="1030">
    <literal><![CDATA[
      (1 / x) \ L(1 / x,y,z) = x * L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(387(a,1),573(a,1,2,1))].">
      <j1 rule="para" parents="387 573"/>
    </justification>
  </clause>

  <clause id="1031">
    <literal><![CDATA[
      (1 / x) \ L((1 / x) * y,z,u) = x * L(x \ y,z,u)
    ]]></literal>
    <justification jstring="[para(513(a,1),573(a,1,2,1))].">
      <j1 rule="para" parents="513 573"/>
    </justification>
  </clause>

  <clause id="1032">
    <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(577(a,1),306(a,1,2))].">
      <j1 rule="para" parents="577 306"/>
    </justification>
  </clause>

  <clause id="1033">
    <literal><![CDATA[
      L(x * (y \ 1),z,u) / (y \ 1) = L(x / y,z,u) * y
    ]]></literal>
    <justification jstring="[para(554(a,1),610(a,1,1,1))].">
      <j1 rule="para" parents="554 610"/>
    </justification>
  </clause>

  <clause id="1034">
    <literal><![CDATA[
      (R(x / y,z,u) * y) * (y \ 1) = R(x * (y \ 1),z,u)
    ]]></literal>
    <justification jstring="[hyper(386,a,647,a)].">
      <j1 rule="hyper" parents="386 647"/>
    </justification>
  </clause>

  <clause id="1035">
    <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(662(a,2),43(a,1)),flip(a)].">
      <j1 rule="para" parents="662 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1036">
    <literal><![CDATA[
      L(x,y \ z,y) != z \ (y * (u * (y \ z)))
    ]]></literal>
    <literal><![CDATA[
      T(u,y \ z) = x
    ]]></literal>
    <justification jstring="[para(754(a,1),50(a,1)),flip(a)].">
      <j1 rule="para" parents="754 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1037">
    <literal><![CDATA[
      x * ((x \ y) * T((x \ y) \ z,u)) = y * T(y \ (x * z),u)
    ]]></literal>
    <justification jstring="[hyper(126,a,791,a(flip),b,98,a),flip(a)].">
      <j1 rule="hyper" parents="126 791 98"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1038">
    <literal><![CDATA[
      x \ (y * T(y \ (x * z),u)) = (x \ y) * T((x \ y) \ z,u)
    ]]></literal>
    <justification jstring="[para(791(a,1),495(a,1,2,2))].">
      <j1 rule="para" parents="791 495"/>
    </justification>
  </clause>

  <clause id="1040">
    <literal><![CDATA[
      (x * R(y,z,z \ x)) / (z \ x) = ((x * y) / x) * z
    ]]></literal>
    <justification jstring="[hyper(138,a,920,a)].">
      <j1 rule="hyper" parents="138 920"/>
    </justification>
  </clause>

  <clause id="1041">
    <literal><![CDATA[
      R(T(x \ y,x * z),x,z) = T((x * z) \ (y * z),x)
    ]]></literal>
    <justification jstring="[para(113(a,1),1005(a,1,1)),flip(a)].">
      <j1 rule="para" parents="113 1005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1042">
    <literal><![CDATA[
      (x * ((y \ x) / x)) / (y \ x) = ((x * (1 / y)) / x) * y
    ]]></literal>
    <justification jstring="[para(399(a,1),1040(a,1,1,2))].">
      <j1 rule="para" parents="399 1040"/>
    </justification>
  </clause>

  <clause id="1043">
    <literal><![CDATA[
      R(T(x \ 1,x * y),x,y) = T((x * y) \ y,x)
    ]]></literal>
    <justification jstring="[para(7(a,1),1041(a,2,1,2))].">
      <j1 rule="para" parents="7 1041"/>
    </justification>
  </clause>

  <clause id="1044">
    <literal><![CDATA[
      T((x * y) \ ((x * z) * y),x) = R(T(z,x * y),x,y)
    ]]></literal>
    <justification jstring="[para(9(a,1),1041(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 1041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1045">
    <literal><![CDATA[
      T((x * y) \ (z * y),x) != R(u,x,y)
    ]]></literal>
    <literal><![CDATA[
      T(x \ z,x * y) = u
    ]]></literal>
    <justification jstring="[para(1041(a,1),51(a,1))].">
      <j1 rule="para" parents="1041 51"/>
    </justification>
  </clause>

  <clause id="1046">
    <literal><![CDATA[
      x * R(T(y,y * x),z,u) = L(R(y,z,u),x,y) * x
    ]]></literal>
    <justification jstring="[para(637(a,1),667(a,1,2))].">
      <j1 rule="para" parents="637 667"/>
    </justification>
  </clause>

  <clause id="1047">
    <literal><![CDATA[
      R(T(x,x \ y),z,u) = R((x \ y) \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(34,a,252,a,b,676,a)].">
      <j1 rule="hyper" parents="34 252 676"/>
    </justification>
  </clause>

  <clause id="1048">
    <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(121,a,1047,a(flip),b,456,a),flip(a)].">
      <j1 rule="hyper" parents="121 1047 456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1049">
    <literal><![CDATA[
      (x * x) \ ((y \ (z * y)) * (x * x)) = T(z,y * (x * x))
    ]]></literal>
    <justification jstring="[para(725(a,1),682(a,1,2))].">
      <j1 rule="para" parents="725 682"/>
    </justification>
  </clause>

  <clause id="1050">
    <literal><![CDATA[
      T(x,x * (y * T(y \ 1,x))) = x
    ]]></literal>
    <justification jstring="[para(778(a,1),911(a,1,2))].">
      <j1 rule="para" parents="778 911"/>
    </justification>
  </clause>

  <clause id="1051">
    <literal><![CDATA[
      x * (y * T(T(x,y),z)) = T(x,z) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(419,a,829,a),flip(a)].">
      <j1 rule="hyper" parents="419 829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1052">
    <literal><![CDATA[
      T(x,y) * (x * z) = x * (T(x,y) * z)
    ]]></literal>
    <justification jstring="[para(250(a,1),1051(a,1,2)),flip(a)].">
      <j1 rule="para" parents="250 1051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1053">
    <literal><![CDATA[
      x \ (T(x,y) * z) = T(x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(631,a,1052,a)].">
      <j1 rule="hyper" parents="631 1052"/>
    </justification>
  </clause>

  <clause id="1054">
    <literal><![CDATA[
      (T(x,y) * z) / (T(x,y) * (x \ z)) = x
    ]]></literal>
    <justification jstring="[hyper(607,a,1052,a)].">
      <j1 rule="hyper" parents="607 1052"/>
    </justification>
  </clause>

  <clause id="1055">
    <literal><![CDATA[
      x * (T(x,y) * T(z,x)) = T(x,y) * (z * x)
    ]]></literal>
    <justification jstring="[hyper(595,a,1052,a),flip(a)].">
      <j1 rule="hyper" parents="595 1052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1056">
    <literal><![CDATA[
      T(T(x,y),x * (T(x,y) \ z)) = (x * (T(x,y) \ z)) \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(444,a,154,a(flip),b,1052,a)].">
      <j1 rule="hyper" parents="444 154 1052"/>
    </justification>
  </clause>

  <clause id="1057">
    <literal><![CDATA[
      x * (T(x,y) * (x \ z)) = T(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(343,a,1052,a),flip(a)].">
      <j1 rule="hyper" parents="343 1052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1058">
    <literal><![CDATA[
      T(x,y) * (x * (T(x,y) \ z)) = x * z
    ]]></literal>
    <justification jstring="[hyper(333,a,154,a(flip),b,1052,a),flip(a)].">
      <j1 rule="hyper" parents="333 154 1052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1059">
    <literal><![CDATA[
      (x * (T(x,y) * z)) / (x * z) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(138,a,1052,a)].">
      <j1 rule="hyper" parents="138 1052"/>
    </justification>
  </clause>

  <clause id="1060">
    <literal><![CDATA[
      T(x,y) \ (x * (T(x,y) * z)) = x * z
    ]]></literal>
    <justification jstring="[hyper(129,a,1052,a)].">
      <j1 rule="hyper" parents="129 1052"/>
    </justification>
  </clause>

  <clause id="1062">
    <literal><![CDATA[
      x * (T(x,y) \ (x \ z)) = T(x,y) \ z
    ]]></literal>
    <justification jstring="[hyper(121,a,72,a(flip),b,1052,a),flip(a)].">
      <j1 rule="hyper" parents="121 72 1052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1063">
    <literal><![CDATA[
      x * (T(x,y) \ 1) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(121,a,69,a(flip),b,1052,a),flip(a)].">
      <j1 rule="hyper" parents="121 69 1052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1064">
    <literal><![CDATA[
      (x / y) * (T(x / y,z) * y) = T(x / y,z) * x
    ]]></literal>
    <justification jstring="[para(12(a,1),1052(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12 1052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1065">
    <literal><![CDATA[
      T(x,y) * (x * z) != x * u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * z = u
    ]]></literal>
    <justification jstring="[para(1052(a,2),43(a,1))].">
      <j1 rule="para" parents="1052 43"/>
    </justification>
  </clause>

  <clause id="1066">
    <literal><![CDATA[
      (x / y) * (T(x / y,y) * z) = (y \ x) * ((x / y) * z)
    ]]></literal>
    <justification jstring="[para(113(a,1),1052(a,1,1)),flip(a)].">
      <j1 rule="para" parents="113 1052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1067">
    <literal><![CDATA[
      T((T(x,y) \ x) / x,x) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(286,a,1063,a)].">
      <j1 rule="hyper" parents="286 1063"/>
    </justification>
  </clause>

  <clause id="1068">
    <literal><![CDATA[
      (T(x,y) \ x) / (T(x,y) \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(138,a,1063,a)].">
      <j1 rule="hyper" parents="138 1063"/>
    </justification>
  </clause>

  <clause id="1069">
    <literal><![CDATA[
      x \ (T(x,y) \ x) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(129,a,1063,a)].">
      <j1 rule="hyper" parents="129 1063"/>
    </justification>
  </clause>

  <clause id="1070">
    <literal><![CDATA[
      L(T(x,y) \ 1,x,1 / x) = (1 / x) * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(126,a,1063,a(flip),b,438,a),flip(a)].">
      <j1 rule="hyper" parents="126 1063 438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1071">
    <literal><![CDATA[
      T((1 / x) * (T(x,y) \ x),x) = (1 / x) * ((T(x,y) \ 1) * x)
    ]]></literal>
    <justification jstring="[para(1063(a,1),841(a,1,1,2))].">
      <j1 rule="para" parents="1063 841"/>
    </justification>
  </clause>

  <clause id="1072">
    <literal><![CDATA[
      (T(x,y) \ T(x,z)) / (T(x,y) \ 1) = T(x,z)
    ]]></literal>
    <justification jstring="[para(1068(a,1),1018(a,2,1))].">
      <j1 rule="para" parents="1068 1018"/>
    </justification>
  </clause>

  <clause id="1073">
    <literal><![CDATA[
      (T(x,y) * z) / u != x
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * (x \ z) = u
    ]]></literal>
    <justification jstring="[para(1054(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="1054 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1074">
    <literal><![CDATA[
      T(x,y) * z != x * u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * (x \ z) = u
    ]]></literal>
    <justification jstring="[para(1054(a,1),131(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1054 131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1075">
    <literal><![CDATA[
      x * (T(x,y) \ y) = T(y,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(253,a,111,a,b,1058,a),flip(a)].">
      <j1 rule="hyper" parents="253 111 1058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1076">
    <literal><![CDATA[
      (x / y) * ((y \ x) \ y) = T(y,T(x / y,y))
    ]]></literal>
    <justification jstring="[para(113(a,1),1075(a,1,2,1))].">
      <j1 rule="para" parents="113 1075"/>
    </justification>
  </clause>

  <clause id="1077">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ x,x) = L(x,T(x,y) \ x,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(34,a,463,a,b,1055,a),flip(a)].">
      <j1 rule="hyper" parents="34 463 1055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1078">
    <literal><![CDATA[
      T(x,y) * (T(x,z) \ 1) = T(x,z) \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(140,a,1072,a)].">
      <j1 rule="hyper" parents="140 1072"/>
    </justification>
  </clause>

  <clause id="1079">
    <literal><![CDATA[
      (x / y) * ((y \ x) \ y) = T(y,y \ x)
    ]]></literal>
    <justification jstring="[para(113(a,1),1076(a,2,2))].">
      <j1 rule="para" parents="113 1076"/>
    </justification>
  </clause>

  <clause id="1080">
    <literal><![CDATA[
      ((x * y) / x) * (y \ x) = T(x,x \ (x * y))
    ]]></literal>
    <justification jstring="[para(9(a,1),1079(a,1,2,1))].">
      <j1 rule="para" parents="9 1079"/>
    </justification>
  </clause>

  <clause id="1081">
    <literal><![CDATA[
      T(x,y) = ((x * y) / x) * (y \ x)
    ]]></literal>
    <justification jstring="[para(9(a,1),1080(a,2,2)),flip(a)].">
      <j1 rule="para" parents="9 1080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1082">
    <literal><![CDATA[
      ((x * y) / x) \ T(x,y) = y \ x
    ]]></literal>
    <justification jstring="[hyper(827,a,1081,a)].">
      <j1 rule="hyper" parents="827 1081"/>
    </justification>
  </clause>

  <clause id="1083">
    <literal><![CDATA[
      T((x * y) / x,y \ x) = (y \ x) \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(444,a,1081,a,b,xx)].">
      <j1 rule="hyper" parents="444 1081"/>
    </justification>
  </clause>

  <clause id="1085">
    <literal><![CDATA[
      ((x * y) * x) / (x * y) = T(x * y,x) / y
    ]]></literal>
    <justification jstring="[hyper(123,a,1081,a,b,155,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="123 1081 155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1086">
    <literal><![CDATA[
      T(x,y) / (y \ x) = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(123,a,1081,a,b,xx)].">
      <j1 rule="hyper" parents="123 1081"/>
    </justification>
  </clause>

  <clause id="1087">
    <literal><![CDATA[
      ((x * (x / y)) / x) * y = T(x,x / y)
    ]]></literal>
    <justification jstring="[hyper(596,a,1081,a(flip))].">
      <j1 rule="hyper" parents="596 1081"/>
    </justification>
  </clause>

  <clause id="1088">
    <literal><![CDATA[
      T(x,x / y) / y = (x * (x / y)) / x
    ]]></literal>
    <justification jstring="[hyper(466,a,1081,a(flip))].">
      <j1 rule="hyper" parents="466 1081"/>
    </justification>
  </clause>

  <clause id="1089">
    <literal><![CDATA[
      (x / (x / y)) * (y \ (x / y)) = T(x / y,y)
    ]]></literal>
    <justification jstring="[para(12(a,1),1081(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="12 1081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1090">
    <literal><![CDATA[
      ((x * R(y,y \ 1,x)) / x) * ((y \ 1) * x) = T(x,R(y,y \ 1,x))
    ]]></literal>
    <justification jstring="[para(430(a,1),1081(a,2,2)),flip(a)].">
      <j1 rule="para" parents="430 1081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1091">
    <literal><![CDATA[
      x * ((y * (x \ y)) / y) = T(y,y / x)
    ]]></literal>
    <justification jstring="[hyper(63,a,906,a(flip),b,1087,a)].">
      <j1 rule="hyper" parents="63 906 1087"/>
    </justification>
  </clause>

  <clause id="1092">
    <literal><![CDATA[
      x \ T(y,y / x) = (y * (x \ y)) / y
    ]]></literal>
    <justification jstring="[hyper(121,a,1087,a(flip),b,906,a(flip))].">
      <j1 rule="hyper" parents="121 1087 906"/>
    </justification>
  </clause>

  <clause id="1094">
    <literal><![CDATA[
      T(T(x,x / y) / y,x) = x / y
    ]]></literal>
    <justification jstring="[para(1088(a,2),238(a,1,1))].">
      <j1 rule="para" parents="1088 238"/>
    </justification>
  </clause>

  <clause id="1095">
    <literal><![CDATA[
      (x / y) * ((x * y) / x) = T(x,x / (x / y))
    ]]></literal>
    <justification jstring="[para(79(a,1),1091(a,1,2,1,2))].">
      <j1 rule="para" parents="79 1091"/>
    </justification>
  </clause>

  <clause id="1096">
    <literal><![CDATA[
      x * ((y * (x \ y)) / y) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ T(y,y / x) = u
    ]]></literal>
    <justification jstring="[para(1091(a,2),827(a,1))].">
      <j1 rule="para" parents="1091 827"/>
    </justification>
  </clause>

  <clause id="1097">
    <literal><![CDATA[
      T(x \ T(y,y / x),y) = x \ y
    ]]></literal>
    <justification jstring="[para(1092(a,2),238(a,1,1))].">
      <j1 rule="para" parents="1092 238"/>
    </justification>
  </clause>

  <clause id="1098">
    <literal><![CDATA[
      T((x \ y) \ T(y,x),y) = (x \ y) \ y
    ]]></literal>
    <justification jstring="[para(76(a,1),1097(a,1,1,2,2))].">
      <j1 rule="para" parents="76 1097"/>
    </justification>
  </clause>

  <clause id="1099">
    <literal><![CDATA[
      T((x \ y) \ T(y,x),y) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(333,a,112,a,b,1098,a),flip(a)].">
      <j1 rule="hyper" parents="333 112 1098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1100">
    <literal><![CDATA[
      T((x \ y) \ T(y,x),x * y) = L(T(x,x \ y),y,x)
    ]]></literal>
    <justification jstring="[para(1083(a,1),964(a,1,1))].">
      <j1 rule="para" parents="1083 964"/>
    </justification>
  </clause>

  <clause id="1101">
    <literal><![CDATA[
      T(T(x * y,x) / y,x * y) = x
    ]]></literal>
    <justification jstring="[para(1085(a,1),238(a,1,1))].">
      <j1 rule="para" parents="1085 238"/>
    </justification>
  </clause>

  <clause id="1102">
    <literal><![CDATA[
      T(T(x * y,x) / y,y) = R(x,y,T(x,y))
    ]]></literal>
    <justification jstring="[para(1085(a,1),947(a,1,1))].">
      <j1 rule="para" parents="1085 947"/>
    </justification>
  </clause>

  <clause id="1103">
    <literal><![CDATA[
      T(T(R(x,y,y \ 1),x * y) / (y \ 1),(x * y) * (y \ 1)) = x * y
    ]]></literal>
    <justification jstring="[para(385(a,1),1101(a,1,1,1,1))].">
      <j1 rule="para" parents="385 1101"/>
    </justification>
  </clause>

  <clause id="1104">
    <literal><![CDATA[
      x \ T(y * x,y) = R(y,x,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(423,a,1102,a)].">
      <j1 rule="hyper" parents="423 1102"/>
    </justification>
  </clause>

  <clause id="1105">
    <literal><![CDATA[
      L(R(x,y,T(x,y)),y,x) = x
    ]]></literal>
    <justification jstring="[para(1104(a,1),492(a,1,1))].">
      <j1 rule="para" parents="1104 492"/>
    </justification>
  </clause>

  <clause id="1106">
    <literal><![CDATA[
      L(x,y,z) != z
    ]]></literal>
    <literal><![CDATA[
      R(z,y,T(z,y)) = x
    ]]></literal>
    <justification jstring="[para(1105(a,1),50(a,1)),flip(a)].">
      <j1 rule="para" parents="1105 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1107">
    <literal><![CDATA[
      (x * y) / ((x * y) / x) = y / (x \ ((x * y) / x))
    ]]></literal>
    <justification jstring="[hyper(123,a,238,a(flip),b,1089,a),flip(a)].">
      <j1 rule="hyper" parents="123 238 1089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1108">
    <literal><![CDATA[
      T(x,x / (x / T(y,x))) = (x / T(y,x)) * y
    ]]></literal>
    <justification jstring="[para(239(a,1),1095(a,1,2)),flip(a)].">
      <j1 rule="para" parents="239 1095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1109">
    <literal><![CDATA[
      (x / y) * (y * T(y \ x,z)) = T(x / y,z) * x
    ]]></literal>
    <justification jstring="[para(471(a,1),1064(a,1,2))].">
      <j1 rule="para" parents="471 1064"/>
    </justification>
  </clause>

  <clause id="1110">
    <literal><![CDATA[
      (1 / x) \ T(1 / x,y) = x * T(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(121,a,8,a(flip),b,1109,a)].">
      <j1 rule="hyper" parents="121 8 1109"/>
    </justification>
  </clause>

  <clause id="1111">
    <literal><![CDATA[
      T(x / y,z) * u != (x / y) * (y * T(y \ x,z))
    ]]></literal>
    <literal><![CDATA[
      u = x
    ]]></literal>
    <justification jstring="[para(1109(a,2),43(a,2))].">
      <j1 rule="para" parents="1109 43"/>
    </justification>
  </clause>

  <clause id="1112">
    <literal><![CDATA[
      (x * y) * T((x * y) \ z,x) = ((x \ (z / y)) * x) * y
    ]]></literal>
    <justification jstring="[hyper(739,a,831,a)].">
      <j1 rule="hyper" parents="739 831"/>
    </justification>
  </clause>

  <clause id="1113">
    <literal><![CDATA[
      (T(1 / x,y) * x) * (x \ z) = z * T(z \ (x \ z),y)
    ]]></literal>
    <justification jstring="[hyper(739,a,955,a),flip(a)].">
      <j1 rule="hyper" parents="739 955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1114">
    <literal><![CDATA[
      (x \ (y * (z \ x))) * x = (z * T(z \ y,x)) * (z \ x)
    ]]></literal>
    <justification jstring="[para(471(a,1),992(a,2,1))].">
      <j1 rule="para" parents="471 992"/>
    </justification>
  </clause>

  <clause id="1115">
    <literal><![CDATA[
      ((1 / x) \ x) * ((y * x) \ z) = (y * (1 / x)) \ z
    ]]></literal>
    <justification jstring="[hyper(63,a,733,a(flip),b,994,a)].">
      <j1 rule="hyper" parents="63 733 994"/>
    </justification>
  </clause>

  <clause id="1116">
    <literal><![CDATA[
      (x * x) * (y * R(z / x,x,x)) = T(y * (z * x),x \ (x \ 1))
    ]]></literal>
    <justification jstring="[para(108(a,2),996(a,1,2,2))].">
      <j1 rule="para" parents="108 996"/>
    </justification>
  </clause>

  <clause id="1117">
    <literal><![CDATA[
      x \ ((L(y,z,x) * x) * z) = z * R(T(y,x * z),x,z)
    ]]></literal>
    <justification jstring="[para(27(a,2),1020(a,2,2))].">
      <j1 rule="para" parents="27 1020"/>
    </justification>
  </clause>

  <clause id="1118">
    <literal><![CDATA[
      x * L(x \ ((1 / x) \ y),z,u) = (1 / x) \ L(y,z,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),1031(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 1031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1119">
    <literal><![CDATA[
      L(x * (y \ 1),z,u) / (y \ 1) = y * L(y \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(333,a,668,a(flip),b,1033,a),flip(a)].">
      <j1 rule="hyper" parents="333 668 1033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1120">
    <literal><![CDATA[
      (x * R(x \ y,z,u)) * (x \ 1) = R(y * (x \ 1),z,u)
    ]]></literal>
    <justification jstring="[para(675(a,1),1034(a,1,1))].">
      <j1 rule="para" parents="675 1034"/>
    </justification>
  </clause>

  <clause id="1121">
    <literal><![CDATA[
      (x * ((y \ x) / x)) / (y \ x) = y * ((x * (y \ 1)) / x)
    ]]></literal>
    <justification jstring="[hyper(333,a,906,a(flip),b,1042,a),flip(a)].">
      <j1 rule="hyper" parents="333 906 1042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1122">
    <literal><![CDATA[
      (x * x) \ (T(y,z) * (x * x)) = T(y,z * (x * x))
    ]]></literal>
    <justification jstring="[para(22(a,2),1049(a,1,2,1))].">
      <j1 rule="para" parents="22 1049"/>
    </justification>
  </clause>

  <clause id="1123">
    <literal><![CDATA[
      T(T(x,y),z * z) = T(x,y * (z * z))
    ]]></literal>
    <justification jstring="[hyper(347,a,1122,a)].">
      <j1 rule="hyper" parents="347 1122"/>
    </justification>
  </clause>

  <clause id="1124">
    <literal><![CDATA[
      T(T(x,y * y),z) = T(x,z * (y * y))
    ]]></literal>
    <justification jstring="[hyper(63,a,115,a(flip),b,1122,a)].">
      <j1 rule="hyper" parents="63 115 1122"/>
    </justification>
  </clause>

  <clause id="1125">
    <literal><![CDATA[
      (x / y) * ((y \ x) * z) = (y \ x) * ((x / y) * z)
    ]]></literal>
    <justification jstring="[para(113(a,1),1066(a,1,2,1))].">
      <j1 rule="para" parents="113 1066"/>
    </justification>
  </clause>

  <clause id="1126">
    <literal><![CDATA[
      (x \ (x * y)) * (((x * y) / x) * z) = ((x * y) / x) * (y * z)
    ]]></literal>
    <justification jstring="[para(238(a,1),1066(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="238 1066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1127">
    <literal><![CDATA[
      ((x / y) \ x) * ((x / (x / y)) * z) = (x / (x / y)) * (y * z)
    ]]></literal>
    <justification jstring="[para(258(a,1),1066(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="258 1066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1128">
    <literal><![CDATA[
      (1 / x) * ((x \ 1) * x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(333,a,78,a(flip),b,1125,a),flip(a)].">
      <j1 rule="hyper" parents="333 78 1125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1130">
    <literal><![CDATA[
      L(T(x \ 1,x),x,1 / x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,574,a,b,1128,a)].">
      <j1 rule="hyper" parents="63 574 1128"/>
    </justification>
  </clause>

  <clause id="1131">
    <literal><![CDATA[
      (1 / x) * K(x \ 1,x) = x \ 1
    ]]></literal>
    <justification jstring="[para(276(a,2),1128(a,1,2))].">
      <j1 rule="para" parents="276 1128"/>
    </justification>
  </clause>

  <clause id="1132">
    <literal><![CDATA[
      (1 / x) \ (x \ 1) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(129,a,1131,a)].">
      <j1 rule="hyper" parents="129 1131"/>
    </justification>
  </clause>

  <clause id="1133">
    <literal><![CDATA[
      K((x \ 1) \ 1,x \ 1) = x \ ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(121,a,1131,a(flip),b,186,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="121 1131 186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1134">
    <literal><![CDATA[
      (1 / x) \ L(x \ 1,y,z) = x * L(T(x \ 1,x),y,z)
    ]]></literal>
    <justification jstring="[para(1130(a,1),573(a,1,2,1))].">
      <j1 rule="para" parents="1130 573"/>
    </justification>
  </clause>

  <clause id="1136">
    <literal><![CDATA[
      ((x \ (x / y)) * x) * y = x * (y * T(y \ 1,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,778,a(flip),b,1112,a),flip(a)].">
      <j1 rule="hyper" parents="63 778 1112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1137">
    <literal><![CDATA[
      x * ((y \ x) * T((y \ x) \ 1,x)) = ((x \ y) * x) * (y \ x)
    ]]></literal>
    <justification jstring="[para(76(a,1),1136(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="76 1136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1138">
    <literal><![CDATA[
      (x * T(x \ 1,y)) * (x \ z) = z * T(z \ (x \ z),y)
    ]]></literal>
    <justification jstring="[para(471(a,1),1113(a,1,1))].">
      <j1 rule="para" parents="471 1113"/>
    </justification>
  </clause>

  <clause id="1139">
    <literal><![CDATA[
      x \ (y \ ((L(z,x,y) * y) * x)) = R(T(z,y * x),y,x)
    ]]></literal>
    <justification jstring="[hyper(121,a,1117,a,b,xx)].">
      <j1 rule="hyper" parents="121 1117"/>
    </justification>
  </clause>

  <clause id="1140">
    <literal><![CDATA[
      L(x \ ((1 / x) \ y),z,u) = x \ ((1 / x) \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(129,a,1118,a),flip(a)].">
      <j1 rule="hyper" parents="129 1118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1141">
    <literal><![CDATA[
      L(x \ 1,y,z) / (x \ 1) = x * L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(7(a,1),1119(a,1,1,1))].">
      <j1 rule="para" parents="7 1119"/>
    </justification>
  </clause>

  <clause id="1142">
    <literal><![CDATA[
      L(x \ 1,x,y) / (x \ 1) = x * ((y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(333,a,390,a(flip),b,1141,a),flip(a)].">
      <j1 rule="hyper" parents="333 390 1141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1143">
    <literal><![CDATA[
      (x * ((y * x) \ y)) * (x \ 1) = L(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(125,a,390,a(flip),b,1141,a)].">
      <j1 rule="hyper" parents="125 390 1141"/>
    </justification>
  </clause>

  <clause id="1144">
    <literal><![CDATA[
      (x * ((y * x) \ y)) \ L(x \ 1,x,y) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(192,a,1142,a)].">
      <j1 rule="hyper" parents="192 1142"/>
    </justification>
  </clause>

  <clause id="1145">
    <literal><![CDATA[
      L(x \ 1,x,y) \ ((x \ 1) * (x * ((y * x) \ y))) = K(x \ 1,x * ((y * x) \ y))
    ]]></literal>
    <justification jstring="[para(1143(a,1),16(a,2,1)),flip(a)].">
      <j1 rule="para" parents="1143 16"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1146">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) \ L((x \ y) \ 1,x \ y,x) = (x \ y) \ 1
    ]]></literal>
    <justification jstring="[para(10(a,1),1144(a,1,1,2,1))].">
      <j1 rule="para" parents="10 1144"/>
    </justification>
  </clause>

  <clause id="1147">
    <literal><![CDATA[
      R(x * (y \ 1),z,u) / (y \ 1) = y * R(y \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(138,a,1120,a)].">
      <j1 rule="hyper" parents="138 1120"/>
    </justification>
  </clause>

  <clause id="1148">
    <literal><![CDATA[
      (1 / x) * (L(x \ 1,y,z) * x) = L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(126,a,251,a(flip),b,1134,a)].">
      <j1 rule="hyper" parents="126 251 1134"/>
    </justification>
  </clause>

  <clause id="1149">
    <literal><![CDATA[
      (x * y) \ x = (1 / y) * (L(y \ 1,y,x) * y)
    ]]></literal>
    <justification jstring="[hyper(333,a,227,a(flip),b,1148,a)].">
      <j1 rule="hyper" parents="333 227 1148"/>
    </justification>
  </clause>

  <clause id="1150">
    <literal><![CDATA[
      L((x \ y) \ 1,x \ y,x) * (x \ y) = (1 / (x \ y)) \ (y \ x)
    ]]></literal>
    <justification jstring="[hyper(121,a,388,a(flip),b,1148,a),flip(a)].">
      <j1 rule="hyper" parents="121 388 1148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1151">
    <literal><![CDATA[
      (1 / x) * (((y * x) \ y) * x) = (y * x) \ y
    ]]></literal>
    <justification jstring="[para(227(a,1),1149(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="227 1149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1152">
    <literal><![CDATA[
      x * L(x \ (((y * x) \ y) * x),z,u) = (1 / x) \ L((y * x) \ y,z,u)
    ]]></literal>
    <justification jstring="[para(1151(a,1),1031(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1151 1031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1153">
    <literal><![CDATA[
      (x * T(x \ (y \ x),z)) / (y \ x) != u
    ]]></literal>
    <literal><![CDATA[
      y * T(y \ 1,z) = u
    ]]></literal>
    <justification jstring="[para(1138(a,1),268(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1138 268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1154">
    <literal><![CDATA[
      K(x \ 1,x) * (x \ y) = y * T(y \ (x \ y),x)
    ]]></literal>
    <justification jstring="[para(358(a,1),1138(a,1,1))].">
      <j1 rule="para" parents="358 1138"/>
    </justification>
  </clause>

  <clause id="1155">
    <literal><![CDATA[
      (x \ T(x,y)) * ((x \ 1) \ z) = z * T(z \ ((x \ 1) \ z),y)
    ]]></literal>
    <justification jstring="[para(1010(a,1),1138(a,1,1))].">
      <j1 rule="para" parents="1010 1138"/>
    </justification>
  </clause>

  <clause id="1156">
    <literal><![CDATA[
      L((x \ 1) \ ((1 / (x \ 1)) \ y),z,u) = (x \ 1) \ (x \ L(y,z,u))
    ]]></literal>
    <justification jstring="[para(76(a,1),1140(a,2,2,1))].">
      <j1 rule="para" parents="76 1140"/>
    </justification>
  </clause>

  <clause id="1157">
    <literal><![CDATA[
      R(x \ 1,y,z) / (x \ 1) = x * R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(7(a,1),1147(a,1,1,1))].">
      <j1 rule="para" parents="7 1147"/>
    </justification>
  </clause>

  <clause id="1158">
    <literal><![CDATA[
      R(x \ 1,y,z) / (x \ 1) = R(1 / x,y,z) * x
    ]]></literal>
    <justification jstring="[hyper(333,a,675,a,b,1157,a),flip(a)].">
      <j1 rule="hyper" parents="333 675 1157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1159">
    <literal><![CDATA[
      R(x \ 1,y,z) / (x \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      x * R(x \ 1,y,z) = u
    ]]></literal>
    <justification jstring="[para(1158(a,2),903(a,1))].">
      <j1 rule="para" parents="1158 903"/>
    </justification>
  </clause>

  <clause id="1161">
    <literal><![CDATA[
      L((x * (y \ z)) / z,u,w) * z = (L(x / y,u,w) * y) * (y \ z)
    ]]></literal>
    <justification jstring="[para(555(a,1),760(a,1,1,1))].">
      <j1 rule="para" parents="555 760"/>
    </justification>
  </clause>

  <clause id="1162">
    <literal><![CDATA[
      x * ((x \ y) * R((x \ y) \ z,u,w)) = y * R(y \ (x * z),u,w)
    ]]></literal>
    <justification jstring="[hyper(126,a,792,a(flip),b,98,a),flip(a)].">
      <j1 rule="hyper" parents="126 792 98"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1163">
    <literal><![CDATA[
      (x \ 1) * R((x \ 1) \ y,z,u) = x \ R(1 \ (x * y),z,u)
    ]]></literal>
    <justification jstring="[hyper(121,a,792,a(flip),b,275,a),flip(a)].">
      <j1 rule="hyper" parents="121 792 275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1164">
    <literal><![CDATA[
      x \ (y * R(y \ (x * z),u,w)) = (x \ y) * R((x \ y) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(792(a,1),495(a,1,2,2))].">
      <j1 rule="para" parents="792 495"/>
    </justification>
  </clause>

  <clause id="1165">
    <literal><![CDATA[
      x \ (y * L(y \ (x * z),u,w)) = (x \ y) * L((x \ y) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(793(a,1),495(a,1,2,2))].">
      <j1 rule="para" parents="793 495"/>
    </justification>
  </clause>

  <clause id="1166">
    <literal><![CDATA[
      (R(x / (y / z),u,w) * (y / z)) * z = R((x * z) / y,u,w) * y
    ]]></literal>
    <justification jstring="[hyper(125,a,803,a(flip),b,109,a),flip(a)].">
      <j1 rule="hyper" parents="125 803 109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1167">
    <literal><![CDATA[
      (x * y) * L(T(y,x),z,u) = (L(y,z,u) * x) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,457,a(flip),b,847,a),flip(a)].">
      <j1 rule="hyper" parents="63 457 847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1168">
    <literal><![CDATA[
      L(T(x,1 / x),y,z) / x = L(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(411,a,1167,a)].">
      <j1 rule="hyper" parents="411 1167"/>
    </justification>
  </clause>

  <clause id="1169">
    <literal><![CDATA[
      (x * y) * R(T(y,x),z,u) = (R(y,z,u) * x) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,453,a(flip),b,848,a),flip(a)].">
      <j1 rule="hyper" parents="63 453 848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1170">
    <literal><![CDATA[
      L(((x * y) * z) / (x * y),y,x) != u / (x * y)
    ]]></literal>
    <literal><![CDATA[
      x * (y * z) = u
    ]]></literal>
    <justification jstring="[para(892(a,2),46(a,1))].">
      <j1 rule="para" parents="892 46"/>
    </justification>
  </clause>

  <clause id="1171">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ u)) / z) = x * (y * ((z * (y \ (x \ u))) / z))
    ]]></literal>
    <justification jstring="[hyper(126,a,914,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="126 914 18"/>
    </justification>
  </clause>

  <clause id="1172">
    <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(914(a,1),306(a,1,2))].">
      <j1 rule="para" parents="914 306"/>
    </justification>
  </clause>

  <clause id="1173">
    <literal><![CDATA[
      (x / y) * (y * ((z * (y \ 1)) / z)) = x * ((z * (x \ (x / y))) / z)
    ]]></literal>
    <justification jstring="[hyper(126,a,915,a(flip),b,100,a),flip(a)].">
      <j1 rule="hyper" parents="126 915 100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1174">
    <literal><![CDATA[
      (1 / x) \ ((y * ((1 / x) * z)) / y) = x * ((y * (x \ z)) / y)
    ]]></literal>
    <justification jstring="[hyper(121,a,916,a(flip),b,277,a)].">
      <j1 rule="hyper" parents="121 916 277"/>
    </justification>
  </clause>

  <clause id="1175">
    <literal><![CDATA[
      ((x * y) * R(z,x,y)) / y = (((x * y) * z) / (x * y)) * x
    ]]></literal>
    <justification jstring="[hyper(138,a,918,a)].">
      <j1 rule="hyper" parents="138 918"/>
    </justification>
  </clause>

  <clause id="1176">
    <literal><![CDATA[
      ((x * (y / (1 / z))) / x) * (1 / z) = ((x * (y * z)) / x) / z
    ]]></literal>
    <justification jstring="[hyper(123,a,925,a(flip),b,533,a),flip(a)].">
      <j1 rule="hyper" parents="123 925 533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1177">
    <literal><![CDATA[
      (x * y) * T((x * y) \ (y * z),u) = y * (T(x,y) * T(T(x,y) \ z,u))
    ]]></literal>
    <justification jstring="[hyper(126,a,943,a(flip),b,245,a)].">
      <j1 rule="hyper" parents="126 943 245"/>
    </justification>
  </clause>

  <clause id="1178">
    <literal><![CDATA[
      (x * y) / a(z,z \ y,T(x,y)) = L(x,z \ y,z) * y
    ]]></literal>
    <justification jstring="[hyper(333,a,782,a(flip),b,978,a),flip(a)].">
      <j1 rule="hyper" parents="333 782 978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1179">
    <literal><![CDATA[
      (L(x,y \ z,y) * z) \ (x * z) = a(y,y \ z,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(192,a,1178,a)].">
      <j1 rule="hyper" parents="192 1178"/>
    </justification>
  </clause>

  <clause id="1180">
    <literal><![CDATA[
      (x * (y \ 1)) / y = x * (y \ (1 / y))
    ]]></literal>
    <justification jstring="[para(510(a,1),986(a,1,2))].">
      <j1 rule="para" parents="510 986"/>
    </justification>
  </clause>

  <clause id="1181">
    <literal><![CDATA[
      R(x,y,y \ (1 / y)) * (1 / y) = ((x * y) * (y \ 1)) / y
    ]]></literal>
    <justification jstring="[hyper(333,a,367,a,b,1180,a)].">
      <j1 rule="hyper" parents="333 367 1180"/>
    </justification>
  </clause>

  <clause id="1182">
    <literal><![CDATA[
      L((x \ (y * (x * z))) / z,z,x) = T((z * y) / z,x * z)
    ]]></literal>
    <justification jstring="[hyper(333,a,476,a(flip),b,990,a),flip(a)].">
      <j1 rule="hyper" parents="333 476 990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1183">
    <literal><![CDATA[
      L((T(x,y) * (x \ y)) / y,y,x) = (y * K(T(x,y),y)) / y
    ]]></literal>
    <justification jstring="[para(1053(a,1),991(a,1,1,1))].">
      <j1 rule="para" parents="1053 991"/>
    </justification>
  </clause>

  <clause id="1184">
    <literal><![CDATA[
      (x * y) \ (x * (y * (z * (u * u)))) = L(z,y,x) * (u * u)
    ]]></literal>
    <justification jstring="[para(33(a,1),993(a,1,2,2))].">
      <j1 rule="para" parents="33 993"/>
    </justification>
  </clause>

  <clause id="1186">
    <literal><![CDATA[
      T(x,x / y) != z
    ]]></literal>
    <literal><![CDATA[
      y * ((x * (y \ x)) / x) = z
    ]]></literal>
    <justification jstring="[para(1087(a,1),999(a,1))].">
      <j1 rule="para" parents="1087 999"/>
    </justification>
  </clause>

  <clause id="1187">
    <literal><![CDATA[
      R(x,y,y \ (1 / y)) * (1 / y) = R(x,y,y) / y
    ]]></literal>
    <justification jstring="[para(810(a,1),1181(a,2,1))].">
      <j1 rule="para" parents="810 1181"/>
    </justification>
  </clause>

  <clause id="1188">
    <literal><![CDATA[
      R(x,y,y) / y = x * (1 / y)
    ]]></literal>
    <justification jstring="[para(548(a,1),1187(a,1,1)),flip(a)].">
      <j1 rule="para" parents="548 1187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1189">
    <literal><![CDATA[
      R(x / (1 / y),y,y) = x * y
    ]]></literal>
    <justification jstring="[hyper(338,a,1188,a),flip(a)].">
      <j1 rule="hyper" parents="338 1188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1190">
    <literal><![CDATA[
      T(x * (1 / y),y) = y \ R(x,y,y)
    ]]></literal>
    <justification jstring="[para(1188(a,1),113(a,1,1))].">
      <j1 rule="para" parents="1188 113"/>
    </justification>
  </clause>

  <clause id="1191">
    <literal><![CDATA[
      ((x \ 1) \ 1) / x = x * (1 / x)
    ]]></literal>
    <justification jstring="[para(814(a,1),1188(a,1,1))].">
      <j1 rule="para" parents="814 1188"/>
    </justification>
  </clause>

  <clause id="1192">
    <literal><![CDATA[
      R(x * (1 / y),y,y) = R(x,y,y) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(1188(a,1),812(a,1,1))].">
      <j1 rule="para" parents="1188 812"/>
    </justification>
  </clause>

  <clause id="1195">
    <literal><![CDATA[
      ((x \ 1) \ 1) / x = K(x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(333,a,278,a,b,1191,a),flip(a)].">
      <j1 rule="hyper" parents="333 278 1191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1196">
    <literal><![CDATA[
      T(x,1 / x) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(37,a,854,a,b,1191,a)].">
      <j1 rule="hyper" parents="37 854 1191"/>
    </justification>
  </clause>

  <clause id="1197">
    <literal><![CDATA[
      T(x,1 / x) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(333,a,112,a,b,1196,a),flip(a)].">
      <j1 rule="hyper" parents="333 112 1196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1198">
    <literal><![CDATA[
      T(x \ 1,x) = ((x \ 1) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(76(a,1),1196(a,1,2))].">
      <j1 rule="para" parents="76 1196"/>
    </justification>
  </clause>

  <clause id="1199">
    <literal><![CDATA[
      L((x \ 1) \ 1,y,z) / x = L(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[para(1196(a,1),1168(a,1,1,1))].">
      <j1 rule="para" parents="1196 1168"/>
    </justification>
  </clause>

  <clause id="1201">
    <literal><![CDATA[
      (x * T(y,y \ 1)) / x = T((x * y) / x,1 / y)
    ]]></literal>
    <justification jstring="[para(1197(a,1),476(a,1,1,2))].">
      <j1 rule="para" parents="1197 476"/>
    </justification>
  </clause>

  <clause id="1202">
    <literal><![CDATA[
      T(x,x \ 1) / x = K(x,1 / x)
    ]]></literal>
    <justification jstring="[para(1197(a,1),855(a,1,1))].">
      <j1 rule="para" parents="1197 855"/>
    </justification>
  </clause>

  <clause id="1204">
    <literal><![CDATA[
      K(1 / x,1 / (1 / x)) = (x \ 1) / (1 / x)
    ]]></literal>
    <justification jstring="[para(79(a,1),1195(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="79 1195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1205">
    <literal><![CDATA[
      T(x,x \ 1) \ 1 = T(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,326,a,b,1198,a)].">
      <j1 rule="hyper" parents="333 326 1198"/>
    </justification>
  </clause>

  <clause id="1206">
    <literal><![CDATA[
      (x \ 1) \ (1 / x) = T(x,x \ 1) / x
    ]]></literal>
    <justification jstring="[hyper(333,a,765,a,b,1202,a)].">
      <j1 rule="hyper" parents="333 765 1202"/>
    </justification>
  </clause>

  <clause id="1207">
    <literal><![CDATA[
      K(x,1 / x) \ T(x,x \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(192,a,1202,a)].">
      <j1 rule="hyper" parents="192 1202"/>
    </justification>
  </clause>

  <clause id="1208">
    <literal><![CDATA[
      T(x,x \ 1) / x != y
    ]]></literal>
    <literal><![CDATA[
      K(x,1 / x) = y
    ]]></literal>
    <justification jstring="[para(1207(a,1),301(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1207 301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1210">
    <literal><![CDATA[
      L(1 / x,y,z) * (1 / (1 / x)) = L(x \ 1,y,z) / (1 / x)
    ]]></literal>
    <justification jstring="[para(79(a,1),1199(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="79 1199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1211">
    <literal><![CDATA[
      T(L(x,y,z) * (1 / x),x) = x \ L((x \ 1) \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(1199(a,1),113(a,1,1))].">
      <j1 rule="para" parents="1199 113"/>
    </justification>
  </clause>

  <clause id="1212">
    <literal><![CDATA[
      T((x * y) / x,1 / y) = T((x * y) / x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(479,a,1201,a),flip(a)].">
      <j1 rule="hyper" parents="479 1201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1213">
    <literal><![CDATA[
      T((x * T(y,x)) / x,T(y,x) \ 1) = T(y,1 / T(y,x))
    ]]></literal>
    <justification jstring="[para(239(a,1),1212(a,1,1)),flip(a)].">
      <j1 rule="para" parents="239 1212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1214">
    <literal><![CDATA[
      T(x,1 / T(x,y)) = T(x,T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[para(239(a,1),1213(a,1,1)),flip(a)].">
      <j1 rule="para" parents="239 1213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1215">
    <literal><![CDATA[
      R(L((x \ (y * (x * x))) / x,x,x),x,x) = (x * x) \ ((x * y) * x)
    ]]></literal>
    <justification jstring="[para(1182(a,2),951(a,1,1))].">
      <j1 rule="para" parents="1182 951"/>
    </justification>
  </clause>

  <clause id="1216">
    <literal><![CDATA[
      L(x * (y * y),z,u) = L(x,z,u) * (y * y)
    ]]></literal>
    <justification jstring="[hyper(504,a,1184,a)].">
      <j1 rule="hyper" parents="504 1184"/>
    </justification>
  </clause>

  <clause id="1217">
    <literal><![CDATA[
      (x / y) \ (L(y \ 1,y,x / y) * ((x / y) * y)) = K(x \ (x / y),(x / y) * y)
    ]]></literal>
    <justification jstring="[para(393(a,1),427(a,2,1))].">
      <j1 rule="para" parents="393 427"/>
    </justification>
  </clause>

  <clause id="1218">
    <literal><![CDATA[
      (x * x) \ ((y * z) \ (y * (z * ((x * x) * u)))) = L(L(u,x * x,z),z * (x * x),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,727,a(flip),b,498,a)].">
      <j1 rule="hyper" parents="63 727 498"/>
    </justification>
  </clause>

  <clause id="1220">
    <literal><![CDATA[
      (x * ((y \ 1) * y)) \ (x * (y * L(z,y,y))) = L(L(y * z,y,y \ 1),(y \ 1) * y,x)
    ]]></literal>
    <justification jstring="[para(715(a,1),498(a,1,2,2))].">
      <j1 rule="para" parents="715 498"/>
    </justification>
  </clause>

  <clause id="1221">
    <literal><![CDATA[
      ((x * y) * (z * (u * u))) / ((y * z) * (u * u)) = R(R(x,y,z),y * z,u * u)
    ]]></literal>
    <justification jstring="[para(33(a,1),541(a,1,1))].">
      <j1 rule="para" parents="33 541"/>
    </justification>
  </clause>

  <clause id="1222">
    <literal><![CDATA[
      T((x * y) * (x \ 1),z) = (x * T(y,z)) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(824,a,819,a),flip(a)].">
      <j1 rule="hyper" parents="824 819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1223">
    <literal><![CDATA[
      (x * T(x \ y,z)) * (x \ 1) = T(y * (x \ 1),z)
    ]]></literal>
    <justification jstring="[para(10(a,1),1222(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 1222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1224">
    <literal><![CDATA[
      T((x * y) * (x \ 1),y) = (x * y) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(110(a,1),1222(a,2,1,2))].">
      <j1 rule="para" parents="110 1222"/>
    </justification>
  </clause>

  <clause id="1225">
    <literal><![CDATA[
      K((x * y) * (x \ 1),y) = 1
    ]]></literal>
    <justification jstring="[hyper(55,a,1224,a)].">
      <j1 rule="hyper" parents="55 1224"/>
    </justification>
  </clause>

  <clause id="1226">
    <literal><![CDATA[
      K(((1 / x) * y) * x,y) = 1
    ]]></literal>
    <justification jstring="[para(79(a,1),1225(a,1,1,2))].">
      <j1 rule="para" parents="79 1225"/>
    </justification>
  </clause>

  <clause id="1227">
    <literal><![CDATA[
      K(x * y,(1 / y) \ x) = 1
    ]]></literal>
    <justification jstring="[para(10(a,1),1226(a,1,1,1))].">
      <j1 rule="para" parents="10 1226"/>
    </justification>
  </clause>

  <clause id="1228">
    <literal><![CDATA[
      T(x * y,(1 / y) \ x) = x * y
    ]]></literal>
    <justification jstring="[hyper(56,a,1227,a)].">
      <j1 rule="hyper" parents="56 1227"/>
    </justification>
  </clause>

  <clause id="1229">
    <literal><![CDATA[
      T(x * (y \ 1),z) / (y \ 1) = y * T(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(138,a,1223,a)].">
      <j1 rule="hyper" parents="138 1223"/>
    </justification>
  </clause>

  <clause id="1230">
    <literal><![CDATA[
      T(x * ((y \ 1) \ 1),z) / ((y \ 1) \ 1) = y \ T(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,953,a(flip),b,1229,a),flip(a)].">
      <j1 rule="hyper" parents="333 953 1229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1231">
    <literal><![CDATA[
      T((x * x) * ((y / x) / (x * x)),x) = ((x \ 1) \ y) / (x * x)
    ]]></literal>
    <justification jstring="[para(809(a,1),907(a,1,1))].">
      <j1 rule="para" parents="809 907"/>
    </justification>
  </clause>

  <clause id="1232">
    <literal><![CDATA[
      (x * y) * R((x * y) \ y,z,u) = (R(1 / x,z,u) * x) * y
    ]]></literal>
    <justification jstring="[hyper(903,a,932,a)].">
      <j1 rule="hyper" parents="903 932"/>
    </justification>
  </clause>

  <clause id="1233">
    <literal><![CDATA[
      (T((x / y) / z,u) * z) * y = (z * y) * T((z * y) \ x,u)
    ]]></literal>
    <justification jstring="[hyper(333,a,471,a(flip),b,938,a),flip(a)].">
      <j1 rule="hyper" parents="333 471 938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1234">
    <literal><![CDATA[
      x * (y * T(y \ (x \ z),x)) = ((x \ (z / y)) * x) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,1112,a(flip),b,940,a),flip(a)].">
      <j1 rule="hyper" parents="63 1112 940"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1235">
    <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(276(a,2),940(a,1,1))].">
      <j1 rule="para" parents="276 940"/>
    </justification>
  </clause>

  <clause id="1236">
    <literal><![CDATA[
      ((x \ (y / (z \ 1))) * x) * (z \ 1) = x * (z \ T(z * (x \ y),x))
    ]]></literal>
    <justification jstring="[para(953(a,1),1234(a,1,2)),flip(a)].">
      <j1 rule="para" parents="953 1234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1237">
    <literal><![CDATA[
      ((x \ (y / y)) * x) * y = x * (K(x \ 1,x) * (x \ y))
    ]]></literal>
    <justification jstring="[para(1154(a,2),1234(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1154 1234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1238">
    <literal><![CDATA[
      x * (K(x \ 1,x) * (x \ y)) = ((x \ 1) * x) * y
    ]]></literal>
    <justification jstring="[para(73(a,1),1237(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="73 1237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1240">
    <literal><![CDATA[
      x * (K(x \ 1,x) * (x \ y)) = K(x \ 1,x) * y
    ]]></literal>
    <justification jstring="[para(276(a,2),1238(a,2,1))].">
      <j1 rule="para" parents="276 1238"/>
    </justification>
  </clause>

  <clause id="1241">
    <literal><![CDATA[
      K(x \ 1,x) * x = x * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(173(a,1),1240(a,1,2)),flip(a)].">
      <j1 rule="para" parents="173 1240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1242">
    <literal><![CDATA[
      T(x,K(x \ 1,x)) = x
    ]]></literal>
    <justification jstring="[hyper(254,a,1241,a)].">
      <j1 rule="hyper" parents="254 1241"/>
    </justification>
  </clause>

  <clause id="1243">
    <literal><![CDATA[
      T(x,(x \ 1) * x) = x
    ]]></literal>
    <justification jstring="[para(276(a,1),1242(a,1,2))].">
      <j1 rule="para" parents="276 1242"/>
    </justification>
  </clause>

  <clause id="1244">
    <literal><![CDATA[
      R(x,x \ 1,x) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(1243(a,1),845(a,1,1))].">
      <j1 rule="para" parents="1243 845"/>
    </justification>
  </clause>

  <clause id="1245">
    <literal><![CDATA[
      T(x,x \ 1) \ x = (x \ 1) * x
    ]]></literal>
    <justification jstring="[para(1244(a,1),430(a,1,1))].">
      <j1 rule="para" parents="1244 430"/>
    </justification>
  </clause>

  <clause id="1246">
    <literal><![CDATA[
      x / K(x \ 1,x) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(600,a,1245,a)].">
      <j1 rule="hyper" parents="600 1245"/>
    </justification>
  </clause>

  <clause id="1247">
    <literal><![CDATA[
      T(x,x \ 1) * K(x \ 1,x) = x
    ]]></literal>
    <justification jstring="[hyper(126,a,276,a,b,1245,a)].">
      <j1 rule="hyper" parents="126 276 1245"/>
    </justification>
  </clause>

  <clause id="1248">
    <literal><![CDATA[
      ((x \ 1) \ 1) * K(x \ 1,x) = x
    ]]></literal>
    <justification jstring="[hyper(125,a,112,a(flip),b,1246,a)].">
      <j1 rule="hyper" parents="125 112 1246"/>
    </justification>
  </clause>

  <clause id="1249">
    <literal><![CDATA[
      (1 / x) \ T((1 / x) * y,z) = x * T(x \ y,z)
    ]]></literal>
    <justification jstring="[para(79(a,1),1008(a,2,2,1,1))].">
      <j1 rule="para" parents="79 1008"/>
    </justification>
  </clause>

  <clause id="1250">
    <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="[para(960(a,1),1249(a,1,2))].">
      <j1 rule="para" parents="960 1249"/>
    </justification>
  </clause>

  <clause id="1251">
    <literal><![CDATA[
      x * (y * L(T(x,y),z,u)) = L(x,z,u) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(420,a,1025,a),flip(a)].">
      <j1 rule="hyper" parents="420 1025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1252">
    <literal><![CDATA[
      L(x,y,z) * (x * u) = x * (L(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(251(a,1),1251(a,1,2)),flip(a)].">
      <j1 rule="para" parents="251 1251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1253">
    <literal><![CDATA[
      x \ (L(x,y,z) * (u * x)) = L(x,y,z) * T(u,x)
    ]]></literal>
    <justification jstring="[hyper(650,a,1252,a)].">
      <j1 rule="hyper" parents="650 1252"/>
    </justification>
  </clause>

  <clause id="1254">
    <literal><![CDATA[
      x \ (L(x,y,z) * u) = L(x,y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(631,a,1252,a)].">
      <j1 rule="hyper" parents="631 1252"/>
    </justification>
  </clause>

  <clause id="1255">
    <literal><![CDATA[
      L(x,y,z) * (x \ 1) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(412,a,1252,a),flip(a)].">
      <j1 rule="hyper" parents="412 1252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1256">
    <literal><![CDATA[
      x * (L(x,y,z) * (x \ u)) = L(x,y,z) * u
    ]]></literal>
    <justification jstring="[hyper(343,a,1252,a),flip(a)].">
      <j1 rule="hyper" parents="343 1252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1257">
    <literal><![CDATA[
      L(x,y,z) \ (x * (L(x,y,z) * u)) = x * u
    ]]></literal>
    <justification jstring="[hyper(129,a,1252,a)].">
      <j1 rule="hyper" parents="129 1252"/>
    </justification>
  </clause>

  <clause id="1258">
    <literal><![CDATA[
      L(x,y,z) \ (x * u) = x * (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(121,a,154,a(flip),b,1252,a)].">
      <j1 rule="hyper" parents="121 154 1252"/>
    </justification>
  </clause>

  <clause id="1259">
    <literal><![CDATA[
      x * (L(x,y,z) \ (x \ u)) = L(x,y,z) \ u
    ]]></literal>
    <justification jstring="[hyper(121,a,72,a(flip),b,1252,a),flip(a)].">
      <j1 rule="hyper" parents="121 72 1252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1260">
    <literal><![CDATA[
      x * (L(x,y,z) \ 1) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(121,a,69,a(flip),b,1252,a),flip(a)].">
      <j1 rule="hyper" parents="121 69 1252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1261">
    <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(444,a,154,a(flip),b,1252,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="444 154 1252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1262">
    <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(121,a,1252,a(flip),b,88,a)].">
      <j1 rule="hyper" parents="121 1252 88"/>
    </justification>
  </clause>

  <clause id="1263">
    <literal><![CDATA[
      L(x,y,z) \ (x \ L(x,y,z)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(129,a,1255,a)].">
      <j1 rule="hyper" parents="129 1255"/>
    </justification>
  </clause>

  <clause id="1264">
    <literal><![CDATA[
      (x \ 1) * L((x \ 1) \ 1,y,z) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,670,a,b,1255,a)].">
      <j1 rule="hyper" parents="63 670 1255"/>
    </justification>
  </clause>

  <clause id="1265">
    <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(1255(a,1),692(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1255 692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1266">
    <literal><![CDATA[
      x \ T(x * (x \ L(x,y,z)),u) = T(L(x,y,z),u) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(1255(a,1),1007(a,1,2,1,2))].">
      <j1 rule="para" parents="1255 1007"/>
    </justification>
  </clause>

  <clause id="1267">
    <literal><![CDATA[
      (x \ y) \ L(x \ y,y \ x,1 / (y \ x)) = L(1 / (y \ x),y \ x,y) * ((x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(931(a,1),1255(a,1,1)),flip(a)].">
      <j1 rule="para" parents="931 1255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1268">
    <literal><![CDATA[
      x \ (L(x,y,z) \ x) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(129,a,1260,a)].">
      <j1 rule="hyper" parents="129 1260"/>
    </justification>
  </clause>

  <clause id="1269">
    <literal><![CDATA[
      (x \ y) \ (((y \ x) \ 1) \ L((y \ x) \ 1,y \ x,y)) = ((y \ x) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(388(a,1),1263(a,1,1))].">
      <j1 rule="para" parents="388 1263"/>
    </justification>
  </clause>

  <clause id="1270">
    <literal><![CDATA[
      L(x,y,z) * u != x * w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) * (x \ u) = w
    ]]></literal>
    <justification jstring="[para(1256(a,1),43(a,1))].">
      <j1 rule="para" parents="1256 43"/>
    </justification>
  </clause>

  <clause id="1271">
    <literal><![CDATA[
      T((x * y) / x,L(y,z,u) * x) = L((y * x) / x,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(1257(a,1),1182(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="1257 1182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1272">
    <literal><![CDATA[
      T(L(x,y,z),x * (L(x,y,z) \ u)) = (L(x,y,z) \ (x * u)) \ (x * u)
    ]]></literal>
    <justification jstring="[para(1258(a,1),112(a,1,2))].">
      <j1 rule="para" parents="1258 112"/>
    </justification>
  </clause>

  <clause id="1273">
    <literal><![CDATA[
      L(x \ 1,y,z) \ K(x \ 1,x) = (x \ 1) * (L(x \ 1,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(276(a,2),1258(a,1,2))].">
      <j1 rule="para" parents="276 1258"/>
    </justification>
  </clause>

  <clause id="1274">
    <literal><![CDATA[
      L(x,y,z) \ (x \ u) = x \ (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(129,a,1259,a),flip(a)].">
      <j1 rule="hyper" parents="129 1259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1275">
    <literal><![CDATA[
      x * (L(x,y,z) \ (x \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) \ u = w
    ]]></literal>
    <justification jstring="[para(1274(a,2),273(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1274 273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1276">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ z,y) = x \ ((y \ (x * z)) * y)
    ]]></literal>
    <justification jstring="[hyper(121,a,111,a(flip),b,1037,a),flip(a)].">
      <j1 rule="hyper" parents="121 111 1037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1277">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ 1,y) = x \ ((y \ x) * y)
    ]]></literal>
    <justification jstring="[para(8(a,1),1276(a,2,2,1,2))].">
      <j1 rule="para" parents="8 1276"/>
    </justification>
  </clause>

  <clause id="1278">
    <literal><![CDATA[
      T(((x * y) \ x) \ 1,x) = ((x * y) \ x) \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(121,a,433,a,b,1277,a),flip(a)].">
      <j1 rule="hyper" parents="121 433 1277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1279">
    <literal><![CDATA[
      ((x * y) \ x) * T(((x * y) \ x) \ 1,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(1278(a,2),273(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1278 273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1280">
    <literal><![CDATA[
      T(L(x \ 1,x,y) \ 1,y) = ((y * x) \ y) \ K(x,y)
    ]]></literal>
    <justification jstring="[para(227(a,2),1278(a,1,1,1))].">
      <j1 rule="para" parents="227 1278"/>
    </justification>
  </clause>

  <clause id="1281">
    <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(1278(a,1),959(a,1,1))].">
      <j1 rule="para" parents="1278 959"/>
    </justification>
  </clause>

  <clause id="1282">
    <literal><![CDATA[
      K(x,y) = L(x \ 1,x,y) * T(L(x \ 1,x,y) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(126,a,1280,a,b,389,a),flip(a)].">
      <j1 rule="hyper" parents="126 1280 389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1283">
    <literal><![CDATA[
      T(x,x * K(y,x)) = x
    ]]></literal>
    <justification jstring="[para(1282(a,2),1050(a,1,2,2))].">
      <j1 rule="para" parents="1282 1050"/>
    </justification>
  </clause>

  <clause id="1284">
    <literal><![CDATA[
      T(x * K(y,x),x) = x * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(54,a,1283,a)].">
      <j1 rule="hyper" parents="54 1283"/>
    </justification>
  </clause>

  <clause id="1285">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ 1,z) = x \ (y * T(y \ x,z))
    ]]></literal>
    <justification jstring="[para(8(a,1),1038(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="8 1038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1286">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ (x \ z),u) = x \ (y * T(y \ z,u))
    ]]></literal>
    <justification jstring="[para(10(a,1),1038(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="10 1038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1287">
    <literal><![CDATA[
      x * T(x \ y,y \ x) = y * K((y \ x) \ 1,y \ x)
    ]]></literal>
    <justification jstring="[hyper(594,a,1285,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="594 1285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1288">
    <literal><![CDATA[
      T(x,x * (y \ (z * T(z \ y,x)))) = x
    ]]></literal>
    <justification jstring="[para(1285(a,1),1050(a,1,2,2))].">
      <j1 rule="para" parents="1285 1050"/>
    </justification>
  </clause>

  <clause id="1289">
    <literal><![CDATA[
      T(x,x * (T(x,y) \ ((y \ x) * ((y \ x) \ x)))) = x
    ]]></literal>
    <justification jstring="[para(1098(a,1),1288(a,1,2,2,2,2))].">
      <j1 rule="para" parents="1098 1288"/>
    </justification>
  </clause>

  <clause id="1290">
    <literal><![CDATA[
      T(x,x * (T(x,y) \ x)) = x
    ]]></literal>
    <justification jstring="[para(10(a,1),1289(a,1,2,2,2))].">
      <j1 rule="para" parents="10 1289"/>
    </justification>
  </clause>

  <clause id="1291">
    <literal><![CDATA[
      T(T(x,y),x * (T(x,z) \ x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(1290(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1290 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1292">
    <literal><![CDATA[
      (x * y) * K(((x * y) \ x) \ 1,(x * y) \ x) = x * T(y,(x * y) \ x)
    ]]></literal>
    <justification jstring="[para(9(a,1),1287(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 1287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1293">
    <literal><![CDATA[
      (x * x) / T(x,y) = x * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(197,a,1291,a(flip),b,1056,a(flip))].">
      <j1 rule="hyper" parents="197 1291 1056"/>
    </justification>
  </clause>

  <clause id="1294">
    <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(1293(a,2),639(a,1,2))].">
      <j1 rule="para" parents="1293 639"/>
    </justification>
  </clause>

  <clause id="1295">
    <literal><![CDATA[
      ((x * y) / x) * (y * z) = y * (((x * y) / x) * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),1126(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 1126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1296">
    <literal><![CDATA[
      x \ (((y * x) / y) * z) = ((y * x) / y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(631,a,1295,a)].">
      <j1 rule="hyper" parents="631 1295"/>
    </justification>
  </clause>

  <clause id="1297">
    <literal><![CDATA[
      ((x * y) / x) * (y \ 1) = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(412,a,1295,a),flip(a)].">
      <j1 rule="hyper" parents="412 1295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1298">
    <literal><![CDATA[
      x * (((y * x) / y) \ 1) = ((y * x) / y) \ x
    ]]></literal>
    <justification jstring="[hyper(121,a,69,a(flip),b,1295,a),flip(a)].">
      <j1 rule="hyper" parents="121 69 1295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1299">
    <literal><![CDATA[
      (x \ 1) * ((y * ((x \ 1) \ 1)) / y) = x \ ((y * x) / y)
    ]]></literal>
    <justification jstring="[hyper(63,a,1002,a,b,1297,a)].">
      <j1 rule="hyper" parents="63 1002 1297"/>
    </justification>
  </clause>

  <clause id="1300">
    <literal><![CDATA[
      ((x * y) / x) * (y \ ((((x * y) / x) \ y) * z)) = L(z,((x * y) / x) \ y,(x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(784,a,1296,a),flip(a)].">
      <j1 rule="hyper" parents="784 1296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1301">
    <literal><![CDATA[
      (x / (x / y)) * (y * z) = y * ((x / (x / y)) * z)
    ]]></literal>
    <justification jstring="[hyper(654,a,1127,a),flip(a)].">
      <j1 rule="hyper" parents="654 1127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1303">
    <literal><![CDATA[
      (1 / (1 / x)) * (x * (1 / x)) = x
    ]]></literal>
    <justification jstring="[hyper(333,a,78,a(flip),b,1301,a),flip(a)].">
      <j1 rule="hyper" parents="333 78 1301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1304">
    <literal><![CDATA[
      (1 / (1 / x)) * K(x,1 / x) = x
    ]]></literal>
    <justification jstring="[para(278(a,2),1303(a,1,2))].">
      <j1 rule="para" parents="278 1303"/>
    </justification>
  </clause>

  <clause id="1305">
    <literal><![CDATA[
      ((x \ y) * x) * (y \ x) = x * (y \ ((x \ y) * x))
    ]]></literal>
    <justification jstring="[para(1277(a,1),1137(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1277 1137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1306">
    <literal><![CDATA[
      ((x \ y) * x) * (y \ x) = x * K(x \ y,x)
    ]]></literal>
    <justification jstring="[para(89(a,1),1305(a,2,2))].">
      <j1 rule="para" parents="89 1305"/>
    </justification>
  </clause>

  <clause id="1307">
    <literal><![CDATA[
      (x * y) * ((y * x) \ y) = y * K(y \ (y * x),y)
    ]]></literal>
    <justification jstring="[para(9(a,1),1306(a,1,1,1))].">
      <j1 rule="para" parents="9 1306"/>
    </justification>
  </clause>

  <clause id="1308">
    <literal><![CDATA[
      (x * y) * ((y * x) \ y) = y * K(x,y)
    ]]></literal>
    <justification jstring="[para(9(a,1),1307(a,2,2,1))].">
      <j1 rule="para" parents="9 1307"/>
    </justification>
  </clause>

  <clause id="1309">
    <literal><![CDATA[
      x \ (y * K(x / y,y)) = (y * (x / y)) \ y
    ]]></literal>
    <justification jstring="[hyper(334,a,1308,a)].">
      <j1 rule="hyper" parents="334 1308"/>
    </justification>
  </clause>

  <clause id="1310">
    <literal><![CDATA[
      (x * y) * L(x \ 1,x,y) = y * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,390,a,b,1308,a)].">
      <j1 rule="hyper" parents="63 390 1308"/>
    </justification>
  </clause>

  <clause id="1312">
    <literal><![CDATA[
      (x \ 1) * R((x \ 1) \ y,z,u) = x \ R(x * y,z,u)
    ]]></literal>
    <justification jstring="[para(65(a,1),1163(a,2,2,1))].">
      <j1 rule="para" parents="65 1163"/>
    </justification>
  </clause>

  <clause id="1313">
    <literal><![CDATA[
      (x \ 1) * R((x \ 1) \ 1,y,z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(165(a,1),1163(a,2,2,1))].">
      <j1 rule="para" parents="165 1163"/>
    </justification>
  </clause>

  <clause id="1314">
    <literal><![CDATA[
      R(x,y,z) * (x \ 1) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,676,a(flip),b,1313,a)].">
      <j1 rule="hyper" parents="63 676 1313"/>
    </justification>
  </clause>

  <clause id="1316">
    <literal><![CDATA[
      (1 / x) \ R(1 / x,y,z) = R(1 / x,y,z) * x
    ]]></literal>
    <justification jstring="[hyper(596,a,1314,a),flip(a)].">
      <j1 rule="hyper" parents="596 1314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1317">
    <literal><![CDATA[
      (x \ R(x,y,z)) / R(T(x,x \ 1),y,z) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(123,a,1314,a(flip),b,252,a)].">
      <j1 rule="hyper" parents="123 1314 252"/>
    </justification>
  </clause>

  <clause id="1318">
    <literal><![CDATA[
      (x \ R(x,y,z)) * u != (x \ 1) * R(x,y,z)
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,R(x,y,z)) = u
    ]]></literal>
    <justification jstring="[para(1314(a,1),322(a,1,1))].">
      <j1 rule="para" parents="1314 322"/>
    </justification>
  </clause>

  <clause id="1319">
    <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(1314(a,1),692(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1314 692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1321">
    <literal><![CDATA[
      (1 / x) \ R(1 / x,y,z) = x * R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,675,a(flip),b,1316,a),flip(a)].">
      <j1 rule="hyper" parents="333 675 1316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1324">
    <literal><![CDATA[
      x * R(x \ 1,y,y \ 1) = a(1 / x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(771,a,1321,a),flip(a)].">
      <j1 rule="hyper" parents="771 1321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1325">
    <literal><![CDATA[
      (1 / x) * ((y / (x * y)) * x) = R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[hyper(126,a,692,a,b,1321,a)].">
      <j1 rule="hyper" parents="126 692 1321"/>
    </justification>
  </clause>

  <clause id="1326">
    <literal><![CDATA[
      (x / y) * R((x / y) \ 1,x / y,y) = (1 / (x / y)) \ (y / x)
    ]]></literal>
    <justification jstring="[para(400(a,1),1321(a,1,2)),flip(a)].">
      <j1 rule="para" parents="400 1321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1327">
    <literal><![CDATA[
      x * R(x \ 1,y,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      a(1 / x,y,y \ 1) = z
    ]]></literal>
    <justification jstring="[para(1321(a,1),771(a,1))].">
      <j1 rule="para" parents="1321 771"/>
    </justification>
  </clause>

  <clause id="1328">
    <literal><![CDATA[
      ((x / (y * x)) * y) \ (x / (y * x)) = T(1 / y,(x / (y * x)) * y)
    ]]></literal>
    <justification jstring="[hyper(444,a,230,a(flip),b,1325,a),flip(a)].">
      <j1 rule="hyper" parents="444 230 1325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1329">
    <literal><![CDATA[
      ((x \ y) / y) / (((x \ y) / (x * (x \ y))) * x) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(123,a,399,a(flip),b,1325,a)].">
      <j1 rule="hyper" parents="123 399 1325"/>
    </justification>
  </clause>

  <clause id="1330">
    <literal><![CDATA[
      x \ R(x * (y * (x \ 1)),z,u) = (x \ 1) * R(T(y,x \ 1),z,u)
    ]]></literal>
    <justification jstring="[para(22(a,2),1312(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="22 1312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1331">
    <literal><![CDATA[
      ((x \ y) / y) / (((x \ y) / y) * x) = 1 / x
    ]]></literal>
    <justification jstring="[para(10(a,1),1329(a,1,2,1,2))].">
      <j1 rule="para" parents="10 1329"/>
    </justification>
  </clause>

  <clause id="1332">
    <literal><![CDATA[
      (1 / x) \ ((x \ y) / y) = ((x \ y) / y) * x
    ]]></literal>
    <justification jstring="[hyper(192,a,1331,a)].">
      <j1 rule="hyper" parents="192 1331"/>
    </justification>
  </clause>

  <clause id="1333">
    <literal><![CDATA[
      (1 / x) \ ((y * (1 / x)) / y) = x * ((y * (x \ 1)) / y)
    ]]></literal>
    <justification jstring="[para(8(a,1),1174(a,1,2,1,2))].">
      <j1 rule="para" parents="8 1174"/>
    </justification>
  </clause>

  <clause id="1334">
    <literal><![CDATA[
      (1 / x) * ((y * ((1 / x) \ z)) / y) = ((y * (z * x)) / y) / x
    ]]></literal>
    <justification jstring="[hyper(999,a,1176,a)].">
      <j1 rule="hyper" parents="999 1176"/>
    </justification>
  </clause>

  <clause id="1335">
    <literal><![CDATA[
      ((x * (x * y)) / x) / y = T(x,x / (1 / y))
    ]]></literal>
    <justification jstring="[hyper(63,a,1087,a(flip),b,1176,a),flip(a)].">
      <j1 rule="hyper" parents="63 1087 1176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1336">
    <literal><![CDATA[
      T(x,x / (1 / (x \ y))) = ((x * y) / x) / (x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),1335(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10 1335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1337">
    <literal><![CDATA[
      T((x * x) * (y / ((x * x) * x)),x) = ((x \ 1) \ y) / (x * x)
    ]]></literal>
    <justification jstring="[para(447(a,1),1231(a,1,1,2))].">
      <j1 rule="para" parents="447 1231"/>
    </justification>
  </clause>

  <clause id="1338">
    <literal><![CDATA[
      (x * y) * R((x * y) \ y,z,u) = (x * R(x \ 1,z,u)) * y
    ]]></literal>
    <justification jstring="[para(675(a,1),1232(a,2,1))].">
      <j1 rule="para" parents="675 1232"/>
    </justification>
  </clause>

  <clause id="1339">
    <literal><![CDATA[
      (T((x / y) / z,u) * z) * y = z * (y * T(y \ (z \ x),u))
    ]]></literal>
    <justification jstring="[hyper(333,a,940,a(flip),b,1233,a),flip(a)].">
      <j1 rule="hyper" parents="333 940 1233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1340">
    <literal><![CDATA[
      T(L(x,y,z),u) * (x \ 1) = x \ T(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(10(a,1),1266(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 1266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1342">
    <literal><![CDATA[
      T(L(x,y,z),u) * (x \ 1) = x \ L(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(25(a,2),1340(a,2,2))].">
      <j1 rule="para" parents="25 1340"/>
    </justification>
  </clause>

  <clause id="1343">
    <literal><![CDATA[
      L(T(x,y),z,u) * (x \ 1) = x \ L(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(25(a,2),1342(a,1,1))].">
      <j1 rule="para" parents="25 1342"/>
    </justification>
  </clause>

  <clause id="1344">
    <literal><![CDATA[
      T(x,y) * T((y \ (x * y)) \ (y \ z),u) = y \ ((x * y) * T((x * y) \ z,u))
    ]]></literal>
    <justification jstring="[para(22(a,2),1286(a,1,1))].">
      <j1 rule="para" parents="22 1286"/>
    </justification>
  </clause>

  <clause id="1345">
    <literal><![CDATA[
      (1 / x) * ((y * ((1 / x) \ 1)) / y) = ((y * x) / y) / x
    ]]></literal>
    <justification jstring="[para(7(a,1),1334(a,2,1,1,2))].">
      <j1 rule="para" parents="7 1334"/>
    </justification>
  </clause>

  <clause id="1346">
    <literal><![CDATA[
      (1 / x) * ((y * x) / y) = ((y * x) / y) / x
    ]]></literal>
    <justification jstring="[para(79(a,1),1345(a,1,2,1,2))].">
      <j1 rule="para" parents="79 1345"/>
    </justification>
  </clause>

  <clause id="1347">
    <literal><![CDATA[
      ((x * (y \ 1)) / x) / (y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      y * ((x * (y \ 1)) / x) = z
    ]]></literal>
    <justification jstring="[para(1346(a,1),351(a,1))].">
      <j1 rule="para" parents="1346 351"/>
    </justification>
  </clause>

  <clause id="1348">
    <literal><![CDATA[
      T(x,x * R(x \ 1,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(253,a,1026,a(flip),b,1338,a(flip))].">
      <j1 rule="hyper" parents="253 1026 1338"/>
    </justification>
  </clause>

  <clause id="1349">
    <literal><![CDATA[
      T(x * R(x \ 1,y,z),x) = x * R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(253,a,1338,a(flip),b,1026,a(flip))].">
      <j1 rule="hyper" parents="253 1338 1026"/>
    </justification>
  </clause>

  <clause id="1352">
    <literal><![CDATA[
      T(x \ 1,R(x,y,z) * (x \ 1)) = x \ 1
    ]]></literal>
    <justification jstring="[para(676(a,1),1348(a,1,2))].">
      <j1 rule="para" parents="676 1348"/>
    </justification>
  </clause>

  <clause id="1353">
    <literal><![CDATA[
      T(x \ 1,x \ R(x,y,z)) = x \ 1
    ]]></literal>
    <justification jstring="[para(1313(a,1),1348(a,1,2))].">
      <j1 rule="para" parents="1313 1348"/>
    </justification>
  </clause>

  <clause id="1354">
    <literal><![CDATA[
      T(T(x \ 1,y),x \ R(x,z,u)) = T(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(1353(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1353 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1356">
    <literal><![CDATA[
      R(x \ 1,R(x,y,z),x \ 1) = T(x \ 1,R(x,y,z))
    ]]></literal>
    <justification jstring="[para(1352(a,1),845(a,1,1))].">
      <j1 rule="para" parents="1352 845"/>
    </justification>
  </clause>

  <clause id="1357">
    <literal><![CDATA[
      (x * T(x \ (y / z),u)) * z = x * (z * T(z \ (x \ y),u))
    ]]></literal>
    <justification jstring="[para(471(a,1),1339(a,1,1))].">
      <j1 rule="para" parents="471 1339"/>
    </justification>
  </clause>

  <clause id="1358">
    <literal><![CDATA[
      x * (y * T(y \ (x \ (z * y)),u)) = (x * T(x \ z,u)) * y
    ]]></literal>
    <justification jstring="[para(11(a,1),1357(a,1,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="11 1357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1359">
    <literal><![CDATA[
      x * (y * T(y \ (x \ y),z)) = (x * T(x \ 1,z)) * y
    ]]></literal>
    <justification jstring="[para(73(a,1),1357(a,1,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="73 1357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1360">
    <literal><![CDATA[
      x * ((y \ z) * T((y \ z) \ (x \ z),u)) = (x * T(x \ y,u)) * (y \ z)
    ]]></literal>
    <justification jstring="[para(76(a,1),1357(a,1,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="76 1357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1361">
    <literal><![CDATA[
      x \ (y * (x * T(x \ (y \ z),u))) != w
    ]]></literal>
    <literal><![CDATA[
      T(y * T(y \ (z / x),u),x) = w
    ]]></literal>
    <justification jstring="[para(1357(a,1),347(a,1,2))].">
      <j1 rule="para" parents="1357 347"/>
    </justification>
  </clause>

  <clause id="1362">
    <literal><![CDATA[
      (x \ 1) * (y * T(y \ ((x \ 1) \ z),u)) = (x \ T(x * (z / y),u)) * y
    ]]></literal>
    <justification jstring="[para(953(a,1),1357(a,1,1)),flip(a)].">
      <j1 rule="para" parents="953 1357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1363">
    <literal><![CDATA[
      (x * y) * T((x * y) \ y,z) = (x * T(x \ 1,z)) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,940,a,b,1359,a)].">
      <j1 rule="hyper" parents="63 940 1359"/>
    </justification>
  </clause>

  <clause id="1364">
    <literal><![CDATA[
      (x * T(x \ 1,y)) * x = x * (x * T(x \ 1,y))
    ]]></literal>
    <justification jstring="[para(66(a,1),1359(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="66 1359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1365">
    <literal><![CDATA[
      T(x,x * T(x \ 1,y)) = x
    ]]></literal>
    <justification jstring="[hyper(254,a,1364,a)].">
      <j1 rule="hyper" parents="254 1364"/>
    </justification>
  </clause>

  <clause id="1366">
    <literal><![CDATA[
      R(x,(x * T(x \ 1,y)) / x,x) = T(x,(x * T(x \ 1,y)) / x)
    ]]></literal>
    <justification jstring="[para(1365(a,1),851(a,1,1))].">
      <j1 rule="para" parents="1365 851"/>
    </justification>
  </clause>

  <clause id="1367">
    <literal><![CDATA[
      T(x \ 1,T(x,y) * (x \ 1)) = x \ 1
    ]]></literal>
    <justification jstring="[para(473(a,1),1365(a,1,2))].">
      <j1 rule="para" parents="473 1365"/>
    </justification>
  </clause>

  <clause id="1368">
    <literal><![CDATA[
      T(x \ 1,x \ T(x,y)) = x \ 1
    ]]></literal>
    <justification jstring="[para(1010(a,1),1365(a,1,2))].">
      <j1 rule="para" parents="1010 1365"/>
    </justification>
  </clause>

  <clause id="1369">
    <literal><![CDATA[
      T(x \ T(x,y),x \ 1) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(54,a,1368,a)].">
      <j1 rule="hyper" parents="54 1368"/>
    </justification>
  </clause>

  <clause id="1370">
    <literal><![CDATA[
      R(x \ 1,T(x,y),x \ 1) = T(x \ 1,T(x,y))
    ]]></literal>
    <justification jstring="[para(1367(a,1),845(a,1,1))].">
      <j1 rule="para" parents="1367 845"/>
    </justification>
  </clause>

  <clause id="1371">
    <literal><![CDATA[
      T((x * y) \ (y * x),y \ 1) = L(y \ T(y,x),y,x)
    ]]></literal>
    <justification jstring="[para(1369(a,1),786(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1369 786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1372">
    <literal><![CDATA[
      K(x,y) = T((y * x) \ (x * y),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(333,a,785,a,b,1371,a)].">
      <j1 rule="hyper" parents="333 785 1371"/>
    </justification>
  </clause>

  <clause id="1373">
    <literal><![CDATA[
      T(K(x,y),x \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[para(16(a,2),1372(a,2,1)),flip(a)].">
      <j1 rule="para" parents="16 1372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1374">
    <literal><![CDATA[
      T(x \ 1,K(x,y)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(54,a,1373,a)].">
      <j1 rule="hyper" parents="54 1373"/>
    </justification>
  </clause>

  <clause id="1375">
    <literal><![CDATA[
      (x \ 1) * K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * (x \ 1) = z
    ]]></literal>
    <justification jstring="[para(1373(a,1),300(a,1,2))].">
      <j1 rule="para" parents="1373 300"/>
    </justification>
  </clause>

  <clause id="1376">
    <literal><![CDATA[
      K(x,y) * (x \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ 1) * K(x,y) = z
    ]]></literal>
    <justification jstring="[para(1374(a,1),300(a,1,2))].">
      <j1 rule="para" parents="1374 300"/>
    </justification>
  </clause>

  <clause id="1377">
    <literal><![CDATA[
      T((x * y) \ x,K(y,z)) = L(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(1374(a,1),394(a,2,1))].">
      <j1 rule="para" parents="1374 394"/>
    </justification>
  </clause>

  <clause id="1378">
    <literal><![CDATA[
      T((x * y) \ x,K(y,z)) = (x * y) \ x
    ]]></literal>
    <justification jstring="[hyper(333,a,227,a(flip),b,1377,a),flip(a)].">
      <j1 rule="hyper" parents="333 227 1377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1379">
    <literal><![CDATA[
      T(K(x,y),(z * x) \ z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(54,a,1378,a)].">
      <j1 rule="hyper" parents="54 1378"/>
    </justification>
  </clause>

  <clause id="1380">
    <literal><![CDATA[
      T(K(x \ 1,y),x) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(166(a,1),1379(a,1,2))].">
      <j1 rule="para" parents="166 1379"/>
    </justification>
  </clause>

  <clause id="1381">
    <literal><![CDATA[
      T(K(x,y),1 / x) = K(x,y)
    ]]></literal>
    <justification jstring="[para(167(a,1),1379(a,1,2))].">
      <j1 rule="para" parents="167 1379"/>
    </justification>
  </clause>

  <clause id="1382">
    <literal><![CDATA[
      T(1 / x,K(x,y)) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(54,a,1381,a)].">
      <j1 rule="hyper" parents="54 1381"/>
    </justification>
  </clause>

  <clause id="1383">
    <literal><![CDATA[
      K(x,y) * (1 / x) = (1 / x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(126,a,1381,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="126 1381 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1384">
    <literal><![CDATA[
      T((1 * x) / y,K(y / x,z)) = R(1 / (y / x),y / x,x)
    ]]></literal>
    <justification jstring="[para(1382(a,1),802(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1382 802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1386">
    <literal><![CDATA[
      K(x \ 1,y) * x = x * K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(126,a,1380,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="126 1380 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1387">
    <literal><![CDATA[
      T((1 * x) / y,K(y / x,z)) = x / y
    ]]></literal>
    <justification jstring="[hyper(333,a,400,a(flip),b,1384,a),flip(a)].">
      <j1 rule="hyper" parents="333 400 1384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1388">
    <literal><![CDATA[
      T(x / y,K(y / x,z)) = x / y
    ]]></literal>
    <justification jstring="[para(7(a,1),1387(a,1,1,1))].">
      <j1 rule="para" parents="7 1387"/>
    </justification>
  </clause>

  <clause id="1389">
    <literal><![CDATA[
      T(x \ y,K(x / y,z)) = T(y / x,x)
    ]]></literal>
    <justification jstring="[para(1388(a,1),259(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1388 259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1390">
    <literal><![CDATA[
      T(x \ y,K(x / y,z)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(333,a,113,a(flip),b,1389,a),flip(a)].">
      <j1 rule="hyper" parents="333 113 1389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1391">
    <literal><![CDATA[
      x * T(x \ (x \ (y * x)),z) = T(x * T(x \ y,z),x)
    ]]></literal>
    <justification jstring="[hyper(254,a,1358,a),flip(a)].">
      <j1 rule="hyper" parents="254 1358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1392">
    <literal><![CDATA[
      (x * y) * T((x * y) \ (z * y),u) = (x * T(x \ z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,940,a,b,1358,a)].">
      <j1 rule="hyper" parents="63 940 1358"/>
    </justification>
  </clause>

  <clause id="1393">
    <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(99(a,2),1358(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="99 1358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1394">
    <literal><![CDATA[
      T(x * T(x \ y,z),x) = x * T(x \ T(y,x),z)
    ]]></literal>
    <justification jstring="[para(22(a,2),1391(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="22 1391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1395">
    <literal><![CDATA[
      x \ T(x * T(x \ y,z),x) = T(x \ T(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(827,a,1394,a)].">
      <j1 rule="hyper" parents="827 1394"/>
    </justification>
  </clause>

  <clause id="1396">
    <literal><![CDATA[
      x * T(x \ T(y,x),x) = T((x \ y) * x,x)
    ]]></literal>
    <justification jstring="[para(111(a,1),1394(a,1,1)),flip(a)].">
      <j1 rule="para" parents="111 1394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1397">
    <literal><![CDATA[
      T((x \ y) * x,x) = (x \ T(y,x)) * x
    ]]></literal>
    <justification jstring="[hyper(300,a,1396,a),flip(a)].">
      <j1 rule="hyper" parents="300 1396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1398">
    <literal><![CDATA[
      T((x \ y) * x,x) / x = x \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(123,a,1396,a(flip),b,111,a(flip))].">
      <j1 rule="hyper" parents="123 1396 111"/>
    </justification>
  </clause>

  <clause id="1399">
    <literal><![CDATA[
      T(x,y) \ T((y \ x) * y,y) = K(y \ T(x,y),y)
    ]]></literal>
    <justification jstring="[para(1396(a,1),434(a,1,2))].">
      <j1 rule="para" parents="1396 434"/>
    </justification>
  </clause>

  <clause id="1400">
    <literal><![CDATA[
      x * (T((x \ y) * x,x) / x) = T(y,x)
    ]]></literal>
    <justification jstring="[para(1397(a,2),75(a,1,2,1))].">
      <j1 rule="para" parents="1397 75"/>
    </justification>
  </clause>

  <clause id="1401">
    <literal><![CDATA[
      T(x * y,y) / y = y \ T(y * x,y)
    ]]></literal>
    <justification jstring="[para(9(a,1),1398(a,1,1,1,1))].">
      <j1 rule="para" parents="9 1398"/>
    </justification>
  </clause>

  <clause id="1403">
    <literal><![CDATA[
      x \ T(x * (y / x),x) = T(y,x) / x
    ]]></literal>
    <justification jstring="[para(80(a,1),1398(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="80 1398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1404">
    <literal><![CDATA[
      T(x * (y / x),x) = x * (T(y,x) / x)
    ]]></literal>
    <justification jstring="[para(80(a,1),1400(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="80 1400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1405">
    <literal><![CDATA[
      x \ T(x * T((x * y) / x,z),x) = T(x * T(y,z),x) / x
    ]]></literal>
    <justification jstring="[para(472(a,1),1401(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="472 1401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1406">
    <literal><![CDATA[
      x \ T(x * L((x * y) / x,z,u),x) = T(x * L(y,z,u),x) / x
    ]]></literal>
    <justification jstring="[para(669(a,1),1401(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="669 1401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1407">
    <literal><![CDATA[
      T(x * ((x * R(x \ 1,y,z)) / x),x) = x * ((x * R(x \ 1,y,z)) / x)
    ]]></literal>
    <justification jstring="[para(1349(a,1),1404(a,2,2,1))].">
      <j1 rule="para" parents="1349 1404"/>
    </justification>
  </clause>

  <clause id="1408">
    <literal><![CDATA[
      T(x \ T(x * y,x),z) = x \ T(x * T(y,z),x)
    ]]></literal>
    <justification jstring="[para(9(a,1),1395(a,1,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 1395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1409">
    <literal><![CDATA[
      T(x * y,x) \ T(y * x,x) = K(x \ T(x * y,x),x)
    ]]></literal>
    <justification jstring="[para(9(a,1),1399(a,1,2,1,1))].">
      <j1 rule="para" parents="9 1399"/>
    </justification>
  </clause>

  <clause id="1410">
    <literal><![CDATA[
      x \ T(x * T(y / x,z),x) = T(T(y,x) / x,z)
    ]]></literal>
    <justification jstring="[para(1403(a,1),1408(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1403 1408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1411">
    <literal><![CDATA[
      T(x * T(y / x,z),x) = x * T(T(y,x) / x,z)
    ]]></literal>
    <justification jstring="[hyper(142,a,1410,a),flip(a)].">
      <j1 rule="hyper" parents="142 1410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1412">
    <literal><![CDATA[
      T(x * T(1 / x,y),x) = x * T(1 / x,y)
    ]]></literal>
    <justification jstring="[para(201(a,1),1411(a,2,2,1,1))].">
      <j1 rule="para" parents="201 1411"/>
    </justification>
  </clause>

  <clause id="1413">
    <literal><![CDATA[
      ((x / y) * T((x / y) \ z,u)) * y = x * T(((x / y) * y) \ (z * y),u)
    ]]></literal>
    <justification jstring="[hyper(339,a,1392,a),flip(a)].">
      <j1 rule="hyper" parents="339 1392"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1414">
    <literal><![CDATA[
      (x * T(x \ (x * y),z)) * y = (x * y) * T(y,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),1392(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 1392"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1415">
    <literal><![CDATA[
      (x * T(y,z)) * y = (x * y) * T(y,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),1414(a,1,1,2,1))].">
      <j1 rule="para" parents="9 1414"/>
    </justification>
  </clause>

  <clause id="1416">
    <literal><![CDATA[
      (x * y) / T(y,z) = (x / T(y,z)) * y
    ]]></literal>
    <justification jstring="[hyper(621,a,1415,a)].">
      <j1 rule="hyper" parents="621 1415"/>
    </justification>
  </clause>

  <clause id="1417">
    <literal><![CDATA[
      (1 / T(x,y)) * x = x / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(411,a,1415,a),flip(a)].">
      <j1 rule="hyper" parents="411 1415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1418">
    <literal><![CDATA[
      (x * T(y,z)) \ ((x * y) * T(y,z)) = y
    ]]></literal>
    <justification jstring="[hyper(129,a,1415,a)].">
      <j1 rule="hyper" parents="129 1415"/>
    </justification>
  </clause>

  <clause id="1419">
    <literal><![CDATA[
      (x * T(y,z)) / y = (x / y) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(123,a,152,a(flip),b,1415,a)].">
      <j1 rule="hyper" parents="123 152 1415"/>
    </justification>
  </clause>

  <clause id="1420">
    <literal><![CDATA[
      ((x / T(y,z)) / y) * T(y,z) = x / y
    ]]></literal>
    <justification jstring="[hyper(123,a,83,a(flip),b,1415,a),flip(a)].">
      <j1 rule="hyper" parents="123 83 1415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1421">
    <literal><![CDATA[
      (1 / x) * T(x,y) = T(x,y) / x
    ]]></literal>
    <justification jstring="[hyper(123,a,77,a(flip),b,1415,a),flip(a)].">
      <j1 rule="hyper" parents="123 77 1415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1422">
    <literal><![CDATA[
      (x * T(y,z)) * y != u * T(y,z)
    ]]></literal>
    <literal><![CDATA[
      x * y = u
    ]]></literal>
    <justification jstring="[para(1415(a,2),44(a,1))].">
      <j1 rule="para" parents="1415 44"/>
    </justification>
  </clause>

  <clause id="1423">
    <literal><![CDATA[
      (x * (y / z)) * T(y / z,z) = (x * (z \ y)) * (y / z)
    ]]></literal>
    <justification jstring="[para(113(a,1),1415(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="113 1415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1424">
    <literal><![CDATA[
      (x / T(x,y)) / x = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(138,a,1417,a)].">
      <j1 rule="hyper" parents="138 1417"/>
    </justification>
  </clause>

  <clause id="1425">
    <literal><![CDATA[
      (1 / T(x,y)) \ (x / T(x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(129,a,1417,a)].">
      <j1 rule="hyper" parents="129 1417"/>
    </justification>
  </clause>

  <clause id="1426">
    <literal><![CDATA[
      T(x,y) \ (T(x,y) / x) = T(1 / x,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(444,a,xx,b,1421,a),flip(a)].">
      <j1 rule="hyper" parents="444 1421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1427">
    <literal><![CDATA[
      (T(x,y) / x) / T(x,y) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(138,a,1421,a)].">
      <j1 rule="hyper" parents="138 1421"/>
    </justification>
  </clause>

  <clause id="1428">
    <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(1421(a,1),639(a,1,2))].">
      <j1 rule="para" parents="1421 639"/>
    </justification>
  </clause>

  <clause id="1429">
    <literal><![CDATA[
      (1 / T(x,y)) * x != z
    ]]></literal>
    <literal><![CDATA[
      x / T(x,y) = z
    ]]></literal>
    <justification jstring="[para(1424(a,1),264(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1424 264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1430">
    <literal><![CDATA[
      T(x,x / (x / T(y,x))) * T(y,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(125,a,1108,a,b,1416,a)].">
      <j1 rule="hyper" parents="125 1108 1416"/>
    </justification>
  </clause>

  <clause id="1431">
    <literal><![CDATA[
      T(x / T(x,y),x) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(253,a,1416,a(flip),b,1293,a(flip))].">
      <j1 rule="hyper" parents="253 1416 1293"/>
    </justification>
  </clause>

  <clause id="1432">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ x,x) = (T(x,y) \ x) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(125,a,1431,a(flip),b,474,a),flip(a)].">
      <j1 rule="hyper" parents="125 1431 474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1433">
    <literal><![CDATA[
      R(T(x,y * T(x,z)),y,T(x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(1418(a,1),1044(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1418 1044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1434">
    <literal><![CDATA[
      ((x / T(y,z)) / y) * T(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x / y = u
    ]]></literal>
    <justification jstring="[para(1419(a,1),422(a,1))].">
      <j1 rule="para" parents="1419 422"/>
    </justification>
  </clause>

  <clause id="1435">
    <literal><![CDATA[
      T(x,x / (x / T(y,x))) * (y * x) = x * (x * y)
    ]]></literal>
    <justification jstring="[para(1430(a,1),1055(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1430 1055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1436">
    <literal><![CDATA[
      x * T(y,z) != u * y
    ]]></literal>
    <literal><![CDATA[
      (u / T(y,z)) * y = x
    ]]></literal>
    <justification jstring="[para(12(a,1),1422(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12 1422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1437">
    <literal><![CDATA[
      T(x,x / (x / T(y,x))) = (x * (x * y)) / (y * x)
    ]]></literal>
    <justification jstring="[hyper(138,a,1435,a),flip(a)].">
      <j1 rule="hyper" parents="138 1435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1438">
    <literal><![CDATA[
      (x * (x * y)) / (y * x) = (x / T(y,x)) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,1108,a(flip),b,1437,a),flip(a)].">
      <j1 rule="hyper" parents="63 1108 1437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1439">
    <literal><![CDATA[
      R(((x * (x * y)) / x) / y,y,x) = (x / T(y,x)) * y
    ]]></literal>
    <justification jstring="[hyper(882,a,1438,a)].">
      <j1 rule="hyper" parents="882 1438"/>
    </justification>
  </clause>

  <clause id="1440">
    <literal><![CDATA[
      R(T(x,x / (1 / y)),y,x) = (x / T(y,x)) * y
    ]]></literal>
    <justification jstring="[para(1335(a,1),1439(a,1,1))].">
      <j1 rule="para" parents="1335 1439"/>
    </justification>
  </clause>

  <clause id="1441">
    <literal><![CDATA[
      (x * (y / z)) * (z \ y) = (x * (z \ y)) * (y / z)
    ]]></literal>
    <justification jstring="[para(113(a,1),1423(a,1,2))].">
      <j1 rule="para" parents="113 1423"/>
    </justification>
  </clause>

  <clause id="1442">
    <literal><![CDATA[
      (x * (y \ (y * z))) * ((y * z) / y) = (x * ((y * z) / y)) * z
    ]]></literal>
    <justification jstring="[para(238(a,1),1423(a,1,2)),flip(a)].">
      <j1 rule="para" parents="238 1423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1443">
    <literal><![CDATA[
      (x * (y \ z)) / (z / y) = (x / (z / y)) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(621,a,1441,a)].">
      <j1 rule="hyper" parents="621 1441"/>
    </justification>
  </clause>

  <clause id="1445">
    <literal><![CDATA[
      (1 / (x / y)) * (y \ x) = (y \ x) / (x / y)
    ]]></literal>
    <justification jstring="[hyper(411,a,1441,a),flip(a)].">
      <j1 rule="hyper" parents="411 1441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1446">
    <literal><![CDATA[
      (x * (y / x)) * (x \ y) = y * (y / x)
    ]]></literal>
    <justification jstring="[hyper(333,a,153,a(flip),b,1441,a),flip(a)].">
      <j1 rule="hyper" parents="333 153 1441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1447">
    <literal><![CDATA[
      (x * (y / z)) / (z \ y) = (x / (z \ y)) * (y / z)
    ]]></literal>
    <justification jstring="[hyper(123,a,152,a(flip),b,1441,a)].">
      <j1 rule="hyper" parents="123 152 1441"/>
    </justification>
  </clause>

  <clause id="1448">
    <literal><![CDATA[
      ((x / y) * (x / (x / y))) * y = x * (x / (x / y))
    ]]></literal>
    <justification jstring="[hyper(596,a,1446,a)].">
      <j1 rule="hyper" parents="596 1446"/>
    </justification>
  </clause>

  <clause id="1449">
    <literal><![CDATA[
      (x \ y) \ ((x \ y) / (y / x)) = T(1 / (y / x),x \ y)
    ]]></literal>
    <justification jstring="[hyper(444,a,xx,b,1445,a),flip(a)].">
      <j1 rule="hyper" parents="444 1445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1450">
    <literal><![CDATA[
      ((x / (y \ z)) / (z / y)) * (y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      x / (z / y) = u
    ]]></literal>
    <justification jstring="[para(1443(a,1),422(a,1))].">
      <j1 rule="para" parents="1443 422"/>
    </justification>
  </clause>

  <clause id="1451">
    <literal><![CDATA[
      T(x * T(y,z),x) / x = T(T(x * y,x) / x,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,1410,a(flip),b,1405,a),flip(a)].">
      <j1 rule="hyper" parents="63 1410 1405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1452">
    <literal><![CDATA[
      (x * ((y * z) / y)) * z = (x * z) * ((y * z) / y)
    ]]></literal>
    <justification jstring="[para(9(a,1),1442(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 1442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1453">
    <literal><![CDATA[
      (x * y) / ((z * y) / z) = (x / ((z * y) / z)) * y
    ]]></literal>
    <justification jstring="[hyper(621,a,1452,a)].">
      <j1 rule="hyper" parents="621 1452"/>
    </justification>
  </clause>

  <clause id="1454">
    <literal><![CDATA[
      (1 / ((x * y) / x)) * y = y / ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(411,a,1452,a),flip(a)].">
      <j1 rule="hyper" parents="411 1452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1456">
    <literal><![CDATA[
      ((x / y) * y) * ((x * y) / x) = T(x,x / (x / y)) * y
    ]]></literal>
    <justification jstring="[para(1095(a,1),1452(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1095 1452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1457">
    <literal><![CDATA[
      T(x,x / (x / y)) * y = x * ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(339,a,1456,a),flip(a)].">
      <j1 rule="hyper" parents="339 1456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1458">
    <literal><![CDATA[
      T(x,x / (x / y)) * (x \ y) = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(1074,a,1457,a)].">
      <j1 rule="hyper" parents="1074 1457"/>
    </justification>
  </clause>

  <clause id="1460">
    <literal><![CDATA[
      ((x * y) / x) / (x \ y) = T(x,x / (x / y))
    ]]></literal>
    <justification jstring="[hyper(138,a,1458,a)].">
      <j1 rule="hyper" parents="138 1458"/>
    </justification>
  </clause>

  <clause id="1461">
    <literal><![CDATA[
      T(x,x / (1 / (x \ y))) = T(x,x / (x / y))
    ]]></literal>
    <justification jstring="[hyper(63,a,1336,a,b,1460,a)].">
      <j1 rule="hyper" parents="63 1336 1460"/>
    </justification>
  </clause>

  <clause id="1462">
    <literal><![CDATA[
      T(x,x / (x / (x * y))) = T(x,x / (1 / y))
    ]]></literal>
    <justification jstring="[para(9(a,1),1461(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="9 1461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1463">
    <literal><![CDATA[
      ((x / (y * y)) * z) / ((y * y) \ z) = R(x,y \ (y \ 1),z)
    ]]></literal>
    <justification jstring="[para(722(a,1),732(a,1,1,1))].">
      <j1 rule="para" parents="722 732"/>
    </justification>
  </clause>

  <clause id="1464">
    <literal><![CDATA[
      (x * ((y * y) \ z)) / ((y * y) \ z) = R(x,y \ (y \ 1),z)
    ]]></literal>
    <justification jstring="[para(707(a,1),1463(a,1,1))].">
      <j1 rule="para" parents="707 1463"/>
    </justification>
  </clause>

  <clause id="1465">
    <literal><![CDATA[
      R(x,y \ (y \ 1),z) = x
    ]]></literal>
    <justification jstring="[hyper(269,a,1464,a),flip(a)].">
      <j1 rule="hyper" parents="269 1464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1468">
    <literal><![CDATA[
      R(x,(1 / y) \ y,z) = x
    ]]></literal>
    <justification jstring="[para(79(a,1),1465(a,1,2,2))].">
      <j1 rule="para" parents="79 1465"/>
    </justification>
  </clause>

  <clause id="1469">
    <literal><![CDATA[
      ((1 / x) \ x) * (x \ y) = (1 / x) \ y
    ]]></literal>
    <justification jstring="[para(1468(a,1),759(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1468 759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1470">
    <literal><![CDATA[
      x / (x \ 1) = (1 / x) \ x
    ]]></literal>
    <justification jstring="[hyper(123,a,79,a(flip),b,1469,a)].">
      <j1 rule="hyper" parents="123 79 1469"/>
    </justification>
  </clause>

  <clause id="1471">
    <literal><![CDATA[
      (1 / (1 / x)) \ (1 / x) = (1 / x) / x
    ]]></literal>
    <justification jstring="[para(79(a,1),1470(a,1,2)),flip(a)].">
      <j1 rule="para" parents="79 1470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1473">
    <literal><![CDATA[
      x * ((x \ y) * ((z * ((x \ y) \ u)) / z)) = y * ((z * (y \ (x * u))) / z)
    ]]></literal>
    <justification jstring="[hyper(126,a,917,a(flip),b,98,a),flip(a)].">
      <j1 rule="hyper" parents="126 917 98"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1474">
    <literal><![CDATA[
      x \ (y * ((z * (y \ (x * u))) / z)) = (x \ y) * ((z * ((x \ y) \ u)) / z)
    ]]></literal>
    <justification jstring="[para(917(a,1),495(a,1,2,2))].">
      <j1 rule="para" parents="917 495"/>
    </justification>
  </clause>

  <clause id="1475">
    <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="[hyper(126,a,945,a(flip),b,245,a)].">
      <j1 rule="hyper" parents="126 945 245"/>
    </justification>
  </clause>

  <clause id="1476">
    <literal><![CDATA[
      T(x * (y * z),z \ (z \ 1)) = (z * z) * (x * (y * (z \ 1)))
    ]]></literal>
    <justification jstring="[para(812(a,1),1116(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="812 1116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1477">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) \ (y \ x) = (x \ y) \ 1
    ]]></literal>
    <justification jstring="[para(388(a,1),1146(a,1,2))].">
      <j1 rule="para" parents="388 1146"/>
    </justification>
  </clause>

  <clause id="1478">
    <literal><![CDATA[
      (x \ y) / ((y \ x) \ 1) = (y \ x) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(198,a,1477,a)].">
      <j1 rule="hyper" parents="198 1477"/>
    </justification>
  </clause>

  <clause id="1479">
    <literal><![CDATA[
      (1 / (x \ y)) \ (y \ x) = (y \ x) * (x \ y)
    ]]></literal>
    <justification jstring="[para(388(a,1),1150(a,1,1)),flip(a)].">
      <j1 rule="para" parents="388 1150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1480">
    <literal><![CDATA[
      (1 / (x \ y)) * ((y \ x) * (x \ y)) = y \ x
    ]]></literal>
    <justification jstring="[hyper(142,a,1479,a)].">
      <j1 rule="hyper" parents="142 1479"/>
    </justification>
  </clause>

  <clause id="1481">
    <literal><![CDATA[
      (x \ (x * y)) * ((x * y) \ x) = (1 / ((x * y) \ x)) \ y
    ]]></literal>
    <justification jstring="[para(9(a,1),1479(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9 1479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1483">
    <literal><![CDATA[
      (1 / ((x * y) \ x)) \ y = y * ((x * y) \ x)
    ]]></literal>
    <justification jstring="[para(9(a,1),1481(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 1481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1484">
    <literal><![CDATA[
      (1 / ((x * y) \ x)) * (y * ((x * y) \ x)) = y
    ]]></literal>
    <justification jstring="[hyper(142,a,1483,a)].">
      <j1 rule="hyper" parents="142 1483"/>
    </justification>
  </clause>

  <clause id="1485">
    <literal><![CDATA[
      T((x * y) / x,L(y,z,u) * x) = L(y,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(11(a,1),1271(a,2,1))].">
      <j1 rule="para" parents="11 1271"/>
    </justification>
  </clause>

  <clause id="1486">
    <literal><![CDATA[
      x * T(y,L(y,z,u) * x) = L(y,x,L(y,z,u)) * x
    ]]></literal>
    <justification jstring="[hyper(125,a,1485,a(flip),b,476,a),flip(a)].">
      <j1 rule="hyper" parents="125 1485 476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1487">
    <literal><![CDATA[
      L(T(x,y),y,L(x,z,u)) = T(x,L(x,z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(34,a,251,a,b,1486,a)].">
      <j1 rule="hyper" parents="34 251 1486"/>
    </justification>
  </clause>

  <clause id="1488">
    <literal><![CDATA[
      (1 / (x / y)) * ((y / x) * (x / y)) = y / x
    ]]></literal>
    <justification jstring="[hyper(126,a,834,a(flip),b,1326,a(flip))].">
      <j1 rule="hyper" parents="126 834 1326"/>
    </justification>
  </clause>

  <clause id="1489">
    <literal><![CDATA[
      T(1 / (x / y),(y / x) * (x / y)) = ((y / x) * (x / y)) \ (y / x)
    ]]></literal>
    <justification jstring="[hyper(444,a,xx,b,1488,a)].">
      <j1 rule="hyper" parents="444 1488"/>
    </justification>
  </clause>

  <clause id="1490">
    <literal><![CDATA[
      T(x,(x * T(x \ 1,y)) / x) = R(x,T(1 / x,y),x)
    ]]></literal>
    <justification jstring="[para(474(a,1),1366(a,1,2)),flip(a)].">
      <j1 rule="para" parents="474 1366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1491">
    <literal><![CDATA[
      R(x,T(1 / x,y),x) = T(x,T(1 / x,y))
    ]]></literal>
    <justification jstring="[para(474(a,1),1490(a,1,2)),flip(a)].">
      <j1 rule="para" parents="474 1490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1492">
    <literal><![CDATA[
      (x / y) * (y * T(y \ 1,z)) = x * T(x \ (x / y),z)
    ]]></literal>
    <justification jstring="[hyper(339,a,941,a),flip(a)].">
      <j1 rule="hyper" parents="339 941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1494">
    <literal><![CDATA[
      (x / y) * K(y \ 1,y) = x * T(x \ (x / y),y)
    ]]></literal>
    <justification jstring="[para(358(a,1),1492(a,1,2))].">
      <j1 rule="para" parents="358 1492"/>
    </justification>
  </clause>

  <clause id="1495">
    <literal><![CDATA[
      ((x / y) * K(y \ 1,y)) * y = x * (y * T(y \ (x \ x),y))
    ]]></literal>
    <justification jstring="[para(1494(a,2),1357(a,1,1))].">
      <j1 rule="para" parents="1494 1357"/>
    </justification>
  </clause>

  <clause id="1496">
    <literal><![CDATA[
      ((x / y) * K(y \ 1,y)) * y = x * (y * T(y \ 1,y))
    ]]></literal>
    <justification jstring="[para(66(a,1),1495(a,2,2,2,1,2))].">
      <j1 rule="para" parents="66 1495"/>
    </justification>
  </clause>

  <clause id="1498">
    <literal><![CDATA[
      ((x / y) * K(y \ 1,y)) * y = x * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(358(a,1),1496(a,2,2))].">
      <j1 rule="para" parents="358 1496"/>
    </justification>
  </clause>

  <clause id="1499">
    <literal><![CDATA[
      (x * K(y \ 1,y)) * y = (x * y) * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(11(a,1),1498(a,1,1,1))].">
      <j1 rule="para" parents="11 1498"/>
    </justification>
  </clause>

  <clause id="1500">
    <literal><![CDATA[
      (x * y) * R((x * y) \ (z * y),u,w) = (R(z / x,u,w) * x) * y
    ]]></literal>
    <justification jstring="[hyper(903,a,1019,a)].">
      <j1 rule="hyper" parents="903 1019"/>
    </justification>
  </clause>

  <clause id="1501">
    <literal><![CDATA[
      (L((x / y) / z,u,w) * z) * y = (z * y) * L((z * y) \ x,u,w)
    ]]></literal>
    <justification jstring="[hyper(333,a,668,a(flip),b,1022,a),flip(a)].">
      <j1 rule="hyper" parents="333 668 1022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1502">
    <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(276(a,2),1024(a,1,1))].">
      <j1 rule="para" parents="276 1024"/>
    </justification>
  </clause>

  <clause id="1503">
    <literal><![CDATA[
      R((x * y) / (x * z),u,w) * (x * z) = x * (z * R(z \ y,u,w))
    ]]></literal>
    <justification jstring="[hyper(687,a,1027,a)].">
      <j1 rule="hyper" parents="687 1027"/>
    </justification>
  </clause>

  <clause id="1504">
    <literal><![CDATA[
      x * ((x * y) * R((x * y) \ y,z,u)) = (x * R(x \ 1,z,u)) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,1338,a(flip),b,1027,a),flip(a)].">
      <j1 rule="hyper" parents="63 1338 1027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1505">
    <literal><![CDATA[
      x * (y * R(y \ (x \ y),z,u)) = (x * R(x \ 1,z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,1338,a(flip),b,1028,a),flip(a)].">
      <j1 rule="hyper" parents="63 1338 1028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1506">
    <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(276(a,2),1028(a,1,1))].">
      <j1 rule="para" parents="276 1028"/>
    </justification>
  </clause>

  <clause id="1507">
    <literal><![CDATA[
      x * (y * R(y \ (x * y),z,u)) = R(x,z,u) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(421,a,1029,a),flip(a)].">
      <j1 rule="hyper" parents="421 1029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1508">
    <literal><![CDATA[
      x * (y * R(T(x,y),z,u)) = R(x,z,u) * (x * y)
    ]]></literal>
    <justification jstring="[para(22(a,2),1507(a,1,2,2,1))].">
      <j1 rule="para" parents="22 1507"/>
    </justification>
  </clause>

  <clause id="1509">
    <literal><![CDATA[
      R(x,y,z) * (x * u) = x * (R(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(252(a,1),1508(a,1,2)),flip(a)].">
      <j1 rule="para" parents="252 1508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1510">
    <literal><![CDATA[
      x \ (R(x,y,z) * u) = R(x,y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(631,a,1509,a)].">
      <j1 rule="hyper" parents="631 1509"/>
    </justification>
  </clause>

  <clause id="1511">
    <literal><![CDATA[
      x \ ((x * x) * y) = R(x,x,y) * y
    ]]></literal>
    <justification jstring="[hyper(622,a,1509,a)].">
      <j1 rule="hyper" parents="622 1509"/>
    </justification>
  </clause>

  <clause id="1512">
    <literal><![CDATA[
      (R(x,y,z) * u) / (R(x,y,z) * (x \ u)) = x
    ]]></literal>
    <justification jstring="[hyper(607,a,1509,a)].">
      <j1 rule="hyper" parents="607 1509"/>
    </justification>
  </clause>

  <clause id="1513">
    <literal><![CDATA[
      x * (R(x,y,z) * T(u,x)) = R(x,y,z) * (u * x)
    ]]></literal>
    <justification jstring="[hyper(595,a,1509,a),flip(a)].">
      <j1 rule="hyper" parents="595 1509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1514">
    <literal><![CDATA[
      R(x,y,z) \ (x * (R(x,y,z) * u)) = x * u
    ]]></literal>
    <justification jstring="[hyper(129,a,1509,a)].">
      <j1 rule="hyper" parents="129 1509"/>
    </justification>
  </clause>

  <clause id="1515">
    <literal><![CDATA[
      x * (R(x,y,z) \ 1) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(121,a,69,a(flip),b,1509,a),flip(a)].">
      <j1 rule="hyper" parents="121 69 1509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1516">
    <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(444,a,154,a(flip),b,1509,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="444 154 1509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1517">
    <literal><![CDATA[
      (x \ ((x * x) * y)) / y != z
    ]]></literal>
    <literal><![CDATA[
      R(x,x,y) = z
    ]]></literal>
    <justification jstring="[para(1511(a,2),268(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1511 268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1518">
    <literal><![CDATA[
      L(R(x,y,z) \ 1,x,1 / x) = (1 / x) * (R(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(126,a,1515,a(flip),b,438,a),flip(a)].">
      <j1 rule="hyper" parents="126 1515 438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1519">
    <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(1515(a,1),1007(a,1,2,1,2))].">
      <j1 rule="para" parents="1515 1007"/>
    </justification>
  </clause>

  <clause id="1520">
    <literal><![CDATA[
      R(x,y,z) * (x \ (y * z)) = x \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[para(107(a,1),1510(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 1510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1521">
    <literal><![CDATA[
      R(x,y,y \ z) * (x \ z) = x \ ((x * y) * (y \ z))
    ]]></literal>
    <justification jstring="[para(367(a,1),1510(a,1,2)),flip(a)].">
      <j1 rule="para" parents="367 1510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1522">
    <literal><![CDATA[
      x \ (R(x,y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) * (x \ u) = w
    ]]></literal>
    <justification jstring="[para(1512(a,1),345(a,1,1))].">
      <j1 rule="para" parents="1512 345"/>
    </justification>
  </clause>

  <clause id="1523">
    <literal><![CDATA[
      R(x,y,z) = (x \ ((x * y) * z)) / (x \ (y * z))
    ]]></literal>
    <justification jstring="[hyper(138,a,1520,a),flip(a)].">
      <j1 rule="hyper" parents="138 1520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1524">
    <literal><![CDATA[
      R(x,y,x) * T(y,x) = T(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(253,a,107,a(flip),b,1513,a),flip(a)].">
      <j1 rule="hyper" parents="253 107 1513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1525">
    <literal><![CDATA[
      R(x,y,x) \ T(x * y,x) = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(129,a,1524,a)].">
      <j1 rule="hyper" parents="129 1524"/>
    </justification>
  </clause>

  <clause id="1526">
    <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(1491(a,1),1524(a,1,1))].">
      <j1 rule="para" parents="1491 1524"/>
    </justification>
  </clause>

  <clause id="1527">
    <literal><![CDATA[
      x \ ((x * (x \ y)) * ((x \ y) \ z)) = ((y * ((x \ y) \ z)) / z) * (x \ z)
    ]]></literal>
    <justification jstring="[para(758(a,1),1521(a,1,1)),flip(a)].">
      <j1 rule="para" parents="758 1521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1528">
    <literal><![CDATA[
      (((x * y) / x) * (y \ 1)) * x = T(x,R(y,y \ 1,x))
    ]]></literal>
    <justification jstring="[hyper(926,a,1090,a)].">
      <j1 rule="hyper" parents="926 1090"/>
    </justification>
  </clause>

  <clause id="1529">
    <literal><![CDATA[
      (x \ ((y * x) / y)) * y = T(y,R(x,x \ 1,y))
    ]]></literal>
    <justification jstring="[para(1297(a,1),1528(a,1,1))].">
      <j1 rule="para" parents="1297 1528"/>
    </justification>
  </clause>

  <clause id="1530">
    <literal><![CDATA[
      T(x,R(y,y \ 1,x)) / x = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(138,a,1529,a)].">
      <j1 rule="hyper" parents="138 1529"/>
    </justification>
  </clause>

  <clause id="1531">
    <literal><![CDATA[
      T(x,R(T(y,x),T(y,x) \ 1,x)) = (T(y,x) \ y) * x
    ]]></literal>
    <justification jstring="[para(239(a,1),1529(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="239 1529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1532">
    <literal><![CDATA[
      (1 / x) \ ((y * (1 / x)) / y) = T(y,R(1 / x,x,y)) / y
    ]]></literal>
    <justification jstring="[para(79(a,1),1530(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="79 1530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1533">
    <literal><![CDATA[
      (x * ((y * (x \ 1)) / y)) * y = T(y,R(1 / x,x,y))
    ]]></literal>
    <justification jstring="[hyper(125,a,1333,a(flip),b,1532,a(flip))].">
      <j1 rule="hyper" parents="125 1333 1532"/>
    </justification>
  </clause>

  <clause id="1534">
    <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(1063(a,1),1533(a,1,1,2,1))].">
      <j1 rule="para" parents="1063 1533"/>
    </justification>
  </clause>

  <clause id="1535">
    <literal><![CDATA[
      L((x \ 1) \ (x \ y),z,u) = (x \ 1) \ (x \ L(y,z,u))
    ]]></literal>
    <justification jstring="[para(76(a,1),1156(a,1,1,2,1))].">
      <j1 rule="para" parents="76 1156"/>
    </justification>
  </clause>

  <clause id="1537">
    <literal><![CDATA[
      (L(x / y,z,u) * y) * (y \ w) = w * L(w \ (x * (y \ w)),z,u)
    ]]></literal>
    <justification jstring="[hyper(895,a,1161,a),flip(a)].">
      <j1 rule="hyper" parents="895 1161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1538">
    <literal><![CDATA[
      (x \ y) * R((x \ y) \ 1,z,u) = x \ (y * R(y \ x,z,u))
    ]]></literal>
    <justification jstring="[para(8(a,1),1164(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="8 1164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1539">
    <literal><![CDATA[
      (x * y) \ ((x * (y * z)) * R((x * (y * z)) \ (x * y),u,w)) = L(z,y,x) * R(((x * y) \ (x * (y * z))) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(18(a,2),1538(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18 1538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1540">
    <literal><![CDATA[
      x \ ((y * x) * R((y * x) \ x,z,u)) = T(y,x) * R((x \ (y * x)) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(22(a,2),1538(a,1,1)),flip(a)].">
      <j1 rule="para" parents="22 1538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1541">
    <literal><![CDATA[
      (x \ y) * L((x \ y) \ 1,z,u) = x \ (y * L(y \ x,z,u))
    ]]></literal>
    <justification jstring="[para(8(a,1),1165(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="8 1165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1542">
    <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(18(a,2),1541(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18 1541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1543">
    <literal><![CDATA[
      (R(1 / (x / y),z,u) * (x / y)) * y = R(y / x,z,u) * x
    ]]></literal>
    <justification jstring="[para(7(a,1),1166(a,2,1,1,1))].">
      <j1 rule="para" parents="7 1166"/>
    </justification>
  </clause>

  <clause id="1544">
    <literal><![CDATA[
      (R(1 / (x / y),z,u) * (x / y)) * y = x * R(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(333,a,675,a(flip),b,1543,a),flip(a)].">
      <j1 rule="hyper" parents="333 675 1543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1545">
    <literal><![CDATA[
      ((x / y) * R((x / y) \ 1,z,u)) * y = x * R(x \ y,z,u)
    ]]></literal>
    <justification jstring="[para(675(a,1),1544(a,1,1))].">
      <j1 rule="para" parents="675 1544"/>
    </justification>
  </clause>

  <clause id="1546">
    <literal><![CDATA[
      (x / y) * R((x / y) \ 1,z,u) = (x * R(x \ y,z,u)) / y
    ]]></literal>
    <justification jstring="[hyper(138,a,1545,a),flip(a)].">
      <j1 rule="hyper" parents="138 1545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1547">
    <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(20(a,2),1546(a,1,1)),flip(a)].">
      <j1 rule="para" parents="20 1546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1548">
    <literal><![CDATA[
      (x / y) \ (x * ((z * (x \ (x / y))) / z)) = y * ((z * (y \ 1)) / z)
    ]]></literal>
    <justification jstring="[hyper(129,a,1173,a)].">
      <j1 rule="hyper" parents="129 1173"/>
    </justification>
  </clause>

  <clause id="1549">
    <literal><![CDATA[
      R(L(((x \ y) * (x * x)) / x,x,x),x,x) = (x * x) \ ((x * y) * x)
    ]]></literal>
    <justification jstring="[para(441(a,1),1215(a,1,1,1,1))].">
      <j1 rule="para" parents="441 1215"/>
    </justification>
  </clause>

  <clause id="1550">
    <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(1328(a,1),426(a,1))].">
      <j1 rule="para" parents="1328 426"/>
    </justification>
  </clause>

  <clause id="1551">
    <literal><![CDATA[
      x \ R(x * (y * (x \ 1)),z,u) = R(y,z,u) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(333,a,252,a(flip),b,1330,a),flip(a)].">
      <j1 rule="hyper" parents="333 252 1330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1552">
    <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(1063(a,1),1551(a,1,2,1,2))].">
      <j1 rule="para" parents="1063 1551"/>
    </justification>
  </clause>

  <clause id="1553">
    <literal><![CDATA[
      (x * y) * R((x * y) \ (z * y),u,w) = (x * R(x \ z,u,w)) * y
    ]]></literal>
    <justification jstring="[para(675(a,1),1500(a,2,1))].">
      <j1 rule="para" parents="675 1500"/>
    </justification>
  </clause>

  <clause id="1554">
    <literal><![CDATA[
      (L((x / y) / z,u,w) * z) * y = z * (y * L(y \ (z \ x),u,w))
    ]]></literal>
    <justification jstring="[hyper(333,a,1024,a(flip),b,1501,a),flip(a)].">
      <j1 rule="hyper" parents="333 1024 1501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1555">
    <literal><![CDATA[
      R((x * y) / (x * z),u,w) * (x * z) = x * (R(y / z,u,w) * z)
    ]]></literal>
    <justification jstring="[para(675(a,2),1503(a,2,2))].">
      <j1 rule="para" parents="675 1503"/>
    </justification>
  </clause>

  <clause id="1556">
    <literal><![CDATA[
      T(x,T(1 / x,y)) * T(x \ 1,y) = T(x * T(1 / x,y),x)
    ]]></literal>
    <justification jstring="[para(259(a,1),1526(a,1,2))].">
      <j1 rule="para" parents="259 1526"/>
    </justification>
  </clause>

  <clause id="1557">
    <literal><![CDATA[
      T(x,T(1 / x,y)) * T(x \ 1,y) = x * T(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,1412,a(flip),b,1556,a),flip(a)].">
      <j1 rule="hyper" parents="333 1412 1556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1558">
    <literal><![CDATA[
      (x * L(x \ y,z,u)) * (x \ w) = w * L(w \ (y * (x \ w)),z,u)
    ]]></literal>
    <justification jstring="[para(668(a,1),1537(a,1,1))].">
      <j1 rule="para" parents="668 1537"/>
    </justification>
  </clause>

  <clause id="1559">
    <literal><![CDATA[
      (x / y) \ (x * ((x / y) / x)) = y * ((x * (y \ 1)) / x)
    ]]></literal>
    <justification jstring="[para(10(a,1),1548(a,1,2,2,1))].">
      <j1 rule="para" parents="10 1548"/>
    </justification>
  </clause>

  <clause id="1560">
    <literal><![CDATA[
      K(x,(x / y) / x) = y * ((x * (y \ 1)) / x)
    ]]></literal>
    <justification jstring="[hyper(483,a,1559,a)].">
      <j1 rule="hyper" parents="483 1559"/>
    </justification>
  </clause>

  <clause id="1561">
    <literal><![CDATA[
      x * ((y * (x \ 1)) / y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,(y / x) / y) = z
    ]]></literal>
    <justification jstring="[para(1559(a,1),483(a,1))].">
      <j1 rule="para" parents="1559 483"/>
    </justification>
  </clause>

  <clause id="1562">
    <literal><![CDATA[
      K(x,(x / (y \ 1)) / x) = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(333,a,1299,a(flip),b,1560,a),flip(a)].">
      <j1 rule="hyper" parents="333 1299 1560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1563">
    <literal><![CDATA[
      (x \ y) * ((y * ((x \ y) \ 1)) / y) = K(y,x / y)
    ]]></literal>
    <justification jstring="[para(76(a,1),1560(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="76 1560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1564">
    <literal><![CDATA[
      x * ((T(x,y) * (x \ 1)) / T(x,y)) = K(T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[para(1427(a,1),1560(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1427 1560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1565">
    <literal><![CDATA[
      K(x,(x / ((T(x,y) \ 1) \ 1)) / x) = (T(x,y) \ 1) \ ((T(x,y) \ x) / x)
    ]]></literal>
    <justification jstring="[para(1063(a,1),1562(a,2,2,1))].">
      <j1 rule="para" parents="1063 1562"/>
    </justification>
  </clause>

  <clause id="1567">
    <literal><![CDATA[
      x * (((x \ 1) * T((x \ 1) \ 1,y)) / T(x,y)) = K(T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[para(473(a,2),1564(a,1,2,1))].">
      <j1 rule="para" parents="473 1564"/>
    </justification>
  </clause>

  <clause id="1568">
    <literal><![CDATA[
      R(L((x \ y) / (x / (x * x)),x,x),x,x) = (x * x) \ ((x * y) * x)
    ]]></literal>
    <justification jstring="[para(801(a,1),1549(a,1,1,1))].">
      <j1 rule="para" parents="801 1549"/>
    </justification>
  </clause>

  <clause id="1569">
    <literal><![CDATA[
      x * (y * R(y \ (x \ (z * y)),u,w)) = (x * R(x \ z,u,w)) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,1028,a(flip),b,1553,a)].">
      <j1 rule="hyper" parents="63 1028 1553"/>
    </justification>
  </clause>

  <clause id="1570">
    <literal><![CDATA[
      (x \ (y * x)) * R((x \ (y * x)) \ x,z,u) = T(y * R(y \ x,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(253,a,1553,a(flip),b,1162,a),flip(a)].">
      <j1 rule="hyper" parents="253 1553 1162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1571">
    <literal><![CDATA[
      x * R(x \ (x \ (y * x)),z,u) = T(x * R(x \ y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(253,a,1553,a(flip),b,1028,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="253 1553 1028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1572">
    <literal><![CDATA[
      (x \ (y * z)) * R((x \ (y * z)) \ z,u,w) = x \ ((y * R(y \ x,u,w)) * z)
    ]]></literal>
    <justification jstring="[hyper(121,a,1553,a(flip),b,1162,a),flip(a)].">
      <j1 rule="hyper" parents="121 1553 1162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1573">
    <literal><![CDATA[
      (x * R(x \ (x * y),z,u)) * y = (x * y) * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),1553(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 1553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1575">
    <literal><![CDATA[
      (x * R(y,z,u)) * y = (x * y) * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),1573(a,1,1,2,1))].">
      <j1 rule="para" parents="9 1573"/>
    </justification>
  </clause>

  <clause id="1576">
    <literal><![CDATA[
      (x * y) / R(y,z,u) = (x / R(y,z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(621,a,1575,a)].">
      <j1 rule="hyper" parents="621 1575"/>
    </justification>
  </clause>

  <clause id="1577">
    <literal><![CDATA[
      ((x / y) / R(y,z,u)) * y = x / R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(620,a,1575,a),flip(a)].">
      <j1 rule="hyper" parents="620 1575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1578">
    <literal><![CDATA[
      (1 / R(x,y,z)) * x = x / R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(411,a,1575,a),flip(a)].">
      <j1 rule="hyper" parents="411 1575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1579">
    <literal><![CDATA[
      ((1 / x) * R(x,y,z)) * x = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,77,a(flip),b,1575,a),flip(a)].">
      <j1 rule="hyper" parents="333 77 1575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1580">
    <literal><![CDATA[
      (x * R(y,z,u)) \ ((x * y) * R(y,z,u)) = y
    ]]></literal>
    <justification jstring="[hyper(129,a,1575,a)].">
      <j1 rule="hyper" parents="129 1575"/>
    </justification>
  </clause>

  <clause id="1581">
    <literal><![CDATA[
      (1 / x) * R(x,y,z) = R(x,y,z) / x
    ]]></literal>
    <justification jstring="[hyper(123,a,77,a(flip),b,1575,a),flip(a)].">
      <j1 rule="hyper" parents="123 77 1575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1583">
    <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(1581(a,1),254(a,2)),flip(a)].">
      <j1 rule="para" parents="1581 254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1585">
    <literal><![CDATA[
      R(T(x,y * R(x,z,u)),y,R(x,z,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(1580(a,1),1044(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1580 1044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1586">
    <literal><![CDATA[
      (x * R(y / x,z,u)) \ (y * R(y / x,z,u)) = T(y / x,x)
    ]]></literal>
    <justification jstring="[hyper(952,a,1585,a)].">
      <j1 rule="hyper" parents="952 1585"/>
    </justification>
  </clause>

  <clause id="1587">
    <literal><![CDATA[
      (x * R(y,z,u)) * T(y,x) = (y * x) * R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(126,a,1585,a(flip),b,674,a)].">
      <j1 rule="hyper" parents="126 1585 674"/>
    </justification>
  </clause>

  <clause id="1591">
    <literal><![CDATA[
      T(x * R(x \ y,z,u),x) = x * R(x \ T(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(22(a,2),1571(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="22 1571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1592">
    <literal><![CDATA[
      x \ T(x * R(x \ y,z,u),x) = R(x \ T(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(827,a,1591,a)].">
      <j1 rule="hyper" parents="827 1591"/>
    </justification>
  </clause>

  <clause id="1593">
    <literal><![CDATA[
      (x * R(y / x,z,u)) \ (y * R(y / x,z,u)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(333,a,113,a(flip),b,1586,a),flip(a)].">
      <j1 rule="hyper" parents="333 113 1586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1594">
    <literal><![CDATA[
      (x * L(x \ (y / z),u,w)) * z = x * (z * L(z \ (x \ y),u,w))
    ]]></literal>
    <justification jstring="[para(668(a,1),1554(a,1,1))].">
      <j1 rule="para" parents="668 1554"/>
    </justification>
  </clause>

  <clause id="1595">
    <literal><![CDATA[
      R((x * (y * z)) / (x * z),u,w) * (x * z) = x * (R(y,u,w) * z)
    ]]></literal>
    <justification jstring="[para(11(a,1),1555(a,2,2,1,1))].">
      <j1 rule="para" parents="11 1555"/>
    </justification>
  </clause>

  <clause id="1596">
    <literal><![CDATA[
      ((x / y) * L((x / y) \ z,u,w)) * y = x * L(x \ (z * ((x / y) \ x)),u,w)
    ]]></literal>
    <justification jstring="[hyper(596,a,1558,a)].">
      <j1 rule="hyper" parents="596 1558"/>
    </justification>
  </clause>

  <clause id="1597">
    <literal><![CDATA[
      (x * L(x \ 1,y,z)) * (x \ u) = u * L(u \ (x \ u),y,z)
    ]]></literal>
    <justification jstring="[para(7(a,1),1558(a,2,2,1,2))].">
      <j1 rule="para" parents="7 1558"/>
    </justification>
  </clause>

  <clause id="1598">
    <literal><![CDATA[
      R(L((x \ y) / (x \ 1),x,x),x,x) = (x * x) \ ((x * y) * x)
    ]]></literal>
    <justification jstring="[para(284(a,1),1568(a,1,1,1,2))].">
      <j1 rule="para" parents="284 1568"/>
    </justification>
  </clause>

  <clause id="1599">
    <literal><![CDATA[
      L(R((x \ y) / (x \ 1),x,x),x,x) = (x * x) \ ((x * y) * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,29,a(flip),b,1598,a)].">
      <j1 rule="hyper" parents="63 29 1598"/>
    </justification>
  </clause>

  <clause id="1600">
    <literal><![CDATA[
      R(x,y,z) * (z * R(z \ (y * z),u,w)) = (R(x,y,z) * R(R(x,y,z) \ (x * y),u,w)) * z
    ]]></literal>
    <justification jstring="[para(187(a,1),1569(a,1,2,2,1,2))].">
      <j1 rule="para" parents="187 1569"/>
    </justification>
  </clause>

  <clause id="1601">
    <literal><![CDATA[
      x * (y * L(y \ (x \ (z * y)),u,w)) = (x * L(x \ z,u,w)) * y
    ]]></literal>
    <justification jstring="[para(11(a,1),1594(a,1,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="11 1594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1602">
    <literal><![CDATA[
      x * (y * L(y \ (x \ y),z,u)) = (x * L(x \ 1,z,u)) * y
    ]]></literal>
    <justification jstring="[para(73(a,1),1594(a,1,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="73 1594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1603">
    <literal><![CDATA[
      (x * y) * L((x * y) \ y,z,u) = (x * L(x \ 1,z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,1024,a,b,1602,a)].">
      <j1 rule="hyper" parents="63 1024 1602"/>
    </justification>
  </clause>

  <clause id="1604">
    <literal><![CDATA[
      x * ((x * y) * L((x * y) \ y,z,u)) = (x * L(x \ 1,z,u)) * (x * y)
    ]]></literal>
    <justification jstring="[para(9(a,1),1602(a,1,2,2,1,2))].">
      <j1 rule="para" parents="9 1602"/>
    </justification>
  </clause>

  <clause id="1605">
    <literal><![CDATA[
      (x * L(x \ 1,y,z)) * x = x * (x * L(x \ 1,y,z))
    ]]></literal>
    <justification jstring="[para(66(a,1),1602(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="66 1602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1606">
    <literal><![CDATA[
      T(x,x * L(x \ 1,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(254,a,1605,a)].">
      <j1 rule="hyper" parents="254 1605"/>
    </justification>
  </clause>

  <clause id="1607">
    <literal><![CDATA[
      K(x,x * L(x \ 1,y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(120,a,1605,a,b,88,a),flip(a)].">
      <j1 rule="hyper" parents="120 1605 88"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1608">
    <literal><![CDATA[
      T(x \ y,(x \ y) * (y \ x)) = x \ y
    ]]></literal>
    <justification jstring="[para(388(a,1),1606(a,1,2,2))].">
      <j1 rule="para" parents="388 1606"/>
    </justification>
  </clause>

  <clause id="1609">
    <literal><![CDATA[
      T(x \ 1,L(x,y,z) * (x \ 1)) = x \ 1
    ]]></literal>
    <justification jstring="[para(670(a,1),1606(a,1,2))].">
      <j1 rule="para" parents="670 1606"/>
    </justification>
  </clause>

  <clause id="1610">
    <literal><![CDATA[
      L(x \ y,y \ x,x \ y) * (y \ x) = (y \ x) * (x \ y)
    ]]></literal>
    <justification jstring="[para(1608(a,1),640(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1608 640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1611">
    <literal><![CDATA[
      R(x \ 1,L(x,y,z),x \ 1) = T(x \ 1,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(1609(a,1),845(a,1,1))].">
      <j1 rule="para" parents="1609 845"/>
    </justification>
  </clause>

  <clause id="1612">
    <literal><![CDATA[
      L(x \ y,y \ x,x \ y) = L(1 / (y \ x),y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(35,a,889,a,b,1610,a),flip(a)].">
      <j1 rule="hyper" parents="35 889 1610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1613">
    <literal><![CDATA[
      x \ (y * L(y \ x,x \ y,y \ x)) = (x \ y) * (1 / (x \ y))
    ]]></literal>
    <justification jstring="[para(1612(a,2),495(a,1,2,2))].">
      <j1 rule="para" parents="1612 495"/>
    </justification>
  </clause>

  <clause id="1614">
    <literal><![CDATA[
      T(x * L(x \ 1,T(x,y),y),y) = T(x,y) * ((x * y) \ y)
    ]]></literal>
    <justification jstring="[hyper(253,a,1603,a(flip),b,489,a(flip))].">
      <j1 rule="hyper" parents="253 1603 489"/>
    </justification>
  </clause>

  <clause id="1615">
    <literal><![CDATA[
      L((x \ y) \ 1,x \ y,y \ x) = 1 / (x \ y)
    ]]></literal>
    <justification jstring="[hyper(34,a,1541,a,b,1613,a(flip))].">
      <j1 rule="hyper" parents="34 1541 1613"/>
    </justification>
  </clause>

  <clause id="1616">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) \ (x \ y) = 1 / (y \ x)
    ]]></literal>
    <justification jstring="[hyper(523,a,1615,a)].">
      <j1 rule="hyper" parents="523 1615"/>
    </justification>
  </clause>

  <clause id="1617">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) * (1 / (y \ x)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(126,a,1615,a(flip),b,227,a(flip))].">
      <j1 rule="hyper" parents="126 1615 227"/>
    </justification>
  </clause>

  <clause id="1618">
    <literal><![CDATA[
      L(((x * y) \ x) \ 1,(x * y) \ x,y) = 1 / ((x * y) \ x)
    ]]></literal>
    <justification jstring="[para(9(a,1),1615(a,1,3))].">
      <j1 rule="para" parents="9 1615"/>
    </justification>
  </clause>

  <clause id="1620">
    <literal><![CDATA[
      (((x * y) \ x) * y) \ ((x * y) \ x) = 1 / (x \ (x * y))
    ]]></literal>
    <justification jstring="[para(9(a,1),1616(a,1,1,2))].">
      <j1 rule="para" parents="9 1616"/>
    </justification>
  </clause>

  <clause id="1621">
    <literal><![CDATA[
      (T(x,y) * ((x * y) \ y)) \ (y \ (x * y)) = 1 / ((x * y) \ y)
    ]]></literal>
    <justification jstring="[para(22(a,2),1616(a,1,1,1))].">
      <j1 rule="para" parents="22 1616"/>
    </justification>
  </clause>

  <clause id="1622">
    <literal><![CDATA[
      (((x * y) \ x) * y) \ ((x * y) \ x) = 1 / y
    ]]></literal>
    <justification jstring="[para(9(a,1),1620(a,2,2))].">
      <j1 rule="para" parents="9 1620"/>
    </justification>
  </clause>

  <clause id="1623">
    <literal><![CDATA[
      (((x * y) \ x) * y) * (1 / y) = (x * y) \ x
    ]]></literal>
    <justification jstring="[hyper(142,a,1622,a)].">
      <j1 rule="hyper" parents="142 1622"/>
    </justification>
  </clause>

  <clause id="1624">
    <literal><![CDATA[
      (x * y) \ x = (L(y \ 1,y,x) * y) * (1 / y)
    ]]></literal>
    <justification jstring="[para(227(a,2),1623(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="227 1623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1625">
    <literal><![CDATA[
      L(x \ 1,x,y) / (1 / x) = L(x \ 1,x,y) * x
    ]]></literal>
    <justification jstring="[hyper(652,a,1624,a)].">
      <j1 rule="hyper" parents="652 1624"/>
    </justification>
  </clause>

  <clause id="1626">
    <literal><![CDATA[
      (x * ((y * x) \ y)) \ x = 1 / ((y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(523,a,1618,a)].">
      <j1 rule="hyper" parents="523 1618"/>
    </justification>
  </clause>

  <clause id="1627">
    <literal><![CDATA[
      (((x * (y * z)) / (x * z)) * x) * z = x * (R(y,x,z) * z)
    ]]></literal>
    <justification jstring="[hyper(299,a,1595,a)].">
      <j1 rule="hyper" parents="299 1595"/>
    </justification>
  </clause>

  <clause id="1628">
    <literal><![CDATA[
      R(T(x,y),z,u) * (x * w) = x * (R(T(x,y),z,u) * w)
    ]]></literal>
    <justification jstring="[para(1059(a,1),1595(a,1,1,1))].">
      <j1 rule="para" parents="1059 1595"/>
    </justification>
  </clause>

  <clause id="1629">
    <literal><![CDATA[
      R(T(x,y),z,u) \ (x * w) = x * (R(T(x,y),z,u) \ w)
    ]]></literal>
    <justification jstring="[hyper(121,a,154,a(flip),b,1628,a)].">
      <j1 rule="hyper" parents="121 154 1628"/>
    </justification>
  </clause>

  <clause id="1630">
    <literal><![CDATA[
      x * L(x \ (x \ (y * x)),z,u) = T(x * L(x \ y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(254,a,1601,a),flip(a)].">
      <j1 rule="hyper" parents="254 1601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1631">
    <literal><![CDATA[
      (x * y) * L((x * y) \ (z * y),u,w) = (x * L(x \ z,u,w)) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,1024,a,b,1601,a)].">
      <j1 rule="hyper" parents="63 1024 1601"/>
    </justification>
  </clause>

  <clause id="1632">
    <literal><![CDATA[
      ((x * y) * L((x * y) \ x,z,u)) * y = (x * y) * (y * L(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[para(66(a,1),1601(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="66 1601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1633">
    <literal><![CDATA[
      T(x * L(x \ y,z,u),x) = x * L(x \ T(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(22(a,2),1630(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="22 1630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1634">
    <literal><![CDATA[
      x \ T(x * L(x \ y,z,u),x) = L(x \ T(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(827,a,1633,a)].">
      <j1 rule="hyper" parents="827 1633"/>
    </justification>
  </clause>

  <clause id="1635">
    <literal><![CDATA[
      L(x \ T(x * y,x),z,u) = x \ T(x * L(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(9(a,1),1634(a,1,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 1634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1636">
    <literal><![CDATA[
      x \ T(x * L(y / x,z,u),x) = L(T(y,x) / x,z,u)
    ]]></literal>
    <justification jstring="[para(1403(a,1),1635(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1403 1635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1637">
    <literal><![CDATA[
      L(T(x * y,x) / x,z,u) = T(x * L(y,z,u),x) / x
    ]]></literal>
    <justification jstring="[hyper(63,a,1406,a(flip),b,1636,a),flip(a)].">
      <j1 rule="hyper" parents="63 1406 1636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1638">
    <literal><![CDATA[
      a(x,y,z) = L(L(z,y,x) \ z,L(z,y,x),x * y)
    ]]></literal>
    <justification jstring="[hyper(333,a,14,a,b,524,a)].">
      <j1 rule="hyper" parents="333 14 524"/>
    </justification>
  </clause>

  <clause id="1639">
    <literal><![CDATA[
      L(L(L(x,y,z) \ u,w,v5),L(x,y,z),z * y) = L((z * (y * x)) \ ((z * y) * u),w,v5)
    ]]></literal>
    <justification jstring="[para(524(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="524 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1640">
    <literal><![CDATA[
      L(L(x,y,z) \ x,L(x,y,z),z * y) != u
    ]]></literal>
    <literal><![CDATA[
      a(z,y,x) = u
    ]]></literal>
    <justification jstring="[para(524(a,2),752(a,1))].">
      <j1 rule="para" parents="524 752"/>
    </justification>
  </clause>

  <clause id="1641">
    <literal><![CDATA[
      a(x,y,z) = L(L(z,y,x) \ z,(x * y) \ (x * (y * z)),x * y)
    ]]></literal>
    <justification jstring="[para(18(a,1),1638(a,2,2))].">
      <j1 rule="para" parents="18 1638"/>
    </justification>
  </clause>

  <clause id="1642">
    <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(1641(a,2),838(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1641 838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1643">
    <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="[hyper(125,a,922,a(flip),b,542,a)].">
      <j1 rule="hyper" parents="125 922 542"/>
    </justification>
  </clause>

  <clause id="1644">
    <literal><![CDATA[
      T(x,R(y,R(z,u,u),u * u) * ((z * u) * u)) = T(T(x,u * u),y * R(z,u,u))
    ]]></literal>
    <justification jstring="[para(546(a,2),1124(a,2,2)),flip(a)].">
      <j1 rule="para" parents="546 1124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1645">
    <literal><![CDATA[
      L(x,y,T(z,z \ u)) = L(x,y,(z \ u) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,699,a(flip),b,700,a)].">
      <j1 rule="hyper" parents="63 699 700"/>
    </justification>
  </clause>

  <clause id="1646">
    <literal><![CDATA[
      a(x,y,(y * y) \ z) = (x * ((y \ 1) * z)) \ ((x * (y \ 1)) * z)
    ]]></literal>
    <justification jstring="[para(976(a,1),720(a,1,2)),flip(a)].">
      <j1 rule="para" parents="976 720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1647">
    <literal><![CDATA[
      a(x,y,(y * y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y \ 1,z) = u
    ]]></literal>
    <justification jstring="[para(1646(a,2),752(a,1))].">
      <j1 rule="para" parents="1646 752"/>
    </justification>
  </clause>

  <clause id="1648">
    <literal><![CDATA[
      (1 / x) * T((1 / x) \ y,z) = T(y * x,z) / x
    ]]></literal>
    <justification jstring="[para(663(a,1),738(a,1,1)),flip(a)].">
      <j1 rule="para" parents="663 738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1649">
    <literal><![CDATA[
      (1 / x) \ (T(y * x,z) / x) = T((1 / x) \ y,z)
    ]]></literal>
    <justification jstring="[hyper(129,a,1648,a)].">
      <j1 rule="hyper" parents="129 1648"/>
    </justification>
  </clause>

  <clause id="1650">
    <literal><![CDATA[
      (1 / x) * T((1 / x) \ 1,y) = T(x,y) / x
    ]]></literal>
    <justification jstring="[para(7(a,1),1648(a,2,1,1))].">
      <j1 rule="para" parents="7 1648"/>
    </justification>
  </clause>

  <clause id="1651">
    <literal><![CDATA[
      T(((1 / x) * y) * x,z) / x = (1 / x) * T(y,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),1648(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 1648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1653">
    <literal><![CDATA[
      ((x \ (y / (1 / z))) * x) * (1 / z) = x * (T((x \ y) * z,x) / z)
    ]]></literal>
    <justification jstring="[para(1648(a,1),1234(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1648 1234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1654">
    <literal><![CDATA[
      T(1 / (1 / x),y) * (1 / x) = T(x,y) / x
    ]]></literal>
    <justification jstring="[hyper(63,a,471,a,b,1650,a)].">
      <j1 rule="hyper" parents="63 471 1650"/>
    </justification>
  </clause>

  <clause id="1655">
    <literal><![CDATA[
      T(1 / x,T(x,y) / x) = 1 / x
    ]]></literal>
    <justification jstring="[para(1650(a,1),1365(a,1,2))].">
      <j1 rule="para" parents="1650 1365"/>
    </justification>
  </clause>

  <clause id="1656">
    <literal><![CDATA[
      T((x * (1 / y)) / x,T(y,z) / y) = (x * (1 / y)) / x
    ]]></literal>
    <justification jstring="[para(1655(a,1),476(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1655 476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1657">
    <literal><![CDATA[
      T(x,y) / x != z
    ]]></literal>
    <literal><![CDATA[
      (1 / x) * T((1 / x) \ 1,y) = z
    ]]></literal>
    <justification jstring="[para(1654(a,1),739(a,1))].">
      <j1 rule="para" parents="1654 739"/>
    </justification>
  </clause>

  <clause id="1658">
    <literal><![CDATA[
      T((1 / x) \ (y / x),z) = (1 / x) \ (T(y,z) / x)
    ]]></literal>
    <justification jstring="[para(12(a,1),1649(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="12 1649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1659">
    <literal><![CDATA[
      (1 / x) * T((1 / x) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y * x,z) / x = u
    ]]></literal>
    <justification jstring="[para(1649(a,1),273(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1649 273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1660">
    <literal><![CDATA[
      T(x * ((1 / x) * y),x) = x * ((1 / x) * T(y,x))
    ]]></literal>
    <justification jstring="[hyper(126,a,1651,a(flip),b,1401,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="126 1651 1401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1661">
    <literal><![CDATA[
      ((1 / x) * T(y,z)) * x != u
    ]]></literal>
    <literal><![CDATA[
      T(((1 / x) * y) * x,z) = u
    ]]></literal>
    <justification jstring="[para(1651(a,1),264(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1651 264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1662">
    <literal><![CDATA[
      ((1 / x) \ (y / x)) * (1 / x) = T(y,1 / x) / x
    ]]></literal>
    <justification jstring="[hyper(143,a,1658,a)].">
      <j1 rule="hyper" parents="143 1658"/>
    </justification>
  </clause>

  <clause id="1663">
    <literal><![CDATA[
      (1 / T(x,y)) \ (T(x,z) / T(x,y)) = T(x,z)
    ]]></literal>
    <justification jstring="[para(1425(a,1),1658(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1425 1658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1664">
    <literal><![CDATA[
      (T(x,y) / T(x,z)) / T(x,y) = 1 / T(x,z)
    ]]></literal>
    <justification jstring="[hyper(198,a,1663,a)].">
      <j1 rule="hyper" parents="198 1663"/>
    </justification>
  </clause>

  <clause id="1666">
    <literal><![CDATA[
      T(x,1 / T(x,y)) / T(x,y) = x * (1 / T(x,y))
    ]]></literal>
    <justification jstring="[hyper(38,a,22,a(flip),b,1663,a),flip(a)].">
      <j1 rule="hyper" parents="38 22 1663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1667">
    <literal><![CDATA[
      T((T(x,y) / T(x,z)) * T(x,z),u) / T(x,z) = (1 / T(x,z)) * T(T(x,y),u)
    ]]></literal>
    <justification jstring="[para(1663(a,1),1648(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1663 1648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1668">
    <literal><![CDATA[
      T(x,y) \ (T(x,y) / T(x,z)) = T(1 / T(x,z),T(x,y))
    ]]></literal>
    <justification jstring="[para(1664(a,1),113(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1664 113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1669">
    <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(1664(a,1),1560(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1664 1560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1670">
    <literal><![CDATA[
      T(x * ((1 / x) * ((1 / x) \ (x \ (y * (1 / x))))),x) = (x * T(x \ y,x)) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(333,a,1358,a(flip),b,1660,a),flip(a)].">
      <j1 rule="hyper" parents="333 1358 1660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1671">
    <literal><![CDATA[
      K(1 / x,(1 / x) \ (y / x)) = (T(y,1 / x) / x) \ (y / x)
    ]]></literal>
    <justification jstring="[para(1662(a,1),90(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1662 90"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1672">
    <literal><![CDATA[
      T(x,T(x,y) \ 1) / T(x,y) = x * (1 / T(x,y))
    ]]></literal>
    <justification jstring="[para(1214(a,1),1666(a,1,1))].">
      <j1 rule="para" parents="1214 1666"/>
    </justification>
  </clause>

  <clause id="1673">
    <literal><![CDATA[
      ((x * (1 / T(x,y))) / x) * T(x,y) = T(x,T(x,y) \ 1) / x
    ]]></literal>
    <justification jstring="[para(1672(a,1),1420(a,1,1,1))].">
      <j1 rule="para" parents="1672 1420"/>
    </justification>
  </clause>

  <clause id="1674">
    <literal><![CDATA[
      T(x,y) * ((x * (T(x,y) \ 1)) / x) = T(x,T(x,y) \ 1) / x
    ]]></literal>
    <justification jstring="[hyper(999,a,1673,a)].">
      <j1 rule="hyper" parents="999 1673"/>
    </justification>
  </clause>

  <clause id="1675">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ x) / x) = T(x,T(x,y) \ 1) / x
    ]]></literal>
    <justification jstring="[para(1063(a,1),1674(a,1,2,1))].">
      <j1 rule="para" parents="1063 1674"/>
    </justification>
  </clause>

  <clause id="1676">
    <literal><![CDATA[
      (x \ (y / (1 / x))) * x = T(y,x) / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(123,a,1400,a(flip),b,1653,a),flip(a)].">
      <j1 rule="hyper" parents="123 1400 1653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1677">
    <literal><![CDATA[
      ((x * (y * (z \ 1))) / x) / (z \ 1) = z * ((x * (z \ y)) / x)
    ]]></literal>
    <justification jstring="[para(924(a,1),1001(a,1,1))].">
      <j1 rule="para" parents="924 1001"/>
    </justification>
  </clause>

  <clause id="1678">
    <literal><![CDATA[
      (x \ 1) * ((y * ((x \ 1) \ K(x \ 1,x))) / y) = ((y * x) / y) / ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(972(a,1),1677(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="972 1677"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1679">
    <literal><![CDATA[
      T(T(R(x,y,y \ 1),x * y) / (y \ 1),R(x,y,y \ 1)) = x * y
    ]]></literal>
    <justification jstring="[para(385(a,1),1103(a,1,2))].">
      <j1 rule="para" parents="385 1103"/>
    </justification>
  </clause>

  <clause id="1680">
    <literal><![CDATA[
      T(T(x,x * y) * y,R(x,y,y \ 1)) = x * y
    ]]></literal>
    <justification jstring="[para(611(a,1),1679(a,1,1))].">
      <j1 rule="para" parents="611 1679"/>
    </justification>
  </clause>

  <clause id="1681">
    <literal><![CDATA[
      T(T(T(x,x * y) * y,z),R(x,y,y \ 1)) = T(x * y,z)
    ]]></literal>
    <justification jstring="[para(1680(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1680 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1682">
    <literal><![CDATA[
      T(x * y,R(x,y,y \ 1)) = T(x * y,T(x,y))
    ]]></literal>
    <justification jstring="[para(1006(a,1),1681(a,1,1))].">
      <j1 rule="para" parents="1006 1681"/>
    </justification>
  </clause>

  <clause id="1683">
    <literal><![CDATA[
      T((x / y) * y,T(x / y,y)) = T(x,R(x / y,y,y \ 1))
    ]]></literal>
    <justification jstring="[para(12(a,1),1682(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12 1682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1684">
    <literal><![CDATA[
      T((x / y) * y,T(x / y,y)) = T(x,x * (y \ 1))
    ]]></literal>
    <justification jstring="[para(554(a,1),1683(a,2,2))].">
      <j1 rule="para" parents="554 1683"/>
    </justification>
  </clause>

  <clause id="1685">
    <literal><![CDATA[
      T(x,T(x / y,y)) = T(x,x * (y \ 1))
    ]]></literal>
    <justification jstring="[para(12(a,1),1684(a,1,1))].">
      <j1 rule="para" parents="12 1684"/>
    </justification>
  </clause>

  <clause id="1686">
    <literal><![CDATA[
      T(x,x * (y \ 1)) = T(x,y \ x)
    ]]></literal>
    <justification jstring="[para(113(a,1),1685(a,1,2)),flip(a)].">
      <j1 rule="para" parents="113 1685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1688">
    <literal><![CDATA[
      L(T(x,x * (L(x,y,z) \ u)),y,z) = (L(x,y,z) \ (x * u)) \ (x * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,25,a,b,1272,a)].">
      <j1 rule="hyper" parents="63 25 1272"/>
    </justification>
  </clause>

  <clause id="1689">
    <literal><![CDATA[
      (T(x,y) * ((T(x,y) \ x) / x)) * x = T(x,(1 * x) / (x * T(x,y)))
    ]]></literal>
    <justification jstring="[para(558(a,1),1534(a,2,2))].">
      <j1 rule="para" parents="558 1534"/>
    </justification>
  </clause>

  <clause id="1690">
    <literal><![CDATA[
      (T(x,y) * ((T(x,y) \ x) / x)) * x = T(x,x / (x * T(x,y)))
    ]]></literal>
    <justification jstring="[para(7(a,1),1689(a,2,2,1))].">
      <j1 rule="para" parents="7 1689"/>
    </justification>
  </clause>

  <clause id="1691">
    <literal><![CDATA[
      (T(x,T(x,y) \ 1) / x) * x = T(x,x / (x * T(x,y)))
    ]]></literal>
    <justification jstring="[para(1675(a,1),1690(a,1,1))].">
      <j1 rule="para" parents="1675 1690"/>
    </justification>
  </clause>

  <clause id="1692">
    <literal><![CDATA[
      T(x,x / (x * T(x,y))) = T(x,T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(265,a,1691,a),flip(a)].">
      <j1 rule="hyper" parents="265 1691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1694">
    <literal><![CDATA[
      L(T(x,x * (L(x,y,z) \ u)),y,z) = (x * (L(x,y,z) \ u)) \ (x * u)
    ]]></literal>
    <justification jstring="[para(1258(a,1),1688(a,2,1))].">
      <j1 rule="para" parents="1258 1688"/>
    </justification>
  </clause>

  <clause id="1695">
    <literal><![CDATA[
      (1 / x) \ L((y * x) \ y,z,u) = L((y * x) \ y,z,u) * x
    ]]></literal>
    <justification jstring="[hyper(935,a,1152,a),flip(a)].">
      <j1 rule="hyper" parents="935 1152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1696">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ (x * u))) / z) = x * (y * ((z * (y \ u)) / z))
    ]]></literal>
    <justification jstring="[para(9(a,1),1171(a,2,2,2,1,2,2))].">
      <j1 rule="para" parents="9 1171"/>
    </justification>
  </clause>

  <clause id="1697">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ x)) / z) = x * (y * ((z * (y \ 1)) / z))
    ]]></literal>
    <justification jstring="[para(66(a,1),1171(a,2,2,2,1,2,2))].">
      <j1 rule="para" parents="66 1171"/>
    </justification>
  </clause>

  <clause id="1698">
    <literal><![CDATA[
      x \ T(x,x / (x * y)) = y * ((x * (y \ 1)) / x)
    ]]></literal>
    <justification jstring="[hyper(1096,a,1697,a)].">
      <j1 rule="hyper" parents="1096 1697"/>
    </justification>
  </clause>

  <clause id="1699">
    <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(97(a,1),1697(a,1,1))].">
      <j1 rule="para" parents="97 1697"/>
    </justification>
  </clause>

  <clause id="1700">
    <literal><![CDATA[
      x * (T(x,T(x,y) \ 1) / x) = T(x,x / (x * T(x,y)))
    ]]></literal>
    <justification jstring="[hyper(126,a,1674,a(flip),b,1698,a)].">
      <j1 rule="hyper" parents="126 1674 1698"/>
    </justification>
  </clause>

  <clause id="1701">
    <literal><![CDATA[
      x \ y != z * ((x * (z \ 1)) / x)
    ]]></literal>
    <literal><![CDATA[
      T(x,x / (x * z)) = y
    ]]></literal>
    <justification jstring="[para(1698(a,1),47(a,1)),flip(a)].">
      <j1 rule="para" parents="1698 47"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1702">
    <literal><![CDATA[
      x * (T(x,T(x,y) \ 1) / x) = T(x,T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(333,a,1692,a(flip),b,1700,a),flip(a)].">
      <j1 rule="hyper" parents="333 1692 1700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1703">
    <literal><![CDATA[
      x * (T(x,y) * ((T(x,y) \ x) / x)) = T(x,T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[para(1675(a,2),1702(a,1,2))].">
      <j1 rule="para" parents="1675 1702"/>
    </justification>
  </clause>

  <clause id="1704">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ y,z) = T(x * T(x \ y,z),y)
    ]]></literal>
    <justification jstring="[hyper(253,a,1392,a(flip),b,1177,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="253 1392 1177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1705">
    <literal><![CDATA[
      x * (T(y,x) * T(T(y,x) \ y,z)) = (y * x) * T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(16(a,2),1177(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="16 1177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1706">
    <literal><![CDATA[
      x * L(y,T(y,x) \ y,T(y,x)) = (y * x) * T(K(x,y),y)
    ]]></literal>
    <justification jstring="[para(1077(a,1),1705(a,1,2))].">
      <j1 rule="para" parents="1077 1705"/>
    </justification>
  </clause>

  <clause id="1709">
    <literal><![CDATA[
      (x \ T(x * (y / z),z)) * z = (x \ 1) * ((z \ ((x \ 1) \ y)) * z)
    ]]></literal>
    <justification jstring="[hyper(595,a,1362,a),flip(a)].">
      <j1 rule="hyper" parents="595 1362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1710">
    <literal><![CDATA[
      (x \ T(x * (y / y),z)) * y = (x \ 1) * ((x \ T(x,z)) * ((x \ 1) \ y))
    ]]></literal>
    <justification jstring="[para(1155(a,2),1362(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1155 1362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1711">
    <literal><![CDATA[
      T((x \ (x * (y / x))) * x,x) = (x \ 1) * ((x \ ((x \ 1) \ y)) * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1397,a,b,1709,a)].">
      <j1 rule="hyper" parents="63 1397 1709"/>
    </justification>
  </clause>

  <clause id="1712">
    <literal><![CDATA[
      T(x,y) = (y \ 1) * ((y \ ((y \ 1) \ x)) * y)
    ]]></literal>
    <justification jstring="[para(80(a,1),1711(a,1,1))].">
      <j1 rule="para" parents="80 1711"/>
    </justification>
  </clause>

  <clause id="1713">
    <literal><![CDATA[
      (x \ ((x \ 1) \ y)) * x = (x \ 1) \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(827,a,1712,a),flip(a)].">
      <j1 rule="hyper" parents="827 1712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1714">
    <literal><![CDATA[
      (x \ 1) * ((x \ y) * x) = T((x \ 1) * y,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),1712(a,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="9 1712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1715">
    <literal><![CDATA[
      T((x \ 1) * (x * y),x) = (x \ 1) * (y * x)
    ]]></literal>
    <justification jstring="[para(9(a,1),1714(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 1714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1716">
    <literal><![CDATA[
      T(((x / y) \ 1) * x,x / y) = ((x / y) \ 1) * (y * (x / y))
    ]]></literal>
    <justification jstring="[para(79(a,1),1714(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="79 1714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1717">
    <literal><![CDATA[
      (x \ 1) \ T((x \ 1) * y,x) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ y) * x = z
    ]]></literal>
    <justification jstring="[para(1714(a,1),342(a,1,2))].">
      <j1 rule="para" parents="1714 342"/>
    </justification>
  </clause>

  <clause id="1718">
    <literal><![CDATA[
      T((x \ 1) * ((y \ x) * y),x) = (x \ 1) * (K(y \ x,y) * x)
    ]]></literal>
    <justification jstring="[para(89(a,1),1714(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="89 1714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1719">
    <literal><![CDATA[
      ((x \ 1) * y) \ T((x \ 1) * y,x) = L(K(x \ y,x),y,x \ 1)
    ]]></literal>
    <justification jstring="[para(1714(a,1),480(a,1,2))].">
      <j1 rule="para" parents="1714 480"/>
    </justification>
  </clause>

  <clause id="1720">
    <literal><![CDATA[
      ((x \ 1) * (x * y)) * x = x * ((x \ 1) * (y * x))
    ]]></literal>
    <justification jstring="[hyper(126,a,1715,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="126 1715 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1721">
    <literal><![CDATA[
      ((x \ 1) * (x * y)) * x = L(y * x,x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,275,a(flip),b,1720,a),flip(a)].">
      <j1 rule="hyper" parents="333 275 1720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1722">
    <literal><![CDATA[
      T(x * ((x * R(x \ 1,y,z)) / x),x) = x * R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(685(a,1),1407(a,2,2))].">
      <j1 rule="para" parents="685 1407"/>
    </justification>
  </clause>

  <clause id="1723">
    <literal><![CDATA[
      T(x * R(1 / x,y,z),x) = x * R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(685(a,1),1722(a,1,1,2))].">
      <j1 rule="para" parents="685 1722"/>
    </justification>
  </clause>

  <clause id="1724">
    <literal><![CDATA[
      T(x * (y / (x * y)),x) = x * R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[para(230(a,1),1723(a,1,1,2))].">
      <j1 rule="para" parents="230 1723"/>
    </justification>
  </clause>

  <clause id="1725">
    <literal><![CDATA[
      T(x * (y / (x * y)),x) = x * (y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(333,a,397,a(flip),b,1724,a),flip(a)].">
      <j1 rule="hyper" parents="333 397 1724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1726">
    <literal><![CDATA[
      T(x,x * (y / (x * y))) = x
    ]]></literal>
    <justification jstring="[hyper(54,a,1725,a)].">
      <j1 rule="hyper" parents="54 1725"/>
    </justification>
  </clause>

  <clause id="1727">
    <literal><![CDATA[
      T(x / y,(x / y) * (y / x)) = x / y
    ]]></literal>
    <justification jstring="[para(12(a,1),1726(a,1,2,2,2))].">
      <j1 rule="para" parents="12 1726"/>
    </justification>
  </clause>

  <clause id="1728">
    <literal><![CDATA[
      T(x \ y,(y / x) * (x / y)) = T(y / x,x)
    ]]></literal>
    <justification jstring="[para(1727(a,1),259(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1727 259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1729">
    <literal><![CDATA[
      T(x \ y,(y / x) * (x / y)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(333,a,113,a(flip),b,1728,a),flip(a)].">
      <j1 rule="hyper" parents="333 113 1728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1730">
    <literal><![CDATA[
      ((x / y) * T((x / y) \ z,u)) * y = x * T(x \ (z * y),u)
    ]]></literal>
    <justification jstring="[para(12(a,1),1413(a,2,2,1,1))].">
      <j1 rule="para" parents="12 1413"/>
    </justification>
  </clause>

  <clause id="1731">
    <literal><![CDATA[
      (x * T(x \ (y * z),u)) / z = (x / z) * T((x / z) \ y,u)
    ]]></literal>
    <justification jstring="[hyper(138,a,1730,a)].">
      <j1 rule="hyper" parents="138 1730"/>
    </justification>
  </clause>

  <clause id="1732">
    <literal><![CDATA[
      (x * (y * T(y \ (x \ (z * u)),w))) / u = ((x * y) / u) * T(((x * y) / u) \ z,w)
    ]]></literal>
    <justification jstring="[hyper(123,a,940,a(flip),b,1730,a)].">
      <j1 rule="hyper" parents="123 940 1730"/>
    </justification>
  </clause>

  <clause id="1733">
    <literal><![CDATA[
      (x / y) * T((x / y) \ z,x) = ((x \ (z * y)) * x) / y
    ]]></literal>
    <justification jstring="[hyper(123,a,111,a(flip),b,1730,a),flip(a)].">
      <j1 rule="hyper" parents="123 111 1730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1734">
    <literal><![CDATA[
      ((x / y) * T((x / y) \ 1,z)) * y = x * T(x \ y,z)
    ]]></literal>
    <justification jstring="[para(7(a,1),1730(a,2,2,1,2))].">
      <j1 rule="para" parents="7 1730"/>
    </justification>
  </clause>

  <clause id="1735">
    <literal><![CDATA[
      (x / y) * T((x / y) \ 1,z) = (x * T(x \ y,z)) / y
    ]]></literal>
    <justification jstring="[hyper(138,a,1734,a),flip(a)].">
      <j1 rule="hyper" parents="138 1734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1738">
    <literal><![CDATA[
      (x \ y) * ((z * ((x \ y) \ 1)) / z) = x \ (y * ((z * (y \ x)) / z))
    ]]></literal>
    <justification jstring="[para(8(a,1),1474(a,1,2,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8 1474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1740">
    <literal><![CDATA[
      x * K(y,(y / (x \ z)) / y) = z * ((y * (z \ x)) / y)
    ]]></literal>
    <justification jstring="[hyper(126,a,1560,a,b,1738,a(flip))].">
      <j1 rule="hyper" parents="126 1560 1738"/>
    </justification>
  </clause>

  <clause id="1741">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ y)) / z) = y * K(z,(z / T(x,y)) / z)
    ]]></literal>
    <justification jstring="[para(22(a,2),1740(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="22 1740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1742">
    <literal><![CDATA[
      (x * R(x \ 1,y,z)) * (x * u) = x * ((x * R(x \ 1,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(1338(a,1),1504(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1338 1504"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1743">
    <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(1313(a,1),1742(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1313 1742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1744">
    <literal><![CDATA[
      ((x * ((y \ x) \ z)) / z) * (y \ z) = y \ (x * ((y \ x) \ z))
    ]]></literal>
    <justification jstring="[para(10(a,1),1527(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 1527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1746">
    <literal><![CDATA[
      R(x,y,z) * (T(x,u) \ 1) = T(x,u) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),1552(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 1552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1747">
    <literal><![CDATA[
      T(x,y) * R((y \ (x * y)) \ y,z,u) = T(x * R(x \ y,z,u),y)
    ]]></literal>
    <justification jstring="[para(22(a,2),1570(a,1,1))].">
      <j1 rule="para" parents="22 1570"/>
    </justification>
  </clause>

  <clause id="1748">
    <literal><![CDATA[
      T(x,y) * R(T(x,y) \ y,z,u) = T(x * R(x \ y,z,u),y)
    ]]></literal>
    <justification jstring="[para(22(a,2),1747(a,1,2,1,1))].">
      <j1 rule="para" parents="22 1747"/>
    </justification>
  </clause>

  <clause id="1749">
    <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(9(a,1),1748(a,2,1,2,1))].">
      <j1 rule="para" parents="9 1748"/>
    </justification>
  </clause>

  <clause id="1750">
    <literal><![CDATA[
      (x * L(x \ 1,y,z)) * (x * u) = x * ((x * L(x \ 1,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(1603(a,1),1604(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1603 1604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1751">
    <literal><![CDATA[
      (x \ 1) * (((x \ 1) * L((x \ 1) \ 1,y,z)) * u) = (x \ L(x,y,z)) * ((x \ 1) * u)
    ]]></literal>
    <justification jstring="[para(1264(a,1),1750(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1264 1750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1752">
    <literal><![CDATA[
      (x * (y * L(y \ 1,z,u))) * y = (x * y) * (y * L(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[para(929(a,1),1632(a,1,1))].">
      <j1 rule="para" parents="929 1632"/>
    </justification>
  </clause>

  <clause id="1753">
    <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(1078(a,1),1669(a,1,2,1))].">
      <j1 rule="para" parents="1078 1669"/>
    </justification>
  </clause>

  <clause id="1754">
    <literal><![CDATA[
      (x \ 1) * ((x \ T(x,y)) * ((x \ 1) \ z)) = (x \ T(x * 1,y)) * z
    ]]></literal>
    <justification jstring="[para(73(a,1),1710(a,1,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="73 1710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1755">
    <literal><![CDATA[
      (x \ 1) * ((x \ T(x,y)) * ((x \ 1) \ z)) = (x \ T(x,y)) * z
    ]]></literal>
    <justification jstring="[para(8(a,1),1754(a,2,1,2,1))].">
      <j1 rule="para" parents="8 1754"/>
    </justification>
  </clause>

  <clause id="1757">
    <literal><![CDATA[
      (x \ T(x,y)) * ((x \ 1) \ ((x \ T(x,y)) \ (x \ 1))) = 1
    ]]></literal>
    <justification jstring="[hyper(120,a,10,a(flip),b,1755,a),flip(a)].">
      <j1 rule="hyper" parents="120 10 1755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1758">
    <literal><![CDATA[
      L(x / (y \ 1),z,u) * (y \ 1) = y \ L(1 \ (y * x),z,u)
    ]]></literal>
    <justification jstring="[para(793(a,1),886(a,1,2)),flip(a)].">
      <j1 rule="para" parents="793 886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1759">
    <literal><![CDATA[
      L(x / (y \ 1),z,u) * (y \ 1) = y \ L(y * x,z,u)
    ]]></literal>
    <justification jstring="[para(65(a,1),1758(a,2,2,1))].">
      <j1 rule="para" parents="65 1758"/>
    </justification>
  </clause>

  <clause id="1760">
    <literal><![CDATA[
      (x \ 1) * L((x \ 1) \ y,z,u) = x \ L(x * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(895,a,1759,a)].">
      <j1 rule="hyper" parents="895 1759"/>
    </justification>
  </clause>

  <clause id="1761">
    <literal><![CDATA[
      x \ L(x * (y \ z),x \ 1,y) = (x \ 1) * ((y * (x \ 1)) \ z)
    ]]></literal>
    <justification jstring="[para(311(a,1),1760(a,1,2)),flip(a)].">
      <j1 rule="para" parents="311 1760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1762">
    <literal><![CDATA[
      L(R(x / (1 / y),1 / y,y),z,u) / y = (1 / y) * L((1 / y) \ x,z,u)
    ]]></literal>
    <justification jstring="[para(29(a,1),888(a,1,1))].">
      <j1 rule="para" parents="29 888"/>
    </justification>
  </clause>

  <clause id="1763">
    <literal><![CDATA[
      (x \ y) \ (((y \ x) \ 1) \ (x \ y)) = ((y \ x) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(388(a,1),1269(a,1,2,2))].">
      <j1 rule="para" parents="388 1269"/>
    </justification>
  </clause>

  <clause id="1764">
    <literal><![CDATA[
      (x \ y) * (((y \ x) \ 1) \ 1) = ((y \ x) \ 1) \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(142,a,1763,a)].">
      <j1 rule="hyper" parents="142 1763"/>
    </justification>
  </clause>

  <clause id="1765">
    <literal><![CDATA[
      ((x \ y) \ 1) * ((((x \ y) \ 1) \ (y \ x)) / (y \ x)) = (((y \ x) * (x \ y)) / (y \ x)) * ((x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(1764(a,1),1002(a,1,2,1))].">
      <j1 rule="para" parents="1764 1002"/>
    </justification>
  </clause>

  <clause id="1766">
    <literal><![CDATA[
      ((x \ y) \ 1) * ((((x \ y) \ 1) \ (y \ x)) / (y \ x)) = K(y \ x,((y \ x) / ((x \ y) \ 1)) / (y \ x))
    ]]></literal>
    <justification jstring="[para(1764(a,1),1560(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="1764 1560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1767">
    <literal><![CDATA[
      (T(x,y) * (1 / x)) / T(x,y) = L(1 / x,T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1656,a(flip),b,1428,a)].">
      <j1 rule="hyper" parents="63 1656 1428"/>
    </justification>
  </clause>

  <clause id="1769">
    <literal><![CDATA[
      T(L(1 / x,T(x,y),1 / x),x) = (T(x,y) * (x \ 1)) / T(x,y)
    ]]></literal>
    <justification jstring="[para(1767(a,1),741(a,1,1))].">
      <j1 rule="para" parents="1767 741"/>
    </justification>
  </clause>

  <clause id="1770">
    <literal><![CDATA[
      (T(x,y) * (x \ 1)) / T(x,y) = L(x \ 1,T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[hyper(896,a,1769,a),flip(a)].">
      <j1 rule="hyper" parents="896 1769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1771">
    <literal><![CDATA[
      x * L(x \ 1,T(x,y),1 / x) = K(T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[para(1770(a,1),1564(a,1,2))].">
      <j1 rule="para" parents="1770 1564"/>
    </justification>
  </clause>

  <clause id="1772">
    <literal><![CDATA[
      (1 / x) * L((1 / x) \ y,z,u) = L(y * x,z,u) / x
    ]]></literal>
    <justification jstring="[para(645(a,1),1762(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="645 1762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1773">
    <literal><![CDATA[
      (1 / x) * L((1 / x) \ 1,y,z) = L(x,y,z) / x
    ]]></literal>
    <justification jstring="[para(7(a,1),1772(a,2,1,1))].">
      <j1 rule="para" parents="7 1772"/>
    </justification>
  </clause>

  <clause id="1774">
    <literal><![CDATA[
      (1 / x) * L(x,y,z) = L(x,y,z) / x
    ]]></literal>
    <justification jstring="[para(79(a,1),1773(a,1,2,1))].">
      <j1 rule="para" parents="79 1773"/>
    </justification>
  </clause>

  <clause id="1775">
    <literal><![CDATA[
      ((x * y) * (z * (u * u))) / (y * (z * (u * u))) = R(R(x,y,z),y * z,u * u)
    ]]></literal>
    <justification jstring="[para(33(a,1),1221(a,1,2))].">
      <j1 rule="para" parents="33 1221"/>
    </justification>
  </clause>

  <clause id="1776">
    <literal><![CDATA[
      x \ ((y * x) * T((y * x) \ z,u)) = T(y,x) * T(T(y,x) \ (x \ z),u)
    ]]></literal>
    <justification jstring="[para(22(a,2),1344(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="22 1344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1777">
    <literal><![CDATA[
      x \ (y * (x * T(x \ (y \ z),u))) = T(y,x) * T(T(y,x) \ (x \ z),u)
    ]]></literal>
    <justification jstring="[para(940(a,1),1776(a,1,2))].">
      <j1 rule="para" parents="940 1776"/>
    </justification>
  </clause>

  <clause id="1778">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ (y \ z),u) = T(x * T(x \ (z / y),u),y)
    ]]></literal>
    <justification jstring="[hyper(1361,a,1777,a),flip(a)].">
      <j1 rule="hyper" parents="1361 1777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1779">
    <literal><![CDATA[
      T(x * T(x \ ((y * z) / y),u),y) = T(x,y) * T(T(x,y) \ z,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),1778(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="9 1778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1780">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ T(z,y),u) = T(x * T(x \ z,u),y)
    ]]></literal>
    <justification jstring="[para(239(a,1),1779(a,1,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="239 1779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1781">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ 1,z) = T(x * T(x \ 1,z),y)
    ]]></literal>
    <justification jstring="[para(201(a,1),1780(a,1,2,1,2))].">
      <j1 rule="para" parents="201 1780"/>
    </justification>
  </clause>

  <clause id="1782">
    <literal><![CDATA[
      T(x * T(x \ 1,T(x,y)),y) = (T(x,y) \ 1) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(300,a,1781,a),flip(a)].">
      <j1 rule="hyper" parents="300 1781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1783">
    <literal><![CDATA[
      T(x,y) \ T(x * T(x \ 1,z),y) = T(T(x,y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(129,a,1781,a)].">
      <j1 rule="hyper" parents="129 1781"/>
    </justification>
  </clause>

  <clause id="1784">
    <literal><![CDATA[
      T(T(x,y) \ 1,x \ T(x,z)) = T(x,y) \ T(x * (x \ 1),y)
    ]]></literal>
    <justification jstring="[para(1368(a,1),1783(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="1368 1783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1785">
    <literal><![CDATA[
      T(T(x,y) \ 1,x \ T(x,z)) = T(x,y) \ T(1,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),1784(a,2,2,1))].">
      <j1 rule="para" parents="10 1784"/>
    </justification>
  </clause>

  <clause id="1787">
    <literal><![CDATA[
      T(T(x,y) \ 1,x \ T(x,z)) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[para(201(a,1),1785(a,2,2))].">
      <j1 rule="para" parents="201 1785"/>
    </justification>
  </clause>

  <clause id="1789">
    <literal><![CDATA[
      x * (T(y,x) * L(T(y,x) \ z,u,w)) = y * (x * L(x \ (y \ (x * z)),u,w))
    ]]></literal>
    <justification jstring="[hyper(1032,a,1475,a),flip(a)].">
      <j1 rule="hyper" parents="1032 1475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1790">
    <literal><![CDATA[
      T(x,y) * L(T(x,y) \ y,z,u) = T(x * L(x \ y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(253,a,1631,a(flip),b,1475,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="253 1631 1475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1791">
    <literal><![CDATA[
      T(x,y) * (R(x,z,u) \ 1) = R(x,z,u) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),1519(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 1519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1793">
    <literal><![CDATA[
      x \ ((y * x) * R((y * x) \ x,z,u)) = T(y,x) * R(T(y,x) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(22(a,2),1540(a,2,2,1,1))].">
      <j1 rule="para" parents="22 1540"/>
    </justification>
  </clause>

  <clause id="1794">
    <literal><![CDATA[
      x \ ((y * R(y \ 1,z,u)) * x) = T(y,x) * R(T(y,x) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(1338(a,1),1793(a,1,2))].">
      <j1 rule="para" parents="1338 1793"/>
    </justification>
  </clause>

  <clause id="1795">
    <literal><![CDATA[
      T(x,y) * R(T(x,y) \ 1,z,u) = T(x * R(x \ 1,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(347,a,1794,a),flip(a)].">
      <j1 rule="hyper" parents="347 1794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1797">
    <literal><![CDATA[
      T(x * R(x \ 1,T(x,y),z),y) = (z / (T(x,y) * z)) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,692,a,b,1795,a),flip(a)].">
      <j1 rule="hyper" parents="63 692 1795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1798">
    <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(1012(a,1),1797(a,2,1,2))].">
      <j1 rule="para" parents="1012 1797"/>
    </justification>
  </clause>

  <clause id="1799">
    <literal><![CDATA[
      ((x \ 1) / (x \ T(x,y))) * T(x,y) = T(x * T(x \ 1,T(x,y)),y)
    ]]></literal>
    <justification jstring="[para(1370(a,1),1798(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1370 1798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1800">
    <literal><![CDATA[
      (x \ 1) / (x \ T(x,y)) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(35,a,1782,a(flip),b,1799,a),flip(a)].">
      <j1 rule="hyper" parents="35 1782 1799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1801">
    <literal><![CDATA[
      T(T(x,y) \ 1,x \ T(x,y)) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ T(x,y)) \ (x \ 1) = z
    ]]></literal>
    <justification jstring="[para(1800(a,1),423(a,1,1))].">
      <j1 rule="para" parents="1800 423"/>
    </justification>
  </clause>

  <clause id="1802">
    <literal><![CDATA[
      (x \ T(x,y)) \ (x \ 1) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(1801,a,1787,a)].">
      <j1 rule="hyper" parents="1801 1787"/>
    </justification>
  </clause>

  <clause id="1803">
    <literal><![CDATA[
      (x \ T(x,y)) * (T(x,y) \ 1) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(142,a,1802,a)].">
      <j1 rule="hyper" parents="142 1802"/>
    </justification>
  </clause>

  <clause id="1804">
    <literal><![CDATA[
      (x * T(x \ 1,y)) \ ((1 / x) \ 1) = T(1 / x,y) \ 1
    ]]></literal>
    <justification jstring="[para(1110(a,1),1802(a,1,1))].">
      <j1 rule="para" parents="1110 1802"/>
    </justification>
  </clause>

  <clause id="1805">
    <literal><![CDATA[
      (x \ T(x,y)) * ((x \ 1) \ (T(x,y) \ 1)) = 1
    ]]></literal>
    <justification jstring="[para(1802(a,1),1757(a,1,2,2))].">
      <j1 rule="para" parents="1802 1757"/>
    </justification>
  </clause>

  <clause id="1806">
    <literal><![CDATA[
      (x \ T(x,y)) \ (x \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) \ 1 = z
    ]]></literal>
    <justification jstring="[para(1803(a,1),342(a,1,2))].">
      <j1 rule="para" parents="1803 342"/>
    </justification>
  </clause>

  <clause id="1807">
    <literal><![CDATA[
      (x \ T(x,y)) * z != 1
    ]]></literal>
    <literal><![CDATA[
      (x \ 1) \ (T(x,y) \ 1) = z
    ]]></literal>
    <justification jstring="[para(1805(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="1805 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1808">
    <literal><![CDATA[
      (x * T(x \ 1,y)) \ x = T(1 / x,y) \ 1
    ]]></literal>
    <justification jstring="[para(79(a,1),1804(a,1,2))].">
      <j1 rule="para" parents="79 1804"/>
    </justification>
  </clause>

  <clause id="1809">
    <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(676(a,1),1572(a,2,2,1))].">
      <j1 rule="para" parents="676 1572"/>
    </justification>
  </clause>

  <clause id="1810">
    <literal><![CDATA[
      ((x / y) * L((x / y) \ z,u,w)) * y = x * L(x \ (z * y),u,w)
    ]]></literal>
    <justification jstring="[para(79(a,1),1596(a,2,2,1,2,2))].">
      <j1 rule="para" parents="79 1596"/>
    </justification>
  </clause>

  <clause id="1811">
    <literal><![CDATA[
      (x * L(x \ (y * z),u,w)) / z = (x / z) * L((x / z) \ y,u,w)
    ]]></literal>
    <justification jstring="[hyper(138,a,1810,a)].">
      <j1 rule="hyper" parents="138 1810"/>
    </justification>
  </clause>

  <clause id="1812">
    <literal><![CDATA[
      ((x / y) * L((x / y) \ 1,z,u)) * y = x * L(x \ y,z,u)
    ]]></literal>
    <justification jstring="[para(7(a,1),1810(a,2,2,1,2))].">
      <j1 rule="para" parents="7 1810"/>
    </justification>
  </clause>

  <clause id="1813">
    <literal><![CDATA[
      ((x / y) * L((x / y) \ x,z,u)) * y = x * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),1810(a,2,2,1))].">
      <j1 rule="para" parents="9 1810"/>
    </justification>
  </clause>

  <clause id="1814">
    <literal><![CDATA[
      ((x / y) * L(y,z,u)) * y = x * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(79(a,1),1813(a,1,1,2,1))].">
      <j1 rule="para" parents="79 1813"/>
    </justification>
  </clause>

  <clause id="1815">
    <literal><![CDATA[
      ((x / y) * L(y,z,u)) \ (x * L(y,z,u)) = y
    ]]></literal>
    <justification jstring="[hyper(129,a,1814,a)].">
      <j1 rule="hyper" parents="129 1814"/>
    </justification>
  </clause>

  <clause id="1816">
    <literal><![CDATA[
      ((x * y) / z) * L(z,y,x) = (x * (y * z)) / z
    ]]></literal>
    <justification jstring="[hyper(123,a,97,a(flip),b,1814,a),flip(a)].">
      <j1 rule="hyper" parents="123 97 1814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1817">
    <literal><![CDATA[
      (x * L(y,z,u)) * y = (x * y) * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(11(a,1),1814(a,1,1,1))].">
      <j1 rule="para" parents="11 1814"/>
    </justification>
  </clause>

  <clause id="1818">
    <literal><![CDATA[
      (x * L(y,z,u)) \ ((x * y) * L(y,z,u)) = y
    ]]></literal>
    <justification jstring="[para(11(a,1),1815(a,1,1,1))].">
      <j1 rule="para" parents="11 1815"/>
    </justification>
  </clause>

  <clause id="1819">
    <literal><![CDATA[
      ((x / L(y,z,u)) * y) \ (x * y) = L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(625,a,1817,a)].">
      <j1 rule="hyper" parents="625 1817"/>
    </justification>
  </clause>

  <clause id="1820">
    <literal><![CDATA[
      (x * y) / L(y,z,u) = (x / L(y,z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(621,a,1817,a)].">
      <j1 rule="hyper" parents="621 1817"/>
    </justification>
  </clause>

  <clause id="1821">
    <literal><![CDATA[
      (1 / L(x,y,z)) * x = x / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(411,a,1817,a),flip(a)].">
      <j1 rule="hyper" parents="411 1817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1822">
    <literal><![CDATA[
      ((1 / L(x,y,z)) * x) * L(x,y,z) = x
    ]]></literal>
    <justification jstring="[hyper(213,a,1817,a),flip(a)].">
      <j1 rule="hyper" parents="213 1817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1823">
    <literal><![CDATA[
      (x * (y * y)) / y = x * L(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(123,a,97,a(flip),b,1817,a)].">
      <j1 rule="hyper" parents="123 97 1817"/>
    </justification>
  </clause>

  <clause id="1824">
    <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(1817(a,1),349(a,1,1))].">
      <j1 rule="para" parents="1817 349"/>
    </justification>
  </clause>

  <clause id="1825">
    <literal><![CDATA[
      x * L(y,z,u) != y
    ]]></literal>
    <literal><![CDATA[
      (1 / L(y,z,u)) * y = x
    ]]></literal>
    <justification jstring="[para(1822(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="1822 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1826">
    <literal><![CDATA[
      ((x * L(y,z,u)) / L(y,z,u)) * T(((x * L(y,z,u)) / L(y,z,u)) \ (x * y),w) = ((x * L(y,z,u)) * T(y,w)) / L(y,z,u)
    ]]></literal>
    <justification jstring="[para(1818(a,1),1731(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1818 1731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1827">
    <literal><![CDATA[
      ((x / L(x,y,z)) * x) \ 1 = L(x,y,z) / (x * x)
    ]]></literal>
    <justification jstring="[hyper(123,a,1819,a(flip),b,443,a),flip(a)].">
      <j1 rule="hyper" parents="123 1819 443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1828">
    <literal><![CDATA[
      (x * y) / L(y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      (x / L(y,z,u)) * y = w
    ]]></literal>
    <justification jstring="[para(1819(a,1),301(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1819 301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1829">
    <literal><![CDATA[
      L(x,y,z) = ((z * y) / x) \ ((z * (y * x)) / x)
    ]]></literal>
    <justification jstring="[hyper(129,a,1816,a),flip(a)].">
      <j1 rule="hyper" parents="129 1816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1830">
    <literal><![CDATA[
      (x * (y * z)) / z != L(z,y,x) * u
    ]]></literal>
    <literal><![CDATA[
      T((x * y) / z,L(z,y,x)) = u
    ]]></literal>
    <justification jstring="[para(1816(a,1),254(a,2)),flip(a)].">
      <j1 rule="para" parents="1816 254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1831">
    <literal><![CDATA[
      ((x * (y / z)) / z) \ ((x * y) / z) = L(z,y / z,x)
    ]]></literal>
    <justification jstring="[para(12(a,1),1829(a,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="12 1829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1832">
    <literal><![CDATA[
      (x / y) * L((x / y) \ 1,z,u) = (x * L(x \ y,z,u)) / y
    ]]></literal>
    <justification jstring="[hyper(138,a,1812,a),flip(a)].">
      <j1 rule="hyper" parents="138 1812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1833">
    <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(20(a,2),1832(a,1,1)),flip(a)].">
      <j1 rule="para" parents="20 1832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1834">
    <literal><![CDATA[
      (x / y) * L((x / y) \ (z / y),u,w) = (x * L(x \ z,u,w)) / y
    ]]></literal>
    <justification jstring="[para(12(a,1),1811(a,1,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="12 1811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1835">
    <literal><![CDATA[
      ((x * y) / x) * L(((x * y) / x) \ y,z,u) = ((x * y) * L(K(y,x),z,u)) / x
    ]]></literal>
    <justification jstring="[para(16(a,2),1811(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="16 1811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1836">
    <literal><![CDATA[
      (x * L(x \ (y * x),z,u)) / y = (x / y) * L(T(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(865(a,2),1834(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="865 1834"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1837">
    <literal><![CDATA[
      (x / y) * L(T(y,x),z,u) = (L(y,z,u) * x) / y
    ]]></literal>
    <justification jstring="[para(666(a,1),1836(a,1,1)),flip(a)].">
      <j1 rule="para" parents="666 1836"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1838">
    <literal><![CDATA[
      (L(x,y,z) * (u * x)) / x = u * L(T(x,u * x),y,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),1837(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 1837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1839">
    <literal><![CDATA[
      T(x * L(T(y,x * y),z,u),y) = y \ (L(y,z,u) * (x * y))
    ]]></literal>
    <justification jstring="[para(1838(a,1),113(a,1,1))].">
      <j1 rule="para" parents="1838 113"/>
    </justification>
  </clause>

  <clause id="1840">
    <literal><![CDATA[
      T(x * L(T(y,x * y),z,u),y) = L(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,1253,a(flip),b,1839,a),flip(a)].">
      <j1 rule="hyper" parents="333 1253 1839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1841">
    <literal><![CDATA[
      (1 / T(x,y)) * T(T(x,z),u) = T(T(x,z),u) / T(x,y)
    ]]></literal>
    <justification jstring="[para(12(a,1),1667(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="12 1667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1843">
    <literal><![CDATA[
      T(T(x,y),z) / T(x,x \ 1) = (x \ 1) * T(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(281(a,1),1841(a,1,1)),flip(a)].">
      <j1 rule="para" parents="281 1841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1844">
    <literal><![CDATA[
      T(T(x,x \ 1),y) / T(x,x \ 1) = T(x,y) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(333,a,250,a(flip),b,1843,a),flip(a)].">
      <j1 rule="hyper" parents="333 250 1843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1845">
    <literal><![CDATA[
      T(T(x,x \ 1),y) / T(x,x \ 1) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,1012,a(flip),b,1844,a),flip(a)].">
      <j1 rule="hyper" parents="333 1012 1844"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1846">
    <literal><![CDATA[
      ((x * y) / x) / ((y \ 1) \ 1) = (y \ 1) * ((x * y) / x)
    ]]></literal>
    <justification jstring="[para(359(a,1),1678(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="359 1678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1847">
    <literal><![CDATA[
      (T(x,y) \ 1) * ((y * T(x,y)) / y) = x / ((T(x,y) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(239(a,1),1846(a,1,1)),flip(a)].">
      <j1 rule="para" parents="239 1846"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1848">
    <literal><![CDATA[
      x / ((T(x,y) \ 1) \ 1) = (T(x,y) \ 1) * x
    ]]></literal>
    <justification jstring="[para(239(a,1),1847(a,1,2)),flip(a)].">
      <j1 rule="para" parents="239 1847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1849">
    <literal><![CDATA[
      (T(x,y) \ 1) \ ((T(x,y) \ x) / x) = K(x,((T(x,y) \ 1) * x) / x)
    ]]></literal>
    <justification jstring="[para(1848(a,1),1565(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1848 1565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1850">
    <literal><![CDATA[
      (T(x,y) \ 1) \ ((T(x,y) \ x) / x) = K(x,T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[para(11(a,1),1849(a,2,2))].">
      <j1 rule="para" parents="11 1849"/>
    </justification>
  </clause>

  <clause id="1851">
    <literal><![CDATA[
      (T(x,y) \ 1) * K(x,T(x,y) \ 1) = (T(x,y) \ x) / x
    ]]></literal>
    <justification jstring="[hyper(142,a,1850,a)].">
      <j1 rule="hyper" parents="142 1850"/>
    </justification>
  </clause>

  <clause id="1853">
    <literal><![CDATA[
      R(R(x,y,z),y * z,u * u) = R(x,y,z * (u * u))
    ]]></literal>
    <justification jstring="[hyper(544,a,1775,a),flip(a)].">
      <j1 rule="hyper" parents="544 1775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1854">
    <literal><![CDATA[
      R(x,y,z * (u * u)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(547,a,1853,a),flip(a)].">
      <j1 rule="hyper" parents="547 1853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1855">
    <literal><![CDATA[
      R(x,y,z * (u * u)) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(1853(a,1),547(a,1))].">
      <j1 rule="para" parents="1853 547"/>
    </justification>
  </clause>

  <clause id="1857">
    <literal><![CDATA[
      R(x,y,z * (u * (w * w))) = R(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(33(a,1),1854(a,1,3))].">
      <j1 rule="para" parents="33 1854"/>
    </justification>
  </clause>

  <clause id="1858">
    <literal><![CDATA[
      R(x,y,z \ 1) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(223(a,1),1854(a,1,3)),flip(a)].">
      <j1 rule="para" parents="223 1854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1859">
    <literal><![CDATA[
      R(x,y,1 / z) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(228(a,1),1854(a,1,3))].">
      <j1 rule="para" parents="228 1854"/>
    </justification>
  </clause>

  <clause id="1860">
    <literal><![CDATA[
      R(x,y,T(z,u * u)) = R(x,y,(u * u) \ z)
    ]]></literal>
    <justification jstring="[para(680(a,1),1854(a,1,3))].">
      <j1 rule="para" parents="680 1854"/>
    </justification>
  </clause>

  <clause id="1862">
    <literal><![CDATA[
      R(x,y,(z \ 1) \ 1) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,1858,a(flip),b,1858,a),flip(a)].">
      <j1 rule="hyper" parents="333 1858 1858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1863">
    <literal><![CDATA[
      R(x,y,1 / z) = R(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(333,a,1858,a,b,1859,a),flip(a)].">
      <j1 rule="hyper" parents="333 1858 1859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1865">
    <literal><![CDATA[
      R(x,y,1 / y) / (y \ 1) = x * y
    ]]></literal>
    <justification jstring="[hyper(123,a,1859,a,b,810,a)].">
      <j1 rule="hyper" parents="123 1859 810"/>
    </justification>
  </clause>

  <clause id="1866">
    <literal><![CDATA[
      R(x,y,(1 / z) * (u * u)) = R(x,y,(u * u) \ z)
    ]]></literal>
    <justification jstring="[para(794(a,1),1859(a,1,3))].">
      <j1 rule="para" parents="794 1859"/>
    </justification>
  </clause>

  <clause id="1867">
    <literal><![CDATA[
      R(x,y,z) * (y * ((z \ 1) \ 1)) = (x * y) * ((z \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(125,a,1862,a(flip),b,20,a(flip))].">
      <j1 rule="hyper" parents="125 1862 20"/>
    </justification>
  </clause>

  <clause id="1868">
    <literal><![CDATA[
      a(x,y \ 1,(y \ 1) \ 1) = x \ R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(121,a,1862,a(flip),b,768,a),flip(a)].">
      <j1 rule="hyper" parents="121 1862 768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1869">
    <literal><![CDATA[
      T(R(x,y,1 / y),z) / (y \ 1) = T(x,z) * y
    ]]></literal>
    <justification jstring="[para(1863(a,2),611(a,1,1,1))].">
      <j1 rule="para" parents="1863 611"/>
    </justification>
  </clause>

  <clause id="1870">
    <literal><![CDATA[
      R(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(223(a,1),1855(a,1,3))].">
      <j1 rule="para" parents="223 1855"/>
    </justification>
  </clause>

  <clause id="1871">
    <literal><![CDATA[
      R(x,y,1 / z) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(228(a,1),1855(a,1,3))].">
      <j1 rule="para" parents="228 1855"/>
    </justification>
  </clause>

  <clause id="1872">
    <literal><![CDATA[
      R(x,y,z \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(1863(a,1),1871(a,1))].">
      <j1 rule="para" parents="1863 1871"/>
    </justification>
  </clause>

  <clause id="1873">
    <literal><![CDATA[
      R(x,y,z * (u \ 1)) = R(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(223(a,1),1857(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="223 1857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1874">
    <literal><![CDATA[
      R(x,y,(z \ 1) * z) = x
    ]]></literal>
    <justification jstring="[hyper(547,a,1873,a),flip(a)].">
      <j1 rule="hyper" parents="547 1873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1875">
    <literal><![CDATA[
      R(x,y,z * (1 / z)) = x
    ]]></literal>
    <justification jstring="[para(79(a,1),1874(a,1,3,1))].">
      <j1 rule="para" parents="79 1874"/>
    </justification>
  </clause>

  <clause id="1876">
    <literal><![CDATA[
      R(x,y,K(z \ 1,z)) = x
    ]]></literal>
    <justification jstring="[para(276(a,2),1874(a,1,3))].">
      <j1 rule="para" parents="276 1874"/>
    </justification>
  </clause>

  <clause id="1877">
    <literal><![CDATA[
      (x * (y * (1 / y))) / z = x / (z / (y * (1 / y)))
    ]]></literal>
    <justification jstring="[hyper(63,a,556,a(flip),b,1875,a)].">
      <j1 rule="hyper" parents="63 556 1875"/>
    </justification>
  </clause>

  <clause id="1878">
    <literal><![CDATA[
      R(x,y,K(z,1 / z)) = x
    ]]></literal>
    <justification jstring="[para(278(a,2),1875(a,1,3))].">
      <j1 rule="para" parents="278 1875"/>
    </justification>
  </clause>

  <clause id="1879">
    <literal><![CDATA[
      (x * y) * K(z \ 1,z) = x * (y * K(z \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(125,a,1876,a(flip),b,20,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="125 1876 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1880">
    <literal><![CDATA[
      (x \ 1) * K(y \ 1,y) = x \ K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(1876(a,1),430(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1876 430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1881">
    <literal><![CDATA[
      x \ (y * K(z \ 1,z)) = (x \ y) * K(z \ 1,z)
    ]]></literal>
    <justification jstring="[para(1876(a,1),529(a,1,1))].">
      <j1 rule="para" parents="1876 529"/>
    </justification>
  </clause>

  <clause id="1882">
    <literal><![CDATA[
      x * (y * K(z \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      (x * y) * K(z \ 1,z) = u
    ]]></literal>
    <justification jstring="[para(1876(a,1),299(a,1,1))].">
      <j1 rule="para" parents="1876 299"/>
    </justification>
  </clause>

  <clause id="1883">
    <literal><![CDATA[
      (x * y) * K(z,1 / z) = x * (y * K(z,1 / z))
    ]]></literal>
    <justification jstring="[hyper(125,a,1878,a(flip),b,20,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="125 1878 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1885">
    <literal><![CDATA[
      ((x * y) * ((y * y) \ z)) / ((y \ 1) * z) = R(x,y,T(z,y * y))
    ]]></literal>
    <justification jstring="[hyper(333,a,719,a,b,1860,a)].">
      <j1 rule="hyper" parents="333 719 1860"/>
    </justification>
  </clause>

  <clause id="1886">
    <literal><![CDATA[
      R(x,y,(z * z) \ u) = R(x,y,1 / u)
    ]]></literal>
    <justification jstring="[hyper(1855,a,1866,a),flip(a)].">
      <j1 rule="hyper" parents="1855 1866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1888">
    <literal><![CDATA[
      R(x,y,(z * z) \ u) = R(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(333,a,1859,a(flip),b,1886,a),flip(a)].">
      <j1 rule="hyper" parents="333 1859 1886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1889">
    <literal><![CDATA[
      R(x,y,T(z,u * u)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,1860,a,b,1888,a)].">
      <j1 rule="hyper" parents="63 1860 1888"/>
    </justification>
  </clause>

  <clause id="1890">
    <literal><![CDATA[
      R(x,y,(z \ 1) \ u) = R(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(710(a,1),1888(a,1,3)),flip(a)].">
      <j1 rule="para" parents="710 1888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1892">
    <literal><![CDATA[
      L(K(x \ 1,x),y,z) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(501,a,1879,a)].">
      <j1 rule="hyper" parents="501 1879"/>
    </justification>
  </clause>

  <clause id="1893">
    <literal><![CDATA[
      a(x,y,K(z \ 1,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(120,a,1879,a(flip),b,84,a),flip(a)].">
      <j1 rule="hyper" parents="120 1879 84"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1894">
    <literal><![CDATA[
      (x * (1 / y)) * K(y \ 1,y) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[para(1131(a,1),1879(a,2,2))].">
      <j1 rule="para" parents="1131 1879"/>
    </justification>
  </clause>

  <clause id="1895">
    <literal><![CDATA[
      (x * T(y,y \ 1)) * K(y \ 1,y) = x * y
    ]]></literal>
    <justification jstring="[para(1247(a,1),1879(a,2,2))].">
      <j1 rule="para" parents="1247 1879"/>
    </justification>
  </clause>

  <clause id="1896">
    <literal><![CDATA[
      (x * ((y \ 1) \ 1)) * K(y \ 1,y) = x * y
    ]]></literal>
    <justification jstring="[para(1248(a,1),1879(a,2,2))].">
      <j1 rule="para" parents="1248 1879"/>
    </justification>
  </clause>

  <clause id="1897">
    <literal><![CDATA[
      (x * y) * K(z \ 1,z) != u
    ]]></literal>
    <literal><![CDATA[
      x * (y * K(z \ 1,z)) = u
    ]]></literal>
    <justification jstring="[para(1892(a,1),306(a,1,2))].">
      <j1 rule="para" parents="1892 306"/>
    </justification>
  </clause>

  <clause id="1898">
    <literal><![CDATA[
      (x / (1 / y)) * (y \ 1) = x * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(339,a,1894,a),flip(a)].">
      <j1 rule="hyper" parents="339 1894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1899">
    <literal><![CDATA[
      (x / (y \ 1)) * (1 / y) = x / K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(123,a,12,a(flip),b,1894,a),flip(a)].">
      <j1 rule="hyper" parents="123 12 1894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1900">
    <literal><![CDATA[
      (x / ((y \ 1) \ 1)) * y = x * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(460(a,1),1895(a,1,1)),flip(a)].">
      <j1 rule="para" parents="460 1895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1901">
    <literal><![CDATA[
      (x * K(y \ 1,y)) * ((y \ 1) \ 1) = x * y
    ]]></literal>
    <justification jstring="[hyper(35,a,1499,a(flip),b,1896,a),flip(a)].">
      <j1 rule="hyper" parents="35 1499 1896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1903">
    <literal><![CDATA[
      (x / (y \ 1)) * K(y \ 1,y) = x / (1 / y)
    ]]></literal>
    <justification jstring="[hyper(1450,a,1898,a),flip(a)].">
      <j1 rule="hyper" parents="1450 1898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1904">
    <literal><![CDATA[
      T(1 / (1 / x),x \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(253,a,1898,a,b,317,a(flip))].">
      <j1 rule="hyper" parents="253 1898 317"/>
    </justification>
  </clause>

  <clause id="1905">
    <literal><![CDATA[
      (x * (y \ 1)) / (1 / y) = x * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,1443,a,b,1898,a)].">
      <j1 rule="hyper" parents="63 1443 1898"/>
    </justification>
  </clause>

  <clause id="1906">
    <literal><![CDATA[
      (x \ 1) / (1 / x) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,1898,a(flip),b,1445,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 1898 1445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1907">
    <literal><![CDATA[
      (x \ 1) / (1 / x) = (x \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(126,a,1904,a(flip),b,1449,a),flip(a)].">
      <j1 rule="hyper" parents="126 1904 1449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1908">
    <literal><![CDATA[
      T(T(1 / (1 / x),y),x \ 1) = T(x,y)
    ]]></literal>
    <justification jstring="[para(1904(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1904 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1909">
    <literal><![CDATA[
      K(x \ 1,x) * (1 / x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(140,a,1906,a)].">
      <j1 rule="hyper" parents="140 1906"/>
    </justification>
  </clause>

  <clause id="1910">
    <literal><![CDATA[
      K(1 / x,1 / (1 / x)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1204,a,b,1906,a)].">
      <j1 rule="hyper" parents="63 1204 1906"/>
    </justification>
  </clause>

  <clause id="1911">
    <literal><![CDATA[
      L(x \ 1,x,x \ 1) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(424,a,1907,a)].">
      <j1 rule="hyper" parents="424 1907"/>
    </justification>
  </clause>

  <clause id="1912">
    <literal><![CDATA[
      x * L(x \ (y \ x),y,y \ 1) = (y * (1 / y)) * (y \ x)
    ]]></literal>
    <justification jstring="[para(1911(a,1),1597(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1911 1597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1913">
    <literal><![CDATA[
      x * (y * L(y \ (x \ y),x,x \ 1)) = (x * (1 / x)) * y
    ]]></literal>
    <justification jstring="[para(1911(a,1),1602(a,2,1,2))].">
      <j1 rule="para" parents="1911 1602"/>
    </justification>
  </clause>

  <clause id="1914">
    <literal><![CDATA[
      T(x * ((y \ 1) \ 1),z) * K(y \ 1,y) = (y \ T(y * x,z)) * y
    ]]></literal>
    <justification jstring="[para(1230(a,1),1900(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1230 1900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1915">
    <literal><![CDATA[
      x * K(x \ 1,x) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(351,a,1903,a)].">
      <j1 rule="hyper" parents="351 1903"/>
    </justification>
  </clause>

  <clause id="1916">
    <literal><![CDATA[
      (x * ((y * x) \ y)) * K(x \ 1,x) = L(x \ 1,x,y) / (1 / x)
    ]]></literal>
    <justification jstring="[para(1142(a,1),1903(a,1,1))].">
      <j1 rule="para" parents="1142 1903"/>
    </justification>
  </clause>

  <clause id="1917">
    <literal><![CDATA[
      K(x \ 1,x) * x = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1386,a,b,1915,a)].">
      <j1 rule="hyper" parents="63 1386 1915"/>
    </justification>
  </clause>

  <clause id="1918">
    <literal><![CDATA[
      (x \ (1 / y)) * K(y \ 1,y) = x \ (y \ 1)
    ]]></literal>
    <justification jstring="[para(1131(a,1),1881(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1131 1881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1919">
    <literal><![CDATA[
      (x \ ((y \ 1) \ 1)) * K(y \ 1,y) = x \ y
    ]]></literal>
    <justification jstring="[para(1248(a,1),1881(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1248 1881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1920">
    <literal><![CDATA[
      x * K(x,1 / x) = T(x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(405,a,1883,a),flip(a)].">
      <j1 rule="hyper" parents="405 1883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1921">
    <literal><![CDATA[
      x \ T(x,x \ 1) = K(x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(121,a,1197,a(flip),b,1920,a)].">
      <j1 rule="hyper" parents="121 1197 1920"/>
    </justification>
  </clause>

  <clause id="1922">
    <literal><![CDATA[
      x \ ((x \ 1) \ 1) = K(x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(121,a,1196,a(flip),b,1920,a)].">
      <j1 rule="hyper" parents="121 1196 1920"/>
    </justification>
  </clause>

  <clause id="1924">
    <literal><![CDATA[
      (x * y) * ((z \ 1) \ 1) != u * (y * ((z \ 1) \ 1))
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(1867(a,1),44(a,1))].">
      <j1 rule="para" parents="1867 44"/>
    </justification>
  </clause>

  <clause id="1925">
    <literal><![CDATA[
      R(x,y,T(z,y * y)) = ((x * (y \ 1)) * z) / ((y \ 1) * z)
    ]]></literal>
    <justification jstring="[para(976(a,1),1885(a,1,1)),flip(a)].">
      <j1 rule="para" parents="976 1885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1926">
    <literal><![CDATA[
      R(x,y,T(z,y * y)) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y \ 1,z) = u
    ]]></literal>
    <justification jstring="[para(1925(a,2),544(a,1))].">
      <j1 rule="para" parents="1925 544"/>
    </justification>
  </clause>

  <clause id="1927">
    <literal><![CDATA[
      R(x,y \ 1,z) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(1926,a,1889,a)].">
      <j1 rule="hyper" parents="1926 1889"/>
    </justification>
  </clause>

  <clause id="1928">
    <literal><![CDATA[
      R(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y \ 1,z) = u
    ]]></literal>
    <justification jstring="[para(1889(a,1),1926(a,1))].">
      <j1 rule="para" parents="1889 1926"/>
    </justification>
  </clause>

  <clause id="1929">
    <literal><![CDATA[
      R(x,y \ 1,z) = R(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(1872,a,1927,a)].">
      <j1 rule="hyper" parents="1872 1927"/>
    </justification>
  </clause>

  <clause id="1930">
    <literal><![CDATA[
      R(x,y \ 1,z \ 1) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(1870,a,1927,a)].">
      <j1 rule="hyper" parents="1870 1927"/>
    </justification>
  </clause>

  <clause id="1931">
    <literal><![CDATA[
      R(x / (1 / y),y \ 1,y) = x * y
    ]]></literal>
    <justification jstring="[hyper(333,a,1189,a(flip),b,1927,a),flip(a)].">
      <j1 rule="hyper" parents="333 1189 1927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1932">
    <literal><![CDATA[
      R(x,x,y) = y / ((x \ 1) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,225,a(flip),b,1927,a),flip(a)].">
      <j1 rule="hyper" parents="63 225 1927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1933">
    <literal><![CDATA[
      R(x,1 / y,z) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(79(a,1),1927(a,1,2)),flip(a)].">
      <j1 rule="para" parents="79 1927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1934">
    <literal><![CDATA[
      R(x,x,y) \ y = (x \ 1) * y
    ]]></literal>
    <justification jstring="[para(1927(a,1),430(a,1,1))].">
      <j1 rule="para" parents="1927 430"/>
    </justification>
  </clause>

  <clause id="1935">
    <literal><![CDATA[
      R(x,y \ 1,y) / y = x * (1 / y)
    ]]></literal>
    <justification jstring="[para(1927(a,2),1188(a,1,1))].">
      <j1 rule="para" parents="1927 1188"/>
    </justification>
  </clause>

  <clause id="1936">
    <literal><![CDATA[
      x \ R(y,x \ 1,x) = T(y * (1 / x),x)
    ]]></literal>
    <justification jstring="[para(1927(a,2),1190(a,2,2)),flip(a)].">
      <j1 rule="para" parents="1927 1190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1937">
    <literal><![CDATA[
      R(x,1 / y,z) = R(x,y \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,1927,a,b,1933,a),flip(a)].">
      <j1 rule="hyper" parents="333 1927 1933"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1938">
    <literal><![CDATA[
      R(x,1 / y,1 / z) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,1859,a(flip),b,1933,a),flip(a)].">
      <j1 rule="hyper" parents="333 1859 1933"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1939">
    <literal><![CDATA[
      R(x,1 / y,1 / z) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(1933(a,2),1871(a,1))].">
      <j1 rule="para" parents="1933 1871"/>
    </justification>
  </clause>

  <clause id="1940">
    <literal><![CDATA[
      R(x \ 1,x,y) = y / (((x \ 1) \ 1) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,1927,a(flip),b,1932,a)].">
      <j1 rule="hyper" parents="63 1927 1932"/>
    </justification>
  </clause>

  <clause id="1941">
    <literal><![CDATA[
      R(x,y \ 1,z) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(1929(a,2),1872(a,1))].">
      <j1 rule="para" parents="1929 1872"/>
    </justification>
  </clause>

  <clause id="1942">
    <literal><![CDATA[
      R(x,y \ 1,(z \ 1) \ 1) = R(x,1 / y,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,1862,a,b,1937,a)].">
      <j1 rule="hyper" parents="333 1862 1937"/>
    </justification>
  </clause>

  <clause id="1943">
    <literal><![CDATA[
      (x * (1 / y)) * y = R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,533,a,b,1937,a)].">
      <j1 rule="hyper" parents="63 533 1937"/>
    </justification>
  </clause>

  <clause id="1946">
    <literal><![CDATA[
      R(x,1 / y,z) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y \ 1,z) = u
    ]]></literal>
    <justification jstring="[para(1933(a,2),1928(a,1))].">
      <j1 rule="para" parents="1933 1928"/>
    </justification>
  </clause>

  <clause id="1947">
    <literal><![CDATA[
      ((1 / x) * (y * x)) \ (y * R(y / (1 / x),x \ 1,x)) = (1 / x) \ y
    ]]></literal>
    <justification jstring="[para(1931(a,1),1593(a,1,1,2))].">
      <j1 rule="para" parents="1931 1593"/>
    </justification>
  </clause>

  <clause id="1948">
    <literal><![CDATA[
      R(x * K(y \ 1,y),y \ 1,y) = (x * (y \ 1)) * y
    ]]></literal>
    <justification jstring="[para(1905(a,1),1931(a,1,1))].">
      <j1 rule="para" parents="1905 1931"/>
    </justification>
  </clause>

  <clause id="1949">
    <literal><![CDATA[
      x / y != z * (1 / y)
    ]]></literal>
    <literal><![CDATA[
      R(z,y \ 1,y) = x
    ]]></literal>
    <justification jstring="[para(1935(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="1935 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1950">
    <literal><![CDATA[
      (x * (1 / y)) * y != z
    ]]></literal>
    <literal><![CDATA[
      R(x,y \ 1,y) = z
    ]]></literal>
    <justification jstring="[para(1935(a,1),264(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1935 264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1951">
    <literal><![CDATA[
      R(x,(y \ 1) \ 1,z) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(1927(a,2),1941(a,1))].">
      <j1 rule="para" parents="1927 1941"/>
    </justification>
  </clause>

  <clause id="1952">
    <literal><![CDATA[
      T(R(x \ 1,x,y),((x \ 1) \ 1) * y) = (((x \ 1) \ 1) * y) \ y
    ]]></literal>
    <justification jstring="[para(1940(a,2),113(a,1,1))].">
      <j1 rule="para" parents="1940 113"/>
    </justification>
  </clause>

  <clause id="1953">
    <literal><![CDATA[
      x / (T(y,y \ 1) * x) = R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(112(a,2),1940(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="112 1940"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1954">
    <literal><![CDATA[
      R(x \ 1,x,y) \ y = T(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(192,a,1953,a)].">
      <j1 rule="hyper" parents="192 1953"/>
    </justification>
  </clause>

  <clause id="1955">
    <literal><![CDATA[
      x / (T(y,y \ 1) * x) != z
    ]]></literal>
    <literal><![CDATA[
      R(y \ 1,y,x) = z
    ]]></literal>
    <justification jstring="[para(1954(a,1),301(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1954 301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1956">
    <literal><![CDATA[
      R(x,y \ 1,T(z \ 1,z)) = R(x,1 / y,z \ 1)
    ]]></literal>
    <justification jstring="[para(1198(a,2),1942(a,1,3))].">
      <j1 rule="para" parents="1198 1942"/>
    </justification>
  </clause>

  <clause id="1957">
    <literal><![CDATA[
      R(x,(y \ 1) \ 1,T(z \ 1,z)) = R(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[para(76(a,1),1956(a,2,2))].">
      <j1 rule="para" parents="76 1956"/>
    </justification>
  </clause>

  <clause id="1958">
    <literal><![CDATA[
      R(x,T(y,y \ 1),T(z \ 1,z)) = R(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[para(112(a,2),1957(a,1,2))].">
      <j1 rule="para" parents="112 1957"/>
    </justification>
  </clause>

  <clause id="1959">
    <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(1136(a,1),1948(a,2,1))].">
      <j1 rule="para" parents="1136 1948"/>
    </justification>
  </clause>

  <clause id="1960">
    <literal><![CDATA[
      (x * ((y * x) \ y)) * K(x \ 1,x) = L(x \ 1,x,y) * x
    ]]></literal>
    <justification jstring="[hyper(333,a,1625,a(flip),b,1916,a),flip(a)].">
      <j1 rule="hyper" parents="333 1625 1916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1961">
    <literal><![CDATA[
      R(T(x \ 1,((x \ 1) \ 1) * y),x,y) = (((x \ 1) \ 1) * y) \ y
    ]]></literal>
    <justification jstring="[hyper(63,a,27,a,b,1952,a)].">
      <j1 rule="hyper" parents="63 27 1952"/>
    </justification>
  </clause>

  <clause id="1962">
    <literal><![CDATA[
      ((1 / x) * (y * x)) \ (y * (y * x)) = (1 / x) \ y
    ]]></literal>
    <justification jstring="[para(1931(a,1),1947(a,1,2,2))].">
      <j1 rule="para" parents="1931 1947"/>
    </justification>
  </clause>

  <clause id="1963">
    <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(253,a,1594,a,b,1789,a)].">
      <j1 rule="hyper" parents="253 1594 1789"/>
    </justification>
  </clause>

  <clause id="1964">
    <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(239(a,1),1963(a,1,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="239 1963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1965">
    <literal><![CDATA[
      T(x,y) * L(T(x,y) \ 1,z,u) = T(x * L(x \ 1,z,u),y)
    ]]></literal>
    <justification jstring="[para(201(a,1),1964(a,1,2,1,2))].">
      <j1 rule="para" parents="201 1964"/>
    </justification>
  </clause>

  <clause id="1966">
    <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(1964(a,2),827(a,1))].">
      <j1 rule="para" parents="1964 827"/>
    </justification>
  </clause>

  <clause id="1967">
    <literal><![CDATA[
      T(x,y) \ T(x * L(x \ 1,z,u),y) = L(T(x,y) \ 1,z,u)
    ]]></literal>
    <justification jstring="[hyper(129,a,1965,a)].">
      <j1 rule="hyper" parents="129 1965"/>
    </justification>
  </clause>

  <clause id="1968">
    <literal><![CDATA[
      T(x * L(x \ 1,T(x,y),z),y) = T(x,y) * ((z * T(x,y)) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,390,a(flip),b,1965,a),flip(a)].">
      <j1 rule="hyper" parents="63 390 1965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1970">
    <literal><![CDATA[
      T(x,y) * L(T(x,y) \ 1,x,1 / x) = T(x * T(1 / x,1),y)
    ]]></literal>
    <justification jstring="[para(788(a,1),1965(a,2,1,2))].">
      <j1 rule="para" parents="788 1965"/>
    </justification>
  </clause>

  <clause id="1971">
    <literal><![CDATA[
      T(x,y) * L(T(x,y) \ 1,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x * L(x \ 1,z,u),y) = w
    ]]></literal>
    <justification jstring="[para(1967(a,1),273(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1967 273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1972">
    <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(388(a,1),1967(a,1,2,1,2))].">
      <j1 rule="para" parents="388 1967"/>
    </justification>
  </clause>

  <clause id="1973">
    <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(1421(a,1),1968(a,2,2,1))].">
      <j1 rule="para" parents="1421 1968"/>
    </justification>
  </clause>

  <clause id="1974">
    <literal><![CDATA[
      T(x,y) * ((1 / x) * (T(x,y) \ x)) = T(x * T(1 / x,1),y)
    ]]></literal>
    <justification jstring="[para(1070(a,1),1970(a,1,2))].">
      <j1 rule="para" parents="1070 1970"/>
    </justification>
  </clause>

  <clause id="1975">
    <literal><![CDATA[
      T(x,y) * ((1 / x) * (T(x,y) \ x)) = T(x * (1 / x),y)
    ]]></literal>
    <justification jstring="[para(199(a,1),1974(a,2,1,2))].">
      <j1 rule="para" parents="199 1974"/>
    </justification>
  </clause>

  <clause id="1976">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) / x) \ (1 / x)) = T(K(T(x,y),1 / x),y)
    ]]></literal>
    <justification jstring="[para(1771(a,1),1973(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1771 1973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1977">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ (u * y))) / z) = (((z * (u / x)) / z) * x) * y
    ]]></literal>
    <justification jstring="[hyper(926,a,1003,a),flip(a)].">
      <j1 rule="hyper" parents="926 1003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1978">
    <literal><![CDATA[
      (((x * ((y / z) / u)) / x) * u) * z = (u * z) * ((x * ((u * z) \ y)) / x)
    ]]></literal>
    <justification jstring="[para(12(a,1),1977(a,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 1977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1979">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ (u * y))) / z) = (x * ((z * (x \ u)) / z)) * y
    ]]></literal>
    <justification jstring="[para(906(a,1),1977(a,2,1))].">
      <j1 rule="para" parents="906 1977"/>
    </justification>
  </clause>

  <clause id="1980">
    <literal><![CDATA[
      (x * y) * ((x * ((x * y) \ z)) / x) = (x * ((z / y) / x)) * y
    ]]></literal>
    <justification jstring="[hyper(339,a,1978,a),flip(a)].">
      <j1 rule="hyper" parents="339 1978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1981">
    <literal><![CDATA[
      (x * y) * ((x * ((x * y) \ z)) / x) != u
    ]]></literal>
    <literal><![CDATA[
      (x * ((z / y) / x)) * y = u
    ]]></literal>
    <justification jstring="[para(1978(a,1),339(a,1))].">
      <j1 rule="para" parents="1978 339"/>
    </justification>
  </clause>

  <clause id="1982">
    <literal><![CDATA[
      x * (y * ((x * (y \ (x \ z))) / x)) = (x * ((z / y) / x)) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,1171,a(flip),b,1980,a)].">
      <j1 rule="hyper" parents="63 1171 1980"/>
    </justification>
  </clause>

  <clause id="1983">
    <literal><![CDATA[
      (x * ((x / y) / x)) * y = T(x,x / (x * y))
    ]]></literal>
    <justification jstring="[hyper(63,a,1091,a(flip),b,1980,a),flip(a)].">
      <j1 rule="hyper" parents="63 1091 1980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1984">
    <literal><![CDATA[
      T(x,x / (x * y)) != z
    ]]></literal>
    <literal><![CDATA[
      T(x * ((x / y) / x),y) = y \ z
    ]]></literal>
    <justification jstring="[para(1983(a,1),296(a,1))].">
      <j1 rule="para" parents="1983 296"/>
    </justification>
  </clause>

  <clause id="1985">
    <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),1982(a,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="365 1982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1986">
    <literal><![CDATA[
      T(x,x / (x * y)) != z
    ]]></literal>
    <literal><![CDATA[
      (x * ((x / y) / x)) * y = z
    ]]></literal>
    <justification jstring="[para(1091(a,1),1981(a,1))].">
      <j1 rule="para" parents="1091 1981"/>
    </justification>
  </clause>

  <clause id="1987">
    <literal><![CDATA[
      ((x / y) * ((z * ((x / y) \ u)) / z)) * y = x * ((z * (((x / y) * y) \ (u * y))) / z)
    ]]></literal>
    <justification jstring="[hyper(339,a,1979,a),flip(a)].">
      <j1 rule="hyper" parents="339 1979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1988">
    <literal><![CDATA[
      x * (y * ((z * (y \ (x \ (u * y)))) / z)) = (x * ((z * (x \ u)) / z)) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,1171,a(flip),b,1979,a)].">
      <j1 rule="hyper" parents="63 1171 1979"/>
    </justification>
  </clause>

  <clause id="1989">
    <literal><![CDATA[
      (x \ (y * x)) * ((z * ((x \ (y * x)) \ x)) / z) = T(y * ((z * (y \ x)) / z),x)
    ]]></literal>
    <justification jstring="[hyper(253,a,1979,a(flip),b,1473,a),flip(a)].">
      <j1 rule="hyper" parents="253 1979 1473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1990">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ y)) / z) = (x * ((z * (x \ 1)) / z)) * y
    ]]></literal>
    <justification jstring="[para(7(a,1),1979(a,1,2,1,2,2))].">
      <j1 rule="para" parents="7 1979"/>
    </justification>
  </clause>

  <clause id="1992">
    <literal><![CDATA[
      (x * ((y * (x \ 1)) / y)) * x = x * (x * ((y * (x \ 1)) / y))
    ]]></literal>
    <justification jstring="[hyper(63,a,1697,a(flip),b,1990,a),flip(a)].">
      <j1 rule="hyper" parents="63 1697 1990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1993">
    <literal><![CDATA[
      T(x * ((y * (x \ 1)) / y),z) = K(y,(y / T(x,z)) / y)
    ]]></literal>
    <justification jstring="[hyper(253,a,1990,a(flip),b,1741,a(flip))].">
      <j1 rule="hyper" parents="253 1990 1741"/>
    </justification>
  </clause>

  <clause id="1995">
    <literal><![CDATA[
      (x * ((y / (z * (x \ y))) / x)) * (z * (x \ y)) = x * ((z * ((x * (z \ 1)) / x)) * (x \ y))
    ]]></literal>
    <justification jstring="[para(1990(a,1),1982(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1990 1982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1996">
    <literal><![CDATA[
      T(x,y) * ((z * (T(x,y) \ 1)) / z) = T(x * ((z * (x \ 1)) / z),y)
    ]]></literal>
    <justification jstring="[hyper(333,a,1560,a(flip),b,1993,a)].">
      <j1 rule="hyper" parents="333 1560 1993"/>
    </justification>
  </clause>

  <clause id="1997">
    <literal><![CDATA[
      K(x,(x / T(y \ x,z)) / x) = T(K(x,y / x),z)
    ]]></literal>
    <justification jstring="[para(1563(a,1),1993(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1563 1993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1998">
    <literal><![CDATA[
      T(K(x,y / x),K(y / x,z)) = K(x,(x / (y \ x)) / x)
    ]]></literal>
    <justification jstring="[para(1390(a,1),1997(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="1390 1997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1999">
    <literal><![CDATA[
      T(K(x,y / x),K(y / x,z)) = K(x,y / x)
    ]]></literal>
    <justification jstring="[para(76(a,1),1998(a,2,2,1))].">
      <j1 rule="para" parents="76 1998"/>
    </justification>
  </clause>

  <clause id="2001">
    <literal><![CDATA[
      T(K(x,y),K((y * x) / x,z)) = K(x,(y * x) / x)
    ]]></literal>
    <justification jstring="[para(11(a,1),1999(a,1,1,2))].">
      <j1 rule="para" parents="11 1999"/>
    </justification>
  </clause>

  <clause id="2002">
    <literal><![CDATA[
      T(K(x,y),K(y,z)) = K(x,(y * x) / x)
    ]]></literal>
    <justification jstring="[para(11(a,1),2001(a,1,2,1))].">
      <j1 rule="para" parents="11 2001"/>
    </justification>
  </clause>

  <clause id="2003">
    <literal><![CDATA[
      T(K(x,y),K(y,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(11(a,1),2002(a,2,2))].">
      <j1 rule="para" parents="11 2002"/>
    </justification>
  </clause>

  <clause id="2004">
    <literal><![CDATA[
      T(K(x,y),K(z,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(54,a,2003,a)].">
      <j1 rule="hyper" parents="54 2003"/>
    </justification>
  </clause>

  <clause id="2005">
    <literal><![CDATA[
      K(x,y) * K(z,x) = K(z,x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(126,a,2003,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="126 2003 22"/>
    </justification>
  </clause>

  <clause id="2006">
    <literal><![CDATA[
      K(x,y) * K(z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,x) * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(2003(a,1),300(a,1,2))].">
      <j1 rule="para" parents="2003 300"/>
    </justification>
  </clause>

  <clause id="2007">
    <literal><![CDATA[
      T(K(x,y),z) * K(y,u) = K(y,u) * T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(2003(a,1),250(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2003 250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2008">
    <literal><![CDATA[
      L(K(x,y),z,u) * K(y,w) = K(y,w) * L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(2003(a,1),251(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2003 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2009">
    <literal><![CDATA[
      R(K(x,y),z,u) * K(y,w) = K(y,w) * R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(2003(a,1),252(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2003 252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2010">
    <literal><![CDATA[
      K(x,y) * L(K(z,x),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(K(z,x),u,w) * K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(2003(a,1),420(a,1,2,1))].">
      <j1 rule="para" parents="2003 420"/>
    </justification>
  </clause>

  <clause id="2011">
    <literal><![CDATA[
      K(x,y) * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(2004(a,1),300(a,1,2))].">
      <j1 rule="para" parents="2004 300"/>
    </justification>
  </clause>

  <clause id="2012">
    <literal><![CDATA[
      R(K(x,y),z,u) * K(w,x) = K(w,x) * R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(2004(a,1),252(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2004 252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2014">
    <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(2004(a,1),421(a,1,2,1))].">
      <j1 rule="para" parents="2004 421"/>
    </justification>
  </clause>

  <clause id="2015">
    <literal><![CDATA[
      (1 / x) * ((1 / x) * ((y * ((1 / x) \ 1)) / y)) = (((y * x) / y) / x) * (1 / x)
    ]]></literal>
    <justification jstring="[para(1345(a,1),1992(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1345 1992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2016">
    <literal><![CDATA[
      T(x,y) * ((x * (T(x,y) \ 1)) / x) = T(x * (1 / x),y)
    ]]></literal>
    <justification jstring="[para(10(a,1),1996(a,2,1,2,1))].">
      <j1 rule="para" parents="10 1996"/>
    </justification>
  </clause>

  <clause id="2017">
    <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(473(a,2),1996(a,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="473 1996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2018">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ x) / x) = T(x * (1 / x),y)
    ]]></literal>
    <justification jstring="[para(1063(a,1),2016(a,1,2,1))].">
      <j1 rule="para" parents="1063 2016"/>
    </justification>
  </clause>

  <clause id="2019">
    <literal><![CDATA[
      (1 / x) * (T(x,y) \ x) = (T(x,y) \ x) / x
    ]]></literal>
    <justification jstring="[hyper(34,a,1975,a,b,2018,a)].">
      <j1 rule="hyper" parents="34 1975 2018"/>
    </justification>
  </clause>

  <clause id="2020">
    <literal><![CDATA[
      T((T(x,y) \ x) / x,x) = (1 / x) * ((T(x,y) \ 1) * x)
    ]]></literal>
    <justification jstring="[para(2019(a,1),1071(a,1,1))].">
      <j1 rule="para" parents="2019 1071"/>
    </justification>
  </clause>

  <clause id="2021">
    <literal><![CDATA[
      (1 / x) * ((T(x,y) \ 1) * x) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,1067,a(flip),b,2020,a),flip(a)].">
      <j1 rule="hyper" parents="63 1067 2020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2022">
    <literal><![CDATA[
      (x * ((y * (x \ z)) / y)) * y = x * (y * ((x \ (z * y)) / y))
    ]]></literal>
    <justification jstring="[para(10(a,1),1988(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10 1988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2023">
    <literal><![CDATA[
      T(x,y) * ((z * ((y \ (x * y)) \ y)) / z) = T(x * ((z * (x \ y)) / z),y)
    ]]></literal>
    <justification jstring="[para(22(a,2),1989(a,1,1))].">
      <j1 rule="para" parents="22 1989"/>
    </justification>
  </clause>

  <clause id="2024">
    <literal><![CDATA[
      T(x,y) * ((z * (T(x,y) \ y)) / z) = T(x * ((z * (x \ y)) / z),y)
    ]]></literal>
    <justification jstring="[para(22(a,2),2023(a,1,2,1,2,1))].">
      <j1 rule="para" parents="22 2023"/>
    </justification>
  </clause>

  <clause id="2025">
    <literal><![CDATA[
      (((x * y) / x) / y) * (1 / y) = (1 / y) * (((x * y) / x) / y)
    ]]></literal>
    <justification jstring="[para(1345(a,1),2015(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1345 2015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2026">
    <literal><![CDATA[
      ((1 / x) * (((y * x) / y) / x)) / (1 / x) = ((y * x) / y) / x
    ]]></literal>
    <justification jstring="[hyper(138,a,2025,a)].">
      <j1 rule="hyper" parents="138 2025"/>
    </justification>
  </clause>

  <clause id="2027">
    <literal><![CDATA[
      R(((x * y) / x) / y,y,x) = ((1 / y) * ((x * y) / (y * x))) / (1 / y)
    ]]></literal>
    <justification jstring="[para(2026(a,1),923(a,1,1))].">
      <j1 rule="para" parents="2026 923"/>
    </justification>
  </clause>

  <clause id="2028">
    <literal><![CDATA[
      ((1 / x) * ((y * x) / (x * y))) / (1 / x) = (y * x) / (x * y)
    ]]></literal>
    <justification jstring="[hyper(632,a,2027,a),flip(a)].">
      <j1 rule="hyper" parents="632 2027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2029">
    <literal><![CDATA[
      T((x * y) / (y * x),y * x) = ((1 / y) * ((y * x) \ (x * y))) / (1 / y)
    ]]></literal>
    <justification jstring="[para(2028(a,1),741(a,1,1))].">
      <j1 rule="para" parents="2028 741"/>
    </justification>
  </clause>

  <clause id="2030">
    <literal><![CDATA[
      ((1 / x) * ((x * y) \ (y * x))) / (1 / x) = (x * y) \ (y * x)
    ]]></literal>
    <justification jstring="[hyper(423,a,2029,a),flip(a)].">
      <j1 rule="hyper" parents="423 2029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2031">
    <literal><![CDATA[
      K(x,y) = ((1 / y) * ((y * x) \ (x * y))) / (1 / y)
    ]]></literal>
    <justification jstring="[hyper(333,a,16,a,b,2030,a)].">
      <j1 rule="hyper" parents="333 16 2030"/>
    </justification>
  </clause>

  <clause id="2032">
    <literal><![CDATA[
      ((1 / x) * K(y,x)) / (1 / x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(16(a,2),2031(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="16 2031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2033">
    <literal><![CDATA[
      T(1 / x,K(y,x)) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(283,a,2032,a)].">
      <j1 rule="hyper" parents="283 2032"/>
    </justification>
  </clause>

  <clause id="2034">
    <literal><![CDATA[
      K(x,y) * (1 / y) = (1 / y) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(140,a,2032,a)].">
      <j1 rule="hyper" parents="140 2032"/>
    </justification>
  </clause>

  <clause id="2037">
    <literal><![CDATA[
      ((1 / x) * K(y,x)) * x = R(K(y,x),x \ 1,x)
    ]]></literal>
    <justification jstring="[para(2032(a,1),1931(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2032 1931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2038">
    <literal><![CDATA[
      K(1 / x,K(y,x)) = 1
    ]]></literal>
    <justification jstring="[hyper(55,a,2033,a)].">
      <j1 rule="hyper" parents="55 2033"/>
    </justification>
  </clause>

  <clause id="2039">
    <literal><![CDATA[
      T(x \ 1,K(y,x)) = T(1 / x,x)
    ]]></literal>
    <justification jstring="[para(2033(a,1),259(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2033 259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2040">
    <literal><![CDATA[
      K(x,K(y,x \ 1)) = 1
    ]]></literal>
    <justification jstring="[para(76(a,1),2038(a,1,1))].">
      <j1 rule="para" parents="76 2038"/>
    </justification>
  </clause>

  <clause id="2041">
    <literal><![CDATA[
      T(x,K(y,x \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(56,a,2040,a)].">
      <j1 rule="hyper" parents="56 2040"/>
    </justification>
  </clause>

  <clause id="2042">
    <literal><![CDATA[
      K(x,y \ 1) * y = y * K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(126,a,2041,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="126 2041 22"/>
    </justification>
  </clause>

  <clause id="2043">
    <literal><![CDATA[
      L(x,y,z) * K(u,x \ 1) = K(u,x \ 1) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(2041(a,1),251(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2041 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2044">
    <literal><![CDATA[
      T(x \ 1,K(y,x)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(333,a,113,a(flip),b,2039,a),flip(a)].">
      <j1 rule="hyper" parents="333 113 2039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2045">
    <literal><![CDATA[
      T((x * y) \ x,K(z,y)) = L(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(2044(a,1),394(a,2,1))].">
      <j1 rule="para" parents="2044 394"/>
    </justification>
  </clause>

  <clause id="2047">
    <literal><![CDATA[
      T(x \ y,K(z,y \ x)) = L((y \ x) \ 1,y \ x,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),2045(a,1,1,1))].">
      <j1 rule="para" parents="10 2045"/>
    </justification>
  </clause>

  <clause id="2048">
    <literal><![CDATA[
      T(x \ y,K(z,y \ x)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(333,a,388,a(flip),b,2047,a),flip(a)].">
      <j1 rule="hyper" parents="333 388 2047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2049">
    <literal><![CDATA[
      K(x,y \ z) * (z \ y) = (z \ y) * K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(126,a,2048,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="126 2048 22"/>
    </justification>
  </clause>

  <clause id="2053">
    <literal><![CDATA[
      (x \ 1) * (L(x \ 1,x,y) \ (x * ((y * x) \ y))) = K(x \ 1,x * ((y * x) \ y))
    ]]></literal>
    <justification jstring="[hyper(63,a,1258,a(flip),b,1145,a)].">
      <j1 rule="hyper" parents="63 1258 1145"/>
    </justification>
  </clause>

  <clause id="2054">
    <literal><![CDATA[
      ((x * y) \ x) * K(y \ 1,y * ((x * y) \ x)) = (y \ 1) * (y * ((x * y) \ x))
    ]]></literal>
    <justification jstring="[hyper(126,a,1145,a(flip),b,389,a(flip))].">
      <j1 rule="hyper" parents="126 1145 389"/>
    </justification>
  </clause>

  <clause id="2055">
    <literal><![CDATA[
      (x / y) \ (L(y \ 1,y,x / y) * x) = K(x \ (x / y),(x / y) * y)
    ]]></literal>
    <justification jstring="[para(12(a,1),1217(a,1,2,2))].">
      <j1 rule="para" parents="12 1217"/>
    </justification>
  </clause>

  <clause id="2056">
    <literal><![CDATA[
      K(x \ (x / y),(x / y) * y) = y * T(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(983,a,2055,a),flip(a)].">
      <j1 rule="hyper" parents="983 2055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2057">
    <literal><![CDATA[
      K(x \ (x / y),x) = y * T(y \ 1,x)
    ]]></literal>
    <justification jstring="[para(12(a,1),2056(a,1,2))].">
      <j1 rule="para" parents="12 2056"/>
    </justification>
  </clause>

  <clause id="2058">
    <literal><![CDATA[
      T(x * T(x \ 1,y),z) = K(y \ (y / T(x,z)),y)
    ]]></literal>
    <justification jstring="[hyper(333,a,1781,a(flip),b,2057,a)].">
      <j1 rule="hyper" parents="333 1781 2057"/>
    </justification>
  </clause>

  <clause id="2059">
    <literal><![CDATA[
      K(x \ (x / (y / z)),x) = (y * T(y \ z,x)) / z
    ]]></literal>
    <justification jstring="[hyper(333,a,1735,a(flip),b,2057,a),flip(a)].">
      <j1 rule="hyper" parents="333 1735 2057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2060">
    <literal><![CDATA[
      K(x \ (x / (1 / y)),x) = T(y,x) / y
    ]]></literal>
    <justification jstring="[hyper(333,a,1650,a(flip),b,2057,a),flip(a)].">
      <j1 rule="hyper" parents="333 1650 2057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2061">
    <literal><![CDATA[
      K(x \ (x / (y \ z)),x) = y \ (z * T(z \ y,x))
    ]]></literal>
    <justification jstring="[hyper(333,a,1285,a(flip),b,2057,a),flip(a)].">
      <j1 rule="hyper" parents="333 1285 2057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2062">
    <literal><![CDATA[
      K(x \ (x / (y \ 1)),x) = y \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,1010,a(flip),b,2057,a),flip(a)].">
      <j1 rule="hyper" parents="333 1010 2057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2063">
    <literal><![CDATA[
      x * T(x \ y,z) = y * K(z \ (z / (y \ x)),z)
    ]]></literal>
    <justification jstring="[hyper(126,a,2057,a,b,1285,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="126 2057 1285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2064">
    <literal><![CDATA[
      K(x \ (x / (y / z)),x) * z = y * T(y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(125,a,2057,a,b,1735,a(flip))].">
      <j1 rule="hyper" parents="125 2057 1735"/>
    </justification>
  </clause>

  <clause id="2065">
    <literal><![CDATA[
      T(x,y) = K(y \ (y / (1 / x)),y) * x
    ]]></literal>
    <justification jstring="[hyper(125,a,2057,a,b,1650,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="125 2057 1650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2066">
    <literal><![CDATA[
      K(x \ (x / y),x) / y = T(1 / y,x)
    ]]></literal>
    <justification jstring="[hyper(123,a,2057,a,b,471,a)].">
      <j1 rule="hyper" parents="123 2057 471"/>
    </justification>
  </clause>

  <clause id="2067">
    <literal><![CDATA[
      x \ K(y \ (y / x),y) = T(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(121,a,2057,a,b,xx)].">
      <j1 rule="hyper" parents="121 2057"/>
    </justification>
  </clause>

  <clause id="2068">
    <literal><![CDATA[
      K(T(1 / x,T(x,y)),T(x,y)) = x * T(x \ 1,T(x,y))
    ]]></literal>
    <justification jstring="[para(1426(a,1),2057(a,1,1))].">
      <j1 rule="para" parents="1426 2057"/>
    </justification>
  </clause>

  <clause id="2070">
    <literal><![CDATA[
      K(T(1 / (1 / x),x \ 1),x \ 1) = T(x,x \ 1) / x
    ]]></literal>
    <justification jstring="[para(1449(a,1),2060(a,1,1))].">
      <j1 rule="para" parents="1449 2060"/>
    </justification>
  </clause>

  <clause id="2071">
    <literal><![CDATA[
      K(x \ (x / (((x * y) / x) \ 1)),x) = ((x * y) / x) \ y
    ]]></literal>
    <justification jstring="[para(238(a,1),2062(a,2,2))].">
      <j1 rule="para" parents="238 2062"/>
    </justification>
  </clause>

  <clause id="2072">
    <literal><![CDATA[
      K((x * y) \ x,x * y) / y = T(1 / y,x * y)
    ]]></literal>
    <justification jstring="[para(11(a,1),2066(a,1,1,1,2))].">
      <j1 rule="para" parents="11 2066"/>
    </justification>
  </clause>

  <clause id="2075">
    <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(1086(a,1),2067(a,1,2,1,2))].">
      <j1 rule="para" parents="1086 2067"/>
    </justification>
  </clause>

  <clause id="2076">
    <literal><![CDATA[
      (x * T(x \ 1,y)) * z = z * K(y \ (y / T(x,z)),y)
    ]]></literal>
    <justification jstring="[hyper(126,a,2058,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="126 2058 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2077">
    <literal><![CDATA[
      T(x * T(x \ 1,y),x \ y) = K(y \ (x \ y),y)
    ]]></literal>
    <justification jstring="[para(281(a,1),2058(a,2,1,2))].">
      <j1 rule="para" parents="281 2058"/>
    </justification>
  </clause>

  <clause id="2078">
    <literal><![CDATA[
      K(x \ (x / T(L(y \ 1,y,x),z)),x) = T(K(y,x),z)
    ]]></literal>
    <justification jstring="[para(1282(a,2),2058(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1282 2058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2079">
    <literal><![CDATA[
      K((x * (y / z)) \ x,x * (y / z)) = (y * T(y \ z,x * (y / z))) / z
    ]]></literal>
    <justification jstring="[para(11(a,1),2059(a,1,1,2))].">
      <j1 rule="para" parents="11 2059"/>
    </justification>
  </clause>

  <clause id="2080">
    <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(20(a,2),2059(a,1,1,2,2))].">
      <j1 rule="para" parents="20 2059"/>
    </justification>
  </clause>

  <clause id="2081">
    <literal><![CDATA[
      K(x \ (x / ((y * z) / y)),x) = (y * (z * T(z \ 1,x))) / y
    ]]></literal>
    <justification jstring="[para(778(a,1),2059(a,2,1))].">
      <j1 rule="para" parents="778 2059"/>
    </justification>
  </clause>

  <clause id="2082">
    <literal><![CDATA[
      K(x \ (x / ((y \ x) / T(x,y))),x) = ((y \ x) * ((y \ x) \ x)) / T(x,y)
    ]]></literal>
    <justification jstring="[para(1098(a,1),2059(a,2,1,2))].">
      <j1 rule="para" parents="1098 2059"/>
    </justification>
  </clause>

  <clause id="2084">
    <literal><![CDATA[
      K(x \ (x / (y \ (y / z))),x) = y \ ((y / z) * T(z,x))
    ]]></literal>
    <justification jstring="[para(79(a,1),2061(a,2,2,2,1))].">
      <j1 rule="para" parents="79 2061"/>
    </justification>
  </clause>

  <clause id="2085">
    <literal><![CDATA[
      T(x * y,z) / y = x * K(z \ (z / (x \ (1 / y))),z)
    ]]></literal>
    <justification jstring="[hyper(1659,a,2063,a)].">
      <j1 rule="hyper" parents="1659 2063"/>
    </justification>
  </clause>

  <clause id="2086">
    <literal><![CDATA[
      (x \ y) * K(z \ (z / ((x \ y) \ (x \ 1))),z) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,1011,a(flip),b,2063,a),flip(a)].">
      <j1 rule="hyper" parents="63 1011 2063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2087">
    <literal><![CDATA[
      (x * y) * K(z \ (z / ((x * y) \ x)),z) = x * T(y,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),2063(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 2063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2088">
    <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(18(a,2),2063(a,2,2,1,2,2))].">
      <j1 rule="para" parents="18 2063"/>
    </justification>
  </clause>

  <clause id="2090">
    <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(1260(a,2),2077(a,1,2))].">
      <j1 rule="para" parents="1260 2077"/>
    </justification>
  </clause>

  <clause id="2091">
    <literal><![CDATA[
      K(x \ (x / T(y \ x,z)),x) = T(K(x \ y,x),z)
    ]]></literal>
    <justification jstring="[para(388(a,1),2078(a,1,1,2,2,1))].">
      <j1 rule="para" parents="388 2078"/>
    </justification>
  </clause>

  <clause id="2092">
    <literal><![CDATA[
      T(K(x \ y,x),(y \ x) \ z) = K(x \ (x / (((y \ x) \ z) \ z)),x)
    ]]></literal>
    <justification jstring="[para(112(a,1),2091(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="112 2091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2093">
    <literal><![CDATA[
      T(x,x \ 1) / x = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(1904(a,1),2070(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1904 2070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2094">
    <literal><![CDATA[
      K(x,1 / x) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(1208,a,2093,a)].">
      <j1 rule="hyper" parents="1208 2093"/>
    </justification>
  </clause>

  <clause id="2096">
    <literal><![CDATA[
      (x \ 1) * K(x,x \ 1) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(126,a,2093,a(flip),b,1206,a)].">
      <j1 rule="hyper" parents="126 2093 1206"/>
    </justification>
  </clause>

  <clause id="2098">
    <literal><![CDATA[
      K(x,x \ 1) = x * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(384,a,2094,a),flip(a)].">
      <j1 rule="hyper" parents="384 2094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2099">
    <literal><![CDATA[
      x \ ((x \ 1) \ 1) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,1922,a,b,2094,a)].">
      <j1 rule="hyper" parents="63 1922 2094"/>
    </justification>
  </clause>

  <clause id="2100">
    <literal><![CDATA[
      K(1 / x,(1 / x) \ 1) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1910,a(flip),b,2094,a),flip(a)].">
      <j1 rule="hyper" parents="63 1910 2094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2101">
    <literal><![CDATA[
      x * K(x,x \ 1) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(126,a,2094,a(flip),b,1922,a)].">
      <j1 rule="hyper" parents="126 2094 1922"/>
    </justification>
  </clause>

  <clause id="2102">
    <literal><![CDATA[
      x * K(x,x \ 1) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(126,a,2094,a(flip),b,1921,a)].">
      <j1 rule="hyper" parents="126 2094 1921"/>
    </justification>
  </clause>

  <clause id="2104">
    <literal><![CDATA[
      K(x,x \ 1) * x = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(125,a,2094,a(flip),b,1195,a)].">
      <j1 rule="hyper" parents="125 2094 1195"/>
    </justification>
  </clause>

  <clause id="2105">
    <literal><![CDATA[
      x \ K(x,x \ 1) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(121,a,2094,a(flip),b,278,a(flip))].">
      <j1 rule="hyper" parents="121 2094 278"/>
    </justification>
  </clause>

  <clause id="2106">
    <literal><![CDATA[
      K(x \ 1,(x \ 1) \ 1) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(76(a,1),2094(a,1,2)),flip(a)].">
      <j1 rule="para" parents="76 2094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2107">
    <literal><![CDATA[
      K(x,x \ 1) \ 1 = K(1 / x,x)
    ]]></literal>
    <justification jstring="[para(2094(a,1),436(a,1,1))].">
      <j1 rule="para" parents="2094 436"/>
    </justification>
  </clause>

  <clause id="2108">
    <literal><![CDATA[
      K(x,x \ 1) != y
    ]]></literal>
    <literal><![CDATA[
      x * (1 / x) = y
    ]]></literal>
    <justification jstring="[para(2094(a,1),384(a,1))].">
      <j1 rule="para" parents="2094 384"/>
    </justification>
  </clause>

  <clause id="2109">
    <literal><![CDATA[
      (1 / (1 / x)) * K(x,x \ 1) = x
    ]]></literal>
    <justification jstring="[para(2094(a,1),1304(a,1,2))].">
      <j1 rule="para" parents="2094 1304"/>
    </justification>
  </clause>

  <clause id="2110">
    <literal><![CDATA[
      R(x,y,K(z,z \ 1)) = x
    ]]></literal>
    <justification jstring="[para(2094(a,1),1878(a,1,3))].">
      <j1 rule="para" parents="2094 1878"/>
    </justification>
  </clause>

  <clause id="2111">
    <literal><![CDATA[
      x * ((x \ y) * K(z,z \ 1)) = y * K(z,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(125,a,2110,a(flip),b,104,a(flip))].">
      <j1 rule="hyper" parents="125 2110 104"/>
    </justification>
  </clause>

  <clause id="2112">
    <literal><![CDATA[
      (x * y) * K(z,z \ 1) = x * (y * K(z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(125,a,2110,a(flip),b,20,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="125 2110 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2113">
    <literal><![CDATA[
      R(x,y,K(z,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(2110(a,1),51(a,2))].">
      <j1 rule="para" parents="2110 51"/>
    </justification>
  </clause>

  <clause id="2115">
    <literal><![CDATA[
      x \ (y * K(z,z \ 1)) = (x \ y) * K(z,z \ 1)
    ]]></literal>
    <justification jstring="[para(2110(a,1),529(a,1,1))].">
      <j1 rule="para" parents="2110 529"/>
    </justification>
  </clause>

  <clause id="2119">
    <literal><![CDATA[
      x * L(x \ y,y \ x,x \ y) = y * K(y \ x,(y \ x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(126,a,2098,a,b,1613,a),flip(a)].">
      <j1 rule="hyper" parents="126 2098 1613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2120">
    <literal><![CDATA[
      L(x,y,z) * K(x,x \ 1) = x * (L(x,y,z) * (1 / x))
    ]]></literal>
    <justification jstring="[hyper(126,a,2098,a,b,1257,a)].">
      <j1 rule="hyper" parents="126 2098 1257"/>
    </justification>
  </clause>

  <clause id="2122">
    <literal><![CDATA[
      K(x \ 1,x) \ 1 = x * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(63,a,435,a,b,2098,a)].">
      <j1 rule="hyper" parents="63 435 2098"/>
    </justification>
  </clause>

  <clause id="2123">
    <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(2098(a,2),940(a,1,1))].">
      <j1 rule="para" parents="2098 940"/>
    </justification>
  </clause>

  <clause id="2124">
    <literal><![CDATA[
      L(x,y,z) \ K(x,x \ 1) = x * (L(x,y,z) \ (1 / x))
    ]]></literal>
    <justification jstring="[para(2098(a,2),1258(a,1,2))].">
      <j1 rule="para" parents="2098 1258"/>
    </justification>
  </clause>

  <clause id="2125">
    <literal><![CDATA[
      x * L(x \ (y \ x),y,y \ 1) = K(y,y \ 1) * (y \ x)
    ]]></literal>
    <justification jstring="[para(2098(a,2),1912(a,2,1))].">
      <j1 rule="para" parents="2098 1912"/>
    </justification>
  </clause>

  <clause id="2126">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ x) / x) = T(K(x,x \ 1),y)
    ]]></literal>
    <justification jstring="[para(2098(a,2),2018(a,2,1))].">
      <j1 rule="para" parents="2098 2018"/>
    </justification>
  </clause>

  <clause id="2127">
    <literal><![CDATA[
      x \ y != 1 / x
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ 1) = y
    ]]></literal>
    <justification jstring="[para(2105(a,1),47(a,1)),flip(a)].">
      <j1 rule="para" parents="2105 47"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2128">
    <literal><![CDATA[
      K(x,x \ 1) * (x \ 1) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(1375,a,2096,a)].">
      <j1 rule="hyper" parents="1375 2096"/>
    </justification>
  </clause>

  <clause id="2129">
    <literal><![CDATA[
      K((x \ 1) \ 1,x \ 1) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,1133,a,b,2099,a)].">
      <j1 rule="hyper" parents="63 1133 2099"/>
    </justification>
  </clause>

  <clause id="2130">
    <literal><![CDATA[
      x * R(x \ K(x,x \ 1),y,z) = R(1 / x,y,z) / (x \ 1)
    ]]></literal>
    <justification jstring="[para(2128(a,1),1147(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="2128 1147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2131">
    <literal><![CDATA[
      K(1 / x,x) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(79(a,1),2100(a,1,2))].">
      <j1 rule="para" parents="79 2100"/>
    </justification>
  </clause>

  <clause id="2132">
    <literal><![CDATA[
      K(x,x \ 1) \ 1 = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,2107,a,b,2131,a)].">
      <j1 rule="hyper" parents="63 2107 2131"/>
    </justification>
  </clause>

  <clause id="2134">
    <literal><![CDATA[
      (x \ 1) * (K(x,x \ 1) * ((x \ 1) \ y)) = K((x \ 1) \ 1,x \ 1) * y
    ]]></literal>
    <justification jstring="[para(2129(a,1),1240(a,1,2,1))].">
      <j1 rule="para" parents="2129 1240"/>
    </justification>
  </clause>

  <clause id="2135">
    <literal><![CDATA[
      a(x,y,K(z,z \ 1)) = 1
    ]]></literal>
    <justification jstring="[para(2129(a,1),1893(a,1,3))].">
      <j1 rule="para" parents="2129 1893"/>
    </justification>
  </clause>

  <clause id="2136">
    <literal><![CDATA[
      L(K(x,x \ 1),y,z) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(52,a,2135,a)].">
      <j1 rule="hyper" parents="52 2135"/>
    </justification>
  </clause>

  <clause id="2138">
    <literal><![CDATA[
      (x \ y) * K(y,y \ 1) = x \ ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(121,a,2101,a(flip),b,2111,a),flip(a)].">
      <j1 rule="hyper" parents="121 2101 2111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2139">
    <literal><![CDATA[
      x \ (y * K(z,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      (x \ y) * K(z,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(2111(a,1),342(a,1,2))].">
      <j1 rule="para" parents="2111 342"/>
    </justification>
  </clause>

  <clause id="2140">
    <literal><![CDATA[
      R(x * y,L(z,y,x),K(u,u \ 1)) \ (x * ((y * z) * K(u,u \ 1))) = L(z,y,x) * K(u,u \ 1)
    ]]></literal>
    <justification jstring="[para(2112(a,1),568(a,1,2))].">
      <j1 rule="para" parents="2112 568"/>
    </justification>
  </clause>

  <clause id="2141">
    <literal><![CDATA[
      (x * (y \ 1)) * K(y,y \ 1) = x * (1 / y)
    ]]></literal>
    <justification jstring="[para(2096(a,1),2112(a,2,2))].">
      <j1 rule="para" parents="2096 2112"/>
    </justification>
  </clause>

  <clause id="2142">
    <literal><![CDATA[
      (x * y) * K(y,y \ 1) = x * ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(2101(a,1),2112(a,2,2))].">
      <j1 rule="para" parents="2101 2112"/>
    </justification>
  </clause>

  <clause id="2143">
    <literal><![CDATA[
      (x * (1 / (1 / y))) * K(y,y \ 1) = x * y
    ]]></literal>
    <justification jstring="[para(2109(a,1),2112(a,2,2))].">
      <j1 rule="para" parents="2109 2112"/>
    </justification>
  </clause>

  <clause id="2144">
    <literal><![CDATA[
      (x / (y \ 1)) * (1 / y) = x * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(339,a,2141,a),flip(a)].">
      <j1 rule="hyper" parents="339 2141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2145">
    <literal><![CDATA[
      (x * y) * K(T(x,y),T(x,y) \ 1) = y * ((T(x,y) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(583,a,2142,a)].">
      <j1 rule="hyper" parents="583 2142"/>
    </justification>
  </clause>

  <clause id="2146">
    <literal><![CDATA[
      (x / y) * ((y \ 1) \ 1) = x * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(339,a,2142,a),flip(a)].">
      <j1 rule="hyper" parents="339 2142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2147">
    <literal><![CDATA[
      (x * K(y,y \ 1)) / y = x / (1 / (1 / y))
    ]]></literal>
    <justification jstring="[hyper(621,a,2143,a)].">
      <j1 rule="hyper" parents="621 2143"/>
    </justification>
  </clause>

  <clause id="2148">
    <literal><![CDATA[
      x / K(y \ 1,y) = x * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,1899,a(flip),b,2144,a)].">
      <j1 rule="hyper" parents="63 1899 2144"/>
    </justification>
  </clause>

  <clause id="2149">
    <literal><![CDATA[
      (x * K(y,y \ 1)) * K(y \ 1,y) = x
    ]]></literal>
    <justification jstring="[hyper(125,a,2144,a(flip),b,1899,a(flip))].">
      <j1 rule="hyper" parents="125 2144 1899"/>
    </justification>
  </clause>

  <clause id="2151">
    <literal><![CDATA[
      (x * K(y \ 1,y)) * K(y,y \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(269,a,2148,a),flip(a)].">
      <j1 rule="hyper" parents="269 2148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2152">
    <literal><![CDATA[
      (x * K(y \ 1,y)) * K(y,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(2148(a,1),269(a,1))].">
      <j1 rule="para" parents="2148 269"/>
    </justification>
  </clause>

  <clause id="2153">
    <literal><![CDATA[
      x * K(y \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      z * K(y,y \ 1) = x
    ]]></literal>
    <justification jstring="[para(2149(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="2149 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2154">
    <literal><![CDATA[
      (x * K(y,y \ 1)) * y = x * ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(2149(a,1),1901(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2149 1901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2155">
    <literal><![CDATA[
      (x / y) * T(y,y \ 1) = x * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(653,a,2146,a)].">
      <j1 rule="hyper" parents="653 2146"/>
    </justification>
  </clause>

  <clause id="2156">
    <literal><![CDATA[
      T((x / y) * K(y,y \ 1),y) = y \ (x * K(y,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(444,a,2146,a(flip),b,2154,a)].">
      <j1 rule="hyper" parents="444 2146 2154"/>
    </justification>
  </clause>

  <clause id="2157">
    <literal><![CDATA[
      (x * K(y,y \ 1)) / y = (x / y) * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(123,a,2146,a(flip),b,2154,a)].">
      <j1 rule="hyper" parents="123 2146 2154"/>
    </justification>
  </clause>

  <clause id="2158">
    <literal><![CDATA[
      (x / ((y \ 1) \ 1)) * K(y,y \ 1) = x / y
    ]]></literal>
    <justification jstring="[hyper(123,a,12,a(flip),b,2154,a),flip(a)].">
      <j1 rule="hyper" parents="123 12 2154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2159">
    <literal><![CDATA[
      (x * K(y,y \ 1)) \ ((x * y) * K(y,y \ 1)) = y
    ]]></literal>
    <justification jstring="[hyper(121,a,2142,a,b,2154,a)].">
      <j1 rule="hyper" parents="121 2142 2154"/>
    </justification>
  </clause>

  <clause id="2161">
    <literal><![CDATA[
      x * T(K(x,x \ 1),y) = T(x,T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[para(2126(a,1),1703(a,1,2))].">
      <j1 rule="para" parents="2126 1703"/>
    </justification>
  </clause>

  <clause id="2162">
    <literal><![CDATA[
      (x / y) * K(y,y \ 1) = x / (1 / (1 / y))
    ]]></literal>
    <justification jstring="[hyper(63,a,2147,a(flip),b,2157,a),flip(a)].">
      <j1 rule="hyper" parents="63 2147 2157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2163">
    <literal><![CDATA[
      (x / (1 / (1 / y))) / (1 / y) = (x / y) / (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(123,a,2162,a(flip),b,2144,a)].">
      <j1 rule="hyper" parents="123 2162 2144"/>
    </justification>
  </clause>

  <clause id="2164">
    <literal><![CDATA[
      R(T(x,y * K(x,x \ 1)),y,K(x,x \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(2159(a,1),1044(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2159 1044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2165">
    <literal><![CDATA[
      T(x,y * K(x,x \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(2113,a,2164,a)].">
      <j1 rule="hyper" parents="2113 2164"/>
    </justification>
  </clause>

  <clause id="2168">
    <literal><![CDATA[
      T((x * y) / x,K(x \ (x / (((x * y) / x) \ 1)),x)) = (((x * y) / x) \ y) \ y
    ]]></literal>
    <justification jstring="[para(2071(a,2),112(a,1,2))].">
      <j1 rule="para" parents="2071 112"/>
    </justification>
  </clause>

  <clause id="2169">
    <literal><![CDATA[
      K(x \ (x / (x \ (x / y))),x) = x \ ((y * x) / y)
    ]]></literal>
    <justification jstring="[para(861(a,1),2084(a,2,2))].">
      <j1 rule="para" parents="861 2084"/>
    </justification>
  </clause>

  <clause id="2170">
    <literal><![CDATA[
      (x / y) * K(z \ (z / ((x / y) \ (1 / y))),z) = T(x,z) / y
    ]]></literal>
    <justification jstring="[para(12(a,1),2085(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="12 2085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2172">
    <literal><![CDATA[
      K(x,x \ 1) * L(x,y,z) = x * (L(x,y,z) * (1 / x))
    ]]></literal>
    <justification jstring="[hyper(63,a,2043,a(flip),b,2120,a)].">
      <j1 rule="hyper" parents="63 2043 2120"/>
    </justification>
  </clause>

  <clause id="2174">
    <literal><![CDATA[
      T((x / y) * K(y,y \ 1),y) = (y \ x) * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(333,a,2115,a(flip),b,2156,a),flip(a)].">
      <j1 rule="hyper" parents="333 2115 2156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2176">
    <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(2174(a,2),44(a,1))].">
      <j1 rule="para" parents="2174 44"/>
    </justification>
  </clause>

  <clause id="2178">
    <literal><![CDATA[
      x * (K(x,x \ 1) * (x \ y)) = (x * (1 / x)) * y
    ]]></literal>
    <justification jstring="[para(2125(a,1),1913(a,1,2))].">
      <j1 rule="para" parents="2125 1913"/>
    </justification>
  </clause>

  <clause id="2179">
    <literal><![CDATA[
      K(x,x \ 1) * (x \ L(y,1 / x,x)) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(34,a,97,a(flip),b,2178,a),flip(a)].">
      <j1 rule="hyper" parents="34 97 2178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2180">
    <literal><![CDATA[
      x * (K(x,x \ 1) * (x \ y)) = K(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[para(2098(a,2),2178(a,2,1))].">
      <j1 rule="para" parents="2098 2178"/>
    </justification>
  </clause>

  <clause id="2181">
    <literal><![CDATA[
      K(x,x \ 1) * (x \ L(x,y,z)) = L(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(34,a,2172,a(flip),b,2180,a),flip(a)].">
      <j1 rule="hyper" parents="34 2172 2180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2182">
    <literal><![CDATA[
      x * (K(x,x \ 1) * T(y,x)) = K(x,x \ 1) * (y * x)
    ]]></literal>
    <justification jstring="[para(22(a,2),2180(a,1,2,2))].">
      <j1 rule="para" parents="22 2180"/>
    </justification>
  </clause>

  <clause id="2183">
    <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(333,a,1210,a(flip),b,2181,a),flip(a)].">
      <j1 rule="hyper" parents="333 1210 2181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2184">
    <literal><![CDATA[
      x \ K(y,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ 1) * K(y,y \ 1) = z
    ]]></literal>
    <justification jstring="[para(7(a,1),2139(a,1,2))].">
      <j1 rule="para" parents="7 2139"/>
    </justification>
  </clause>

  <clause id="2185">
    <literal><![CDATA[
      K(x \ (x / ((y * x) / y)),x) = (y * K(x \ 1,x)) / y
    ]]></literal>
    <justification jstring="[para(358(a,1),2081(a,2,1,2))].">
      <j1 rule="para" parents="358 2081"/>
    </justification>
  </clause>

  <clause id="2186">
    <literal><![CDATA[
      ((x * y) / x) \ ((x * K(y \ 1,y)) / x) = T(((x * y) / x) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(121,a,2185,a(flip),b,2057,a(flip))].">
      <j1 rule="hyper" parents="121 2185 2057"/>
    </justification>
  </clause>

  <clause id="2187">
    <literal><![CDATA[
      R(1 / x,y,z) / (x \ 1) = x * R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(2105(a,1),2130(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2105 2130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2188">
    <literal><![CDATA[
      (x / y) * R(1 / (x / y),x / y,y) = (y / x) / ((x / y) \ 1)
    ]]></literal>
    <justification jstring="[para(400(a,1),2187(a,1,1)),flip(a)].">
      <j1 rule="para" parents="400 2187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2189">
    <literal><![CDATA[
      (x / y) / ((y / x) \ 1) = (y / x) * (x / y)
    ]]></literal>
    <justification jstring="[para(400(a,1),2188(a,1,2)),flip(a)].">
      <j1 rule="para" parents="400 2188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2190">
    <literal><![CDATA[
      (x / (y \ x)) * ((y \ x) / x) = ((y \ x) / x) / (y \ 1)
    ]]></literal>
    <justification jstring="[para(76(a,1),2189(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="76 2189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2191">
    <literal><![CDATA[
      ((x \ y) / y) / (x \ 1) = x * ((x \ y) / y)
    ]]></literal>
    <justification jstring="[hyper(351,a,2190,a),flip(a)].">
      <j1 rule="hyper" parents="351 2190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2193">
    <literal><![CDATA[
      R(x * ((x \ y) / y),x \ 1,y) = (x \ y) / ((x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(2191(a,1),314(a,1,1))].">
      <j1 rule="para" parents="2191 314"/>
    </justification>
  </clause>

  <clause id="2194">
    <literal><![CDATA[
      R(x * ((x \ y) / y),x,y) = (x \ y) / ((x \ 1) * y)
    ]]></literal>
    <justification jstring="[hyper(1941,a,2193,a)].">
      <j1 rule="hyper" parents="1941 2193"/>
    </justification>
  </clause>

  <clause id="2195">
    <literal><![CDATA[
      (x \ y) / ((x \ 1) * y) != z
    ]]></literal>
    <literal><![CDATA[
      R(x * ((x \ y) / y),x,y) = z
    ]]></literal>
    <justification jstring="[para(2193(a,1),1941(a,1))].">
      <j1 rule="para" parents="2193 1941"/>
    </justification>
  </clause>

  <clause id="2199">
    <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(862(a,1),2075(a,1,2,1))].">
      <j1 rule="para" parents="862 2075"/>
    </justification>
  </clause>

  <clause id="2200">
    <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(142,a,2199,a)].">
      <j1 rule="hyper" parents="142 2199"/>
    </justification>
  </clause>

  <clause id="2201">
    <literal><![CDATA[
      K(T(x / y,T(y,x)),T(y,x)) = x \ (y * T(y \ x,T(y,x)))
    ]]></literal>
    <justification jstring="[hyper(63,a,1285,a(flip),b,2200,a),flip(a)].">
      <j1 rule="hyper" parents="63 1285 2200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2202">
    <literal><![CDATA[
      K(((x / y) * (y / x)) \ (x / y),(x / y) * (y / x)) = (y * (y \ x)) / x
    ]]></literal>
    <justification jstring="[para(1729(a,1),2079(a,2,1,2))].">
      <j1 rule="para" parents="1729 2079"/>
    </justification>
  </clause>

  <clause id="2203">
    <literal><![CDATA[
      K(x \ (x / ((y \ x) / T(x,y))),x) = x / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(363,a,2082,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="363 2082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2204">
    <literal><![CDATA[
      (x \ 1) * (K(x,x \ 1) * ((x \ 1) \ y)) = K(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[para(2129(a,1),2134(a,2,1))].">
      <j1 rule="para" parents="2129 2134"/>
    </justification>
  </clause>

  <clause id="2205">
    <literal><![CDATA[
      (x \ 1) \ (K(x,x \ 1) * y) = K(x,x \ 1) * ((x \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(129,a,2204,a)].">
      <j1 rule="hyper" parents="129 2204"/>
    </justification>
  </clause>

  <clause id="2206">
    <literal><![CDATA[
      K(((x / y) * (y / x)) \ (x / y),(x / y) * (y / x)) = x / x
    ]]></literal>
    <justification jstring="[hyper(363,a,2202,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="363 2202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2207">
    <literal><![CDATA[
      K(((x / y) * (y / x)) \ (x / y),(x / y) * (y / x)) = 1
    ]]></literal>
    <justification jstring="[hyper(333,a,73,a(flip),b,2206,a),flip(a)].">
      <j1 rule="hyper" parents="333 73 2206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2209">
    <literal><![CDATA[
      T(1 / (x / y),(y / x) * (x / y)) = 1 / (x / y)
    ]]></literal>
    <justification jstring="[para(2207(a,1),2072(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2207 2072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2210">
    <literal><![CDATA[
      ((x / y) * (y / x)) \ (x / y) = 1 / (y / x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1489,a(flip),b,2209,a)].">
      <j1 rule="hyper" parents="63 1489 2209"/>
    </justification>
  </clause>

  <clause id="2211">
    <literal><![CDATA[
      K(1 / (x / y),(y / x) * (x / y)) = 1
    ]]></literal>
    <justification jstring="[hyper(55,a,2209,a)].">
      <j1 rule="hyper" parents="55 2209"/>
    </justification>
  </clause>

  <clause id="2213">
    <literal><![CDATA[
      K(1 / x,(y / (x * y)) * ((x * y) / y)) = 1
    ]]></literal>
    <justification jstring="[para(11(a,1),2211(a,1,1,2))].">
      <j1 rule="para" parents="11 2211"/>
    </justification>
  </clause>

  <clause id="2215">
    <literal><![CDATA[
      K(1 / x,(y / (x * y)) * x) = 1
    ]]></literal>
    <justification jstring="[para(11(a,1),2213(a,1,2,2))].">
      <j1 rule="para" parents="11 2213"/>
    </justification>
  </clause>

  <clause id="2216">
    <literal><![CDATA[
      T(1 / x,(y / (x * y)) * x) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(56,a,2215,a)].">
      <j1 rule="hyper" parents="56 2215"/>
    </justification>
  </clause>

  <clause id="2217">
    <literal><![CDATA[
      L(x \ 1,x,y / (x * y)) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(1550,a,2216,a)].">
      <j1 rule="hyper" parents="1550 2216"/>
    </justification>
  </clause>

  <clause id="2219">
    <literal><![CDATA[
      L(x \ 1,x,(x \ y) / y) = 1 / x
    ]]></literal>
    <justification jstring="[para(10(a,1),2217(a,1,3,2))].">
      <j1 rule="para" parents="10 2217"/>
    </justification>
  </clause>

  <clause id="2220">
    <literal><![CDATA[
      L(x \ 1,x,R(1 / x,x,y)) = 1 / x
    ]]></literal>
    <justification jstring="[para(230(a,2),2217(a,1,3))].">
      <j1 rule="para" parents="230 2217"/>
    </justification>
  </clause>

  <clause id="2221">
    <literal><![CDATA[
      (((x \ y) / y) * x) * (1 / x) = (x \ y) / y
    ]]></literal>
    <justification jstring="[hyper(126,a,2219,a(flip),b,227,a(flip))].">
      <j1 rule="hyper" parents="126 2219 227"/>
    </justification>
  </clause>

  <clause id="2222">
    <literal><![CDATA[
      R(1 / x,x,y) / (1 / x) = R(1 / x,x,y) * x
    ]]></literal>
    <justification jstring="[hyper(197,a,2220,a(flip),b,227,a(flip))].">
      <j1 rule="hyper" parents="197 2220 227"/>
    </justification>
  </clause>

  <clause id="2226">
    <literal><![CDATA[
      T(1 / (1 / x),R(1 / x,x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(1583,a,2222,a)].">
      <j1 rule="hyper" parents="1583 2222"/>
    </justification>
  </clause>

  <clause id="2227">
    <literal><![CDATA[
      T(1 / (1 / x),y / (x * y)) = x
    ]]></literal>
    <justification jstring="[para(230(a,1),2226(a,1,2))].">
      <j1 rule="para" parents="230 2226"/>
    </justification>
  </clause>

  <clause id="2228">
    <literal><![CDATA[
      T(x,y / (x * y)) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(2227(a,1),1908(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2227 1908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2229">
    <literal><![CDATA[
      T(x,y / (x * y)) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(333,a,112,a(flip),b,2228,a),flip(a)].">
      <j1 rule="hyper" parents="333 112 2228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2231">
    <literal><![CDATA[
      T(x / y,y / x) = ((x / y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(12(a,1),2229(a,1,2,2))].">
      <j1 rule="para" parents="12 2229"/>
    </justification>
  </clause>

  <clause id="2242">
    <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(863(a,1),1294(a,1,1))].">
      <j1 rule="para" parents="863 1294"/>
    </justification>
  </clause>

  <clause id="2243">
    <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(1077(a,1),2242(a,1,1))].">
      <j1 rule="para" parents="1077 2242"/>
    </justification>
  </clause>

  <clause id="2244">
    <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(1293(a,1),2243(a,1,2))].">
      <j1 rule="para" parents="1293 2243"/>
    </justification>
  </clause>

  <clause id="2245">
    <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(63,a,25,a,b,2244,a)].">
      <j1 rule="hyper" parents="63 25 2244"/>
    </justification>
  </clause>

  <clause id="2246">
    <literal><![CDATA[
      L(x,T(x,y) \ x,T(x,y)) = L(x,T(x,y) \ x,x)
    ]]></literal>
    <justification jstring="[para(1290(a,1),2245(a,1,1))].">
      <j1 rule="para" parents="1290 2245"/>
    </justification>
  </clause>

  <clause id="2247">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ x,x) = L(x,T(x,y) \ x,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1077,a,b,2246,a)].">
      <j1 rule="hyper" parents="63 1077 2246"/>
    </justification>
  </clause>

  <clause id="2248">
    <literal><![CDATA[
      x * L(y,T(y,x) \ y,y) = (y * x) * T(K(x,y),y)
    ]]></literal>
    <justification jstring="[para(2246(a,1),1706(a,1,2))].">
      <j1 rule="para" parents="2246 1706"/>
    </justification>
  </clause>

  <clause id="2249">
    <literal><![CDATA[
      L(x,T(x,y) \ x,x) = (T(x,y) \ x) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,1432,a(flip),b,2247,a),flip(a)].">
      <j1 rule="hyper" parents="63 1432 2247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2250">
    <literal><![CDATA[
      (x * y) * (z * T(z \ L(y \ z,y,x),u)) = (x * (y * T(y \ 1,u))) * z
    ]]></literal>
    <justification jstring="[para(778(a,1),1393(a,1,1)),flip(a)].">
      <j1 rule="para" parents="778 1393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2251">
    <literal><![CDATA[
      (x * y) * ((z \ L(y \ z,y,x)) * z) = (x * (y * T(y \ 1,z))) * z
    ]]></literal>
    <justification jstring="[hyper(595,a,2250,a)].">
      <j1 rule="hyper" parents="595 2250"/>
    </justification>
  </clause>

  <clause id="2252">
    <literal><![CDATA[
      K(x \ 1,x * ((y * x) \ y)) = (x \ 1) * T(x,(y * x) \ y)
    ]]></literal>
    <justification jstring="[para(777(a,1),2053(a,1,2)),flip(a)].">
      <j1 rule="para" parents="777 2053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2253">
    <literal><![CDATA[
      (x * x) \ ((y * z) \ (y * (z * ((x * x) * u)))) = L(u,z * (x * x),y)
    ]]></literal>
    <justification jstring="[para(491(a,1),1218(a,2,1))].">
      <j1 rule="para" parents="491 1218"/>
    </justification>
  </clause>

  <clause id="2254">
    <literal><![CDATA[
      (x * x) \ L((x * x) * y,z,u) = L(y,z * (x * x),u)
    ]]></literal>
    <justification jstring="[para(18(a,2),2253(a,1,2))].">
      <j1 rule="para" parents="18 2253"/>
    </justification>
  </clause>

  <clause id="2255">
    <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(276(a,2),1235(a,1,2,1,1))].">
      <j1 rule="para" parents="276 1235"/>
    </justification>
  </clause>

  <clause id="2256">
    <literal><![CDATA[
      (x * T(x \ y,x)) * (1 / x) = T(y * (1 / x),x)
    ]]></literal>
    <justification jstring="[para(72(a,1),1670(a,1,1)),flip(a)].">
      <j1 rule="para" parents="72 1670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2257">
    <literal><![CDATA[
      ((x \ y) * x) * (1 / x) = T(y * (1 / x),x)
    ]]></literal>
    <justification jstring="[hyper(583,a,2256,a)].">
      <j1 rule="hyper" parents="583 2256"/>
    </justification>
  </clause>

  <clause id="2259">
    <literal><![CDATA[
      T((x * y) * (1 / x),x) = (y * x) * (1 / x)
    ]]></literal>
    <justification jstring="[para(9(a,1),2257(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 2257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2260">
    <literal><![CDATA[
      T(x * (1 / y),y) != z * (1 / y)
    ]]></literal>
    <literal><![CDATA[
      (y \ x) * y = z
    ]]></literal>
    <justification jstring="[para(2257(a,1),44(a,1))].">
      <j1 rule="para" parents="2257 44"/>
    </justification>
  </clause>

  <clause id="2261">
    <literal><![CDATA[
      T((x * y) * (1 / x),x) != z * (1 / x)
    ]]></literal>
    <literal><![CDATA[
      y * x = z
    ]]></literal>
    <justification jstring="[para(2259(a,2),44(a,1))].">
      <j1 rule="para" parents="2259 44"/>
    </justification>
  </clause>

  <clause id="2262">
    <literal><![CDATA[
      ((x * y) / x) * T(((x * y) / x) \ z,u) = (x * (y * T(y \ T(z,x),u))) / x
    ]]></literal>
    <justification jstring="[para(22(a,2),1732(a,1,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="22 1732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2263">
    <literal><![CDATA[
      (x \ R(x,y,z)) * ((x \ 1) * u) = (x \ 1) * ((x \ R(x,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(1313(a,1),1743(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1313 1743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2264">
    <literal><![CDATA[
      (x \ 1) * ((x \ R(x,y,z)) \ 1) = (x \ R(x,y,z)) \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(121,a,69,a(flip),b,2263,a),flip(a)].">
      <j1 rule="hyper" parents="121 69 2263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2265">
    <literal><![CDATA[
      (x \ L(x,y,z)) * ((x \ 1) * u) = (x \ 1) * ((x \ L(x,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(1264(a,1),1751(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1264 1751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2266">
    <literal><![CDATA[
      (x \ 1) * ((x \ L(x,y,z)) \ 1) = (x \ L(x,y,z)) \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(121,a,69,a(flip),b,2265,a),flip(a)].">
      <j1 rule="hyper" parents="121 69 2265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2267">
    <literal><![CDATA[
      ((x / y) * ((z * ((x / y) \ u)) / z)) * y = x * ((z * (x \ (u * y))) / z)
    ]]></literal>
    <justification jstring="[para(12(a,1),1987(a,2,2,1,2,1))].">
      <j1 rule="para" parents="12 1987"/>
    </justification>
  </clause>

  <clause id="2268">
    <literal><![CDATA[
      (x * ((y * (x \ (z * u))) / y)) / u = (x / u) * ((y * ((x / u) \ z)) / y)
    ]]></literal>
    <justification jstring="[hyper(138,a,2267,a)].">
      <j1 rule="hyper" parents="138 2267"/>
    </justification>
  </clause>

  <clause id="2269">
    <literal><![CDATA[
      (x / y) * ((z * ((x / y) \ 1)) / z) = (x * ((z * (x \ y)) / z)) / y
    ]]></literal>
    <justification jstring="[para(7(a,1),2268(a,1,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 2268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2270">
    <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(2098(a,2),2123(a,1,2,1,1))].">
      <j1 rule="para" parents="2098 2123"/>
    </justification>
  </clause>

  <clause id="2271">
    <literal><![CDATA[
      K(x \ 1,x) * ((1 / x) \ L(1 / x,y,z)) = L(x \ 1,y,z) / (1 / x)
    ]]></literal>
    <justification jstring="[para(2100(a,1),2183(a,1,1))].">
      <j1 rule="para" parents="2100 2183"/>
    </justification>
  </clause>

  <clause id="2272">
    <literal><![CDATA[
      K(x \ 1,x) * (x * L(x \ 1,y,z)) = L(x \ 1,y,z) / (1 / x)
    ]]></literal>
    <justification jstring="[para(1030(a,1),2271(a,1,2))].">
      <j1 rule="para" parents="1030 2271"/>
    </justification>
  </clause>

  <clause id="2273">
    <literal><![CDATA[
      K(x \ 1,x) * (x * L(x \ 1,x,y)) = (x * ((y * x) \ y)) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,1916,a,b,2272,a),flip(a)].">
      <j1 rule="hyper" parents="333 1916 2272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2274">
    <literal><![CDATA[
      ((x \ 1) * x) * (x * L(x \ 1,x,y)) = (x * ((y * x) \ y)) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(276(a,1),2273(a,1,1))].">
      <j1 rule="para" parents="276 2273"/>
    </justification>
  </clause>

  <clause id="2275">
    <literal><![CDATA[
      ((x \ 1) * (x * L(x \ 1,x,y))) * x = (x * ((y * x) \ y)) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1752,a,b,2274,a)].">
      <j1 rule="hyper" parents="63 1752 2274"/>
    </justification>
  </clause>

  <clause id="2276">
    <literal><![CDATA[
      (x \ 1) * (x * L(x \ 1,x,y)) = L(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(35,a,1960,a(flip),b,2275,a),flip(a)].">
      <j1 rule="hyper" parents="35 1960 2275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2277">
    <literal><![CDATA[
      (x * y) \ x = (y \ 1) * (y * L(y \ 1,y,x))
    ]]></literal>
    <justification jstring="[hyper(333,a,227,a(flip),b,2276,a)].">
      <j1 rule="hyper" parents="333 227 2276"/>
    </justification>
  </clause>

  <clause id="2278">
    <literal><![CDATA[
      (x \ 1) * (x * ((y * x) \ y)) = (y * x) \ y
    ]]></literal>
    <justification jstring="[para(227(a,1),2277(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="227 2277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2279">
    <literal><![CDATA[
      (x \ 1) \ ((y * x) \ y) = x * ((y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(129,a,2278,a)].">
      <j1 rule="hyper" parents="129 2278"/>
    </justification>
  </clause>

  <clause id="2280">
    <literal><![CDATA[
      K(x \ 1,x * ((y * x) \ y)) = 1
    ]]></literal>
    <justification jstring="[hyper(120,a,2278,a(flip),b,2054,a),flip(a)].">
      <j1 rule="hyper" parents="120 2278 2054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2281">
    <literal><![CDATA[
      T(x,(y * x) \ y) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(121,a,2280,a(flip),b,2252,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="121 2280 2252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2282">
    <literal><![CDATA[
      T(x,(y * x) \ y) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(333,a,112,a,b,2281,a),flip(a)].">
      <j1 rule="hyper" parents="333 112 2281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2283">
    <literal><![CDATA[
      T(x \ y,y \ x) = ((x \ y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(10(a,1),2281(a,1,2,1))].">
      <j1 rule="para" parents="10 2281"/>
    </justification>
  </clause>

  <clause id="2284">
    <literal><![CDATA[
      (x * y) * K(y,y \ 1) = x * T(y,(z * y) \ z)
    ]]></literal>
    <justification jstring="[para(2281(a,2),2142(a,2,2))].">
      <j1 rule="para" parents="2281 2142"/>
    </justification>
  </clause>

  <clause id="2285">
    <literal><![CDATA[
      T(K(x,y),(x * y) \ (y * x)) = T(K(x,y),K(x,y) \ 1)
    ]]></literal>
    <justification jstring="[para(88(a,1),2282(a,1,2,1))].">
      <j1 rule="para" parents="88 2282"/>
    </justification>
  </clause>

  <clause id="2286">
    <literal><![CDATA[
      1 / T(x \ y,y \ x) = (x \ y) \ 1
    ]]></literal>
    <justification jstring="[hyper(197,a,2283,a,b,xx)].">
      <j1 rule="hyper" parents="197 2283"/>
    </justification>
  </clause>

  <clause id="2287">
    <literal><![CDATA[
      T(x \ (x / y),y) = ((x \ (x / y)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(79(a,1),2283(a,1,2))].">
      <j1 rule="para" parents="79 2283"/>
    </justification>
  </clause>

  <clause id="2289">
    <literal><![CDATA[
      x * K((x \ y) \ 1,x \ y) = y * (((y \ x) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(2283(a,1),1287(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2283 1287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2290">
    <literal><![CDATA[
      T(K(x \ (x / (y \ 1)),x),T(y,x) \ y) = ((y \ T(y,x)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(2062(a,2),2283(a,1,1))].">
      <j1 rule="para" parents="2062 2283"/>
    </justification>
  </clause>

  <clause id="2291">
    <literal><![CDATA[
      K(x \ (x / T(y \ x,x \ y)),x) = T(K(x \ y,x),(y \ x) \ 1)
    ]]></literal>
    <justification jstring="[para(2283(a,2),2092(a,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2283 2092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2292">
    <literal><![CDATA[
      1 / T((x * y) \ x,y) = ((x * y) \ x) \ 1
    ]]></literal>
    <justification jstring="[para(9(a,1),2286(a,1,2,2))].">
      <j1 rule="para" parents="9 2286"/>
    </justification>
  </clause>

  <clause id="2293">
    <literal><![CDATA[
      L(x * ((y * x) \ y),x \ 1,y * x) = ((y * x) * (x \ 1)) \ y
    ]]></literal>
    <justification jstring="[para(2279(a,1),311(a,1,1))].">
      <j1 rule="para" parents="2279 311"/>
    </justification>
  </clause>

  <clause id="2294">
    <literal><![CDATA[
      T(K(x,y),K(x,y) \ 1) = T(K(x,y),K(y,x))
    ]]></literal>
    <justification jstring="[para(16(a,2),2285(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16 2285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2295">
    <literal><![CDATA[
      T(K(x,y),K(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      (K(x,y) \ 1) \ 1 = z
    ]]></literal>
    <justification jstring="[para(2294(a,1),432(a,1))].">
      <j1 rule="para" parents="2294 432"/>
    </justification>
  </clause>

  <clause id="2296">
    <literal><![CDATA[
      (K(x,y) \ 1) \ 1 = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(2295,a,2004,a)].">
      <j1 rule="hyper" parents="2295 2004"/>
    </justification>
  </clause>

  <clause id="2297">
    <literal><![CDATA[
      1 / (1 / K(x,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(2296(a,1),193(a,1,2,2))].">
      <j1 rule="para" parents="2296 193"/>
    </justification>
  </clause>

  <clause id="2298">
    <literal><![CDATA[
      L(x * ((y * x) \ y),x \ 1,y * x) = R(y,x,x \ 1) \ y
    ]]></literal>
    <justification jstring="[para(385(a,1),2293(a,2,1))].">
      <j1 rule="para" parents="385 2293"/>
    </justification>
  </clause>

  <clause id="2299">
    <literal><![CDATA[
      T(K(x \ y,x),(y \ x) \ 1) = T(K(x \ y,x),x \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,2091,a(flip),b,2291,a),flip(a)].">
      <j1 rule="hyper" parents="63 2091 2291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2300">
    <literal><![CDATA[
      T(K(x \ (x * y),x),x \ (x * y)) = T(K(y,x),((x * y) \ x) \ 1)
    ]]></literal>
    <justification jstring="[para(9(a,1),2299(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 2299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2301">
    <literal><![CDATA[
      T(K(x,y),((y * x) \ y) \ 1) = T(K(x,y),y \ (y * x))
    ]]></literal>
    <justification jstring="[para(9(a,1),2300(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 2300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2302">
    <literal><![CDATA[
      T(K(x,y),((y * x) \ y) \ 1) = T(K(x,y),x)
    ]]></literal>
    <justification jstring="[para(9(a,1),2301(a,2,2))].">
      <j1 rule="para" parents="9 2301"/>
    </justification>
  </clause>

  <clause id="2304">
    <literal><![CDATA[
      K(x \ 1,x) * T(K(x \ 1,x) \ y,z) = (x \ T(x * (y / x),z)) * x
    ]]></literal>
    <justification jstring="[hyper(333,a,1362,a(flip),b,2255,a),flip(a)].">
      <j1 rule="hyper" parents="333 1362 2255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2305">
    <literal><![CDATA[
      K(x,x \ 1) * T(K(x,x \ 1) \ y,z) = x * (T((x \ y) * x,z) / x)
    ]]></literal>
    <justification jstring="[para(1648(a,1),2270(a,2,2))].">
      <j1 rule="para" parents="1648 2270"/>
    </justification>
  </clause>

  <clause id="2306">
    <literal><![CDATA[
      K(x,x \ 1) * T(K(x,x \ 1) \ y,x) = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,1400,a(flip),b,2305,a),flip(a)].">
      <j1 rule="hyper" parents="333 1400 2305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2307">
    <literal><![CDATA[
      T(K(x,x \ 1) * y,x) = K(x,x \ 1) * T(y,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),2306(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 2306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2308">
    <literal><![CDATA[
      x * T(K(x,x \ 1) * y,x) = K(x,x \ 1) * (y * x)
    ]]></literal>
    <justification jstring="[para(2307(a,2),2182(a,1,2))].">
      <j1 rule="para" parents="2307 2182"/>
    </justification>
  </clause>

  <clause id="2309">
    <literal><![CDATA[
      (K(x,x \ 1) * y) * x = K(x,x \ 1) * (y * x)
    ]]></literal>
    <justification jstring="[hyper(300,a,2308,a)].">
      <j1 rule="hyper" parents="300 2308"/>
    </justification>
  </clause>

  <clause id="2310">
    <literal><![CDATA[
      L(x,y,K(x,x \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(501,a,2309,a)].">
      <j1 rule="hyper" parents="501 2309"/>
    </justification>
  </clause>

  <clause id="2311">
    <literal><![CDATA[
      L(1 / x,y,K(x \ 1,x)) = 1 / x
    ]]></literal>
    <justification jstring="[para(2100(a,1),2310(a,1,3))].">
      <j1 rule="para" parents="2100 2310"/>
    </justification>
  </clause>

  <clause id="2312">
    <literal><![CDATA[
      L(T(1 / x,y),z,K(x \ 1,x)) = T(1 / x,y)
    ]]></literal>
    <justification jstring="[para(2311(a,1),25(a,2,1))].">
      <j1 rule="para" parents="2311 25"/>
    </justification>
  </clause>

  <clause id="2313">
    <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(333,a,458,a(flip),b,775,a),flip(a)].">
      <j1 rule="hyper" parents="333 458 775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2314">
    <literal><![CDATA[
      x * (K(x,y) * T(K(x,y) \ y,z)) = (T(y,z) * x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,939,a(flip),b,2313,a)].">
      <j1 rule="hyper" parents="63 939 2313"/>
    </justification>
  </clause>

  <clause id="2315">
    <literal><![CDATA[
      (T(x,K(y,x)) * y) * K(y,x) = y * ((K(y,x) \ x) * K(y,x))
    ]]></literal>
    <justification jstring="[hyper(595,a,2314,a),flip(a)].">
      <j1 rule="hyper" parents="595 2314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2316">
    <literal><![CDATA[
      (x * K(y \ 1,y)) \ (x * (y * L(z,y,y))) = L(L(y * z,y,y \ 1),(y \ 1) * y,x)
    ]]></literal>
    <justification jstring="[para(276(a,2),1220(a,1,1,2))].">
      <j1 rule="para" parents="276 1220"/>
    </justification>
  </clause>

  <clause id="2317">
    <literal><![CDATA[
      K(x \ (x / R(y,z,u)),x) = (((y * z) * T((y * z) \ z,x)) * u) / (z * u)
    ]]></literal>
    <justification jstring="[para(1392(a,1),2080(a,2,1))].">
      <j1 rule="para" parents="1392 2080"/>
    </justification>
  </clause>

  <clause id="2318">
    <literal><![CDATA[
      K(x \ (x / R(y,z,u)),x) = (((y * T(y \ 1,x)) * z) * u) / (z * u)
    ]]></literal>
    <justification jstring="[para(1363(a,1),2317(a,2,1,1))].">
      <j1 rule="para" parents="1363 2317"/>
    </justification>
  </clause>

  <clause id="2319">
    <literal><![CDATA[
      R(x * T(x \ 1,y),z,u) = K(y \ (y / R(x,z,u)),y)
    ]]></literal>
    <justification jstring="[hyper(333,a,20,a,b,2318,a)].">
      <j1 rule="hyper" parents="333 20 2318"/>
    </justification>
  </clause>

  <clause id="2320">
    <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(333,a,2057,a(flip),b,2319,a)].">
      <j1 rule="hyper" parents="333 2057 2319"/>
    </justification>
  </clause>

  <clause id="2321">
    <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(1317(a,1),2319(a,2,1,2))].">
      <j1 rule="para" parents="1317 2319"/>
    </justification>
  </clause>

  <clause id="2322">
    <literal><![CDATA[
      R(x * T(x \ 1,R(x,y,z)),y,z) != u * R(x,y,z)
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) \ 1 = u
    ]]></literal>
    <justification jstring="[para(2320(a,1),256(a,1))].">
      <j1 rule="para" parents="2320 256"/>
    </justification>
  </clause>

  <clause id="2323">
    <literal><![CDATA[
      (x * y) * K(z \ (z / L(u,y,x)),z) = x * ((y * u) * T((y * u) \ y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,939,a(flip),b,2088,a),flip(a)].">
      <j1 rule="hyper" parents="63 939 2088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2324">
    <literal><![CDATA[
      (x * y) * K(z \ (z / L(u,y,x)),z) = x * (y * (u * T(u \ 1,z)))
    ]]></literal>
    <justification jstring="[para(778(a,1),2323(a,2,2))].">
      <j1 rule="para" parents="778 2323"/>
    </justification>
  </clause>

  <clause id="2325">
    <literal><![CDATA[
      L(x * T(x \ 1,y),z,u) = K(y \ (y / L(x,z,u)),y)
    ]]></literal>
    <justification jstring="[hyper(501,a,2324,a)].">
      <j1 rule="hyper" parents="501 2324"/>
    </justification>
  </clause>

  <clause id="2326">
    <literal><![CDATA[
      (x * y) * (L(z,y,x) * T(L(z,y,x) \ 1,u)) = x * (y * (z * T(z \ 1,u)))
    ]]></literal>
    <justification jstring="[para(2057(a,1),2324(a,1,2))].">
      <j1 rule="para" parents="2057 2324"/>
    </justification>
  </clause>

  <clause id="2327">
    <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(333,a,2057,a(flip),b,2325,a)].">
      <j1 rule="hyper" parents="333 2057 2325"/>
    </justification>
  </clause>

  <clause id="2328">
    <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(73(a,1),2325(a,2,1,2))].">
      <j1 rule="para" parents="73 2325"/>
    </justification>
  </clause>

  <clause id="2329">
    <literal><![CDATA[
      L(1 / (x \ y),x \ y,x) * ((y \ x) \ 1) = (y \ x) \ L(1 / (x \ y),x \ y,x)
    ]]></literal>
    <justification jstring="[para(931(a,1),1267(a,1,2)),flip(a)].">
      <j1 rule="para" parents="931 1267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2330">
    <literal><![CDATA[
      (((x * y) \ x) \ K(y,x)) / (((x * y) \ x) \ 1) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(1279,a,1281,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="1279 1281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2331">
    <literal><![CDATA[
      T(K(x,y),((y * x) \ y) \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      (((y * x) \ y) \ 1) \ (((y * x) \ y) \ K(x,y)) = z
    ]]></literal>
    <justification jstring="[para(2330(a,1),423(a,1,1))].">
      <j1 rule="para" parents="2330 423"/>
    </justification>
  </clause>

  <clause id="2332">
    <literal><![CDATA[
      T(K(x,y),x) != z
    ]]></literal>
    <literal><![CDATA[
      (((y * x) \ y) \ 1) \ (((y * x) \ y) \ K(x,y)) = z
    ]]></literal>
    <justification jstring="[para(2302(a,1),2331(a,1))].">
      <j1 rule="para" parents="2302 2331"/>
    </justification>
  </clause>

  <clause id="2333">
    <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(276(a,2),1502(a,1,2,1,1))].">
      <j1 rule="para" parents="276 1502"/>
    </justification>
  </clause>

  <clause id="2334">
    <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(276(a,2),1506(a,1,2,1,1))].">
      <j1 rule="para" parents="276 1506"/>
    </justification>
  </clause>

  <clause id="2335">
    <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(89(a,1),1809(a,1,1))].">
      <j1 rule="para" parents="89 1809"/>
    </justification>
  </clause>

  <clause id="2336">
    <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(89(a,1),2335(a,1,2,1,1))].">
      <j1 rule="para" parents="89 2335"/>
    </justification>
  </clause>

  <clause id="2337">
    <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(2327(a,1),2090(a,1,1))].">
      <j1 rule="para" parents="2327 2090"/>
    </justification>
  </clause>

  <clause id="2338">
    <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),2337(a,1,1,1))].">
      <j1 rule="para" parents="358 2337"/>
    </justification>
  </clause>

  <clause id="2339">
    <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(1260(a,1),2338(a,1,2))].">
      <j1 rule="para" parents="1260 2338"/>
    </justification>
  </clause>

  <clause id="2340">
    <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(63,a,25,a,b,2339,a)].">
      <j1 rule="hyper" parents="63 25 2339"/>
    </justification>
  </clause>

  <clause id="2341">
    <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(1268(a,1),2340(a,2,1))].">
      <j1 rule="para" parents="1268 2340"/>
    </justification>
  </clause>

  <clause id="2342">
    <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(333,a,1601,a(flip),b,2333,a),flip(a)].">
      <j1 rule="hyper" parents="333 1601 2333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2343">
    <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(333,a,1569,a(flip),b,2334,a),flip(a)].">
      <j1 rule="hyper" parents="333 1569 2334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2344">
    <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(1760(a,1),2342(a,2,1))].">
      <j1 rule="para" parents="1760 2342"/>
    </justification>
  </clause>

  <clause id="2345">
    <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(1312(a,1),2343(a,2,1))].">
      <j1 rule="para" parents="1312 2343"/>
    </justification>
  </clause>

  <clause id="2346">
    <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(22(a,2),1600(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="22 1600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2347">
    <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(252(a,1),2346(a,2,2))].">
      <j1 rule="para" parents="252 2346"/>
    </justification>
  </clause>

  <clause id="2348">
    <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(79(a,1),1250(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="79 1250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2349">
    <literal><![CDATA[
      x * T(x \ T((1 / x) \ 1,y),(1 / x) \ 1) = (1 / x) \ (x \ T(x,y))
    ]]></literal>
    <justification jstring="[para(79(a,1),2348(a,2,2,2,1))].">
      <j1 rule="para" parents="79 2348"/>
    </justification>
  </clause>

  <clause id="2350">
    <literal><![CDATA[
      x * T(x \ T(x,y),(1 / x) \ 1) = (1 / x) \ (x \ T(x,y))
    ]]></literal>
    <justification jstring="[para(79(a,1),2349(a,1,2,1,2,1))].">
      <j1 rule="para" parents="79 2349"/>
    </justification>
  </clause>

  <clause id="2351">
    <literal><![CDATA[
      (1 / x) \ (x \ T(x,y)) = x * T(x \ T(x,y),x)
    ]]></literal>
    <justification jstring="[para(79(a,1),2350(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="79 2350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2352">
    <literal><![CDATA[
      (1 / x) \ (x \ T(x,y)) = (x \ T(x,y)) * x
    ]]></literal>
    <justification jstring="[hyper(333,a,111,a(flip),b,2351,a),flip(a)].">
      <j1 rule="hyper" parents="333 111 2351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2356">
    <literal><![CDATA[
      (x * y) \ (x * ((y * z) * K(u,u \ 1))) = L(z,y,x) * K(u,u \ 1)
    ]]></literal>
    <justification jstring="[para(2110(a,1),2140(a,1,1))].">
      <j1 rule="para" parents="2110 2140"/>
    </justification>
  </clause>

  <clause id="2358">
    <literal><![CDATA[
      (x * y) \ (x * (y * (z * K(u,u \ 1)))) = L(z,y,x) * K(u,u \ 1)
    ]]></literal>
    <justification jstring="[para(2112(a,1),2356(a,1,2,2))].">
      <j1 rule="para" parents="2112 2356"/>
    </justification>
  </clause>

  <clause id="2359">
    <literal><![CDATA[
      L(x * K(y,y \ 1),z,u) = L(x,z,u) * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(504,a,2358,a)].">
      <j1 rule="hyper" parents="504 2358"/>
    </justification>
  </clause>

  <clause id="2360">
    <literal><![CDATA[
      x \ L(y * K(z,z \ 1),u,w) = (x \ L(y,u,w)) * K(z,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(121,a,2359,a,b,2111,a)].">
      <j1 rule="hyper" parents="121 2359 2111"/>
    </justification>
  </clause>

  <clause id="2361">
    <literal><![CDATA[
      L(x \ 1,y,z) * K(x,x \ 1) = L(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(2096(a,1),2359(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2096 2359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2362">
    <literal><![CDATA[
      ((x \ y) \ 1) * ((((x \ y) \ 1) \ (y \ x)) / (y \ x)) = L(1 / (y \ x),y \ x,y) * ((x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(890(a,1),1765(a,2,1))].">
      <j1 rule="para" parents="890 1765"/>
    </justification>
  </clause>

  <clause id="2363">
    <literal><![CDATA[
      ((x \ y) \ 1) * ((((x \ y) \ 1) \ (y \ x)) / (y \ x)) = (x \ y) \ L(1 / (y \ x),y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,2329,a(flip),b,2362,a),flip(a)].">
      <j1 rule="hyper" parents="333 2329 2362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2364">
    <literal><![CDATA[
      ((x \ y) \ 1) * ((((x \ y) \ 1) \ (y \ x)) / (y \ x)) = K(y \ x,((x \ y) * (y \ x)) / (y \ x))
    ]]></literal>
    <justification jstring="[para(1478(a,1),1766(a,2,2,1))].">
      <j1 rule="para" parents="1478 1766"/>
    </justification>
  </clause>

  <clause id="2365">
    <literal><![CDATA[
      ((x \ y) \ 1) * ((((x \ y) \ 1) \ (y \ x)) / (y \ x)) = K(y \ x,x \ y)
    ]]></literal>
    <justification jstring="[para(11(a,1),2364(a,2,2))].">
      <j1 rule="para" parents="11 2364"/>
    </justification>
  </clause>

  <clause id="2366">
    <literal><![CDATA[
      (x \ y) * K(y \ x,x \ y) = L(1 / (y \ x),y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(126,a,2365,a(flip),b,2363,a(flip))].">
      <j1 rule="hyper" parents="126 2365 2363"/>
    </justification>
  </clause>

  <clause id="2368">
    <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(1078(a,1),2017(a,2,2,1))].">
      <j1 rule="para" parents="1078 2017"/>
    </justification>
  </clause>

  <clause id="2369">
    <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(1567(a,1),2368(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1567 2368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2370">
    <literal><![CDATA[
      K(T(x,y),1 / T(x,z)) = T(K(T(x,y),1 / x),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,1753,a(flip),b,2369,a)].">
      <j1 rule="hyper" parents="63 1753 2369"/>
    </justification>
  </clause>

  <clause id="2371">
    <literal><![CDATA[
      K(T(x,y),T(x,y) \ 1) = T(K(T(x,y),1 / x),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,2094,a(flip),b,2370,a)].">
      <j1 rule="hyper" parents="63 2094 2370"/>
    </justification>
  </clause>

  <clause id="2372">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) / x) \ (1 / x)) = K(T(x,y),T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(333,a,1976,a,b,2371,a)].">
      <j1 rule="hyper" parents="333 1976 2371"/>
    </justification>
  </clause>

  <clause id="2373">
    <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(2371(a,2),49(a,1)),flip(a)].">
      <j1 rule="para" parents="2371 49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2374">
    <literal><![CDATA[
      (T(x,y) / x) \ (1 / x) = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(34,a,2098,a(flip),b,2372,a),flip(a)].">
      <j1 rule="hyper" parents="34 2098 2372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2375">
    <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(281(a,1),2374(a,1,2))].">
      <j1 rule="para" parents="281 2374"/>
    </justification>
  </clause>

  <clause id="2376">
    <literal><![CDATA[
      (x \ T(x,y)) \ (x \ 1) = 1 / T(T(x,x \ 1),y)
    ]]></literal>
    <justification jstring="[para(1845(a,1),2375(a,1,1))].">
      <j1 rule="para" parents="1845 2375"/>
    </justification>
  </clause>

  <clause id="2377">
    <literal><![CDATA[
      1 / T(T(x,x \ 1),y) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(1806,a,2376,a),flip(a)].">
      <j1 rule="hyper" parents="1806 2376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2378">
    <literal><![CDATA[
      T(T(x,x \ 1),y) = (T(x,y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(192,a,2377,a),flip(a)].">
      <j1 rule="hyper" parents="192 2377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2379">
    <literal><![CDATA[
      1 / T((x \ 1) \ 1,y) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[para(112(a,1),2377(a,1,2,1))].">
      <j1 rule="para" parents="112 2377"/>
    </justification>
  </clause>

  <clause id="2381">
    <literal><![CDATA[
      T(1 / (1 / x),y) \ 1 = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[para(357(a,1),2377(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="357 2377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2382">
    <literal><![CDATA[
      T((x \ 1) \ 1,y) = (T(x,y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,694,a(flip),b,2378,a)].">
      <j1 rule="hyper" parents="63 694 2378"/>
    </justification>
  </clause>

  <clause id="2383">
    <literal><![CDATA[
      (T(1 / x,y) \ 1) \ 1 = T(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(332(a,1),2378(a,1,1)),flip(a)].">
      <j1 rule="para" parents="332 2378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2384">
    <literal><![CDATA[
      1 / (1 / T(x,y)) = T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[hyper(198,a,2381,a)].">
      <j1 rule="hyper" parents="198 2381"/>
    </justification>
  </clause>

  <clause id="2385">
    <literal><![CDATA[
      T(1 / (1 / (x \ y)),y \ x) = x \ y
    ]]></literal>
    <justification jstring="[hyper(39,a,2286,a(flip),b,2381,a),flip(a)].">
      <j1 rule="hyper" parents="39 2286 2381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2386">
    <literal><![CDATA[
      x * ((T(y,x) \ 1) \ 1) = ((y \ 1) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(126,a,2382,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="126 2382 22"/>
    </justification>
  </clause>

  <clause id="2387">
    <literal><![CDATA[
      T(((x / y) \ 1) \ 1,y) = ((y \ x) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(113(a,1),2382(a,2,1,1))].">
      <j1 rule="para" parents="113 2382"/>
    </justification>
  </clause>

  <clause id="2388">
    <literal><![CDATA[
      (x / T(y,z)) * T((y \ 1) \ 1,z) = x * K(T(y,z),T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(2382(a,2),2146(a,1,2))].">
      <j1 rule="para" parents="2382 2146"/>
    </justification>
  </clause>

  <clause id="2389">
    <literal><![CDATA[
      T(1 / (1 / (x / y)),y) = 1 / (1 / (y \ x))
    ]]></literal>
    <justification jstring="[para(113(a,1),2384(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="113 2384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2390">
    <literal><![CDATA[
      T(1 / (1 / K(x \ (x / (y \ 1)),x)),T(y,x) \ y) = y \ T(y,x)
    ]]></literal>
    <justification jstring="[para(2062(a,2),2385(a,1,1,2,2))].">
      <j1 rule="para" parents="2062 2385"/>
    </justification>
  </clause>

  <clause id="2391">
    <literal><![CDATA[
      T(x,T(x,y) \ 1) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(780,a,2386,a)].">
      <j1 rule="hyper" parents="780 2386"/>
    </justification>
  </clause>

  <clause id="2392">
    <literal><![CDATA[
      (((x / y) \ 1) \ 1) * y = y * (((y \ x) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(113(a,1),2386(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="113 2386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2393">
    <literal><![CDATA[
      T(x,T(x,y) \ 1) = x * K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(333,a,2101,a,b,2391,a),flip(a)].">
      <j1 rule="hyper" parents="333 2101 2391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2394">
    <literal><![CDATA[
      T(K(x,x \ 1),y) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(34,a,2161,a,b,2393,a(flip))].">
      <j1 rule="hyper" parents="34 2161 2393"/>
    </justification>
  </clause>

  <clause id="2395">
    <literal><![CDATA[
      K(T(x,y),T(x,y) \ 1) = K(T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[hyper(2373,a,2394,a),flip(a)].">
      <j1 rule="hyper" parents="2373 2394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2396">
    <literal><![CDATA[
      T(x,K(y,y \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(54,a,2394,a)].">
      <j1 rule="hyper" parents="54 2394"/>
    </justification>
  </clause>

  <clause id="2397">
    <literal><![CDATA[
      K(x,x \ 1) * y = y * K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(126,a,2394,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="126 2394 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2398">
    <literal><![CDATA[
      T(x,y) \ K(x,x \ 1) = (T(x,y) \ x) / x
    ]]></literal>
    <justification jstring="[hyper(121,a,2394,a(flip),b,2126,a)].">
      <j1 rule="hyper" parents="121 2394 2126"/>
    </justification>
  </clause>

  <clause id="2399">
    <literal><![CDATA[
      x * K(y,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,y \ 1) * x = z
    ]]></literal>
    <justification jstring="[para(2394(a,1),300(a,1,2))].">
      <j1 rule="para" parents="2394 300"/>
    </justification>
  </clause>

  <clause id="2403">
    <literal><![CDATA[
      K(x,x \ 1) * y != z
    ]]></literal>
    <literal><![CDATA[
      y * K(x,x \ 1) = z
    ]]></literal>
    <justification jstring="[para(2396(a,1),300(a,1,2))].">
      <j1 rule="para" parents="2396 300"/>
    </justification>
  </clause>

  <clause id="2404">
    <literal><![CDATA[
      T(x,K(y,1 / y)) = x
    ]]></literal>
    <justification jstring="[para(2094(a,2),2396(a,1,2))].">
      <j1 rule="para" parents="2094 2396"/>
    </justification>
  </clause>

  <clause id="2405">
    <literal><![CDATA[
      T(x,y * (1 / y)) = x
    ]]></literal>
    <justification jstring="[para(2098(a,1),2396(a,1,2))].">
      <j1 rule="para" parents="2098 2396"/>
    </justification>
  </clause>

  <clause id="2406">
    <literal><![CDATA[
      T(x,K(y \ 1,y)) = x
    ]]></literal>
    <justification jstring="[para(2100(a,1),2396(a,1,2))].">
      <j1 rule="para" parents="2100 2396"/>
    </justification>
  </clause>

  <clause id="2407">
    <literal><![CDATA[
      T(x,L(K(y,y \ 1),z,u)) = x
    ]]></literal>
    <justification jstring="[para(2136(a,2),2396(a,1,2))].">
      <j1 rule="para" parents="2136 2396"/>
    </justification>
  </clause>

  <clause id="2408">
    <literal><![CDATA[
      K(x,1 / x) * y = y * K(x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(2261,a,2404,a),flip(a)].">
      <j1 rule="hyper" parents="2261 2404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2409">
    <literal><![CDATA[
      (x * (1 / x)) * y = y * (x * (1 / x))
    ]]></literal>
    <justification jstring="[hyper(2261,a,2405,a),flip(a)].">
      <j1 rule="hyper" parents="2261 2405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2410">
    <literal><![CDATA[
      x / (y * (1 / y)) = (y * (1 / y)) \ x
    ]]></literal>
    <justification jstring="[hyper(2176,a,2405,a),flip(a)].">
      <j1 rule="hyper" parents="2176 2405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2411">
    <literal><![CDATA[
      T(x,(y \ 1) * y) = x
    ]]></literal>
    <justification jstring="[para(76(a,1),2405(a,1,2,2))].">
      <j1 rule="para" parents="76 2405"/>
    </justification>
  </clause>

  <clause id="2412">
    <literal><![CDATA[
      K(x \ 1,x) * y = y * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(2261,a,2406,a),flip(a)].">
      <j1 rule="hyper" parents="2261 2406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2413">
    <literal><![CDATA[
      T(K(x \ 1,x),y) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(54,a,2406,a)].">
      <j1 rule="hyper" parents="54 2406"/>
    </justification>
  </clause>

  <clause id="2414">
    <literal><![CDATA[
      (x * K(y \ 1,y)) / x = K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(197,a,2406,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="197 2406 22"/>
    </justification>
  </clause>

  <clause id="2416">
    <literal><![CDATA[
      K(x \ 1,x) * y != z
    ]]></literal>
    <literal><![CDATA[
      y * K(x \ 1,x) = z
    ]]></literal>
    <justification jstring="[para(2406(a,1),300(a,1,2))].">
      <j1 rule="para" parents="2406 300"/>
    </justification>
  </clause>

  <clause id="2417">
    <literal><![CDATA[
      x * (K(y \ 1,y) * z) = x * (z * K(y \ 1,y))
    ]]></literal>
    <justification jstring="[para(2406(a,1),235(a,1,2,2))].">
      <j1 rule="para" parents="2406 235"/>
    </justification>
  </clause>

  <clause id="2418">
    <literal><![CDATA[
      ((x \ 1) * x) * y = y * ((x \ 1) * x)
    ]]></literal>
    <justification jstring="[hyper(2261,a,2411,a),flip(a)].">
      <j1 rule="hyper" parents="2261 2411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2419">
    <literal><![CDATA[
      T((x \ 1) * x,y) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(276(a,1),2413(a,1,1))].">
      <j1 rule="para" parents="276 2413"/>
    </justification>
  </clause>

  <clause id="2421">
    <literal><![CDATA[
      L(K(x \ 1,x),y,z) = K(L(x,y,z) \ 1,x)
    ]]></literal>
    <justification jstring="[para(2413(a,1),2341(a,1,1))].">
      <j1 rule="para" parents="2413 2341"/>
    </justification>
  </clause>

  <clause id="2422">
    <literal><![CDATA[
      L(x * K(y,y \ 1),z,u) = K(y,y \ 1) * L(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(333,a,2359,a,b,2397,a)].">
      <j1 rule="hyper" parents="333 2359 2397"/>
    </justification>
  </clause>

  <clause id="2423">
    <literal><![CDATA[
      K(x,x \ 1) * (y * K(x \ 1,x)) = y
    ]]></literal>
    <justification jstring="[hyper(333,a,2151,a(flip),b,2397,a),flip(a)].">
      <j1 rule="hyper" parents="333 2151 2397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2424">
    <literal><![CDATA[
      K(x,x \ 1) * (y * x) = y * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(333,a,2142,a(flip),b,2397,a),flip(a)].">
      <j1 rule="hyper" parents="333 2142 2397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2425">
    <literal><![CDATA[
      K(x,x \ 1) * (y * (x \ 1)) = y * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(333,a,2141,a(flip),b,2397,a),flip(a)].">
      <j1 rule="hyper" parents="333 2141 2397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2426">
    <literal><![CDATA[
      (K(x,x \ 1) * y) * K(x \ 1,x) = y
    ]]></literal>
    <justification jstring="[hyper(125,a,2397,a,b,2148,a)].">
      <j1 rule="hyper" parents="125 2397 2148"/>
    </justification>
  </clause>

  <clause id="2427">
    <literal><![CDATA[
      x \ (K(y,y \ 1) * z) = (x \ z) * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(121,a,2397,a,b,2111,a)].">
      <j1 rule="hyper" parents="121 2397 2111"/>
    </justification>
  </clause>

  <clause id="2428">
    <literal><![CDATA[
      (K(x,x \ 1) * y) \ ((z * y) * K(x,x \ 1)) = L(T(z,y),y,K(x,x \ 1))
    ]]></literal>
    <justification jstring="[para(2397(a,1),246(a,1,2))].">
      <j1 rule="para" parents="2397 246"/>
    </justification>
  </clause>

  <clause id="2429">
    <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(2397(a,2),674(a,1,1))].">
      <j1 rule="para" parents="2397 674"/>
    </justification>
  </clause>

  <clause id="2430">
    <literal><![CDATA[
      T(x,K(x,x \ 1) * y) = T(x,y)
    ]]></literal>
    <justification jstring="[para(2397(a,2),2165(a,1,2))].">
      <j1 rule="para" parents="2397 2165"/>
    </justification>
  </clause>

  <clause id="2431">
    <literal><![CDATA[
      x \ (K(y,y \ 1) * z) != u
    ]]></literal>
    <literal><![CDATA[
      (x \ z) * K(y,y \ 1) = u
    ]]></literal>
    <justification jstring="[para(2397(a,2),2139(a,1,2))].">
      <j1 rule="para" parents="2397 2139"/>
    </justification>
  </clause>

  <clause id="2432">
    <literal><![CDATA[
      K(x,1 / x) * (y * z) = y * (z * K(x,1 / x))
    ]]></literal>
    <justification jstring="[hyper(333,a,1883,a(flip),b,2408,a),flip(a)].">
      <j1 rule="hyper" parents="333 1883 2408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2433">
    <literal><![CDATA[
      (x * (y * (1 / y))) / z = x / ((y * (1 / y)) \ z)
    ]]></literal>
    <justification jstring="[para(2410(a,1),1877(a,2,2))].">
      <j1 rule="para" parents="2410 1877"/>
    </justification>
  </clause>

  <clause id="2434">
    <literal><![CDATA[
      K(x \ 1,x) * (y * K(x,x \ 1)) = y
    ]]></literal>
    <justification jstring="[hyper(333,a,2149,a(flip),b,2412,a),flip(a)].">
      <j1 rule="hyper" parents="333 2149 2412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2435">
    <literal><![CDATA[
      K(x \ 1,x) * (y * T(x,x \ 1)) = y * x
    ]]></literal>
    <justification jstring="[hyper(333,a,1895,a(flip),b,2412,a),flip(a)].">
      <j1 rule="hyper" parents="333 1895 2412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2436">
    <literal><![CDATA[
      K(x \ 1,x) * (y * (1 / x)) = y * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(333,a,1894,a(flip),b,2412,a),flip(a)].">
      <j1 rule="hyper" parents="333 1894 2412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2437">
    <literal><![CDATA[
      K(x \ 1,x) * (y \ 1) = y \ K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,1880,a(flip),b,2412,a),flip(a)].">
      <j1 rule="hyper" parents="333 1880 2412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2438">
    <literal><![CDATA[
      K(x \ 1,x) * (y * z) = y * (z * K(x \ 1,x))
    ]]></literal>
    <justification jstring="[hyper(333,a,1879,a(flip),b,2412,a),flip(a)].">
      <j1 rule="hyper" parents="333 1879 2412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2439">
    <literal><![CDATA[
      (K(x \ 1,x) * y) * K(x,x \ 1) = y
    ]]></literal>
    <justification jstring="[hyper(34,a,2149,a(flip),b,2412,a),flip(a)].">
      <j1 rule="hyper" parents="34 2149 2412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2440">
    <literal><![CDATA[
      L(x \ (K(y \ 1,y) \ z),x,K(y \ 1,y)) = (x * K(y \ 1,y)) \ z
    ]]></literal>
    <justification jstring="[para(2412(a,1),311(a,2,1))].">
      <j1 rule="para" parents="2412 311"/>
    </justification>
  </clause>

  <clause id="2441">
    <literal><![CDATA[
      x \ (K(y \ 1,y) * z) = (x \ z) * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(2412(a,2),1881(a,1,2))].">
      <j1 rule="para" parents="2412 1881"/>
    </justification>
  </clause>

  <clause id="2442">
    <literal><![CDATA[
      K(x \ 1,x) * y != z
    ]]></literal>
    <literal><![CDATA[
      z * K(x,x \ 1) = y
    ]]></literal>
    <justification jstring="[para(2412(a,2),2153(a,1))].">
      <j1 rule="para" parents="2412 2153"/>
    </justification>
  </clause>

  <clause id="2443">
    <literal><![CDATA[
      T(K(x \ 1,x),y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,x) = z
    ]]></literal>
    <justification jstring="[para(2414(a,1),350(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2414 350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2444">
    <literal><![CDATA[
      ((x * y) / x) \ K(y \ 1,y) = T(((x * y) / x) \ 1,y)
    ]]></literal>
    <justification jstring="[para(2414(a,1),2186(a,1,2))].">
      <j1 rule="para" parents="2414 2186"/>
    </justification>
  </clause>

  <clause id="2445">
    <literal><![CDATA[
      a(x \ 1,x,x \ 1) = (x \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(837,a,2418,a)].">
      <j1 rule="hyper" parents="837 2418"/>
    </justification>
  </clause>

  <clause id="2446">
    <literal><![CDATA[
      a(x \ 1,x,x \ 1) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,276,a,b,2445,a),flip(a)].">
      <j1 rule="hyper" parents="333 276 2445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2447">
    <literal><![CDATA[
      K(x,x \ 1) * (y * x) = y * T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(1895(a,1),2423(a,1,2))].">
      <j1 rule="para" parents="1895 2423"/>
    </justification>
  </clause>

  <clause id="2448">
    <literal><![CDATA[
      K(x,x \ 1) * (y / (1 / x)) = y / (x \ 1)
    ]]></literal>
    <justification jstring="[para(1903(a,1),2423(a,1,2))].">
      <j1 rule="para" parents="1903 2423"/>
    </justification>
  </clause>

  <clause id="2449">
    <literal><![CDATA[
      K(x,x \ 1) * (y \ (x \ 1)) = y \ (1 / x)
    ]]></literal>
    <justification jstring="[para(1918(a,1),2423(a,1,2))].">
      <j1 rule="para" parents="1918 2423"/>
    </justification>
  </clause>

  <clause id="2450">
    <literal><![CDATA[
      K(x,x \ 1) * (K(x \ 1,x) * y) = y
    ]]></literal>
    <justification jstring="[para(2412(a,2),2423(a,1,2))].">
      <j1 rule="para" parents="2412 2423"/>
    </justification>
  </clause>

  <clause id="2451">
    <literal><![CDATA[
      K(x \ 1,x) * (K(x,x \ 1) * y) = y
    ]]></literal>
    <justification jstring="[hyper(63,a,2412,a,b,2426,a)].">
      <j1 rule="hyper" parents="63 2412 2426"/>
    </justification>
  </clause>

  <clause id="2452">
    <literal><![CDATA[
      K(x \ 1,x) \ y = K(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(121,a,2426,a(flip),b,2412,a)].">
      <j1 rule="hyper" parents="121 2426 2412"/>
    </justification>
  </clause>

  <clause id="2453">
    <literal><![CDATA[
      x * K(y \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,y \ 1) * z = x
    ]]></literal>
    <justification jstring="[para(2426(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="2426 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2454">
    <literal><![CDATA[
      ((x \ 1) * (x * y)) * K(x,x \ 1) = L(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(875,a,2434,a),flip(a)].">
      <j1 rule="hyper" parents="875 2434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2455">
    <literal><![CDATA[
      K(x \ 1,x) * (y * x) = y * (1 / (1 / x))
    ]]></literal>
    <justification jstring="[para(2143(a,1),2434(a,1,2))].">
      <j1 rule="para" parents="2143 2434"/>
    </justification>
  </clause>

  <clause id="2456">
    <literal><![CDATA[
      K(x \ 1,x) * (y / x) = y / ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(2158(a,1),2434(a,1,2))].">
      <j1 rule="para" parents="2158 2434"/>
    </justification>
  </clause>

  <clause id="2457">
    <literal><![CDATA[
      K(x \ 1,x) * L(y * K(x,x \ 1),z,u) = L(y,z,u)
    ]]></literal>
    <justification jstring="[para(2359(a,2),2434(a,1,2))].">
      <j1 rule="para" parents="2359 2434"/>
    </justification>
  </clause>

  <clause id="2459">
    <literal><![CDATA[
      K(x,x \ 1) * y != z
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,x) * z = y
    ]]></literal>
    <justification jstring="[para(2450(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="2450 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2460">
    <literal><![CDATA[
      K(x \ 1,x) * y != z
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ 1) * z = y
    ]]></literal>
    <justification jstring="[para(2451(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="2451 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2461">
    <literal><![CDATA[
      K(x,x \ 1) * (K(x \ 1,x) * y) != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(2452(a,1),342(a,1))].">
      <j1 rule="para" parents="2452 342"/>
    </justification>
  </clause>

  <clause id="2462">
    <literal><![CDATA[
      K(x \ 1,x) * T(K(x,x \ 1) * y,z) = (x \ T(x * (y / x),z)) * x
    ]]></literal>
    <justification jstring="[para(2452(a,1),2304(a,1,2,1))].">
      <j1 rule="para" parents="2452 2304"/>
    </justification>
  </clause>

  <clause id="2463">
    <literal><![CDATA[
      K(x \ 1,x) * L(K(x,x \ 1) * (y * x),z,u) = (x \ L(x * y,z,u)) * x
    ]]></literal>
    <justification jstring="[para(2452(a,1),2344(a,1,2,1))].">
      <j1 rule="para" parents="2452 2344"/>
    </justification>
  </clause>

  <clause id="2464">
    <literal><![CDATA[
      K(x \ 1,x) * R(K(x,x \ 1) * (y * x),z,u) = (x \ R(x * y,z,u)) * x
    ]]></literal>
    <justification jstring="[para(2452(a,1),2345(a,1,2,1))].">
      <j1 rule="para" parents="2452 2345"/>
    </justification>
  </clause>

  <clause id="2466">
    <literal><![CDATA[
      (x * (((x \ y) \ 1) \ 1)) / x = ((y / x) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(289,a,2387,a)].">
      <j1 rule="hyper" parents="289 2387"/>
    </justification>
  </clause>

  <clause id="2467">
    <literal><![CDATA[
      (x * (1 / (1 / (x \ y)))) / x = 1 / (1 / (y / x))
    ]]></literal>
    <justification jstring="[hyper(289,a,2389,a)].">
      <j1 rule="hyper" parents="289 2389"/>
    </justification>
  </clause>

  <clause id="2468">
    <literal><![CDATA[
      (x * y) * K(T(x,y),1 / x) = y * ((T(x,y) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(2395(a,1),2145(a,1,2))].">
      <j1 rule="para" parents="2395 2145"/>
    </justification>
  </clause>

  <clause id="2470">
    <literal><![CDATA[
      (T(x,y) \ 1) * K(x,x \ 1) = (T(x,y) \ x) / x
    ]]></literal>
    <justification jstring="[hyper(2184,a,2398,a)].">
      <j1 rule="hyper" parents="2184 2398"/>
    </justification>
  </clause>

  <clause id="2471">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,x) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1892,a(flip),b,2421,a),flip(a)].">
      <j1 rule="hyper" parents="63 1892 2421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2474">
    <literal><![CDATA[
      (K(x,x \ 1) * y) * x = y * T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,2309,a,b,2447,a)].">
      <j1 rule="hyper" parents="63 2309 2447"/>
    </justification>
  </clause>

  <clause id="2475">
    <literal><![CDATA[
      K(1 / x,x) * (y * x) = y * (1 / (1 / x))
    ]]></literal>
    <justification jstring="[para(2131(a,2),2455(a,1,1))].">
      <j1 rule="para" parents="2131 2455"/>
    </justification>
  </clause>

  <clause id="2477">
    <literal><![CDATA[
      (x * (y * (z * K(u \ 1,u)))) \ ((x * y) * (K(u \ 1,u) * z)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * K(u \ 1,u)) = w
    ]]></literal>
    <justification jstring="[para(2417(a,2),752(a,1,2))].">
      <j1 rule="para" parents="2417 752"/>
    </justification>
  </clause>

  <clause id="2480">
    <literal><![CDATA[
      K(x \ 1,x) * (y * z) = y * (K(x \ 1,x) * z)
    ]]></literal>
    <justification jstring="[hyper(333,a,2417,a,b,2438,a),flip(a)].">
      <j1 rule="hyper" parents="333 2417 2438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2481">
    <literal><![CDATA[
      (x * ((y * z) * K(u \ 1,u))) \ (K(u \ 1,u) * ((x * y) * z)) = L(a(x,y,z),x * (y * z),K(u \ 1,u))
    ]]></literal>
    <justification jstring="[para(2438(a,1),519(a,1,1))].">
      <j1 rule="para" parents="2438 519"/>
    </justification>
  </clause>

  <clause id="2482">
    <literal><![CDATA[
      K(x,x \ 1) * (y * (z * K(x \ 1,x))) != u
    ]]></literal>
    <literal><![CDATA[
      y * z = u
    ]]></literal>
    <justification jstring="[para(2438(a,1),2461(a,1,2))].">
      <j1 rule="para" parents="2438 2461"/>
    </justification>
  </clause>

  <clause id="2483">
    <literal><![CDATA[
      x \ (K(y \ 1,y) * z) = K(y \ 1,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(333,a,2412,a,b,2441,a),flip(a)].">
      <j1 rule="hyper" parents="333 2412 2441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2485">
    <literal><![CDATA[
      (x * T(x \ y,y \ x)) / x = ((y / x) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(2283(a,2),2466(a,1,1,2))].">
      <j1 rule="para" parents="2283 2466"/>
    </justification>
  </clause>

  <clause id="2487">
    <literal><![CDATA[
      K(x,T(x,y) \ 1) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(34,a,1851,a,b,2470,a)].">
      <j1 rule="hyper" parents="34 1851 2470"/>
    </justification>
  </clause>

  <clause id="2488">
    <literal><![CDATA[
      T(K(x,x \ 1),y) = K(x,T(x,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(333,a,2394,a,b,2487,a)].">
      <j1 rule="hyper" parents="333 2394 2487"/>
    </justification>
  </clause>

  <clause id="2490">
    <literal><![CDATA[
      K(x,T(x,y) \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ 1) = z
    ]]></literal>
    <justification jstring="[para(2488(a,1),181(a,1)),flip(b)].">
      <j1 rule="para" parents="2488 181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2491">
    <literal><![CDATA[
      T(K(T(x,y),1 / x),z) = K(T(x,y),T(T(x,y),u) \ 1)
    ]]></literal>
    <justification jstring="[para(2395(a,1),2488(a,1,1))].">
      <j1 rule="para" parents="2395 2488"/>
    </justification>
  </clause>

  <clause id="2492">
    <literal><![CDATA[
      K(x,x \ 1) * (y * (K(x \ 1,x) * z)) = y * z
    ]]></literal>
    <justification jstring="[hyper(2460,a,2480,a)].">
      <j1 rule="hyper" parents="2460 2480"/>
    </justification>
  </clause>

  <clause id="2493">
    <literal><![CDATA[
      x \ (y * (K(z \ 1,z) * u)) = (x \ (y * u)) * K(z \ 1,z)
    ]]></literal>
    <justification jstring="[para(2480(a,1),2441(a,1,2))].">
      <j1 rule="para" parents="2480 2441"/>
    </justification>
  </clause>

  <clause id="2494">
    <literal><![CDATA[
      K(x \ 1,x) * (y \ x) = y \ (1 / (1 / x))
    ]]></literal>
    <justification jstring="[para(1917(a,1),2483(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1917 2483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2495">
    <literal><![CDATA[
      x \ (K(y \ 1,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      (x \ z) * K(y \ 1,y) = u
    ]]></literal>
    <justification jstring="[para(2483(a,2),2416(a,1))].">
      <j1 rule="para" parents="2483 2416"/>
    </justification>
  </clause>

  <clause id="2496">
    <literal><![CDATA[
      T(x / y,x \ y) = ((x / y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(475,a,2485,a)].">
      <j1 rule="hyper" parents="475 2485"/>
    </justification>
  </clause>

  <clause id="2497">
    <literal><![CDATA[
      T(x / y,y / x) = T(x / y,x \ y)
    ]]></literal>
    <justification jstring="[hyper(333,a,2231,a,b,2496,a)].">
      <j1 rule="hyper" parents="333 2231 2496"/>
    </justification>
  </clause>

  <clause id="2498">
    <literal><![CDATA[
      T(T(x / y,x \ y),y) = T(y \ x,y / x)
    ]]></literal>
    <justification jstring="[para(2497(a,1),259(a,1,1))].">
      <j1 rule="para" parents="2497 259"/>
    </justification>
  </clause>

  <clause id="2499">
    <literal><![CDATA[
      T(x \ y,x / y) = T(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(740,a,2498,a),flip(a)].">
      <j1 rule="hyper" parents="740 2498"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2500">
    <literal><![CDATA[
      T(x \ y,x / y) = ((x \ y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(333,a,2283,a(flip),b,2499,a),flip(a)].">
      <j1 rule="hyper" parents="333 2283 2499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2501">
    <literal><![CDATA[
      T((x * y) \ y,x) = (((x * y) \ y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(11(a,1),2500(a,1,2))].">
      <j1 rule="para" parents="11 2500"/>
    </justification>
  </clause>

  <clause id="2502">
    <literal><![CDATA[
      T(x \ (y \ x),y) = ((x \ (y \ x)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(76(a,1),2500(a,1,2))].">
      <j1 rule="para" parents="76 2500"/>
    </justification>
  </clause>

  <clause id="2503">
    <literal><![CDATA[
      K(x,x \ 1) * (y * z) = y * (K(x,x \ 1) * z)
    ]]></literal>
    <justification jstring="[para(2451(a,1),2492(a,1,2,2))].">
      <j1 rule="para" parents="2451 2492"/>
    </justification>
  </clause>

  <clause id="2504">
    <literal><![CDATA[
      K(x,x \ 1) * (y * (z * (x \ 1))) = y * (z * (1 / x))
    ]]></literal>
    <justification jstring="[para(2436(a,1),2492(a,1,2,2))].">
      <j1 rule="para" parents="2436 2492"/>
    </justification>
  </clause>

  <clause id="2506">
    <literal><![CDATA[
      (x * ((K(y,y \ 1) * z) * u)) \ ((K(y,y \ 1) * (x * z)) * u) = a(x,K(y,y \ 1) * z,u)
    ]]></literal>
    <justification jstring="[para(2503(a,2),14(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="2503 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2507">
    <literal><![CDATA[
      K(x,x \ 1) * (y * (z / (1 / x))) = y * (z / (x \ 1))
    ]]></literal>
    <justification jstring="[para(2448(a,1),2503(a,2,2))].">
      <j1 rule="para" parents="2448 2503"/>
    </justification>
  </clause>

  <clause id="2508">
    <literal><![CDATA[
      x \ (y * (K(z,z \ 1) * u)) = (x \ (y * u)) * K(z,z \ 1)
    ]]></literal>
    <justification jstring="[para(2503(a,1),2427(a,1,2))].">
      <j1 rule="para" parents="2503 2427"/>
    </justification>
  </clause>

  <clause id="2509">
    <literal><![CDATA[
      K(x,x \ 1) * L(x,y,z) = L(T(x,x \ 1),y,z)
    ]]></literal>
    <justification jstring="[para(2102(a,1),2422(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2102 2422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2510">
    <literal><![CDATA[
      K(x,x \ 1) * L(y * K(x \ 1,x),z,u) = L(y,z,u)
    ]]></literal>
    <justification jstring="[para(2151(a,1),2422(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2151 2422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2511">
    <literal><![CDATA[
      L(x * K(y,y \ 1),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z,u) * K(y,y \ 1) = w
    ]]></literal>
    <justification jstring="[para(2422(a,2),2403(a,1))].">
      <j1 rule="para" parents="2422 2403"/>
    </justification>
  </clause>

  <clause id="2512">
    <literal><![CDATA[
      x \ L(T(x,x \ 1),y,z) = L(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(121,a,2509,a(flip),b,2172,a(flip))].">
      <j1 rule="hyper" parents="121 2509 2172"/>
    </justification>
  </clause>

  <clause id="2513">
    <literal><![CDATA[
      x \ L((x \ 1) \ 1,y,z) = L(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[para(112(a,1),2512(a,1,2,1))].">
      <j1 rule="para" parents="112 2512"/>
    </justification>
  </clause>

  <clause id="2514">
    <literal><![CDATA[
      T(L(x,y,z) * (1 / x),x) = L(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1211,a,b,2513,a)].">
      <j1 rule="hyper" parents="63 1211 2513"/>
    </justification>
  </clause>

  <clause id="2515">
    <literal><![CDATA[
      (x \ L(x,y,z)) * x = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(2260,a,2514,a)].">
      <j1 rule="hyper" parents="2260 2514"/>
    </justification>
  </clause>

  <clause id="2516">
    <literal><![CDATA[
      L(x,y,z) / x = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(138,a,2515,a)].">
      <j1 rule="hyper" parents="138 2515"/>
    </justification>
  </clause>

  <clause id="2517">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ L(x,y,z) = x
    ]]></literal>
    <justification jstring="[hyper(129,a,2515,a)].">
      <j1 rule="hyper" parents="129 2515"/>
    </justification>
  </clause>

  <clause id="2518">
    <literal><![CDATA[
      K(x \ L(x,y,z),x) = 1
    ]]></literal>
    <justification jstring="[hyper(120,a,2515,a(flip),b,317,a),flip(a)].">
      <j1 rule="hyper" parents="120 2515 317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2519">
    <literal><![CDATA[
      R(x \ L(x,y,z),x,u) = (L(x,y,z) * u) / (x * u)
    ]]></literal>
    <justification jstring="[para(2515(a,1),20(a,2,1,1))].">
      <j1 rule="para" parents="2515 20"/>
    </justification>
  </clause>

  <clause id="2521">
    <literal><![CDATA[
      (1 / x) * L(x,y,z) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,1774,a,b,2516,a)].">
      <j1 rule="hyper" parents="63 1774 2516"/>
    </justification>
  </clause>

  <clause id="2523">
    <literal><![CDATA[
      (x \ L(x,y,z)) * x != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(2516(a,1),264(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2516 264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2524">
    <literal><![CDATA[
      T(x,y) * (x \ L(x,z,u)) = (x \ L(x,z,u)) * T(x,y)
    ]]></literal>
    <justification jstring="[para(2517(a,1),473(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2517 473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2525">
    <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(2444(a,2),2077(a,1,1,2))].">
      <j1 rule="para" parents="2444 2077"/>
    </justification>
  </clause>

  <clause id="2527">
    <literal><![CDATA[
      (x * y) * K(T(x,y),1 / x) = ((x \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(333,a,2386,a(flip),b,2468,a),flip(a)].">
      <j1 rule="hyper" parents="333 2386 2468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2528">
    <literal><![CDATA[
      K(T(x,y),T(T(x,y),z) \ 1) = K(T(x,y),1 / T(x,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,2370,a,b,2491,a),flip(a)].">
      <j1 rule="hyper" parents="63 2370 2491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2529">
    <literal><![CDATA[
      L(x * K(y \ 1,y),z,u) = L(x,z,u) * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(34,a,2423,a,b,2510,a),flip(a)].">
      <j1 rule="hyper" parents="34 2423 2510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2530">
    <literal><![CDATA[
      x \ ((x \ L(x,y,z)) * T(x,u)) = T(x,u) * (x \ (x \ L(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(121,a,2524,a(flip),b,1057,a)].">
      <j1 rule="hyper" parents="121 2524 1057"/>
    </justification>
  </clause>

  <clause id="2531">
    <literal><![CDATA[
      K(T(x,y),T(x,y) \ 1) = K(T(x,y),1 / T(x,z))
    ]]></literal>
    <justification jstring="[hyper(2490,a,2528,a)].">
      <j1 rule="hyper" parents="2490 2528"/>
    </justification>
  </clause>

  <clause id="2533">
    <literal><![CDATA[
      K(T(x,y),T(x,y) \ 1) = K(T(x,y),x \ 1)
    ]]></literal>
    <justification jstring="[para(281(a,1),2531(a,2,2))].">
      <j1 rule="para" parents="281 2531"/>
    </justification>
  </clause>

  <clause id="2534">
    <literal><![CDATA[
      K(T(x,y),1 / x) = K(T(x,y),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,2395,a(flip),b,2533,a)].">
      <j1 rule="hyper" parents="63 2395 2533"/>
    </justification>
  </clause>

  <clause id="2535">
    <literal><![CDATA[
      (x * y) * K(T(x,y),x \ 1) = ((x \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[para(2534(a,1),2527(a,1,2))].">
      <j1 rule="para" parents="2534 2527"/>
    </justification>
  </clause>

  <clause id="2536">
    <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(752,a,2508,a),flip(a)].">
      <j1 rule="hyper" parents="752 2508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2537">
    <literal><![CDATA[
      (T(x,y) * z) * K(T(T(x,z),y),T(T(x,z),y) \ 1) = z * T((T(x,z) \ 1) \ 1,y)
    ]]></literal>
    <justification jstring="[para(282(a,1),2388(a,1,1)),flip(a)].">
      <j1 rule="para" parents="282 2388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2538">
    <literal><![CDATA[
      T(K(x \ (x / (y \ 1)),x),T(y,x) \ y) = y \ T(y,x)
    ]]></literal>
    <justification jstring="[para(2297(a,1),2390(a,1,1))].">
      <j1 rule="para" parents="2297 2390"/>
    </justification>
  </clause>

  <clause id="2539">
    <literal><![CDATA[
      ((x \ T(x,y)) \ 1) \ 1 = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,2290,a(flip),b,2538,a)].">
      <j1 rule="hyper" parents="63 2290 2538"/>
    </justification>
  </clause>

  <clause id="2540">
    <literal><![CDATA[
      L(x \ (K(y,y \ 1) * z),x,K(y \ 1,y)) = (x * K(y \ 1,y)) \ z
    ]]></literal>
    <justification jstring="[para(2452(a,1),2440(a,1,1,2))].">
      <j1 rule="para" parents="2452 2440"/>
    </justification>
  </clause>

  <clause id="2541">
    <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(2447(a,1),2463(a,1,2,1))].">
      <j1 rule="para" parents="2447 2463"/>
    </justification>
  </clause>

  <clause id="2542">
    <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(2155(a,1),2541(a,1,2,1))].">
      <j1 rule="para" parents="2155 2541"/>
    </justification>
  </clause>

  <clause id="2543">
    <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(2447(a,1),2464(a,1,2,1))].">
      <j1 rule="para" parents="2447 2464"/>
    </justification>
  </clause>

  <clause id="2544">
    <literal><![CDATA[
      x \ L(x * (y / x),z,u) = L(y,z,u) / x
    ]]></literal>
    <justification jstring="[hyper(123,a,2457,a(flip),b,2542,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="123 2457 2542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2545">
    <literal><![CDATA[
      L(x * (y / x),z,u) = x * (L(y,z,u) / x)
    ]]></literal>
    <justification jstring="[hyper(142,a,2544,a),flip(a)].">
      <j1 rule="hyper" parents="142 2544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2546">
    <literal><![CDATA[
      L(x * y,z,u) / y = y \ L(y * x,z,u)
    ]]></literal>
    <justification jstring="[para(11(a,1),2544(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="11 2544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2547">
    <literal><![CDATA[
      (x \ L(x * y,z,u)) * x = L(y * x,z,u)
    ]]></literal>
    <justification jstring="[hyper(140,a,2546,a)].">
      <j1 rule="hyper" parents="140 2546"/>
    </justification>
  </clause>

  <clause id="2548">
    <literal><![CDATA[
      (x \ 1) \ L((x \ 1) * y,z,u) = x * L(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,1119,a(flip),b,2546,a),flip(a)].">
      <j1 rule="hyper" parents="63 1119 2546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2549">
    <literal><![CDATA[
      L((x \ y) * x,z,u) = (x \ L(y,z,u)) * x
    ]]></literal>
    <justification jstring="[para(10(a,1),2547(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 2547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2550">
    <literal><![CDATA[
      (L(x,y,z) \ x) * L(x,y,z) = x
    ]]></literal>
    <justification jstring="[hyper(207,a,2549,a),flip(a)].">
      <j1 rule="hyper" parents="207 2549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2551">
    <literal><![CDATA[
      L((x * x) \ y,z,u) = (x * x) \ L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(35,a,1216,a(flip),b,2549,a(flip))].">
      <j1 rule="hyper" parents="35 1216 2549"/>
    </justification>
  </clause>

  <clause id="2552">
    <literal><![CDATA[
      L(T((x \ y) * x,z),u,w) = T((x \ L(y,u,w)) * x,z)
    ]]></literal>
    <justification jstring="[para(2549(a,1),25(a,2,1))].">
      <j1 rule="para" parents="2549 25"/>
    </justification>
  </clause>

  <clause id="2553">
    <literal><![CDATA[
      L((x \ (y \ (z \ u))) * x,y,z) = (x \ ((z * y) \ u)) * x
    ]]></literal>
    <justification jstring="[para(311(a,1),2549(a,2,1,2))].">
      <j1 rule="para" parents="311 2549"/>
    </justification>
  </clause>

  <clause id="2554">
    <literal><![CDATA[
      L((x \ ((y \ 1) \ z)) * x,y \ 1,y) = (x \ (y * z)) * x
    ]]></literal>
    <justification jstring="[para(514(a,1),2549(a,2,1,2))].">
      <j1 rule="para" parents="514 2549"/>
    </justification>
  </clause>

  <clause id="2555">
    <literal><![CDATA[
      L((x \ ((y \ z) \ u)) * x,y \ z,y) = (x \ (z \ (y * u))) * x
    ]]></literal>
    <justification jstring="[para(515(a,1),2549(a,2,1,2))].">
      <j1 rule="para" parents="515 2549"/>
    </justification>
  </clause>

  <clause id="2556">
    <literal><![CDATA[
      (1 / L(x,y,z)) * x = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(1825,a,2550,a)].">
      <j1 rule="hyper" parents="1825 2550"/>
    </justification>
  </clause>

  <clause id="2557">
    <literal><![CDATA[
      T(L(x,y,z),L(x,y,z) \ x) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(356,a,2550,a)].">
      <j1 rule="hyper" parents="356 2550"/>
    </justification>
  </clause>

  <clause id="2558">
    <literal><![CDATA[
      x / L(x,y,z) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(138,a,2550,a)].">
      <j1 rule="hyper" parents="138 2550"/>
    </justification>
  </clause>

  <clause id="2559">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ x = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(129,a,2550,a)].">
      <j1 rule="hyper" parents="129 2550"/>
    </justification>
  </clause>

  <clause id="2560">
    <literal><![CDATA[
      x / L(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) \ x = u
    ]]></literal>
    <justification jstring="[para(2550(a,1),268(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2550 268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2562">
    <literal><![CDATA[
      (L(x,y,z) \ x) / x = 1 / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(123,a,2558,a(flip),b,1821,a)].">
      <j1 rule="hyper" parents="123 2558 1821"/>
    </justification>
  </clause>

  <clause id="2563">
    <literal><![CDATA[
      ((L(x,y,z) \ x) * x) \ 1 = L(x,y,z) / (x * x)
    ]]></literal>
    <justification jstring="[para(2558(a,1),1827(a,1,1,1))].">
      <j1 rule="para" parents="2558 1827"/>
    </justification>
  </clause>

  <clause id="2564">
    <literal><![CDATA[
      T(x,L(x,y,z) \ x) = x
    ]]></literal>
    <justification jstring="[hyper(150,a,2557,a)].">
      <j1 rule="hyper" parents="150 2557"/>
    </justification>
  </clause>

  <clause id="2565">
    <literal><![CDATA[
      (L(x,y,z) \ x) * x = x * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(126,a,2564,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="126 2564 22"/>
    </justification>
  </clause>

  <clause id="2566">
    <literal><![CDATA[
      T(L(x,y,z),L(x,u,w) \ x) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(2564(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2564 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2567">
    <literal><![CDATA[
      K(L(x,y,z),L(x,u,w) \ x) = 1
    ]]></literal>
    <justification jstring="[hyper(55,a,2566,a)].">
      <j1 rule="hyper" parents="55 2566"/>
    </justification>
  </clause>

  <clause id="2568">
    <literal><![CDATA[
      (x * x) * L((x * x) \ y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(y,z,u) = w
    ]]></literal>
    <justification jstring="[para(2551(a,2),273(a,1,2)),flip(b)].">
      <j1 rule="para" parents="2551 273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2569">
    <literal><![CDATA[
      (x * x) * L((x * x) \ y,z,u) != w * v5
    ]]></literal>
    <literal><![CDATA[
      L(y,z,u) / v5 = w
    ]]></literal>
    <justification jstring="[para(2551(a,2),362(a,1,2))].">
      <j1 rule="para" parents="2551 362"/>
    </justification>
  </clause>

  <clause id="2571">
    <literal><![CDATA[
      (x * (L(x,y,z) \ x)) \ 1 = L(x,y,z) / (x * x)
    ]]></literal>
    <justification jstring="[para(2565(a,1),2563(a,1,1))].">
      <j1 rule="para" parents="2565 2563"/>
    </justification>
  </clause>

  <clause id="2572">
    <literal><![CDATA[
      (x * y) * ((z \ ((x * y) \ u)) * z) = x * (y * ((z \ (y \ (x \ u))) * z))
    ]]></literal>
    <justification jstring="[hyper(126,a,2553,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="126 2553 18"/>
    </justification>
  </clause>

  <clause id="2573">
    <literal><![CDATA[
      (x \ 1) * ((y \ ((x \ 1) \ z)) * y) = x \ ((y \ (x * z)) * y)
    ]]></literal>
    <justification jstring="[hyper(121,a,2554,a(flip),b,275,a),flip(a)].">
      <j1 rule="hyper" parents="121 2554 275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2574">
    <literal><![CDATA[
      L(x * y,z,u) / y = y * L(y \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(2569,a,1631,a)].">
      <j1 rule="hyper" parents="2569 1631"/>
    </justification>
  </clause>

  <clause id="2575">
    <literal><![CDATA[
      L(x / (y * y),z,u) = L(x,z,u) / (y * y)
    ]]></literal>
    <justification jstring="[hyper(2569,a,668,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="2569 668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2576">
    <literal><![CDATA[
      x \ L(x * y,z,u) = x * L(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,2546,a(flip),b,2574,a)].">
      <j1 rule="hyper" parents="63 2546 2574"/>
    </justification>
  </clause>

  <clause id="2577">
    <literal><![CDATA[
      L((x * x) * y,x,x) = x * (x * y)
    ]]></literal>
    <justification jstring="[hyper(1170,a,2575,a),flip(a)].">
      <j1 rule="hyper" parents="1170 2575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2578">
    <literal><![CDATA[
      L(x,y,z) / (x * x) = L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(284(a,1),2575(a,1,1)),flip(a)].">
      <j1 rule="para" parents="284 2575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2579">
    <literal><![CDATA[
      (x * (L(x,y,z) \ x)) \ 1 = L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,2571,a,b,2578,a)].">
      <j1 rule="hyper" parents="63 2571 2578"/>
    </justification>
  </clause>

  <clause id="2580">
    <literal><![CDATA[
      (x * x) * L((x * x) \ y,z,u) = L(y,z * (x * x),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,2254,a(flip),b,2576,a),flip(a)].">
      <j1 rule="hyper" parents="63 2254 2576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2581">
    <literal><![CDATA[
      x * L(x \ (y \ z),x \ 1,y) = (x \ 1) * ((y * (x \ 1)) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,1761,a(flip),b,2576,a),flip(a)].">
      <j1 rule="hyper" parents="63 1761 2576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2582">
    <literal><![CDATA[
      x * L(x \ 1,y,z) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(8(a,1),2576(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8 2576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2584">
    <literal><![CDATA[
      T(x * L(x \ 1,y,z),u) = T(x,u) \ L(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(1971,a,2582,a)].">
      <j1 rule="hyper" parents="1971 2582"/>
    </justification>
  </clause>

  <clause id="2585">
    <literal><![CDATA[
      (x * L(x \ y,z,u)) / y = (x / y) \ L(x / y,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,1832,a(flip),b,2582,a)].">
      <j1 rule="hyper" parents="63 1832 2582"/>
    </justification>
  </clause>

  <clause id="2586">
    <literal><![CDATA[
      (x \ y) \ L(x \ y,z,u) = x \ (y * L(y \ x,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,1541,a(flip),b,2582,a),flip(a)].">
      <j1 rule="hyper" parents="63 1541 2582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2587">
    <literal><![CDATA[
      x \ L(x,x,y) = x * ((y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,390,a(flip),b,2582,a),flip(a)].">
      <j1 rule="hyper" parents="63 390 2582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2588">
    <literal><![CDATA[
      (x \ 1) * (x \ L(x,y,z)) = L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(126,a,1264,a(flip),b,2582,a(flip))].">
      <j1 rule="hyper" parents="126 1264 2582"/>
    </justification>
  </clause>

  <clause id="2589">
    <literal><![CDATA[
      ((x / y) \ L(x / y,z,u)) * y = x * L(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(125,a,2582,a(flip),b,1832,a(flip))].">
      <j1 rule="hyper" parents="125 2582 1832"/>
    </justification>
  </clause>

  <clause id="2590">
    <literal><![CDATA[
      (x \ L(x,y,z)) / x = L(1 / x,y,z)
    ]]></literal>
    <justification jstring="[hyper(123,a,2582,a(flip),b,668,a)].">
      <j1 rule="hyper" parents="123 2582 668"/>
    </justification>
  </clause>

  <clause id="2591">
    <literal><![CDATA[
      x \ (x \ L(x,y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(x \ 1,y,z) = u
    ]]></literal>
    <justification jstring="[para(2582(a,1),342(a,1,2))].">
      <j1 rule="para" parents="2582 342"/>
    </justification>
  </clause>

  <clause id="2592">
    <literal><![CDATA[
      L(x,y * (z * z),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(2568,a,2580,a),flip(a)].">
      <j1 rule="hyper" parents="2568 2580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2593">
    <literal><![CDATA[
      L(x,y * (z * z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(2580(a,1),2568(a,1))].">
      <j1 rule="para" parents="2580 2568"/>
    </justification>
  </clause>

  <clause id="2595">
    <literal><![CDATA[
      L(x,y / (z * z),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(12(a,1),2592(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12 2592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2596">
    <literal><![CDATA[
      L(x,y \ 1,z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(223(a,1),2592(a,1,2)),flip(a)].">
      <j1 rule="para" parents="223 2592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2597">
    <literal><![CDATA[
      L(x,1 / y,z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(228(a,1),2592(a,1,2))].">
      <j1 rule="para" parents="228 2592"/>
    </justification>
  </clause>

  <clause id="2598">
    <literal><![CDATA[
      L(x,(y \ 1) \ 1,z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,2596,a(flip),b,2596,a),flip(a)].">
      <j1 rule="hyper" parents="333 2596 2596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2599">
    <literal><![CDATA[
      x * ((x \ 1) * y) = L(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,275,a,b,2596,a)].">
      <j1 rule="hyper" parents="63 275 2596"/>
    </justification>
  </clause>

  <clause id="2600">
    <literal><![CDATA[
      L(T(x,y \ 1),y,y) = y * (x * (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,571,a(flip),b,2596,a),flip(a)].">
      <j1 rule="hyper" parents="63 571 2596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2601">
    <literal><![CDATA[
      L((x \ 1) \ y,x,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(63,a,514,a(flip),b,2596,a),flip(a)].">
      <j1 rule="hyper" parents="63 514 2596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2602">
    <literal><![CDATA[
      a(x,x \ 1,y) = L(y,x,x) \ y
    ]]></literal>
    <justification jstring="[para(2596(a,1),766(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2596 766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2603">
    <literal><![CDATA[
      L(x,y,y) != y * z
    ]]></literal>
    <literal><![CDATA[
      (y \ 1) * x = z
    ]]></literal>
    <justification jstring="[para(2596(a,1),572(a,1))].">
      <j1 rule="para" parents="2596 572"/>
    </justification>
  </clause>

  <clause id="2604">
    <literal><![CDATA[
      L(x,1 / y,z) = L(x,y \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,2596,a,b,2597,a),flip(a)].">
      <j1 rule="hyper" parents="333 2596 2597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2605">
    <literal><![CDATA[
      L(x,1 / (1 / y),z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,2597,a(flip),b,2597,a),flip(a)].">
      <j1 rule="hyper" parents="333 2597 2597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2606">
    <literal><![CDATA[
      L(x,x,y) = (y * (1 / x)) \ y
    ]]></literal>
    <justification jstring="[hyper(63,a,232,a(flip),b,2597,a),flip(a)].">
      <j1 rule="hyper" parents="63 232 2597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2607">
    <literal><![CDATA[
      x / L(y,y,x) = x * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(197,a,2597,a(flip),b,232,a(flip))].">
      <j1 rule="hyper" parents="197 2597 232"/>
    </justification>
  </clause>

  <clause id="2608">
    <literal><![CDATA[
      x \ L(y,1 / x,x) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(121,a,2597,a,b,2599,a)].">
      <j1 rule="hyper" parents="121 2597 2599"/>
    </justification>
  </clause>

  <clause id="2610">
    <literal><![CDATA[
      x \ L(y,x,x) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ 1) * y = z
    ]]></literal>
    <justification jstring="[para(2599(a,1),342(a,1,2))].">
      <j1 rule="para" parents="2599 342"/>
    </justification>
  </clause>

  <clause id="2611">
    <literal><![CDATA[
      L((x \ 1) \ y,x,x) \ ((x \ 1) \ y) = ((x \ 1) \ y) / (x * y)
    ]]></literal>
    <justification jstring="[hyper(197,a,2601,a(flip),b,2559,a),flip(a)].">
      <j1 rule="hyper" parents="197 2601 2559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2612">
    <literal><![CDATA[
      L(x,y,y) != y * z
    ]]></literal>
    <literal><![CDATA[
      (y \ 1) \ z = x
    ]]></literal>
    <justification jstring="[para(2601(a,1),50(a,1)),flip(a)].">
      <j1 rule="para" parents="2601 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2613">
    <literal><![CDATA[
      L(x,x \ 1,y) = (y * (1 / x)) \ y
    ]]></literal>
    <justification jstring="[hyper(63,a,2596,a,b,2606,a)].">
      <j1 rule="hyper" parents="63 2596 2606"/>
    </justification>
  </clause>

  <clause id="2614">
    <literal><![CDATA[
      ((x * y) / y) \ ((x * (y * y)) / y) = (x * (1 / y)) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,1829,a(flip),b,2606,a)].">
      <j1 rule="hyper" parents="63 1829 2606"/>
    </justification>
  </clause>

  <clause id="2615">
    <literal><![CDATA[
      x / L(y,y \ 1,x) = x * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(197,a,2596,a,b,2606,a(flip))].">
      <j1 rule="hyper" parents="197 2596 2606"/>
    </justification>
  </clause>

  <clause id="2616">
    <literal><![CDATA[
      x / y != x * (1 / z)
    ]]></literal>
    <literal><![CDATA[
      L(z,z,x) = y
    ]]></literal>
    <justification jstring="[para(2607(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="2607 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2617">
    <literal><![CDATA[
      (x * (1 / y)) \ x != z
    ]]></literal>
    <literal><![CDATA[
      L(y,y,x) = z
    ]]></literal>
    <justification jstring="[para(2607(a,1),345(a,1,1))].">
      <j1 rule="para" parents="2607 345"/>
    </justification>
  </clause>

  <clause id="2618">
    <literal><![CDATA[
      L(x,y * (z / (u * u)),w) = L(x,y * z,w)
    ]]></literal>
    <justification jstring="[para(809(a,1),2595(a,1,2))].">
      <j1 rule="para" parents="809 2595"/>
    </justification>
  </clause>

  <clause id="2619">
    <literal><![CDATA[
      L(x,L(y \ 1,z,u),w) = L(x,L(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(2578(a,1),2595(a,1,2))].">
      <j1 rule="para" parents="2578 2595"/>
    </justification>
  </clause>

  <clause id="2620">
    <literal><![CDATA[
      L(x,T(y,y \ 1),z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(112(a,2),2598(a,1,2))].">
      <j1 rule="para" parents="112 2598"/>
    </justification>
  </clause>

  <clause id="2621">
    <literal><![CDATA[
      L(x,y \ 1,T(z,z \ u)) = L(x,1 / y,(z \ u) \ u)
    ]]></literal>
    <justification jstring="[hyper(333,a,1645,a,b,2604,a)].">
      <j1 rule="hyper" parents="333 1645 2604"/>
    </justification>
  </clause>

  <clause id="2622">
    <literal><![CDATA[
      L(x,((y \ z) \ z) \ 1,u) = L(x,1 / T(y,y \ z),u)
    ]]></literal>
    <justification jstring="[para(326(a,1),2604(a,2,2)),flip(a)].">
      <j1 rule="para" parents="326 2604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2623">
    <literal><![CDATA[
      (x * T(y,y \ 1)) * L(z,y,x) = x * (T(y,y \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(126,a,2620,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="126 2620 18"/>
    </justification>
  </clause>

  <clause id="2624">
    <literal><![CDATA[
      K(x,x \ 1) * ((x \ 1) * y) = (1 / x) * y
    ]]></literal>
    <justification jstring="[para(2608(a,1),2179(a,1,2))].">
      <j1 rule="para" parents="2608 2179"/>
    </justification>
  </clause>

  <clause id="2625">
    <literal><![CDATA[
      K(x \ (x / L(y,y \ 1,x)),z) = K(1 / y,z)
    ]]></literal>
    <justification jstring="[para(2615(a,2),705(a,1,1,2))].">
      <j1 rule="para" parents="2615 705"/>
    </justification>
  </clause>

  <clause id="2626">
    <literal><![CDATA[
      L(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y \ 1,z) = u
    ]]></literal>
    <justification jstring="[para(223(a,1),2593(a,1,2))].">
      <j1 rule="para" parents="223 2593"/>
    </justification>
  </clause>

  <clause id="2627">
    <literal><![CDATA[
      L(x,1 / y,z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(228(a,1),2593(a,1,2))].">
      <j1 rule="para" parents="228 2593"/>
    </justification>
  </clause>

  <clause id="2628">
    <literal><![CDATA[
      L(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,(y \ 1) \ 1,z) = u
    ]]></literal>
    <justification jstring="[para(2596(a,1),2626(a,1))].">
      <j1 rule="para" parents="2596 2626"/>
    </justification>
  </clause>

  <clause id="2629">
    <literal><![CDATA[
      L(x,1 / (1 / y),z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(2597(a,2),2627(a,1))].">
      <j1 rule="para" parents="2597 2627"/>
    </justification>
  </clause>

  <clause id="2630">
    <literal><![CDATA[
      (x * (1 / (1 / y))) \ x != z
    ]]></literal>
    <literal><![CDATA[
      L(1 / y,y,x) = z
    ]]></literal>
    <justification jstring="[para(2606(a,1),2627(a,1))].">
      <j1 rule="para" parents="2606 2627"/>
    </justification>
  </clause>

  <clause id="2631">
    <literal><![CDATA[
      L(x,y \ 1,z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(2604(a,1),2627(a,1))].">
      <j1 rule="para" parents="2604 2627"/>
    </justification>
  </clause>

  <clause id="2632">
    <literal><![CDATA[
      L(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,1 / y,z) = u
    ]]></literal>
    <justification jstring="[para(2605(a,1),2627(a,1))].">
      <j1 rule="para" parents="2605 2627"/>
    </justification>
  </clause>

  <clause id="2633">
    <literal><![CDATA[
      x * ((x \ 1) * y) != z
    ]]></literal>
    <literal><![CDATA[
      L(y,x,x) = z
    ]]></literal>
    <justification jstring="[para(275(a,2),2631(a,1))].">
      <j1 rule="para" parents="275 2631"/>
    </justification>
  </clause>

  <clause id="2634">
    <literal><![CDATA[
      L(x,y * (z \ 1),u) = L(x,y * z,u)
    ]]></literal>
    <justification jstring="[para(284(a,1),2618(a,1,2,2))].">
      <j1 rule="para" parents="284 2618"/>
    </justification>
  </clause>

  <clause id="2635">
    <literal><![CDATA[
      L(x,R(y,z,z) / z,u) = L(x,y * ((1 / z) / (w * w)),u)
    ]]></literal>
    <justification jstring="[para(1188(a,2),2618(a,2,2)),flip(a)].">
      <j1 rule="para" parents="1188 2618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2636">
    <literal><![CDATA[
      L(x,y * (1 / z),u) = L(x,y * z,u)
    ]]></literal>
    <justification jstring="[para(79(a,1),2634(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="79 2634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2637">
    <literal><![CDATA[
      L(x,y * (1 / y),z) = x
    ]]></literal>
    <justification jstring="[hyper(333,a,491,a(flip),b,2636,a),flip(a)].">
      <j1 rule="hyper" parents="333 491 2636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2638">
    <literal><![CDATA[
      (x * (y * (1 / y))) \ z = (y * (1 / y)) \ (x \ z)
    ]]></literal>
    <justification jstring="[hyper(578,a,2637,a),flip(a)].">
      <j1 rule="hyper" parents="578 2637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2639">
    <literal><![CDATA[
      L(x,y * (1 / y),z) != u
    ]]></literal>
    <literal><![CDATA[
      u = x
    ]]></literal>
    <justification jstring="[para(2637(a,1),50(a,1)),flip(a)].">
      <j1 rule="para" parents="2637 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2640">
    <literal><![CDATA[
      L(x,K(y,y \ 1),z) = x
    ]]></literal>
    <justification jstring="[para(2098(a,2),2637(a,1,2))].">
      <j1 rule="para" parents="2098 2637"/>
    </justification>
  </clause>

  <clause id="2641">
    <literal><![CDATA[
      (x * K(y,y \ 1)) * z = x * (K(y,y \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(1170,a,2640,a),flip(a)].">
      <j1 rule="hyper" parents="1170 2640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2642">
    <literal><![CDATA[
      (1 / x) * (y * K(x \ 1,x)) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(2482,a,2624,a),flip(a)].">
      <j1 rule="hyper" parents="2482 2624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2643">
    <literal><![CDATA[
      K(x \ 1,x) * ((1 / x) * y) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(2459,a,2624,a)].">
      <j1 rule="hyper" parents="2459 2624"/>
    </justification>
  </clause>

  <clause id="2644">
    <literal><![CDATA[
      ((x \ 1) * y) * K(x,x \ 1) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(2403,a,2624,a)].">
      <j1 rule="hyper" parents="2403 2624"/>
    </justification>
  </clause>

  <clause id="2645">
    <literal><![CDATA[
      (1 / x) * ((x \ 1) \ y) = K(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(343,a,2624,a),flip(a)].">
      <j1 rule="hyper" parents="343 2624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2646">
    <literal><![CDATA[
      ((1 / x) * y) * K(x \ 1,x) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(34,a,2423,a,b,2624,a)].">
      <j1 rule="hyper" parents="34 2423 2624"/>
    </justification>
  </clause>

  <clause id="2647">
    <literal><![CDATA[
      (x \ 1) \ ((1 / x) * y) = K(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(121,a,2624,a(flip),b,2503,a(flip))].">
      <j1 rule="hyper" parents="121 2624 2503"/>
    </justification>
  </clause>

  <clause id="2648">
    <literal><![CDATA[
      T(x,(1 / x) * y) = T(x,(x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(2624(a,1),2430(a,1,2))].">
      <j1 rule="para" parents="2624 2430"/>
    </justification>
  </clause>

  <clause id="2649">
    <literal><![CDATA[
      T(x \ 1,((x \ 1) \ 1) * y) = T(x \ 1,x * y)
    ]]></literal>
    <justification jstring="[para(76(a,1),2648(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="76 2648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2650">
    <literal><![CDATA[
      ((x \ 1) \ y) * K(x \ 1,x) = (1 / x) \ y
    ]]></literal>
    <justification jstring="[hyper(121,a,10,a(flip),b,2642,a),flip(a)].">
      <j1 rule="hyper" parents="121 10 2642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2651">
    <literal><![CDATA[
      (x \ 1) * (y * ((x \ 1) \ 1)) = (1 / x) * (y * x)
    ]]></literal>
    <justification jstring="[para(1896(a,1),2642(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1896 2642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2652">
    <literal><![CDATA[
      (1 / x) * (x * y) = L(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(875,a,2643,a),flip(a)].">
      <j1 rule="hyper" parents="875 2643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2653">
    <literal><![CDATA[
      ((x \ 1) * y) / L(T(1 / x,y),y,K(x \ 1,x)) = K(x \ 1,x) * y
    ]]></literal>
    <justification jstring="[para(2643(a,1),487(a,1,1))].">
      <j1 rule="para" parents="2643 487"/>
    </justification>
  </clause>

  <clause id="2654">
    <literal><![CDATA[
      L(T(x,y),y,y \ 1) = (1 / y) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(595,a,2652,a),flip(a)].">
      <j1 rule="hyper" parents="595 2652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2655">
    <literal><![CDATA[
      L(x \ y,x,x \ 1) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(343,a,2652,a),flip(a)].">
      <j1 rule="hyper" parents="343 2652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2656">
    <literal><![CDATA[
      (1 / x) \ L(y,x,x \ 1) = x * y
    ]]></literal>
    <justification jstring="[hyper(129,a,2652,a)].">
      <j1 rule="hyper" parents="129 2652"/>
    </justification>
  </clause>

  <clause id="2658">
    <literal><![CDATA[
      L(x,y,y \ 1) \ x = a(1 / y,y,x)
    ]]></literal>
    <justification jstring="[para(2652(a,1),229(a,1,1))].">
      <j1 rule="para" parents="2652 229"/>
    </justification>
  </clause>

  <clause id="2659">
    <literal><![CDATA[
      L(x,y,y \ 1) \ ((1 / y) * (x * y)) = L(K(x,y),y * x,1 / y)
    ]]></literal>
    <justification jstring="[para(2652(a,1),319(a,1,1))].">
      <j1 rule="para" parents="2652 319"/>
    </justification>
  </clause>

  <clause id="2660">
    <literal><![CDATA[
      L((x \ 1) \ y,x \ 1,(x \ 1) \ 1) = x * y
    ]]></literal>
    <justification jstring="[hyper(333,a,186,a(flip),b,2655,a),flip(a)].">
      <j1 rule="hyper" parents="333 186 2655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2661">
    <literal><![CDATA[
      x * ((1 / x) * (y * x)) = L(y,x,x \ 1) * x
    ]]></literal>
    <justification jstring="[para(2655(a,1),666(a,1,2))].">
      <j1 rule="para" parents="2655 666"/>
    </justification>
  </clause>

  <clause id="2662">
    <literal><![CDATA[
      (1 / x) \ y != x * z
    ]]></literal>
    <literal><![CDATA[
      L(z,x,x \ 1) = y
    ]]></literal>
    <justification jstring="[para(2656(a,1),47(a,1)),flip(a)].">
      <j1 rule="para" parents="2656 47"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2663">
    <literal><![CDATA[
      (1 / (1 / x)) \ L(y,1 / x,x) = (1 / x) * y
    ]]></literal>
    <justification jstring="[para(79(a,1),2656(a,1,2,3))].">
      <j1 rule="para" parents="79 2656"/>
    </justification>
  </clause>

  <clause id="2664">
    <literal><![CDATA[
      (1 / x) * (x * y) != z
    ]]></literal>
    <literal><![CDATA[
      L(y,x,x \ 1) = z
    ]]></literal>
    <justification jstring="[para(2656(a,1),273(a,1,2)),flip(b)].">
      <j1 rule="para" parents="2656 273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2665">
    <literal><![CDATA[
      K(x,x \ 1) * ((1 / x) \ y) = (x \ 1) \ y
    ]]></literal>
    <justification jstring="[para(10(a,1),2647(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 2647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2666">
    <literal><![CDATA[
      L(K(x,x \ 1) * y,x \ 1,x) = x * ((1 / x) * y)
    ]]></literal>
    <justification jstring="[para(2647(a,1),514(a,1,1))].">
      <j1 rule="para" parents="2647 514"/>
    </justification>
  </clause>

  <clause id="2667">
    <literal><![CDATA[
      L(K(x,x \ 1) * y,x,x) = x * ((1 / x) * y)
    ]]></literal>
    <justification jstring="[para(2647(a,1),2601(a,1,1))].">
      <j1 rule="para" parents="2647 2601"/>
    </justification>
  </clause>

  <clause id="2669">
    <literal><![CDATA[
      ((1 / x) \ y) * K(x,x \ 1) = (x \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(2153,a,2650,a)].">
      <j1 rule="hyper" parents="2153 2650"/>
    </justification>
  </clause>

  <clause id="2670">
    <literal><![CDATA[
      ((1 / x) \ y) * (1 / x) = ((x \ 1) \ y) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(125,a,2650,a(flip),b,1905,a)].">
      <j1 rule="hyper" parents="125 2650 1905"/>
    </justification>
  </clause>

  <clause id="2672">
    <literal><![CDATA[
      K(x,x \ 1) * (((x \ y) / y) * x) = (x \ 1) \ ((x \ y) / y)
    ]]></literal>
    <justification jstring="[para(1332(a,1),2665(a,1,2))].">
      <j1 rule="para" parents="1332 2665"/>
    </justification>
  </clause>

  <clause id="2673">
    <literal><![CDATA[
      K(x,x \ 1) * (y * ((1 / x) \ z)) = y * ((x \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(2665(a,1),2503(a,2,2))].">
      <j1 rule="para" parents="2665 2503"/>
    </justification>
  </clause>

  <clause id="2674">
    <literal><![CDATA[
      (x \ y) * K(x \ 1,(x \ 1) \ 1) = ((x \ 1) \ 1) \ y
    ]]></literal>
    <justification jstring="[para(76(a,1),2669(a,1,1,1))].">
      <j1 rule="para" parents="76 2669"/>
    </justification>
  </clause>

  <clause id="2675">
    <literal><![CDATA[
      L(x * T(x \ 1,y),x \ 1,y) = K(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,2325,a,b,2625,a)].">
      <j1 rule="hyper" parents="63 2325 2625"/>
    </justification>
  </clause>

  <clause id="2676">
    <literal><![CDATA[
      L(K(x,x \ 1) * (y * x),x,x) = L(y,x,x \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(333,a,2661,a(flip),b,2667,a),flip(a)].">
      <j1 rule="hyper" parents="333 2661 2667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2677">
    <literal><![CDATA[
      L(x * K(y,y \ 1),y,y) = y * ((1 / y) * x)
    ]]></literal>
    <justification jstring="[para(2397(a,1),2667(a,1,1))].">
      <j1 rule="para" parents="2397 2667"/>
    </justification>
  </clause>

  <clause id="2678">
    <literal><![CDATA[
      L((1 / x) * T((1 / x) \ 1,y),x,y) = K(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[para(79(a,1),2675(a,1,2))].">
      <j1 rule="para" parents="79 2675"/>
    </justification>
  </clause>

  <clause id="2679">
    <literal><![CDATA[
      L(x,y,y) * K(y,y \ 1) = y * ((1 / y) * x)
    ]]></literal>
    <justification jstring="[hyper(2511,a,2677,a)].">
      <j1 rule="hyper" parents="2511 2677"/>
    </justification>
  </clause>

  <clause id="2680">
    <literal><![CDATA[
      (x * K(y,y \ 1)) * z = K(y,y \ 1) * (x * z)
    ]]></literal>
    <justification jstring="[hyper(333,a,2503,a,b,2641,a),flip(a)].">
      <j1 rule="hyper" parents="333 2503 2641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2681">
    <literal><![CDATA[
      x * (K(x,x \ 1) * y) = ((x \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[para(2101(a,1),2641(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2101 2641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2682">
    <literal><![CDATA[
      (K(x,x \ 1) * y) * z = y * (K(x,x \ 1) * z)
    ]]></literal>
    <justification jstring="[para(2397(a,2),2641(a,1,1))].">
      <j1 rule="para" parents="2397 2641"/>
    </justification>
  </clause>

  <clause id="2683">
    <literal><![CDATA[
      K(x,x \ 1) * (((x \ 1) \ 1) \ y) = x \ y
    ]]></literal>
    <justification jstring="[hyper(121,a,10,a(flip),b,2681,a),flip(a)].">
      <j1 rule="hyper" parents="121 10 2681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2684">
    <literal><![CDATA[
      K(x,x \ 1) * (x * y) = ((x \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,2503,a,b,2681,a)].">
      <j1 rule="hyper" parents="63 2503 2681"/>
    </justification>
  </clause>

  <clause id="2685">
    <literal><![CDATA[
      ((x \ 1) \ 1) * y != x * z
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ 1) * y = z
    ]]></literal>
    <justification jstring="[para(2681(a,1),43(a,1))].">
      <j1 rule="para" parents="2681 43"/>
    </justification>
  </clause>

  <clause id="2686">
    <literal><![CDATA[
      x * (y * K(x,x \ 1)) = ((x \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[para(2397(a,1),2681(a,1,2))].">
      <j1 rule="para" parents="2397 2681"/>
    </justification>
  </clause>

  <clause id="2687">
    <literal><![CDATA[
      K(x \ 1,x) * (x \ y) = ((x \ 1) \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(2459,a,2683,a)].">
      <j1 rule="hyper" parents="2459 2683"/>
    </justification>
  </clause>

  <clause id="2688">
    <literal><![CDATA[
      (x \ y) * K(x \ 1,x) = ((x \ 1) \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(34,a,2423,a,b,2683,a)].">
      <j1 rule="hyper" parents="34 2423 2683"/>
    </justification>
  </clause>

  <clause id="2689">
    <literal><![CDATA[
      K(x \ 1,x) * (((x \ 1) \ 1) * y) = x * y
    ]]></literal>
    <justification jstring="[hyper(2459,a,2684,a)].">
      <j1 rule="hyper" parents="2459 2684"/>
    </justification>
  </clause>

  <clause id="2690">
    <literal><![CDATA[
      (x * y) * K(x,x \ 1) = ((x \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(2403,a,2684,a)].">
      <j1 rule="hyper" parents="2403 2684"/>
    </justification>
  </clause>

  <clause id="2692">
    <literal><![CDATA[
      x * (y * K(x,x \ 1)) = T(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(333,a,329,a,b,2686,a),flip(a)].">
      <j1 rule="hyper" parents="333 329 2686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2693">
    <literal><![CDATA[
      x * T(x \ (y \ x),y) = ((y \ 1) \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,1154,a(flip),b,2687,a)].">
      <j1 rule="hyper" parents="63 1154 2687"/>
    </justification>
  </clause>

  <clause id="2694">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ y != z
    ]]></literal>
    <literal><![CDATA[
      (x \ y) * K(x \ 1,x) = z
    ]]></literal>
    <justification jstring="[para(2687(a,1),2416(a,1))].">
      <j1 rule="para" parents="2687 2416"/>
    </justification>
  </clause>

  <clause id="2695">
    <literal><![CDATA[
      (((x \ 1) \ 1) \ y) * ((x \ 1) \ 1) = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(2688(a,1),1901(a,1,1))].">
      <j1 rule="para" parents="2688 1901"/>
    </justification>
  </clause>

  <clause id="2696">
    <literal><![CDATA[
      K(x \ 1,x) \ (x * y) != z
    ]]></literal>
    <literal><![CDATA[
      ((x \ 1) \ 1) * y = z
    ]]></literal>
    <justification jstring="[para(2689(a,1),342(a,1,2))].">
      <j1 rule="para" parents="2689 342"/>
    </justification>
  </clause>

  <clause id="2697">
    <literal><![CDATA[
      K(T(x,y),x \ 1) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(34,a,2535,a,b,2690,a)].">
      <j1 rule="hyper" parents="34 2535 2690"/>
    </justification>
  </clause>

  <clause id="2698">
    <literal><![CDATA[
      K(T(x,y),T(x,y) \ 1) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,2533,a,b,2697,a)].">
      <j1 rule="hyper" parents="63 2533 2697"/>
    </justification>
  </clause>

  <clause id="2702">
    <literal><![CDATA[
      T(x,y) \ K(x,x \ 1) = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(121,a,2698,a(flip),b,2098,a(flip))].">
      <j1 rule="hyper" parents="121 2698 2098"/>
    </justification>
  </clause>

  <clause id="2704">
    <literal><![CDATA[
      (1 / T(x,y)) * x = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(125,a,2702,a(flip),b,2398,a(flip))].">
      <j1 rule="hyper" parents="125 2702 2398"/>
    </justification>
  </clause>

  <clause id="2705">
    <literal><![CDATA[
      x / T(x,y) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(1429,a,2704,a)].">
      <j1 rule="hyper" parents="1429 2704"/>
    </justification>
  </clause>

  <clause id="2706">
    <literal><![CDATA[
      (T(x,y) \ x) * T(x,y) = x
    ]]></literal>
    <justification jstring="[hyper(125,a,2704,a(flip),b,1417,a(flip))].">
      <j1 rule="hyper" parents="125 2704 1417"/>
    </justification>
  </clause>

  <clause id="2707">
    <literal><![CDATA[
      (T(x,y) \ x) / x != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ (1 / T(x,y)) = u
    ]]></literal>
    <justification jstring="[para(2704(a,1),415(a,1,1))].">
      <j1 rule="para" parents="2704 415"/>
    </justification>
  </clause>

  <clause id="2708">
    <literal><![CDATA[
      T(x,y) \ x != z
    ]]></literal>
    <literal><![CDATA[
      x / T(x,y) = z
    ]]></literal>
    <justification jstring="[para(2704(a,1),1429(a,1))].">
      <j1 rule="para" parents="2704 1429"/>
    </justification>
  </clause>

  <clause id="2709">
    <literal><![CDATA[
      (T(x,y) \ x) \ x = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(192,a,2705,a)].">
      <j1 rule="hyper" parents="192 2705"/>
    </justification>
  </clause>

  <clause id="2710">
    <literal><![CDATA[
      K(x \ (x / ((y \ x) / T(x,y))),x) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,2203,a,b,2705,a)].">
      <j1 rule="hyper" parents="63 2203 2705"/>
    </justification>
  </clause>

  <clause id="2711">
    <literal><![CDATA[
      L(x,T(x,y) \ x,x) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,2249,a,b,2706,a)].">
      <j1 rule="hyper" parents="63 2249 2706"/>
    </justification>
  </clause>

  <clause id="2713">
    <literal><![CDATA[
      (x * y) * T(K(y,x),x) = y * x
    ]]></literal>
    <justification jstring="[para(2711(a,1),2248(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2711 2248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2714">
    <literal><![CDATA[
      T(K(x,y),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(322,a,2713,a),flip(a)].">
      <j1 rule="hyper" parents="322 2713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2715">
    <literal><![CDATA[
      (x * K(y,x)) / x = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(289,a,2714,a)].">
      <j1 rule="hyper" parents="289 2714"/>
    </justification>
  </clause>

  <clause id="2716">
    <literal><![CDATA[
      T(x,K(y,x)) = x
    ]]></literal>
    <justification jstring="[hyper(54,a,2714,a)].">
      <j1 rule="hyper" parents="54 2714"/>
    </justification>
  </clause>

  <clause id="2717">
    <literal><![CDATA[
      K(x,y) * y = y * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(126,a,2714,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="126 2714 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2718">
    <literal><![CDATA[
      T(L(K(x,y),z,u),y) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(2714(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2714 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2719">
    <literal><![CDATA[
      (x * K(y,x)) / x != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(2714(a,1),302(a,1,1,2)),flip(b)].">
      <j1 rule="para" parents="2714 302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2720">
    <literal><![CDATA[
      T((x \ y) \ y,K(z,(x \ y) \ y)) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(333,a,112,a,b,2716,a),flip(a)].">
      <j1 rule="hyper" parents="333 112 2716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2721">
    <literal><![CDATA[
      T(x,K(y,R(x,z,u))) = x
    ]]></literal>
    <justification jstring="[hyper(151,a,2716,a)].">
      <j1 rule="hyper" parents="151 2716"/>
    </justification>
  </clause>

  <clause id="2722">
    <literal><![CDATA[
      T(x,K(y,L(x,z,u))) = x
    ]]></literal>
    <justification jstring="[hyper(150,a,2716,a)].">
      <j1 rule="hyper" parents="150 2716"/>
    </justification>
  </clause>

  <clause id="2723">
    <literal><![CDATA[
      T(x,K(y,T(x,z))) = x
    ]]></literal>
    <justification jstring="[hyper(147,a,2716,a)].">
      <j1 rule="hyper" parents="147 2716"/>
    </justification>
  </clause>

  <clause id="2724">
    <literal><![CDATA[
      K(x,K(y,x)) = 1
    ]]></literal>
    <justification jstring="[hyper(55,a,2716,a)].">
      <j1 rule="hyper" parents="55 2716"/>
    </justification>
  </clause>

  <clause id="2725">
    <literal><![CDATA[
      T(T(x,y),K(z,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(2716(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2716 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2726">
    <literal><![CDATA[
      K(x,y) * y != z
    ]]></literal>
    <literal><![CDATA[
      y * K(x,y) = z
    ]]></literal>
    <justification jstring="[para(2716(a,1),300(a,1,2))].">
      <j1 rule="para" parents="2716 300"/>
    </justification>
  </clause>

  <clause id="2727">
    <literal><![CDATA[
      T(x,y) * K(z,x) = K(z,x) * T(x,y)
    ]]></literal>
    <justification jstring="[para(2716(a,1),250(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2716 250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2728">
    <literal><![CDATA[
      L(x,y,z) * K(u,x) = K(u,x) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(2716(a,1),251(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2716 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2729">
    <literal><![CDATA[
      R(x,y,z) * K(u,x) = K(u,x) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(2716(a,1),252(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2716 252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2730">
    <literal><![CDATA[
      K(x,y) * T(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(2716(a,1),419(a,1,2,1))].">
      <j1 rule="para" parents="2716 419"/>
    </justification>
  </clause>

  <clause id="2731">
    <literal><![CDATA[
      L(x \ y,x,K(z,y)) = (K(z,y) * x) \ (y * K(z,y))
    ]]></literal>
    <justification jstring="[para(2716(a,1),468(a,1,1,2))].">
      <j1 rule="para" parents="2716 468"/>
    </justification>
  </clause>

  <clause id="2732">
    <literal><![CDATA[
      T(T(x,y),z) * K(u,x) = K(u,x) * T(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(2716(a,1),470(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="2716 470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2733">
    <literal><![CDATA[
      T(x,y \ T(y,x)) = x
    ]]></literal>
    <justification jstring="[para(2062(a,1),2716(a,1,2))].">
      <j1 rule="para" parents="2062 2716"/>
    </justification>
  </clause>

  <clause id="2734">
    <literal><![CDATA[
      T(x,x \ ((y * x) / y)) = x
    ]]></literal>
    <justification jstring="[para(2169(a,1),2716(a,1,2))].">
      <j1 rule="para" parents="2169 2716"/>
    </justification>
  </clause>

  <clause id="2735">
    <literal><![CDATA[
      x * ((K(x,y) \ y) * K(x,y)) = (y * x) * K(x,y)
    ]]></literal>
    <justification jstring="[para(2716(a,1),2315(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="2716 2315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2736">
    <literal><![CDATA[
      K(x,T(y,z)) * y = y * K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(126,a,2723,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="126 2723 22"/>
    </justification>
  </clause>

  <clause id="2738">
    <literal><![CDATA[
      (x \ T(x,y)) * y = y * (x \ T(x,y))
    ]]></literal>
    <justification jstring="[hyper(126,a,2733,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="126 2733 22"/>
    </justification>
  </clause>

  <clause id="2739">
    <literal><![CDATA[
      T(T(x,y),K(z,R(x,u,w))) = T(x,y)
    ]]></literal>
    <justification jstring="[para(2721(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2721 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2740">
    <literal><![CDATA[
      K(x,L(y,z,u)) * y = y * K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(126,a,2722,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="126 2722 22"/>
    </justification>
  </clause>

  <clause id="2741">
    <literal><![CDATA[
      L((T(x,y) * (x \ y)) / y,y,x) = K(T(x,y),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,1183,a,b,2715,a)].">
      <j1 rule="hyper" parents="63 1183 2715"/>
    </justification>
  </clause>

  <clause id="2742">
    <literal><![CDATA[
      T(K(x,y),y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(2715(a,1),350(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2715 350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2743">
    <literal><![CDATA[
      ((x * K(y,z)) * z) / (z * K(y,z)) = R(x,K(y,z),z)
    ]]></literal>
    <justification jstring="[hyper(197,a,2717,a(flip),b,187,a)].">
      <j1 rule="hyper" parents="197 2717 187"/>
    </justification>
  </clause>

  <clause id="2744">
    <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(2717(a,1),543(a,2,2))].">
      <j1 rule="para" parents="2717 543"/>
    </justification>
  </clause>

  <clause id="2745">
    <literal><![CDATA[
      T(K(x,y),T(y,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(54,a,2725,a)].">
      <j1 rule="hyper" parents="54 2725"/>
    </justification>
  </clause>

  <clause id="2746">
    <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(2725(a,1),419(a,1,2,1))].">
      <j1 rule="para" parents="2725 419"/>
    </justification>
  </clause>

  <clause id="2747">
    <literal><![CDATA[
      ((x * y) / x) / y = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(197,a,2734,a(flip),b,112,a(flip))].">
      <j1 rule="hyper" parents="197 2734 112"/>
    </justification>
  </clause>

  <clause id="2748">
    <literal><![CDATA[
      K(K(x,y),T(y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(55,a,2745,a)].">
      <j1 rule="hyper" parents="55 2745"/>
    </justification>
  </clause>

  <clause id="2749">
    <literal><![CDATA[
      K(x \ T(x,y),T(y,z)) = 1
    ]]></literal>
    <justification jstring="[para(2062(a,1),2748(a,1,1))].">
      <j1 rule="para" parents="2062 2748"/>
    </justification>
  </clause>

  <clause id="2750">
    <literal><![CDATA[
      T(x \ T(x,y),T(y,z)) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(56,a,2749,a)].">
      <j1 rule="hyper" parents="56 2749"/>
    </justification>
  </clause>

  <clause id="2751">
    <literal><![CDATA[
      T(x,L(K(y,x),z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(54,a,2718,a)].">
      <j1 rule="hyper" parents="54 2718"/>
    </justification>
  </clause>

  <clause id="2752">
    <literal><![CDATA[
      x * (((y * x) / y) / x) = (y * x) / y
    ]]></literal>
    <justification jstring="[hyper(126,a,2747,a,b,xx)].">
      <j1 rule="hyper" parents="126 2747"/>
    </justification>
  </clause>

  <clause id="2754">
    <literal><![CDATA[
      x * (((x \ (y \ x)) \ 1) \ 1) = ((y \ 1) \ 1) \ x
    ]]></literal>
    <justification jstring="[para(2502(a,1),2693(a,1,2))].">
      <j1 rule="para" parents="2502 2693"/>
    </justification>
  </clause>

  <clause id="2756">
    <literal><![CDATA[
      R(T(x \ 1,x * y),x,y) = (((x \ 1) \ 1) * y) \ y
    ]]></literal>
    <justification jstring="[para(2649(a,1),1961(a,1,1))].">
      <j1 rule="para" parents="2649 1961"/>
    </justification>
  </clause>

  <clause id="2757">
    <literal><![CDATA[
      1 \ ((x \ 1) * (y * ((x \ 1) \ 1))) = (1 / x) * (y * x)
    ]]></literal>
    <justification jstring="[hyper(211,a,2651,a)].">
      <j1 rule="hyper" parents="211 2651"/>
    </justification>
  </clause>

  <clause id="2758">
    <literal><![CDATA[
      (x \ 1) * y != (1 / x) * (z * x)
    ]]></literal>
    <literal><![CDATA[
      z * ((x \ 1) \ 1) = y
    ]]></literal>
    <justification jstring="[para(2651(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="2651 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2760">
    <literal><![CDATA[
      K(x,x \ 1) * ((1 / (1 / x)) * y) = x * y
    ]]></literal>
    <justification jstring="[para(2109(a,1),2680(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2109 2680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2761">
    <literal><![CDATA[
      K(x,x \ 1) * ((y \ x) * z) = (y \ ((x \ 1) \ 1)) * z
    ]]></literal>
    <justification jstring="[para(2138(a,1),2680(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2138 2680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2762">
    <literal><![CDATA[
      (K(x,x \ 1) * y) * z = K(x,x \ 1) * (y * z)
    ]]></literal>
    <justification jstring="[para(2397(a,2),2680(a,1,1))].">
      <j1 rule="para" parents="2397 2680"/>
    </justification>
  </clause>

  <clause id="2763">
    <literal><![CDATA[
      K(x,x \ 1) * ((K(x \ 1,x) * y) * z) = y * z
    ]]></literal>
    <justification jstring="[para(2439(a,1),2680(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2439 2680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2764">
    <literal><![CDATA[
      K(x,x \ 1) * (((x \ 1) * y) * z) = ((1 / x) * y) * z
    ]]></literal>
    <justification jstring="[para(2644(a,1),2680(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2644 2680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2765">
    <literal><![CDATA[
      (x * y) * K(x \ 1,x) = (1 / (1 / x)) * y
    ]]></literal>
    <justification jstring="[hyper(34,a,2423,a,b,2760,a)].">
      <j1 rule="hyper" parents="34 2423 2760"/>
    </justification>
  </clause>

  <clause id="2766">
    <literal><![CDATA[
      K(x,x \ 1) * ((y \ (1 / (1 / x))) * y) = x * K(y \ (1 / (1 / x)),y)
    ]]></literal>
    <justification jstring="[para(317(a,1),2760(a,1,2))].">
      <j1 rule="para" parents="317 2760"/>
    </justification>
  </clause>

  <clause id="2767">
    <literal><![CDATA[
      ((1 / (1 / x)) * y) * (1 / x) = (x * y) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(125,a,2765,a(flip),b,1905,a)].">
      <j1 rule="hyper" parents="125 2765 1905"/>
    </justification>
  </clause>

  <clause id="2768">
    <literal><![CDATA[
      (((x \ 1) \ 1) \ y) * ((x \ 1) \ 1) != y * z
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,x) = z
    ]]></literal>
    <justification jstring="[para(2695(a,2),481(a,1))].">
      <j1 rule="para" parents="2695 481"/>
    </justification>
  </clause>

  <clause id="2769">
    <literal><![CDATA[
      T(x \ 1,T(x,y) \ x) = x \ 1
    ]]></literal>
    <justification jstring="[para(2710(a,1),2044(a,1,2))].">
      <j1 rule="para" parents="2710 2044"/>
    </justification>
  </clause>

  <clause id="2770">
    <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(2710(a,1),2037(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2710 2037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2771">
    <literal><![CDATA[
      T(T(x,y) \ x,x \ 1) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(54,a,2769,a)].">
      <j1 rule="hyper" parents="54 2769"/>
    </justification>
  </clause>

  <clause id="2772">
    <literal><![CDATA[
      (K(x,y) \ y) * K(x,y) = y
    ]]></literal>
    <justification jstring="[hyper(34,a,88,a(flip),b,2735,a),flip(a)].">
      <j1 rule="hyper" parents="34 88 2735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2773">
    <literal><![CDATA[
      x / K(y,x) = K(y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(138,a,2772,a)].">
      <j1 rule="hyper" parents="138 2772"/>
    </justification>
  </clause>

  <clause id="2779">
    <literal><![CDATA[
      (((x \ 1) \ 1) \ y) / y = (((x \ y) / y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(123,a,2754,a(flip),b,2392,a)].">
      <j1 rule="hyper" parents="123 2754 2392"/>
    </justification>
  </clause>

  <clause id="2780">
    <literal><![CDATA[
      (((x / y) \ 1) \ 1) \ x = x * (((x \ y) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(79(a,1),2754(a,1,2,1,1,2)),flip(a)].">
      <j1 rule="para" parents="79 2754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2781">
    <literal><![CDATA[
      R(K(x,x \ 1),y,z) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(1924,a,2762,a)].">
      <j1 rule="hyper" parents="1924 2762"/>
    </justification>
  </clause>

  <clause id="2782">
    <literal><![CDATA[
      L(x,y,K(z,z \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(501,a,2762,a)].">
      <j1 rule="hyper" parents="501 2762"/>
    </justification>
  </clause>

  <clause id="2783">
    <literal><![CDATA[
      K(x,x \ 1) * (1 / y) = K(x,x \ 1) / y
    ]]></literal>
    <justification jstring="[hyper(123,a,78,a(flip),b,2762,a),flip(a)].">
      <j1 rule="hyper" parents="123 78 2762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2785">
    <literal><![CDATA[
      L(x,y,K(z,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(2782(a,1),50(a,2))].">
      <j1 rule="para" parents="2782 50"/>
    </justification>
  </clause>

  <clause id="2786">
    <literal><![CDATA[
      L(x,y,K(1 / z,z)) = x
    ]]></literal>
    <justification jstring="[para(79(a,1),2782(a,1,3,2))].">
      <j1 rule="para" parents="79 2782"/>
    </justification>
  </clause>

  <clause id="2787">
    <literal><![CDATA[
      L(x,y,K(z,1 / z)) = x
    ]]></literal>
    <justification jstring="[para(2094(a,2),2782(a,1,3))].">
      <j1 rule="para" parents="2094 2782"/>
    </justification>
  </clause>

  <clause id="2788">
    <literal><![CDATA[
      L(x,y,z * (1 / z)) = x
    ]]></literal>
    <justification jstring="[para(2098(a,1),2782(a,1,3))].">
      <j1 rule="para" parents="2098 2782"/>
    </justification>
  </clause>

  <clause id="2789">
    <literal><![CDATA[
      L(x,y,K(z \ 1,z)) = x
    ]]></literal>
    <justification jstring="[para(2100(a,1),2782(a,1,3))].">
      <j1 rule="para" parents="2100 2782"/>
    </justification>
  </clause>

  <clause id="2790">
    <literal><![CDATA[
      (K(1 / x,x) * y) * z = K(1 / x,x) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(1170,a,2786,a),flip(a)].">
      <j1 rule="hyper" parents="1170 2786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2791">
    <literal><![CDATA[
      (K(x,1 / x) * y) * z = K(x,1 / x) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(1170,a,2787,a),flip(a)].">
      <j1 rule="hyper" parents="1170 2787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2792">
    <literal><![CDATA[
      K(x,1 / x) * (1 / y) = K(x,1 / x) / y
    ]]></literal>
    <justification jstring="[hyper(197,a,2787,a(flip),b,2613,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="197 2787 2613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2793">
    <literal><![CDATA[
      ((x * (1 / x)) \ y) \ z = y \ ((x * (1 / x)) * z)
    ]]></literal>
    <justification jstring="[hyper(597,a,2788,a),flip(a)].">
      <j1 rule="hyper" parents="597 2788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2794">
    <literal><![CDATA[
      ((x * (1 / x)) * y) \ z = y \ ((x * (1 / x)) \ z)
    ]]></literal>
    <justification jstring="[hyper(578,a,2788,a),flip(a)].">
      <j1 rule="hyper" parents="578 2788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2795">
    <literal><![CDATA[
      ((x * (1 / x)) * y) / z = (x * (1 / x)) * (y / z)
    ]]></literal>
    <justification jstring="[hyper(197,a,2788,a(flip),b,101,a(flip))].">
      <j1 rule="hyper" parents="197 2788 101"/>
    </justification>
  </clause>

  <clause id="2796">
    <literal><![CDATA[
      (K(x \ 1,x) * y) * z = K(x \ 1,x) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(1170,a,2789,a),flip(a)].">
      <j1 rule="hyper" parents="1170 2789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2798">
    <literal><![CDATA[
      (x * K(y \ 1,y)) \ z = x \ (K(y,y \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,2540,a(flip),b,2789,a)].">
      <j1 rule="hyper" parents="63 2540 2789"/>
    </justification>
  </clause>

  <clause id="2799">
    <literal><![CDATA[
      (K(x \ 1,x) * y) / z = K(x \ 1,x) * (y / z)
    ]]></literal>
    <justification jstring="[hyper(197,a,2789,a(flip),b,101,a(flip))].">
      <j1 rule="hyper" parents="197 2789 101"/>
    </justification>
  </clause>

  <clause id="2800">
    <literal><![CDATA[
      L(x,y,K(z \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(2789(a,1),50(a,2))].">
      <j1 rule="para" parents="2789 50"/>
    </justification>
  </clause>

  <clause id="2801">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      L(x,z,K(u \ 1,u)) = y
    ]]></literal>
    <justification jstring="[para(2789(a,1),2593(a,1))].">
      <j1 rule="para" parents="2789 2593"/>
    </justification>
  </clause>

  <clause id="2803">
    <literal><![CDATA[
      K(x,x \ 1) / y != z
    ]]></literal>
    <literal><![CDATA[
      (1 / y) * K(x,x \ 1) = z
    ]]></literal>
    <justification jstring="[para(2783(a,1),2403(a,1))].">
      <j1 rule="para" parents="2783 2403"/>
    </justification>
  </clause>

  <clause id="2804">
    <literal><![CDATA[
      (K(x \ 1,x) * y) \ z = y \ (K(x,x \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(631,a,2763,a),flip(a)].">
      <j1 rule="hyper" parents="631 2763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2805">
    <literal><![CDATA[
      K(x,x \ 1) * ((y \ (1 / (1 / x))) * z) = (y \ x) * z
    ]]></literal>
    <justification jstring="[para(2494(a,1),2763(a,1,2,1))].">
      <j1 rule="para" parents="2494 2763"/>
    </justification>
  </clause>

  <clause id="2806">
    <literal><![CDATA[
      ((1 / (1 / x)) * (((x \ 1) * (x \ y)) / (x \ 1))) * (1 / x) = x * ((x \ 1) * ((x \ (y * (x \ 1))) / (x \ 1)))
    ]]></literal>
    <justification jstring="[hyper(333,a,2022,a(flip),b,2767,a),flip(a)].">
      <j1 rule="hyper" parents="333 2022 2767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2807">
    <literal><![CDATA[
      (x * K(y \ (1 / (1 / x)),y)) * (x \ 1) = ((y \ (1 / (1 / x))) * y) * (1 / x)
    ]]></literal>
    <justification jstring="[para(317(a,1),2767(a,1,1)),flip(a)].">
      <j1 rule="para" parents="317 2767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2808">
    <literal><![CDATA[
      x / (x * (((x \ y) \ 1) \ 1)) = ((x / y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(198,a,2780,a)].">
      <j1 rule="hyper" parents="198 2780"/>
    </justification>
  </clause>

  <clause id="2809">
    <literal><![CDATA[
      x / ((((y / x) \ 1) \ 1) * x) = ((x / y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(197,a,2392,a,b,2780,a)].">
      <j1 rule="hyper" parents="197 2392 2780"/>
    </justification>
  </clause>

  <clause id="2810">
    <literal><![CDATA[
      (K(1 / x,x) * y) \ (y * (1 / (1 / x))) = x
    ]]></literal>
    <justification jstring="[hyper(121,a,2475,a(flip),b,2790,a)].">
      <j1 rule="hyper" parents="121 2475 2790"/>
    </justification>
  </clause>

  <clause id="2811">
    <literal><![CDATA[
      K(1 / x,x) * (y / (1 / (1 / x))) = y / x
    ]]></literal>
    <justification jstring="[para(2810(a,1),336(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2810 336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2812">
    <literal><![CDATA[
      (K(x,1 / x) * y) * z = y * (z * K(x,1 / x))
    ]]></literal>
    <justification jstring="[hyper(333,a,2432,a(flip),b,2791,a),flip(a)].">
      <j1 rule="hyper" parents="333 2432 2791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2814">
    <literal><![CDATA[
      ((K(x \ 1,x) * (y * z)) * u) / (z * u) = R(K(x \ 1,x) * y,z,u)
    ]]></literal>
    <justification jstring="[para(2796(a,1),20(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="2796 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2815">
    <literal><![CDATA[
      (x * K(y \ 1,y)) * z = K(y \ 1,y) * (x * z)
    ]]></literal>
    <justification jstring="[para(2412(a,1),2796(a,1,1))].">
      <j1 rule="para" parents="2412 2796"/>
    </justification>
  </clause>

  <clause id="2816">
    <literal><![CDATA[
      (x * (y * K(z \ 1,z))) * u = K(z \ 1,z) * ((x * y) * u)
    ]]></literal>
    <justification jstring="[para(2438(a,1),2796(a,1,1))].">
      <j1 rule="para" parents="2438 2796"/>
    </justification>
  </clause>

  <clause id="2818">
    <literal><![CDATA[
      (x * K(y \ 1,y)) \ z = (x \ z) * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(333,a,2427,a(flip),b,2798,a),flip(a)].">
      <j1 rule="hyper" parents="333 2427 2798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2819">
    <literal><![CDATA[
      (x * (y * K(z \ 1,z))) \ u = (x * y) \ (K(z,z \ 1) * u)
    ]]></literal>
    <justification jstring="[para(1879(a,1),2798(a,1,1))].">
      <j1 rule="para" parents="1879 2798"/>
    </justification>
  </clause>

  <clause id="2820">
    <literal><![CDATA[
      (x * K(y \ 1,y)) \ (z * K(y \ 1,y)) = x \ z
    ]]></literal>
    <justification jstring="[para(2423(a,1),2798(a,2,2))].">
      <j1 rule="para" parents="2423 2798"/>
    </justification>
  </clause>

  <clause id="2821">
    <literal><![CDATA[
      (x \ y) \ (K(x,x \ 1) * z) = (((x \ 1) \ 1) \ y) \ z
    ]]></literal>
    <justification jstring="[para(2688(a,1),2798(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2688 2798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2822">
    <literal><![CDATA[
      K(x \ 1,x) * (((x \ 1) \ 1) / y) = x / y
    ]]></literal>
    <justification jstring="[para(972(a,1),2799(a,1,1)),flip(a)].">
      <j1 rule="para" parents="972 2799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2823">
    <literal><![CDATA[
      (x / y) * K(x,x \ 1) = ((x \ 1) \ 1) / y
    ]]></literal>
    <justification jstring="[hyper(2442,a,2822,a)].">
      <j1 rule="hyper" parents="2442 2822"/>
    </justification>
  </clause>

  <clause id="2824">
    <literal><![CDATA[
      x / (x * ((y \ 1) \ 1)) = ((x / (x * y)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(9(a,1),2808(a,1,2,2,1,1))].">
      <j1 rule="para" parents="9 2808"/>
    </justification>
  </clause>

  <clause id="2825">
    <literal><![CDATA[
      x / (((y \ 1) \ 1) * x) = ((x / (y * x)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(11(a,1),2809(a,1,2,1,1,1))].">
      <j1 rule="para" parents="11 2809"/>
    </justification>
  </clause>

  <clause id="2828">
    <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(2815(a,1),14(a,2,1)),flip(a)].">
      <j1 rule="para" parents="2815 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2829">
    <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(2815(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="2815 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2830">
    <literal><![CDATA[
      (x * (y * K(z \ 1,z))) \ (x * (K(z \ 1,z) * (y * u))) != w
    ]]></literal>
    <literal><![CDATA[
      L(u,y * K(z \ 1,z),x) = w
    ]]></literal>
    <justification jstring="[para(2815(a,1),504(a,1,2,2))].">
      <j1 rule="para" parents="2815 504"/>
    </justification>
  </clause>

  <clause id="2831">
    <literal><![CDATA[
      K(x \ 1,x) * ((y / (x \ 1)) * z) = (y / (1 / x)) * z
    ]]></literal>
    <justification jstring="[para(1903(a,1),2815(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1903 2815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2832">
    <literal><![CDATA[
      (x \ (x * (y * L(z,y,y)))) * K(y,y \ 1) = L(L(y * z,y,y \ 1),(y \ 1) * y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,2316,a(flip),b,2818,a),flip(a)].">
      <j1 rule="hyper" parents="63 2316 2818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2833">
    <literal><![CDATA[
      (x \ y) * K(x,x \ 1) = (1 / (1 / x)) \ y
    ]]></literal>
    <justification jstring="[para(1915(a,1),2818(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1915 2818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2834">
    <literal><![CDATA[
      ((1 / (1 / x)) \ y) / (1 / x) = (x \ y) / (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(123,a,2833,a(flip),b,2144,a)].">
      <j1 rule="hyper" parents="123 2833 2144"/>
    </justification>
  </clause>

  <clause id="2835">
    <literal><![CDATA[
      (x \ y) * K(x,1 / x) = (1 / (1 / x)) \ y
    ]]></literal>
    <justification jstring="[para(2094(a,2),2833(a,1,2))].">
      <j1 rule="para" parents="2094 2833"/>
    </justification>
  </clause>

  <clause id="2836">
    <literal><![CDATA[
      ((1 / (1 / x)) \ y) * x = (x \ y) * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(2833(a,1),2154(a,1,1))].">
      <j1 rule="para" parents="2833 2154"/>
    </justification>
  </clause>

  <clause id="2837">
    <literal><![CDATA[
      K(x,1 / x) * (x \ y) = (1 / (1 / x)) \ y
    ]]></literal>
    <justification jstring="[hyper(63,a,2408,a,b,2835,a)].">
      <j1 rule="hyper" parents="63 2408 2835"/>
    </justification>
  </clause>

  <clause id="2838">
    <literal><![CDATA[
      K(x,1 / x) * ((x \ y) * z) = ((1 / (1 / x)) \ y) * z
    ]]></literal>
    <justification jstring="[para(2837(a,1),2791(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2837 2791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2839">
    <literal><![CDATA[
      T(x,x \ y) = ((x \ y) * K(z \ 1,z)) \ (y * K(z \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(333,a,112,a,b,2820,a)].">
      <j1 rule="hyper" parents="333 112 2820"/>
    </justification>
  </clause>

  <clause id="2841">
    <literal><![CDATA[
      x \ (y * K(x \ 1,x)) = T(x,x \ 1) \ y
    ]]></literal>
    <justification jstring="[para(1247(a,1),2820(a,1,1))].">
      <j1 rule="para" parents="1247 2820"/>
    </justification>
  </clause>

  <clause id="2842">
    <literal><![CDATA[
      (K(x,x \ 1) * y) \ z = y \ (z * K(x \ 1,x))
    ]]></literal>
    <justification jstring="[para(2426(a,1),2820(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2426 2820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2843">
    <literal><![CDATA[
      R(x \ 1,x,y) = ((y / (x * y)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,1940,a,b,2825,a)].">
      <j1 rule="hyper" parents="63 1940 2825"/>
    </justification>
  </clause>

  <clause id="2846">
    <literal><![CDATA[
      T(x / (1 / (1 / y)),1 / (1 / y)) / (1 / y) = (y \ x) / (y \ 1)
    ]]></literal>
    <justification jstring="[para(113(a,2),2834(a,1,1))].">
      <j1 rule="para" parents="113 2834"/>
    </justification>
  </clause>

  <clause id="2847">
    <literal><![CDATA[
      (K(x,x \ 1) * y) \ z = (y \ z) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,1881,a(flip),b,2842,a),flip(a)].">
      <j1 rule="hyper" parents="333 1881 2842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2848">
    <literal><![CDATA[
      (K(x,x \ 1) * y) \ z = K(x \ 1,x) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(333,a,2412,a,b,2847,a),flip(a)].">
      <j1 rule="hyper" parents="333 2412 2847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2849">
    <literal><![CDATA[
      x / (y * K(z \ 1,z)) = K(z,z \ 1) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(197,a,195,a(flip),b,2847,a)].">
      <j1 rule="hyper" parents="197 195 2847"/>
    </justification>
  </clause>

  <clause id="2850">
    <literal><![CDATA[
      (x * (K(y,y \ 1) * z)) \ u = ((x * z) \ u) * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(2503(a,1),2847(a,1,1))].">
      <j1 rule="para" parents="2503 2847"/>
    </justification>
  </clause>

  <clause id="2851">
    <literal><![CDATA[
      (((x \ 1) * y) \ z) * K(x \ 1,x) = ((1 / x) * y) \ z
    ]]></literal>
    <justification jstring="[para(2624(a,1),2847(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2624 2847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2852">
    <literal><![CDATA[
      (((1 / x) \ y) \ z) * K(x \ 1,x) = ((x \ 1) \ y) \ z
    ]]></literal>
    <justification jstring="[para(2665(a,1),2847(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2665 2847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2853">
    <literal><![CDATA[
      (x * K(y,y \ 1)) \ z = K(y \ 1,y) * (x \ z)
    ]]></literal>
    <justification jstring="[para(2397(a,1),2848(a,1,1))].">
      <j1 rule="para" parents="2397 2848"/>
    </justification>
  </clause>

  <clause id="2854">
    <literal><![CDATA[
      K(x \ 1,x) * ((x * y) \ z) = (((x \ 1) \ 1) * y) \ z
    ]]></literal>
    <justification jstring="[para(2684(a,1),2848(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2684 2848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2855">
    <literal><![CDATA[
      x / (y * (z * K(u \ 1,u))) = K(u,u \ 1) * (x / (y * z))
    ]]></literal>
    <justification jstring="[para(1879(a,1),2849(a,1,2))].">
      <j1 rule="para" parents="1879 2849"/>
    </justification>
  </clause>

  <clause id="2856">
    <literal><![CDATA[
      x / (K(y \ 1,y) * z) = K(y,y \ 1) * (x / z)
    ]]></literal>
    <justification jstring="[para(2412(a,2),2849(a,1,2))].">
      <j1 rule="para" parents="2412 2849"/>
    </justification>
  </clause>

  <clause id="2857">
    <literal><![CDATA[
      (x * K(y,y \ 1)) \ z = x \ (K(y \ 1,y) * z)
    ]]></literal>
    <justification jstring="[hyper(333,a,2483,a,b,2853,a),flip(a)].">
      <j1 rule="hyper" parents="333 2483 2853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2858">
    <literal><![CDATA[
      (x * K(y,y \ 1)) \ 1 = x \ K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,2437,a(flip),b,2853,a),flip(a)].">
      <j1 rule="hyper" parents="333 2437 2853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2859">
    <literal><![CDATA[
      L(x \ 1,y,z) \ K(x \ 1,x) = L(1 / x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(2361(a,1),2858(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2361 2858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2860">
    <literal><![CDATA[
      (x * K(y,y \ 1)) \ (1 / y) = x \ (y \ 1)
    ]]></literal>
    <justification jstring="[para(1909(a,1),2857(a,2,2))].">
      <j1 rule="para" parents="1909 2857"/>
    </justification>
  </clause>

  <clause id="2861">
    <literal><![CDATA[
      ((x \ 1) * y) \ (K(x \ 1,x) * z) = ((1 / x) * y) \ z
    ]]></literal>
    <justification jstring="[para(2644(a,1),2857(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2644 2857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2862">
    <literal><![CDATA[
      ((x \ 1) / y) * K(x,x \ 1) = (1 / x) / y
    ]]></literal>
    <justification jstring="[hyper(197,a,79,a(flip),b,2860,a),flip(a)].">
      <j1 rule="hyper" parents="197 79 2860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2863">
    <literal><![CDATA[
      L(1 / x,y,z) \ (1 / x) = L(x \ 1,y,z) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(2361(a,1),2860(a,1,1))].">
      <j1 rule="para" parents="2361 2860"/>
    </justification>
  </clause>

  <clause id="2864">
    <literal><![CDATA[
      K(x,x \ 1) * ((x \ 1) / y) = (1 / x) / y
    ]]></literal>
    <justification jstring="[hyper(2399,a,2862,a)].">
      <j1 rule="hyper" parents="2399 2862"/>
    </justification>
  </clause>

  <clause id="2865">
    <literal><![CDATA[
      T(x,x \ 1) * y != x * z
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ 1) * y = z
    ]]></literal>
    <justification jstring="[para(112(a,2),2685(a,1,1))].">
      <j1 rule="para" parents="112 2685"/>
    </justification>
  </clause>

  <clause id="2866">
    <literal><![CDATA[
      (1 / x) \ (1 / T(x,y)) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(2707,a,2019,a(flip))].">
      <j1 rule="hyper" parents="2707 2019"/>
    </justification>
  </clause>

  <clause id="2867">
    <literal><![CDATA[
      T((x * y) \ y,x) = (((x \ 1) \ 1) * y) \ y
    ]]></literal>
    <justification jstring="[hyper(63,a,1043,a(flip),b,2756,a)].">
      <j1 rule="hyper" parents="63 1043 2756"/>
    </justification>
  </clause>

  <clause id="2868">
    <literal><![CDATA[
      (T(x,x \ 1) * y) \ y = T((x * y) \ y,x)
    ]]></literal>
    <justification jstring="[para(112(a,2),2867(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="112 2867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2869">
    <literal><![CDATA[
      T(x,y) \ L(T(x,y),z,u) = T(x \ L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(2582(a,1),2584(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2582 2584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2870">
    <literal><![CDATA[
      T(x \ L(x,y,z),L(x,u,w) \ x) = x \ L(T(x,L(x,u,w) \ x),y,z)
    ]]></literal>
    <justification jstring="[para(2564(a,1),2869(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2564 2869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2871">
    <literal><![CDATA[
      x \ ((x * (y * y)) / y) = (x * (1 / y)) \ x
    ]]></literal>
    <justification jstring="[para(11(a,1),2614(a,1,1))].">
      <j1 rule="para" parents="11 2614"/>
    </justification>
  </clause>

  <clause id="2872">
    <literal><![CDATA[
      x \ (x / (y / (y * y))) = (x * (1 / y)) \ x
    ]]></literal>
    <justification jstring="[para(801(a,1),2871(a,1,2))].">
      <j1 rule="para" parents="801 2871"/>
    </justification>
  </clause>

  <clause id="2873">
    <literal><![CDATA[
      (x * (1 / y)) \ x = x \ (x / (y \ 1))
    ]]></literal>
    <justification jstring="[para(284(a,1),2872(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="284 2872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2874">
    <literal><![CDATA[
      L(1 / x,x,y) = y \ (y / ((1 / x) \ 1))
    ]]></literal>
    <justification jstring="[hyper(2630,a,2873,a)].">
      <j1 rule="hyper" parents="2630 2873"/>
    </justification>
  </clause>

  <clause id="2875">
    <literal><![CDATA[
      L(x,x,y) = y \ (y / (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(2617,a,2873,a)].">
      <j1 rule="hyper" parents="2617 2873"/>
    </justification>
  </clause>

  <clause id="2876">
    <literal><![CDATA[
      (x / (y \ 1)) / L(y,y,x) = x
    ]]></literal>
    <justification jstring="[hyper(197,a,2606,a,b,2873,a(flip))].">
      <j1 rule="hyper" parents="197 2606 2873"/>
    </justification>
  </clause>

  <clause id="2877">
    <literal><![CDATA[
      x * L(y,y,x) = x / (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(126,a,2606,a,b,2873,a(flip))].">
      <j1 rule="hyper" parents="126 2606 2873"/>
    </justification>
  </clause>

  <clause id="2878">
    <literal><![CDATA[
      x \ (x / ((y \ 1) \ 1)) = (x * y) \ x
    ]]></literal>
    <justification jstring="[para(76(a,1),2873(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="76 2873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2879">
    <literal><![CDATA[
      (x / (y \ 1)) * y = x * (y * y)
    ]]></literal>
    <justification jstring="[hyper(125,a,2877,a(flip),b,1823,a)].">
      <j1 rule="hyper" parents="125 2877 1823"/>
    </justification>
  </clause>

  <clause id="2880">
    <literal><![CDATA[
      T(x / (y \ 1),y) = y \ (x * (y * y))
    ]]></literal>
    <justification jstring="[hyper(444,a,xx,b,2879,a)].">
      <j1 rule="hyper" parents="444 2879"/>
    </justification>
  </clause>

  <clause id="2881">
    <literal><![CDATA[
      T(x / (y \ 1),y) = (y \ x) * (y * y)
    ]]></literal>
    <justification jstring="[hyper(333,a,441,a(flip),b,2880,a),flip(a)].">
      <j1 rule="hyper" parents="333 441 2880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2882">
    <literal><![CDATA[
      (x \ ((x \ 1) * (y / x))) * (x * x) = ((x \ 1) * (x \ y)) / (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(1000,a,2881,a),flip(a)].">
      <j1 rule="hyper" parents="1000 2881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2883">
    <literal><![CDATA[
      L(1 / x,x,y) = y \ (y / x)
    ]]></literal>
    <justification jstring="[para(79(a,1),2874(a,2,2,2))].">
      <j1 rule="para" parents="79 2874"/>
    </justification>
  </clause>

  <clause id="2884">
    <literal><![CDATA[
      x \ L(x,x,y) = (y \ (y / x)) * x
    ]]></literal>
    <justification jstring="[hyper(125,a,2883,a(flip),b,2590,a),flip(a)].">
      <j1 rule="hyper" parents="125 2883 2590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2885">
    <literal><![CDATA[
      (x \ (x / y)) * y = y * ((x * y) \ x)
    ]]></literal>
    <justification jstring="[hyper(125,a,2883,a(flip),b,887,a)].">
      <j1 rule="hyper" parents="125 2883 887"/>
    </justification>
  </clause>

  <clause id="2886">
    <literal><![CDATA[
      T(x \ (x / y),y) = (x * y) \ x
    ]]></literal>
    <justification jstring="[hyper(253,a,2884,a(flip),b,2587,a(flip))].">
      <j1 rule="hyper" parents="253 2884 2587"/>
    </justification>
  </clause>

  <clause id="2888">
    <literal><![CDATA[
      T(x \ (x / (1 / y)),1 / y) = x \ (x / (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(333,a,2873,a(flip),b,2886,a),flip(a)].">
      <j1 rule="hyper" parents="333 2873 2886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2889">
    <literal><![CDATA[
      ((x \ (x / y)) \ 1) \ 1 = (x * y) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,2287,a(flip),b,2886,a)].">
      <j1 rule="hyper" parents="63 2287 2886"/>
    </justification>
  </clause>

  <clause id="2890">
    <literal><![CDATA[
      1 / ((x * y) \ x) = (x \ (x / y)) \ 1
    ]]></literal>
    <justification jstring="[hyper(197,a,2886,a(flip),b,2287,a(flip))].">
      <j1 rule="hyper" parents="197 2886 2287"/>
    </justification>
  </clause>

  <clause id="2891">
    <literal><![CDATA[
      x * (y \ (y / ((x \ 1) \ 1))) = (y \ (y / x)) * x
    ]]></literal>
    <justification jstring="[para(2878(a,2),2885(a,2,2)),flip(a)].">
      <j1 rule="para" parents="2878 2885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2892">
    <literal><![CDATA[
      ((x \ (x / y)) \ 1) \ 1 = x \ (x / ((y \ 1) \ 1))
    ]]></literal>
    <justification jstring="[hyper(333,a,2878,a,b,2889,a),flip(a)].">
      <j1 rule="hyper" parents="333 2878 2889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2893">
    <literal><![CDATA[
      1 / (x \ (x / (y \ 1))) = (x \ (x / (1 / y))) \ 1
    ]]></literal>
    <justification jstring="[hyper(197,a,2873,a(flip),b,2889,a)].">
      <j1 rule="hyper" parents="197 2873 2889"/>
    </justification>
  </clause>

  <clause id="2894">
    <literal><![CDATA[
      ((x \ y) \ 1) \ 1 = (x * (y \ x)) \ x
    ]]></literal>
    <justification jstring="[para(76(a,1),2889(a,1,1,1,2))].">
      <j1 rule="para" parents="76 2889"/>
    </justification>
  </clause>

  <clause id="2895">
    <literal><![CDATA[
      ((x \ (x / y)) \ 1) \ R(1 / ((x * y) \ x),z,u) = ((x * y) \ x) * R(((x * y) \ x) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(2890(a,1),1321(a,1,1))].">
      <j1 rule="para" parents="2890 1321"/>
    </justification>
  </clause>

  <clause id="2896">
    <literal><![CDATA[
      (1 * L(1 \ ((x * y) \ x),z,u)) / ((x * y) \ x) = ((x \ (x / y)) \ 1) \ L(1 / ((x * y) \ x),z,u)
    ]]></literal>
    <justification jstring="[para(2890(a,1),2585(a,2,1))].">
      <j1 rule="para" parents="2890 2585"/>
    </justification>
  </clause>

  <clause id="2897">
    <literal><![CDATA[
      x / (((y \ x) \ 1) \ 1) = x * (((x \ y) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(126,a,2894,a,b,2878,a),flip(a)].">
      <j1 rule="hyper" parents="126 2894 2878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2898">
    <literal><![CDATA[
      (x \ (x / (1 / (1 / y)))) \ 1 = 1 / (x \ (x / y))
    ]]></literal>
    <justification jstring="[para(79(a,1),2893(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="79 2893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2899">
    <literal><![CDATA[
      1 / (1 / (x \ (x / y))) = x \ (x / (1 / (1 / y)))
    ]]></literal>
    <justification jstring="[hyper(198,a,2898,a)].">
      <j1 rule="hyper" parents="198 2898"/>
    </justification>
  </clause>

  <clause id="2900">
    <literal><![CDATA[
      x * (1 / (1 / (x \ (x / y)))) = x / (1 / (1 / y))
    ]]></literal>
    <justification jstring="[hyper(126,a,2899,a,b,xx)].">
      <j1 rule="hyper" parents="126 2899"/>
    </justification>
  </clause>

  <clause id="2901">
    <literal><![CDATA[
      x / (1 / (1 / (y \ x))) = x * (1 / (1 / (x \ y)))
    ]]></literal>
    <justification jstring="[para(76(a,1),2900(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="76 2900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2902">
    <literal><![CDATA[
      (x / (1 / (1 / y))) / x = 1 / (1 / ((x / y) / x))
    ]]></literal>
    <justification jstring="[para(2900(a,1),2467(a,1,1))].">
      <j1 rule="para" parents="2900 2467"/>
    </justification>
  </clause>

  <clause id="2903">
    <literal><![CDATA[
      (x * (1 / (1 / (x \ y)))) \ x = 1 / (1 / (y \ x))
    ]]></literal>
    <justification jstring="[hyper(192,a,2901,a)].">
      <j1 rule="hyper" parents="192 2901"/>
    </justification>
  </clause>

  <clause id="2904">
    <literal><![CDATA[
      1 / (1 / ((x / (y \ 1)) / x)) = (x / (1 / y)) / x
    ]]></literal>
    <justification jstring="[para(76(a,1),2902(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="76 2902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2905">
    <literal><![CDATA[
      L(1 / (x \ y),x \ y,x) = 1 / (1 / (y \ x))
    ]]></literal>
    <justification jstring="[hyper(2630,a,2903,a)].">
      <j1 rule="hyper" parents="2630 2903"/>
    </justification>
  </clause>

  <clause id="2906">
    <literal><![CDATA[
      (x \ y) * K(y \ x,x \ y) = 1 / (1 / (x \ y))
    ]]></literal>
    <justification jstring="[hyper(63,a,2366,a,b,2905,a)].">
      <j1 rule="hyper" parents="63 2366 2905"/>
    </justification>
  </clause>

  <clause id="2907">
    <literal><![CDATA[
      L(x \ y,y \ x,x \ y) = 1 / (1 / (x \ y))
    ]]></literal>
    <justification jstring="[hyper(63,a,1612,a,b,2905,a)].">
      <j1 rule="hyper" parents="63 1612 2905"/>
    </justification>
  </clause>

  <clause id="2908">
    <literal><![CDATA[
      x * K(x \ y,(x \ y) \ 1) = y * (1 / (1 / (y \ x)))
    ]]></literal>
    <justification jstring="[para(2907(a,1),2119(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2907 2119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2909">
    <literal><![CDATA[
      1 / ((x / (y \ 1)) / x) = ((x / (1 / y)) / x) \ 1
    ]]></literal>
    <justification jstring="[hyper(192,a,2904,a),flip(a)].">
      <j1 rule="hyper" parents="192 2904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2911">
    <literal><![CDATA[
      K((x \ y) \ 1,x \ y) = K(y \ x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(34,a,1915,a,b,2906,a)].">
      <j1 rule="hyper" parents="34 1915 2906"/>
    </justification>
  </clause>

  <clause id="2913">
    <literal><![CDATA[
      K(((x * y) \ x) \ 1,(x * y) \ x) = K(y,(x * y) \ x)
    ]]></literal>
    <justification jstring="[hyper(333,a,705,a(flip),b,2911,a),flip(a)].">
      <j1 rule="hyper" parents="333 705 2911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2915">
    <literal><![CDATA[
      ((x \ y) * z) * K(y \ x,x \ y) = (1 / (1 / (x \ y))) * z
    ]]></literal>
    <justification jstring="[para(2911(a,1),2765(a,1,2))].">
      <j1 rule="para" parents="2911 2765"/>
    </justification>
  </clause>

  <clause id="2916">
    <literal><![CDATA[
      L(x * T(y,y \ 1),y,y) = L(x,y,y \ 1) * y
    ]]></literal>
    <justification jstring="[para(2447(a,1),2676(a,1,1))].">
      <j1 rule="para" parents="2447 2676"/>
    </justification>
  </clause>

  <clause id="2917">
    <literal><![CDATA[
      L(T(x,y),y,y \ 1) = 1 \ ((y \ 1) * (x * ((y \ 1) \ 1)))
    ]]></literal>
    <justification jstring="[hyper(333,a,2654,a,b,2757,a)].">
      <j1 rule="hyper" parents="333 2654 2757"/>
    </justification>
  </clause>

  <clause id="2918">
    <literal><![CDATA[
      (x \ 1) * ((y \ ((x \ 1) \ 1)) * z) = (1 / x) * ((y \ x) * z)
    ]]></literal>
    <justification jstring="[hyper(126,a,2761,a(flip),b,2647,a)].">
      <j1 rule="hyper" parents="126 2761 2647"/>
    </justification>
  </clause>

  <clause id="2919">
    <literal><![CDATA[
      L((x \ ((y \ 1) \ 1)) * z,y \ 1,y) = y * ((1 / y) * ((x \ y) * z))
    ]]></literal>
    <justification jstring="[para(2761(a,1),2666(a,1,1))].">
      <j1 rule="para" parents="2761 2666"/>
    </justification>
  </clause>

  <clause id="2920">
    <literal><![CDATA[
      ((1 / x) * y) * (z * K(x \ 1,x)) = ((x \ 1) * y) * z
    ]]></literal>
    <justification jstring="[hyper(2482,a,2764,a),flip(a)].">
      <j1 rule="hyper" parents="2482 2764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2921">
    <literal><![CDATA[
      K(x,x \ 1) * (((x \ 1) \ y) \ z) = ((1 / x) \ y) \ z
    ]]></literal>
    <justification jstring="[hyper(2453,a,2852,a)].">
      <j1 rule="hyper" parents="2453 2852"/>
    </justification>
  </clause>

  <clause id="2922">
    <literal><![CDATA[
      (x \ 1) * (L(x \ 1,y,z) \ x) = L(1 / x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,1273,a(flip),b,2859,a)].">
      <j1 rule="hyper" parents="63 1273 2859"/>
    </justification>
  </clause>

  <clause id="2923">
    <literal><![CDATA[
      (x * y) * K(y,(x * y) \ x) = x * T(y,(x * y) \ x)
    ]]></literal>
    <justification jstring="[para(2913(a,1),1292(a,1,2))].">
      <j1 rule="para" parents="2913 1292"/>
    </justification>
  </clause>

  <clause id="2924">
    <literal><![CDATA[
      ((1 / x) * (x \ 1)) * ((y * (z * ((x \ 1) \ 1))) * K(x \ 1,x)) = T(y * (z * (x \ 1)),(x \ 1) \ ((x \ 1) \ 1))
    ]]></literal>
    <justification jstring="[hyper(333,a,1476,a,b,2920,a),flip(a)].">
      <j1 rule="hyper" parents="333 1476 2920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2925">
    <literal><![CDATA[
      K(x,(y * x) \ y) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(34,a,2284,a,b,2923,a),flip(a)].">
      <j1 rule="hyper" parents="34 2284 2923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2926">
    <literal><![CDATA[
      L(K(x,x \ 1),y,z) = K(x,(u * x) \ u)
    ]]></literal>
    <justification jstring="[hyper(333,a,2136,a,b,2925,a)].">
      <j1 rule="hyper" parents="333 2136 2925"/>
    </justification>
  </clause>

  <clause id="2928">
    <literal><![CDATA[
      K(x \ y,(x \ y) \ 1) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[para(10(a,1),2925(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 2925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2929">
    <literal><![CDATA[
      K(x,y \ (y / x)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(12(a,1),2925(a,1,2,1))].">
      <j1 rule="para" parents="12 2925"/>
    </justification>
  </clause>

  <clause id="2930">
    <literal><![CDATA[
      K(x \ y,T(y,x) \ ((y * x) / y)) = K(x \ y,(x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(1081(a,2),2925(a,1,2,1))].">
      <j1 rule="para" parents="1081 2925"/>
    </justification>
  </clause>

  <clause id="2931">
    <literal><![CDATA[
      K(x,(y * x) \ y) \ 1 = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(2925(a,2),2132(a,1,1))].">
      <j1 rule="para" parents="2925 2132"/>
    </justification>
  </clause>

  <clause id="2934">
    <literal><![CDATA[
      K((x / y) \ x,z \ (z / y)) = K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,706,a,b,2929,a)].">
      <j1 rule="hyper" parents="63 706 2929"/>
    </justification>
  </clause>

  <clause id="2935">
    <literal><![CDATA[
      L(K(x,x \ 1),y,z) = K(((u * x) \ u) \ 1,(u * x) \ u)
    ]]></literal>
    <justification jstring="[hyper(333,a,2913,a,b,2926,a),flip(a)].">
      <j1 rule="hyper" parents="333 2913 2926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2936">
    <literal><![CDATA[
      (x \ y) * (1 / (x \ y)) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(2108,a,2928,a)].">
      <j1 rule="hyper" parents="2108 2928"/>
    </justification>
  </clause>

  <clause id="2937">
    <literal><![CDATA[
      K((x * y) \ x,((x * y) \ x) \ 1) = K((x * y) \ x,y)
    ]]></literal>
    <justification jstring="[para(9(a,1),2928(a,2,2))].">
      <j1 rule="para" parents="9 2928"/>
    </justification>
  </clause>

  <clause id="2939">
    <literal><![CDATA[
      x * K(x \ y,y \ x) = y * (1 / (1 / (y \ x)))
    ]]></literal>
    <justification jstring="[para(2928(a,1),2908(a,1,2))].">
      <j1 rule="para" parents="2928 2908"/>
    </justification>
  </clause>

  <clause id="2941">
    <literal><![CDATA[
      (x * K(x \ y,y \ x)) \ y = 1 / (1 / (x \ y))
    ]]></literal>
    <justification jstring="[para(2939(a,2),2903(a,1,1))].">
      <j1 rule="para" parents="2939 2903"/>
    </justification>
  </clause>

  <clause id="2942">
    <literal><![CDATA[
      (x * T(y,y \ 1)) * z != x * (T(y,y \ 1) * u)
    ]]></literal>
    <literal><![CDATA[
      L(u,y,x) = z
    ]]></literal>
    <justification jstring="[para(2623(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="2623 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2943">
    <literal><![CDATA[
      L(x,R(y,z,z) / z,u) = L(x,y * (1 / ((w * w) * z)),u)
    ]]></literal>
    <justification jstring="[para(447(a,1),2635(a,2,2,2))].">
      <j1 rule="para" parents="447 2635"/>
    </justification>
  </clause>

  <clause id="2944">
    <literal><![CDATA[
      L(T(x,y) / x,x,y) = K(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[para(1650(a,1),2678(a,1,1))].">
      <j1 rule="para" parents="1650 2678"/>
    </justification>
  </clause>

  <clause id="2945">
    <literal><![CDATA[
      K(1 / (1 / x),y) = (x * K(x,y)) / x
    ]]></literal>
    <justification jstring="[hyper(63,a,901,a(flip),b,2944,a),flip(a)].">
      <j1 rule="hyper" parents="63 901 2944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2946">
    <literal><![CDATA[
      T(K(1 / (1 / x),y),x) = K(x,y)
    ]]></literal>
    <justification jstring="[para(2945(a,2),238(a,1,1))].">
      <j1 rule="para" parents="2945 238"/>
    </justification>
  </clause>

  <clause id="2947">
    <literal><![CDATA[
      L(T(x,y),(y \ 1) \ 1,y \ 1) = 1 \ ((y \ 1) * (x * ((y \ 1) \ 1)))
    ]]></literal>
    <justification jstring="[hyper(2628,a,2917,a)].">
      <j1 rule="hyper" parents="2628 2917"/>
    </justification>
  </clause>

  <clause id="2949">
    <literal><![CDATA[
      K((x * y) \ x,((x * y) \ x) \ 1) = L(K(y,y \ 1),z,u) \ 1
    ]]></literal>
    <justification jstring="[para(2935(a,2),435(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2935 435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2950">
    <literal><![CDATA[
      L(x,R(y,z,z) / z,u) = L(x,y * ((w * w) * z),u)
    ]]></literal>
    <justification jstring="[hyper(333,a,2636,a(flip),b,2943,a),flip(a)].">
      <j1 rule="hyper" parents="333 2636 2943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2951">
    <literal><![CDATA[
      L(x,y * ((z * z) * u),w) = L(x,y * (1 / u),w)
    ]]></literal>
    <justification jstring="[para(1188(a,1),2950(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1188 2950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2952">
    <literal><![CDATA[
      L(x,y * ((z * z) * u),w) = L(x,y * u,w)
    ]]></literal>
    <justification jstring="[hyper(333,a,2636,a(flip),b,2951,a),flip(a)].">
      <j1 rule="hyper" parents="333 2636 2951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2953">
    <literal><![CDATA[
      L(x,y * ((z * z) \ u),w) = L(x,y * u,w)
    ]]></literal>
    <justification jstring="[para(10(a,1),2952(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 2952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2954">
    <literal><![CDATA[
      L(x,(y * y) * z,u) = L(x,z,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),2953(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 2953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2955">
    <literal><![CDATA[
      L(x,(y \ 1) * z,u) = L(x,y * z,u)
    ]]></literal>
    <justification jstring="[para(713(a,1),2953(a,1,2))].">
      <j1 rule="para" parents="713 2953"/>
    </justification>
  </clause>

  <clause id="2956">
    <literal><![CDATA[
      L(x,(y \ 1) \ z,u) = L(x,y \ z,u)
    ]]></literal>
    <justification jstring="[para(708(a,1),2954(a,1,2))].">
      <j1 rule="para" parents="708 2954"/>
    </justification>
  </clause>

  <clause id="2957">
    <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(123,a,2816,a(flip),b,107,a)].">
      <j1 rule="hyper" parents="123 2816 107"/>
    </justification>
  </clause>

  <clause id="2958">
    <literal><![CDATA[
      K(x \ 1,x) * (y / (z * (u * K(x \ 1,x)))) = y / (z * u)
    ]]></literal>
    <justification jstring="[hyper(126,a,2855,a,b,2452,a)].">
      <j1 rule="hyper" parents="126 2855 2452"/>
    </justification>
  </clause>

  <clause id="2959">
    <literal><![CDATA[
      ((x \ (x / y)) * z) * K(y,y \ 1) = (1 / (1 / (x \ (x / y)))) * z
    ]]></literal>
    <justification jstring="[para(2934(a,1),2915(a,1,2))].">
      <j1 rule="para" parents="2934 2915"/>
    </justification>
  </clause>

  <clause id="2960">
    <literal><![CDATA[
      K(x \ y,T(x / y,T(y,x))) = K(x \ y,(x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(862(a,1),2930(a,1,2))].">
      <j1 rule="para" parents="862 2930"/>
    </justification>
  </clause>

  <clause id="2961">
    <literal><![CDATA[
      K(x \ y,T(x / y,T(y,x))) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(333,a,2928,a(flip),b,2960,a),flip(a)].">
      <j1 rule="hyper" parents="333 2928 2960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2962">
    <literal><![CDATA[
      x / (K(y,y \ 1) * z) = K(y \ 1,y) * (x / z)
    ]]></literal>
    <justification jstring="[para(2423(a,1),2958(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2423 2958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2963">
    <literal><![CDATA[
      (x \ 1) * ((y * (x \ 1)) \ z) = x * L(x \ (y \ z),x,y)
    ]]></literal>
    <justification jstring="[para(2596(a,1),2581(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2596 2581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2964">
    <literal><![CDATA[
      (x \ 1) * ((y * (x \ 1)) \ z) = x * ((y * x) \ z)
    ]]></literal>
    <justification jstring="[para(311(a,1),2963(a,2,2))].">
      <j1 rule="para" parents="311 2963"/>
    </justification>
  </clause>

  <clause id="2965">
    <literal><![CDATA[
      ((x \ 1) \ y) / (x * y) = (x * y) \ ((x \ 1) \ y)
    ]]></literal>
    <justification jstring="[para(2601(a,1),2611(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2601 2611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2966">
    <literal><![CDATA[
      K(((x \ 1) \ 1) \ y,(x \ 1) \ 1) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(2768,a,317,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="2768 317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2967">
    <literal><![CDATA[
      K((x * y) \ x,y) = L(K(y,y \ 1),z,u) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,2937,a(flip),b,2949,a)].">
      <j1 rule="hyper" parents="63 2937 2949"/>
    </justification>
  </clause>

  <clause id="2969">
    <literal><![CDATA[
      K((x * y) \ x,y) = K(y,(z * y) \ z) \ 1
    ]]></literal>
    <justification jstring="[para(2926(a,1),2967(a,2,1))].">
      <j1 rule="para" parents="2926 2967"/>
    </justification>
  </clause>

  <clause id="2970">
    <literal><![CDATA[
      K((x * y) \ x,y) = K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,2931,a(flip),b,2969,a),flip(a)].">
      <j1 rule="hyper" parents="333 2931 2969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2971">
    <literal><![CDATA[
      K(x \ (x / y),y) = K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(12(a,1),2970(a,1,1,1))].">
      <j1 rule="para" parents="12 2970"/>
    </justification>
  </clause>

  <clause id="2972">
    <literal><![CDATA[
      K(T(x,y) \ 1,T(x,y)) = K((x * y) \ y,T(x,y))
    ]]></literal>
    <justification jstring="[para(111(a,1),2970(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="111 2970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2973">
    <literal><![CDATA[
      K(x \ (x / y),y) = (y \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(333,a,276,a(flip),b,2971,a),flip(a)].">
      <j1 rule="hyper" parents="333 276 2971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2974">
    <literal><![CDATA[
      K((x * y) \ y,y \ (x * y)) = K(T(x,y) \ 1,T(x,y))
    ]]></literal>
    <justification jstring="[para(22(a,1),2972(a,2,2)),flip(a)].">
      <j1 rule="para" parents="22 2972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2975">
    <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(861(a,1),2972(a,2,1,1))].">
      <j1 rule="para" parents="861 2972"/>
    </justification>
  </clause>

  <clause id="2976">
    <literal><![CDATA[
      ((x \ 1) * (x \ y)) / (x \ 1) = T(y / x,x * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,744,a(flip),b,2882,a),flip(a)].">
      <j1 rule="hyper" parents="63 744 2882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2977">
    <literal><![CDATA[
      ((x \ (x / (y \ 1))) * z) * K(y \ 1,y) = (1 / (1 / (x \ (x / (y \ 1))))) * z
    ]]></literal>
    <justification jstring="[para(2106(a,1),2959(a,1,2))].">
      <j1 rule="para" parents="2106 2959"/>
    </justification>
  </clause>

  <clause id="2978">
    <literal><![CDATA[
      ((x \ 1) * y) / T(1 / x,y) = K(x \ 1,x) * y
    ]]></literal>
    <justification jstring="[para(2312(a,1),2653(a,1,2))].">
      <j1 rule="para" parents="2312 2653"/>
    </justification>
  </clause>

  <clause id="2979">
    <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(2978(a,1),2076(a,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="2978 2076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2982">
    <literal><![CDATA[
      (K(x \ 1,x) * ((y * z) * u)) / (z * u) = R(K(x \ 1,x) * y,z,u)
    ]]></literal>
    <justification jstring="[para(2796(a,1),2814(a,1,1))].">
      <j1 rule="para" parents="2796 2814"/>
    </justification>
  </clause>

  <clause id="2983">
    <literal><![CDATA[
      T(x,(y \ 1) \ 1) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(1036,a,2947,a)].">
      <j1 rule="hyper" parents="1036 2947"/>
    </justification>
  </clause>

  <clause id="2984">
    <literal><![CDATA[
      ((x \ 1) \ 1) * T(y,x) = y * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(126,a,2983,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="126 2983 22"/>
    </justification>
  </clause>

  <clause id="2985">
    <literal><![CDATA[
      (x \ 1) \ T((x \ 1) * y,x) = (((x \ 1) \ 1) \ y) * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(121,a,2983,a(flip),b,962,a)].">
      <j1 rule="hyper" parents="121 2983 962"/>
    </justification>
  </clause>

  <clause id="2986">
    <literal><![CDATA[
      T(x,1 / y) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(79(a,1),2983(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="79 2983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2987">
    <literal><![CDATA[
      T(x,T(y,y \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(112(a,2),2983(a,1,2))].">
      <j1 rule="para" parents="112 2983"/>
    </justification>
  </clause>

  <clause id="2990">
    <literal><![CDATA[
      T(x / (1 / y),y \ 1) = (1 / y) \ x
    ]]></literal>
    <justification jstring="[hyper(423,a,2986,a),flip(a)].">
      <j1 rule="hyper" parents="423 2986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2992">
    <literal><![CDATA[
      T(((1 / x) * y) * x,x \ 1) = R(y,1 / x,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,965,a(flip),b,2986,a),flip(a)].">
      <j1 rule="hyper" parents="63 965 2986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2993">
    <literal><![CDATA[
      (1 / x) * T(y,x \ 1) = y * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(126,a,2986,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="126 2986 22"/>
    </justification>
  </clause>

  <clause id="2994">
    <literal><![CDATA[
      ((x \ 1) \ 1) * T(y,x) = y * T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(126,a,2987,a(flip),b,697,a)].">
      <j1 rule="hyper" parents="126 2987 697"/>
    </justification>
  </clause>

  <clause id="2995">
    <literal><![CDATA[
      T(x,x \ 1) * T(y,x) = y * T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(126,a,2987,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="126 2987 22"/>
    </justification>
  </clause>

  <clause id="2996">
    <literal><![CDATA[
      (T(x,x \ 1) \ 1) \ R(y,T(x,x \ 1),T(x,x \ 1) \ 1) = T(((x \ 1) \ 1) * T(y,x),T(x,x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(2994(a,2),609(a,2,1))].">
      <j1 rule="para" parents="2994 609"/>
    </justification>
  </clause>

  <clause id="2997">
    <literal><![CDATA[
      T(((1 / x) * y) * x,x \ 1) = R(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,1933,a(flip),b,2992,a),flip(a)].">
      <j1 rule="hyper" parents="333 1933 2992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2998">
    <literal><![CDATA[
      T((K(x,x \ 1) * y) * x,x \ 1) = R((x \ 1) \ y,1 / x,x)
    ]]></literal>
    <justification jstring="[para(2645(a,1),2992(a,1,1,1))].">
      <j1 rule="para" parents="2645 2992"/>
    </justification>
  </clause>

  <clause id="2999">
    <literal><![CDATA[
      R((1 / x) * y,x,x) = (x \ 1) * R(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(126,a,2997,a(flip),b,811,a),flip(a)].">
      <j1 rule="hyper" parents="126 2997 811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3000">
    <literal><![CDATA[
      T(x * T(y,y \ 1),y \ 1) = R((y \ 1) \ x,1 / y,y)
    ]]></literal>
    <justification jstring="[para(2474(a,1),2998(a,1,1))].">
      <j1 rule="para" parents="2474 2998"/>
    </justification>
  </clause>

  <clause id="3001">
    <literal><![CDATA[
      (((x \ 1) \ 1) \ y) * ((x \ 1) \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ y) * x = z
    ]]></literal>
    <justification jstring="[para(2985(a,1),1717(a,1))].">
      <j1 rule="para" parents="2985 1717"/>
    </justification>
  </clause>

  <clause id="3002">
    <literal><![CDATA[
      K(x \ 1,x) * (((y * z) * u) / (z * u)) = R(K(x \ 1,x) * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,2799,a(flip),b,2982,a)].">
      <j1 rule="hyper" parents="63 2799 2982"/>
    </justification>
  </clause>

  <clause id="3003">
    <literal><![CDATA[
      R(K(x \ 1,x) * y,z,u) = K(x \ 1,x) * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(20(a,2),3002(a,1,2)),flip(a)].">
      <j1 rule="para" parents="20 3002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3004">
    <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(333,a,2543,a(flip),b,3003,a),flip(a)].">
      <j1 rule="hyper" parents="333 2543 3003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3005">
    <literal><![CDATA[
      K(x,x \ 1) * R(K(x \ 1,x) * y,z,u) = R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(2460,a,3003,a(flip))].">
      <j1 rule="hyper" parents="2460 3003"/>
    </justification>
  </clause>

  <clause id="3006">
    <literal><![CDATA[
      K(x,x \ 1) * R(x \ 1,y,z) = R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(1909(a,1),3005(a,1,2,1))].">
      <j1 rule="para" parents="1909 3005"/>
    </justification>
  </clause>

  <clause id="3007">
    <literal><![CDATA[
      x * K(y \ (1 / (1 / x)),y) = (y \ x) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,2805,a(flip),b,2766,a),flip(a)].">
      <j1 rule="hyper" parents="63 2805 2766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3008">
    <literal><![CDATA[
      x \ L(T(x,L(x,y,z) \ x),y,z) = ((x \ L(x,y,z)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,2283,a(flip),b,2870,a),flip(a)].">
      <j1 rule="hyper" parents="63 2283 2870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3009">
    <literal><![CDATA[
      ((x \ L(x,y,z)) \ 1) \ 1 = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(2564(a,1),3008(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2564 3008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3010">
    <literal><![CDATA[
      (x * (L(x,y,z) \ x)) \ x = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,2894,a(flip),b,3009,a)].">
      <j1 rule="hyper" parents="63 2894 3009"/>
    </justification>
  </clause>

  <clause id="3012">
    <literal><![CDATA[
      (x \ R(x * y,z,u)) * x = R(y * x,z,u)
    ]]></literal>
    <justification jstring="[para(2435(a,1),3004(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2435 3004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3013">
    <literal><![CDATA[
      R((x \ y) * x,z,u) = (x \ R(y,z,u)) * x
    ]]></literal>
    <justification jstring="[para(10(a,1),3012(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 3012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3014">
    <literal><![CDATA[
      (R(x,y,z) \ x) * R(x,y,z) = x
    ]]></literal>
    <justification jstring="[hyper(208,a,3013,a),flip(a)].">
      <j1 rule="hyper" parents="208 3013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3015">
    <literal><![CDATA[
      R((x \ y) * x,z,u) / x = x \ R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(123,a,3013,a,b,xx)].">
      <j1 rule="hyper" parents="123 3013"/>
    </justification>
  </clause>

  <clause id="3016">
    <literal><![CDATA[
      (x \ R(x,y,z)) * x = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(172(a,1),3013(a,1,1)),flip(a)].">
      <j1 rule="para" parents="172 3013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3017">
    <literal><![CDATA[
      R((x \ (y / z)) * x,z,z \ 1) = (x \ (y * (z \ 1))) * x
    ]]></literal>
    <justification jstring="[para(554(a,1),3013(a,2,1,2))].">
      <j1 rule="para" parents="554 3013"/>
    </justification>
  </clause>

  <clause id="3018">
    <literal><![CDATA[
      R((x \ (y / (1 / z))) * x,z \ 1,z) = (x \ (y * z)) * x
    ]]></literal>
    <justification jstring="[para(1931(a,1),3013(a,2,1,2))].">
      <j1 rule="para" parents="1931 3013"/>
    </justification>
  </clause>

  <clause id="3019">
    <literal><![CDATA[
      x / R(x,y,z) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(138,a,3014,a)].">
      <j1 rule="hyper" parents="138 3014"/>
    </justification>
  </clause>

  <clause id="3020">
    <literal><![CDATA[
      T(x \ R(x,y,z),x) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(444,a,xx,b,3016,a)].">
      <j1 rule="hyper" parents="444 3016"/>
    </justification>
  </clause>

  <clause id="3021">
    <literal><![CDATA[
      T(x,x \ R(x,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(356,a,3016,a)].">
      <j1 rule="hyper" parents="356 3016"/>
    </justification>
  </clause>

  <clause id="3022">
    <literal><![CDATA[
      R(x,y,z) / x = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(138,a,3016,a)].">
      <j1 rule="hyper" parents="138 3016"/>
    </justification>
  </clause>

  <clause id="3023">
    <literal><![CDATA[
      (1 / x) * R(x,y,z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(35,a,1579,a,b,3016,a)].">
      <j1 rule="hyper" parents="35 1579 3016"/>
    </justification>
  </clause>

  <clause id="3024">
    <literal><![CDATA[
      R(x,y,z) / x != u
    ]]></literal>
    <literal><![CDATA[
      x \ R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(3016(a,1),268(a,1,1)),flip(b)].">
      <j1 rule="para" parents="3016 268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3025">
    <literal><![CDATA[
      x * (R(x,y,z) / x) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(3016(a,1),75(a,1,2,1))].">
      <j1 rule="para" parents="3016 75"/>
    </justification>
  </clause>

  <clause id="3026">
    <literal><![CDATA[
      R(x,y,z) / x != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (x \ R(x,y,z)) = w
    ]]></literal>
    <justification jstring="[para(3016(a,1),415(a,1,1))].">
      <j1 rule="para" parents="3016 415"/>
    </justification>
  </clause>

  <clause id="3027">
    <literal><![CDATA[
      (x / R(x,y,z)) * u = (R(x,y,z) \ x) * u
    ]]></literal>
    <justification jstring="[hyper(125,a,3019,a,b,11,a)].">
      <j1 rule="hyper" parents="125 3019 11"/>
    </justification>
  </clause>

  <clause id="3028">
    <literal><![CDATA[
      (1 / R(x,y,z)) * x = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,1578,a,b,3019,a)].">
      <j1 rule="hyper" parents="63 1578 3019"/>
    </justification>
  </clause>

  <clause id="3029">
    <literal><![CDATA[
      (x \ 1) \ R(x \ 1,y,z) = x * R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(1159,a,3022,a),flip(a)].">
      <j1 rule="hyper" parents="1159 3022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3031">
    <literal><![CDATA[
      R(T(x \ R(x,y,z),x * u),x,u) != w
    ]]></literal>
    <literal><![CDATA[
      (x * u) \ (R(x,y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(3022(a,1),952(a,1,1,1))].">
      <j1 rule="para" parents="3022 952"/>
    </justification>
  </clause>

  <clause id="3032">
    <literal><![CDATA[
      (x \ 1) \ R(x \ 1,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x * R(x \ 1,y,z) = u
    ]]></literal>
    <justification jstring="[para(3022(a,1),1159(a,1))].">
      <j1 rule="para" parents="3022 1159"/>
    </justification>
  </clause>

  <clause id="3033">
    <literal><![CDATA[
      R(x \ R(x,y,z),x,y * z) = ((x * y) * z) / (x * (y * z))
    ]]></literal>
    <justification jstring="[para(3022(a,1),561(a,1,1))].">
      <j1 rule="para" parents="3022 561"/>
    </justification>
  </clause>

  <clause id="3034">
    <literal><![CDATA[
      x \ R(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) / x = u
    ]]></literal>
    <justification jstring="[para(3025(a,1),342(a,1,2))].">
      <j1 rule="para" parents="3025 342"/>
    </justification>
  </clause>

  <clause id="3035">
    <literal><![CDATA[
      T(x,y) != y \ R(y,z,u)
    ]]></literal>
    <literal><![CDATA[
      y \ R(y,z,u) = x
    ]]></literal>
    <justification jstring="[para(3020(a,1),49(a,1)),flip(a)].">
      <j1 rule="para" parents="3020 49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3037">
    <literal><![CDATA[
      (x \ R(x,y,z)) * K(x \ 1,x) = (x \ 1) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(3023(a,1),2646(a,1,1))].">
      <j1 rule="para" parents="3023 2646"/>
    </justification>
  </clause>

  <clause id="3038">
    <literal><![CDATA[
      T(1 / R(x,y,z),x) = R(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(253,a,3028,a,b,1515,a)].">
      <j1 rule="hyper" parents="253 3028 1515"/>
    </justification>
  </clause>

  <clause id="3039">
    <literal><![CDATA[
      x \ R(x * (y / x),z,u) = R(y,z,u) / x
    ]]></literal>
    <justification jstring="[para(80(a,1),3015(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="80 3015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3040">
    <literal><![CDATA[
      (x / R(x,y,z)) * u != w
    ]]></literal>
    <literal><![CDATA[
      T(R(x,y,z) \ x,u) = u \ w
    ]]></literal>
    <justification jstring="[para(3027(a,2),296(a,1))].">
      <j1 rule="para" parents="3027 296"/>
    </justification>
  </clause>

  <clause id="3041">
    <literal><![CDATA[
      R(x * (y / x),z,u) = x * (R(y,z,u) / x)
    ]]></literal>
    <justification jstring="[hyper(142,a,3039,a),flip(a)].">
      <j1 rule="hyper" parents="142 3039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3042">
    <literal><![CDATA[
      K(x \ 1,R(x,y,z)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(1318,a,3037,a)].">
      <j1 rule="hyper" parents="1318 3037"/>
    </justification>
  </clause>

  <clause id="3044">
    <literal><![CDATA[
      ((x \ (y * (z \ 1))) * x) / (z \ 1) = ((x \ (y / z)) * x) * z
    ]]></literal>
    <justification jstring="[hyper(123,a,3017,a(flip),b,385,a)].">
      <j1 rule="hyper" parents="123 3017 385"/>
    </justification>
  </clause>

  <clause id="3045">
    <literal><![CDATA[
      ((x \ (y / (1 / z))) * x) * (1 / z) = ((x \ (y * z)) * x) / z
    ]]></literal>
    <justification jstring="[hyper(123,a,3018,a(flip),b,1943,a),flip(a)].">
      <j1 rule="hyper" parents="123 3018 1943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3046">
    <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(3033(a,2),2387(a,1,1,1,1))].">
      <j1 rule="para" parents="3033 2387"/>
    </justification>
  </clause>

  <clause id="3047">
    <literal><![CDATA[
      x * (T((x \ y) * z,x) / z) = ((x \ (y * z)) * x) / z
    ]]></literal>
    <justification jstring="[hyper(63,a,1653,a(flip),b,3045,a)].">
      <j1 rule="hyper" parents="63 1653 3045"/>
    </justification>
  </clause>

  <clause id="3048">
    <literal><![CDATA[
      T((x * y) \ (R(x,z,u) * y),x) != w
    ]]></literal>
    <literal><![CDATA[
      (x * y) \ (R(x,z,u) * y) = w
    ]]></literal>
    <justification jstring="[para(1041(a,1),3031(a,1))].">
      <j1 rule="para" parents="1041 3031"/>
    </justification>
  </clause>

  <clause id="3049">
    <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(333,a,537,a,b,2807,a)].">
      <j1 rule="hyper" parents="333 537 2807"/>
    </justification>
  </clause>

  <clause id="3050">
    <literal><![CDATA[
      ((x \ (x / (y \ 1))) * z) * K(y \ 1,y) = (1 / ((x \ (x / (1 / y))) \ 1)) * z
    ]]></literal>
    <justification jstring="[para(2893(a,1),2977(a,2,1,2))].">
      <j1 rule="para" parents="2893 2977"/>
    </justification>
  </clause>

  <clause id="3051">
    <literal><![CDATA[
      ((x \ (x / (y \ 1))) * z) * K(y \ 1,y) = (x \ (x / (1 / y))) * z
    ]]></literal>
    <justification jstring="[hyper(333,a,186,a(flip),b,3050,a),flip(a)].">
      <j1 rule="hyper" parents="333 186 3050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3053">
    <literal><![CDATA[
      R((x \ (x / (1 / y))) * x,y \ 1,y) = (x * ((y \ 1) * T((y \ 1) \ 1,x))) * y
    ]]></literal>
    <justification jstring="[para(3051(a,1),1959(a,1,1))].">
      <j1 rule="para" parents="3051 1959"/>
    </justification>
  </clause>

  <clause id="3054">
    <literal><![CDATA[
      R((x \ (x / (1 / y))) * x,y \ 1,y) = (x * (y \ T(y,x))) * y
    ]]></literal>
    <justification jstring="[para(1010(a,1),3053(a,2,1,2))].">
      <j1 rule="para" parents="1010 3053"/>
    </justification>
  </clause>

  <clause id="3055">
    <literal><![CDATA[
      (x \ (x * y)) * x = (x * (y \ T(y,x))) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,3018,a(flip),b,3054,a)].">
      <j1 rule="hyper" parents="63 3018 3054"/>
    </justification>
  </clause>

  <clause id="3056">
    <literal><![CDATA[
      (x * (y \ T(y,x))) * y = y * x
    ]]></literal>
    <justification jstring="[para(9(a,1),3055(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 3055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3057">
    <literal><![CDATA[
      x * (y \ T(y,x)) = (y * x) / y
    ]]></literal>
    <justification jstring="[hyper(138,a,3056,a),flip(a)].">
      <j1 rule="hyper" parents="138 3056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3058">
    <literal><![CDATA[
      (x \ y) * (x \ T(x,x \ y)) = y / x
    ]]></literal>
    <justification jstring="[hyper(123,a,10,a(flip),b,3056,a),flip(a)].">
      <j1 rule="hyper" parents="123 10 3056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3059">
    <literal><![CDATA[
      x \ ((y * x) / y) = y \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(129,a,3057,a)].">
      <j1 rule="hyper" parents="129 3057"/>
    </justification>
  </clause>

  <clause id="3061">
    <literal><![CDATA[
      T(x,y) \ x = y \ T(y,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(121,a,239,a(flip),b,3057,a)].">
      <j1 rule="hyper" parents="121 239 3057"/>
    </justification>
  </clause>

  <clause id="3062">
    <literal><![CDATA[
      (x / y) \ T(x / y,y) = y \ (x / (x / y))
    ]]></literal>
    <justification jstring="[hyper(121,a,156,a(flip),b,3057,a),flip(a)].">
      <j1 rule="hyper" parents="121 156 3057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3063">
    <literal><![CDATA[
      (x \ T(x,y)) * y = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(63,a,2738,a,b,3057,a)].">
      <j1 rule="hyper" parents="63 2738 3057"/>
    </justification>
  </clause>

  <clause id="3064">
    <literal><![CDATA[
      ((x * y) / x) / y = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(34,a,2752,a,b,3057,a)].">
      <j1 rule="hyper" parents="34 2752 3057"/>
    </justification>
  </clause>

  <clause id="3065">
    <literal><![CDATA[
      x \ ((y * x) / y) != z
    ]]></literal>
    <literal><![CDATA[
      y \ T(y,x) = z
    ]]></literal>
    <justification jstring="[para(3057(a,1),342(a,1,2))].">
      <j1 rule="para" parents="3057 342"/>
    </justification>
  </clause>

  <clause id="3066">
    <literal><![CDATA[
      (x * y) \ ((x * y) / x) = L(x \ 1,T(x,y),y)
    ]]></literal>
    <justification jstring="[para(3057(a,1),1015(a,1,2))].">
      <j1 rule="para" parents="3057 1015"/>
    </justification>
  </clause>

  <clause id="3067">
    <literal><![CDATA[
      ((x * y) / x) * (y \ 1) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,1297,a,b,3059,a)].">
      <j1 rule="hyper" parents="63 1297 3059"/>
    </justification>
  </clause>

  <clause id="3068">
    <literal><![CDATA[
      T(x,R(y,y \ 1,x)) = (x \ T(x,y)) * x
    ]]></literal>
    <justification jstring="[hyper(125,a,3059,a(flip),b,1530,a),flip(a)].">
      <j1 rule="hyper" parents="125 3059 1530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3069">
    <literal><![CDATA[
      L(x \ T(x,y),y,x) = K(x,(x * y) / x)
    ]]></literal>
    <justification jstring="[para(3059(a,1),516(a,1,1))].">
      <j1 rule="para" parents="3059 516"/>
    </justification>
  </clause>

  <clause id="3070">
    <literal><![CDATA[
      R(x \ T(x,y),y,z) \ (((x * y) / x) * z) = y * z
    ]]></literal>
    <justification jstring="[para(3063(a,1),187(a,1,2,1))].">
      <j1 rule="para" parents="3063 187"/>
    </justification>
  </clause>

  <clause id="3071">
    <literal><![CDATA[
      x * ((y * (x \ 1)) / y) = y \ T(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(1347,a,3064,a)].">
      <j1 rule="hyper" parents="1347 3064"/>
    </justification>
  </clause>

  <clause id="3074">
    <literal><![CDATA[
      R(x \ T(x,y),y,((x * y) / x) \ z) \ z = y * (((x * y) / x) \ z)
    ]]></literal>
    <justification jstring="[para(3064(a,1),527(a,1,1,1))].">
      <j1 rule="para" parents="3064 527"/>
    </justification>
  </clause>

  <clause id="3076">
    <literal><![CDATA[
      (x \ y) * (x \ ((x \ y) \ y)) = y / x
    ]]></literal>
    <justification jstring="[para(112(a,1),3058(a,1,2,2))].">
      <j1 rule="para" parents="112 3058"/>
    </justification>
  </clause>

  <clause id="3077">
    <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(3067(a,1),504(a,1,1))].">
      <j1 rule="para" parents="3067 504"/>
    </justification>
  </clause>

  <clause id="3078">
    <literal><![CDATA[
      (x \ y) \ (y / x) = x \ ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[hyper(129,a,3076,a)].">
      <j1 rule="hyper" parents="129 3076"/>
    </justification>
  </clause>

  <clause id="3079">
    <literal><![CDATA[
      ((x * y) / x) * (y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      x \ T(x,y) = z
    ]]></literal>
    <justification jstring="[para(1297(a,2),3065(a,1))].">
      <j1 rule="para" parents="1297 3065"/>
    </justification>
  </clause>

  <clause id="3080">
    <literal><![CDATA[
      K(x,y) = L(x \ T(x,T(y,x)),T(y,x),x)
    ]]></literal>
    <justification jstring="[para(239(a,1),3069(a,2,2)),flip(a)].">
      <j1 rule="para" parents="239 3069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3081">
    <literal><![CDATA[
      (x / y) \ (y \ x) = y \ (x / (x / y))
    ]]></literal>
    <justification jstring="[para(113(a,1),3062(a,1,2))].">
      <j1 rule="para" parents="113 3062"/>
    </justification>
  </clause>

  <clause id="3082">
    <literal><![CDATA[
      K(x,(x / y) / x) = x \ T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(1561,a,3071,a)].">
      <j1 rule="hyper" parents="1561 3071"/>
    </justification>
  </clause>

  <clause id="3083">
    <literal><![CDATA[
      (x * ((y \ x) / x)) / (y \ x) = x \ T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,1121,a,b,3071,a)].">
      <j1 rule="hyper" parents="63 1121 3071"/>
    </justification>
  </clause>

  <clause id="3084">
    <literal><![CDATA[
      x \ (y * ((z * (y \ x)) / z)) = z \ T(z,(x \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,1738,a(flip),b,3071,a)].">
      <j1 rule="hyper" parents="63 1738 3071"/>
    </justification>
  </clause>

  <clause id="3085">
    <literal><![CDATA[
      T(x,x / (x * y)) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(1701,a,3071,a(flip))].">
      <j1 rule="hyper" parents="1701 3071"/>
    </justification>
  </clause>

  <clause id="3086">
    <literal><![CDATA[
      T(x,(y \ x) \ 1) = x * K(x,y / x)
    ]]></literal>
    <justification jstring="[hyper(126,a,1563,a(flip),b,3071,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="126 1563 3071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3087">
    <literal><![CDATA[
      x \ T(x,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,(x / y) / x) = z
    ]]></literal>
    <justification jstring="[para(3071(a,1),1561(a,1))].">
      <j1 rule="para" parents="3071 1561"/>
    </justification>
  </clause>

  <clause id="3088">
    <literal><![CDATA[
      T(x \ T(x,y \ 1),z) = K(x,(x / T(y,z)) / x)
    ]]></literal>
    <justification jstring="[para(3071(a,1),1993(a,1,1))].">
      <j1 rule="para" parents="3071 1993"/>
    </justification>
  </clause>

  <clause id="3089">
    <literal><![CDATA[
      (x * ((y / (z * (x \ y))) / x)) * (z * (x \ y)) = x * ((x \ T(x,z \ 1)) * (x \ y))
    ]]></literal>
    <justification jstring="[para(3071(a,1),1995(a,2,2,1))].">
      <j1 rule="para" parents="3071 1995"/>
    </justification>
  </clause>

  <clause id="3090">
    <literal><![CDATA[
      (x * ((x / y) / x)) * y = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(1986,a,3085,a)].">
      <j1 rule="hyper" parents="1986 3085"/>
    </justification>
  </clause>

  <clause id="3091">
    <literal><![CDATA[
      T(x * ((x / y) / x),y) = y \ T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(1984,a,3085,a)].">
      <j1 rule="hyper" parents="1984 3085"/>
    </justification>
  </clause>

  <clause id="3093">
    <literal><![CDATA[
      T(x,y \ 1) / y = x * ((x / y) / x)
    ]]></literal>
    <justification jstring="[hyper(123,a,3085,a(flip),b,1983,a)].">
      <j1 rule="hyper" parents="123 3085 1983"/>
    </justification>
  </clause>

  <clause id="3094">
    <literal><![CDATA[
      (x * ((x / y) / x)) \ T(x,y \ 1) = y
    ]]></literal>
    <justification jstring="[hyper(121,a,3085,a(flip),b,1983,a)].">
      <j1 rule="hyper" parents="121 3085 1983"/>
    </justification>
  </clause>

  <clause id="3095">
    <literal><![CDATA[
      T(x,y) / (y \ 1) = x * ((x / (y \ 1)) / x)
    ]]></literal>
    <justification jstring="[hyper(123,a,2983,a(flip),b,3090,a)].">
      <j1 rule="hyper" parents="123 2983 3090"/>
    </justification>
  </clause>

  <clause id="3096">
    <literal><![CDATA[
      T(x,(y \ x) \ 1) / (y \ x) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(76(a,1),3093(a,2,2,1))].">
      <j1 rule="para" parents="76 3093"/>
    </justification>
  </clause>

  <clause id="3097">
    <literal><![CDATA[
      T(x,y) / (1 / y) = x * ((x / (1 / y)) / x)
    ]]></literal>
    <justification jstring="[para(79(a,1),3093(a,1,1,2))].">
      <j1 rule="para" parents="79 3093"/>
    </justification>
  </clause>

  <clause id="3098">
    <literal><![CDATA[
      L(((x / y) / x) \ 1,(x / y) / x,x) = (T(x,y \ 1) / y) \ x
    ]]></literal>
    <justification jstring="[para(3093(a,2),227(a,2,1))].">
      <j1 rule="para" parents="3093 227"/>
    </justification>
  </clause>

  <clause id="3099">
    <literal><![CDATA[
      T(((x / y) / x) * ((x \ 1) \ 1),y) * K(x \ 1,x) = (x \ (y \ T(x,y \ 1))) * x
    ]]></literal>
    <justification jstring="[para(3091(a,1),1914(a,2,1,2))].">
      <j1 rule="para" parents="3091 1914"/>
    </justification>
  </clause>

  <clause id="3100">
    <literal><![CDATA[
      x \ (T(x,y) / (1 / y)) = (x / (1 / y)) / x
    ]]></literal>
    <justification jstring="[hyper(121,a,3097,a,b,xx)].">
      <j1 rule="hyper" parents="121 3097"/>
    </justification>
  </clause>

  <clause id="3101">
    <literal><![CDATA[
      T(x \ T(x,y \ 1),z) = x \ T(x,T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(333,a,3082,a(flip),b,3088,a),flip(a)].">
      <j1 rule="hyper" parents="333 3082 3088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3102">
    <literal><![CDATA[
      (T(x,y) * z) * K(T(T(x,z),y),T(T(x,z),y) \ 1) = z * T(T((x \ 1) \ 1,z),y)
    ]]></literal>
    <justification jstring="[para(2382(a,2),2537(a,2,2,1))].">
      <j1 rule="para" parents="2382 2537"/>
    </justification>
  </clause>

  <clause id="3103">
    <literal><![CDATA[
      T((x / y) * K(x,x \ 1),y) * K(x \ 1,x) = (x \ (y \ T(x,y \ 1))) * x
    ]]></literal>
    <justification jstring="[para(2146(a,1),3099(a,1,1,1))].">
      <j1 rule="para" parents="2146 3099"/>
    </justification>
  </clause>

  <clause id="3104">
    <literal><![CDATA[
      T(((x \ 1) \ 1) / y,y) * K(x \ 1,x) = (x \ (y \ T(x,y \ 1))) * x
    ]]></literal>
    <justification jstring="[para(2823(a,1),3103(a,1,1,1))].">
      <j1 rule="para" parents="2823 3103"/>
    </justification>
  </clause>

  <clause id="3105">
    <literal><![CDATA[
      (x \ ((y \ 1) \ 1)) * K(y \ 1,y) = (y \ (x \ T(y,x \ 1))) * y
    ]]></literal>
    <justification jstring="[para(113(a,1),3104(a,1,1))].">
      <j1 rule="para" parents="113 3104"/>
    </justification>
  </clause>

  <clause id="3106">
    <literal><![CDATA[
      x \ (y \ T(x,y \ 1)) = (y \ x) / x
    ]]></literal>
    <justification jstring="[hyper(123,a,1919,a(flip),b,3105,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="123 1919 3105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3107">
    <literal><![CDATA[
      x \ T(y,x \ 1) = y * ((x \ y) / y)
    ]]></literal>
    <justification jstring="[hyper(142,a,3106,a),flip(a)].">
      <j1 rule="hyper" parents="142 3106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3108">
    <literal><![CDATA[
      x * (y * ((x \ y) / y)) = T(y,x \ 1)
    ]]></literal>
    <justification jstring="[para(3106(a,1),72(a,1,2,2))].">
      <j1 rule="para" parents="3106 72"/>
    </justification>
  </clause>

  <clause id="3109">
    <literal><![CDATA[
      (x / y) \ T(x,(x / y) \ 1) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(79(a,1),3107(a,2,2,1))].">
      <j1 rule="para" parents="79 3107"/>
    </justification>
  </clause>

  <clause id="3110">
    <literal><![CDATA[
      R(x,(y \ x) / x,x) = ((y \ T(x,y \ 1)) * x) / (y \ x)
    ]]></literal>
    <justification jstring="[para(3107(a,2),109(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="3107 109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3111">
    <literal><![CDATA[
      (x \ 1) \ T(y,x) = y * (((x \ 1) \ y) / y)
    ]]></literal>
    <justification jstring="[para(2983(a,1),3107(a,1,2))].">
      <j1 rule="para" parents="2983 3107"/>
    </justification>
  </clause>

  <clause id="3112">
    <literal><![CDATA[
      x * ((x * y) * (y / (x * y))) = T(x * y,x \ 1)
    ]]></literal>
    <justification jstring="[para(9(a,1),3108(a,1,2,2,1))].">
      <j1 rule="para" parents="9 3108"/>
    </justification>
  </clause>

  <clause id="3113">
    <literal><![CDATA[
      (((x / y) \ 1) \ y) * ((x / y) \ 1) = x * (y / x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1016,a(flip),b,3109,a)].">
      <j1 rule="hyper" parents="63 1016 3109"/>
    </justification>
  </clause>

  <clause id="3114">
    <literal><![CDATA[
      x * R(y,y,y \ x) = (y \ 1) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(762(a,2),3111(a,2,2)),flip(a)].">
      <j1 rule="para" parents="762 3111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3115">
    <literal><![CDATA[
      ((x \ 1) \ y) * (x \ 1) = (x * y) * (y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(34,a,962,a,b,3112,a)].">
      <j1 rule="hyper" parents="34 962 3112"/>
    </justification>
  </clause>

  <clause id="3116">
    <literal><![CDATA[
      K(((x / y) \ 1) \ y,(x / y) \ 1) = y \ (x * (y / x))
    ]]></literal>
    <justification jstring="[hyper(121,a,3113,a(flip),b,317,a),flip(a)].">
      <j1 rule="hyper" parents="121 3113 317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3117">
    <literal><![CDATA[
      ((x \ 1) * y) * (y / ((x \ 1) * y)) = (x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(3001,a,3115,a),flip(a)].">
      <j1 rule="hyper" parents="3001 3115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3118">
    <literal><![CDATA[
      ((x \ 1) * y) * R(x,x \ 1,y) = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(225(a,2),3117(a,1,2))].">
      <j1 rule="para" parents="225 3117"/>
    </justification>
  </clause>

  <clause id="3119">
    <literal><![CDATA[
      ((((x \ 1) * y) * x) / ((x \ 1) * y)) * (x \ 1) = ((x \ y) * x) / y
    ]]></literal>
    <justification jstring="[hyper(123,a,3118,a(flip),b,918,a),flip(a)].">
      <j1 rule="hyper" parents="123 3118 918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3120">
    <literal><![CDATA[
      ((x \ 1) * y) \ T((x \ 1) * y,x) = ((x \ y) * x) / y
    ]]></literal>
    <justification jstring="[hyper(3079,a,3119,a)].">
      <j1 rule="hyper" parents="3079 3119"/>
    </justification>
  </clause>

  <clause id="3121">
    <literal><![CDATA[
      L(K(x \ y,x),y,x \ 1) = ((x \ y) * x) / y
    ]]></literal>
    <justification jstring="[hyper(63,a,1719,a(flip),b,3120,a)].">
      <j1 rule="hyper" parents="63 1719 3120"/>
    </justification>
  </clause>

  <clause id="3122">
    <literal><![CDATA[
      ((x \ (x * y)) * x) / (x * y) = L(K(y,x),x * y,x \ 1)
    ]]></literal>
    <justification jstring="[para(9(a,1),3121(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 3121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3123">
    <literal><![CDATA[
      L(K(x,y),y * x,y \ 1) = (x * y) / (y * x)
    ]]></literal>
    <justification jstring="[para(9(a,1),3122(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 3122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3124">
    <literal><![CDATA[
      (T(x,y) * z) * K(T(T(x,z),y),T(T(x,z),y) \ 1) = T((x \ 1) \ 1,y) * z
    ]]></literal>
    <justification jstring="[hyper(333,a,250,a(flip),b,3102,a),flip(a)].">
      <j1 rule="hyper" parents="333 250 3102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3125">
    <literal><![CDATA[
      (T(x,y) * z) * K(T(x,z),T(x,z) \ 1) = T((x \ 1) \ 1,y) * z
    ]]></literal>
    <justification jstring="[para(2698(a,1),3124(a,1,2))].">
      <j1 rule="para" parents="2698 3124"/>
    </justification>
  </clause>

  <clause id="3126">
    <literal><![CDATA[
      (T(x,y) * z) * K(x,x \ 1) = T((x \ 1) \ 1,y) * z
    ]]></literal>
    <justification jstring="[para(2698(a,1),3125(a,1,2))].">
      <j1 rule="para" parents="2698 3125"/>
    </justification>
  </clause>

  <clause id="3129">
    <literal><![CDATA[
      T(x,x \ 1) * (T(x,y) * z) = x * (T((x \ 1) \ 1,y) * z)
    ]]></literal>
    <justification jstring="[para(3126(a,1),2692(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3126 2692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3130">
    <literal><![CDATA[
      (1 / x) * (T(((1 / x) \ 1) \ 1,y) * z) = (x \ 1) * (T(1 / x,y) * z)
    ]]></literal>
    <justification jstring="[para(332(a,1),3129(a,1,1)),flip(a)].">
      <j1 rule="para" parents="332 3129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3131">
    <literal><![CDATA[
      (1 / x) * (T(x \ 1,y) * z) = (x \ 1) * (T(1 / x,y) * z)
    ]]></literal>
    <justification jstring="[para(79(a,1),3130(a,1,2,1,1,1))].">
      <j1 rule="para" parents="79 3130"/>
    </justification>
  </clause>

  <clause id="3132">
    <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(2815(a,1),2829(a,1,2))].">
      <j1 rule="para" parents="2815 2829"/>
    </justification>
  </clause>

  <clause id="3133">
    <literal><![CDATA[
      L(L(x * y,x,x \ 1),(x \ 1) * x,z) = (x * L(y,x,x)) * K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(9(a,1),2832(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 2832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3134">
    <literal><![CDATA[
      L(L(x * y,x,x \ 1),(x \ 1) * x,z) = x * (L(y,x,x) * K(x,x \ 1))
    ]]></literal>
    <justification jstring="[hyper(333,a,2112,a(flip),b,3133,a),flip(a)].">
      <j1 rule="hyper" parents="333 2112 3133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3136">
    <literal><![CDATA[
      L(L(x * y,x,x \ 1),(x \ 1) * x,z) = x * (x * ((1 / x) * y))
    ]]></literal>
    <justification jstring="[para(2679(a,1),3134(a,2,2))].">
      <j1 rule="para" parents="2679 3134"/>
    </justification>
  </clause>

  <clause id="3137">
    <literal><![CDATA[
      x * (x * ((1 / x) * y)) = L(x * y,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(2800,a,3136,a),flip(a)].">
      <j1 rule="hyper" parents="2800 3136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3138">
    <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(2815(a,1),2957(a,1,2))].">
      <j1 rule="para" parents="2815 2957"/>
    </justification>
  </clause>

  <clause id="3139">
    <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(877,a,3132,a)].">
      <j1 rule="hyper" parents="877 3132"/>
    </justification>
  </clause>

  <clause id="3140">
    <literal><![CDATA[
      L(x,y,z * K(u \ 1,u)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(2800,a,3139,a),flip(a)].">
      <j1 rule="hyper" parents="2800 3139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3141">
    <literal><![CDATA[
      L(x,y,z * K(u \ 1,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(3139(a,1),2800(a,1))].">
      <j1 rule="para" parents="3139 2800"/>
    </justification>
  </clause>

  <clause id="3143">
    <literal><![CDATA[
      L(x,y,1 / z) = L(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[para(1131(a,1),3140(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1131 3140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3144">
    <literal><![CDATA[
      L(x,y,(z \ 1) \ 1) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(1248(a,1),3140(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1248 3140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3145">
    <literal><![CDATA[
      L(x,y,z / (1 / u)) = L(x,y,z / (u \ 1))
    ]]></literal>
    <justification jstring="[para(1903(a,1),3140(a,1,3))].">
      <j1 rule="para" parents="1903 3140"/>
    </justification>
  </clause>

  <clause id="3146">
    <literal><![CDATA[
      L(x,y,K(z,z \ 1) * u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(2426(a,1),3140(a,1,3)),flip(a)].">
      <j1 rule="para" parents="2426 3140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3147">
    <literal><![CDATA[
      L(x,y,(1 / z) \ u) = L(x,y,(z \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(2650(a,1),3140(a,1,3))].">
      <j1 rule="para" parents="2650 3140"/>
    </justification>
  </clause>

  <clause id="3148">
    <literal><![CDATA[
      L(x,1 / y,1 / z) = L(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(2632,a,3143,a)].">
      <j1 rule="hyper" parents="2632 3143"/>
    </justification>
  </clause>

  <clause id="3149">
    <literal><![CDATA[
      L(x,1 / y,1 / z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(3143(a,2),2627(a,1))].">
      <j1 rule="para" parents="3143 2627"/>
    </justification>
  </clause>

  <clause id="3150">
    <literal><![CDATA[
      L(x,y,R(1 / z,u,w)) = L(x,y,R(z \ 1,u,w))
    ]]></literal>
    <justification jstring="[para(3006(a,1),3146(a,1,3))].">
      <j1 rule="para" parents="3006 3146"/>
    </justification>
  </clause>

  <clause id="3151">
    <literal><![CDATA[
      L(x,y,1 / z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(2597(a,1),3149(a,1))].">
      <j1 rule="para" parents="2597 3149"/>
    </justification>
  </clause>

  <clause id="3152">
    <literal><![CDATA[
      L(x,y,y \ 1) \ ((1 / y) * (x * y)) != z
    ]]></literal>
    <literal><![CDATA[
      L(K(x,y),y * x,y \ 1) = z
    ]]></literal>
    <justification jstring="[para(2659(a,2),3151(a,1))].">
      <j1 rule="para" parents="2659 3151"/>
    </justification>
  </clause>

  <clause id="3153">
    <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(63,a,2856,a(flip),b,3138,a)].">
      <j1 rule="hyper" parents="63 2856 3138"/>
    </justification>
  </clause>

  <clause id="3154">
    <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(2982(a,1),3153(a,1,2))].">
      <j1 rule="para" parents="2982 3153"/>
    </justification>
  </clause>

  <clause id="3155">
    <literal><![CDATA[
      R(x,y * K(z \ 1,z),u) = R(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,3005,a(flip),b,3154,a),flip(a)].">
      <j1 rule="hyper" parents="63 3005 3154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3157">
    <literal><![CDATA[
      R(x,((y \ 1) \ 1) \ z,u) = R(x,y \ z,u)
    ]]></literal>
    <justification jstring="[para(2688(a,1),3155(a,1,2))].">
      <j1 rule="para" parents="2688 3155"/>
    </justification>
  </clause>

  <clause id="3158">
    <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(63,a,2428,a(flip),b,2429,a),flip(a)].">
      <j1 rule="hyper" parents="63 2428 2429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3159">
    <literal><![CDATA[
      R(T(x,y * K(z,z \ 1)),y,K(z,z \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,2782,a(flip),b,3158,a),flip(a)].">
      <j1 rule="hyper" parents="333 2782 3158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3160">
    <literal><![CDATA[
      T(x,y * K(z,z \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(2113,a,3159,a)].">
      <j1 rule="hyper" parents="2113 3159"/>
    </justification>
  </clause>

  <clause id="3163">
    <literal><![CDATA[
      T(x,y * K(z \ 1,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(2100(a,1),3160(a,1,2,2))].">
      <j1 rule="para" parents="2100 3160"/>
    </justification>
  </clause>

  <clause id="3164">
    <literal><![CDATA[
      T(x,y * (z * K(u,u \ 1))) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(2112(a,1),3160(a,1,2))].">
      <j1 rule="para" parents="2112 3160"/>
    </justification>
  </clause>

  <clause id="3165">
    <literal><![CDATA[
      T(x,y * (1 / z)) = T(x,y * (z \ 1))
    ]]></literal>
    <justification jstring="[para(2141(a,1),3160(a,1,2))].">
      <j1 rule="para" parents="2141 3160"/>
    </justification>
  </clause>

  <clause id="3166">
    <literal><![CDATA[
      T(x,y * ((z \ 1) \ 1)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(2142(a,1),3160(a,1,2))].">
      <j1 rule="para" parents="2142 3160"/>
    </justification>
  </clause>

  <clause id="3167">
    <literal><![CDATA[
      T(x,K(y,y \ 1) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[para(2397(a,2),3160(a,1,2))].">
      <j1 rule="para" parents="2397 3160"/>
    </justification>
  </clause>

  <clause id="3168">
    <literal><![CDATA[
      T(x,K(y \ 1,y) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[para(2439(a,1),3160(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2439 3160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3169">
    <literal><![CDATA[
      T(x,(1 / y) * z) = T(x,(y \ 1) * z)
    ]]></literal>
    <justification jstring="[para(2644(a,1),3160(a,1,2))].">
      <j1 rule="para" parents="2644 3160"/>
    </justification>
  </clause>

  <clause id="3170">
    <literal><![CDATA[
      T(x,(1 / y) \ z) = T(x,(y \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(2669(a,1),3160(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2669 3160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3172">
    <literal><![CDATA[
      T(x,(1 / (1 / y)) \ z) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(2833(a,1),3160(a,1,2))].">
      <j1 rule="para" parents="2833 3160"/>
    </justification>
  </clause>

  <clause id="3173">
    <literal><![CDATA[
      T(x,((y \ 1) \ 1) \ z) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(2674(a,1),3160(a,1,2))].">
      <j1 rule="para" parents="2674 3160"/>
    </justification>
  </clause>

  <clause id="3174">
    <literal><![CDATA[
      T(x,y / (1 / z)) = T(x,y / (z \ 1))
    ]]></literal>
    <justification jstring="[para(1903(a,1),3163(a,1,2))].">
      <j1 rule="para" parents="1903 3163"/>
    </justification>
  </clause>

  <clause id="3175">
    <literal><![CDATA[
      T(x,y \ (1 / z)) = T(x,y \ (z \ 1))
    ]]></literal>
    <justification jstring="[para(1918(a,1),3163(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1918 3163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3176">
    <literal><![CDATA[
      T(x,y * (((y \ z) \ 1) \ 1)) = T(x,z)
    ]]></literal>
    <justification jstring="[para(2289(a,1),3163(a,1,2))].">
      <j1 rule="para" parents="2289 3163"/>
    </justification>
  </clause>

  <clause id="3177">
    <literal><![CDATA[
      T(x,(K(y,y \ 1) * z) \ u) = T(x,z \ u)
    ]]></literal>
    <justification jstring="[para(2847(a,2),3163(a,1,2))].">
      <j1 rule="para" parents="2847 3163"/>
    </justification>
  </clause>

  <clause id="3178">
    <literal><![CDATA[
      T(x,((1 / y) * z) \ u) = T(x,((y \ 1) * z) \ u)
    ]]></literal>
    <justification jstring="[para(2851(a,1),3163(a,1,2))].">
      <j1 rule="para" parents="2851 3163"/>
    </justification>
  </clause>

  <clause id="3179">
    <literal><![CDATA[
      T(x,L(T(y,y \ 1),z,u)) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(2509(a,1),3167(a,1,2))].">
      <j1 rule="para" parents="2509 3167"/>
    </justification>
  </clause>

  <clause id="3180">
    <literal><![CDATA[
      T(x,y * (z * (1 / u))) = T(x,y * (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[para(2504(a,1),3167(a,1,2))].">
      <j1 rule="para" parents="2504 3167"/>
    </justification>
  </clause>

  <clause id="3181">
    <literal><![CDATA[
      T(x,y * ((1 / z) \ u)) = T(x,y * ((z \ 1) \ u))
    ]]></literal>
    <justification jstring="[para(2673(a,1),3167(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2673 3167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3182">
    <literal><![CDATA[
      T(x,((1 / y) * z) * u) = T(x,((y \ 1) * z) * u)
    ]]></literal>
    <justification jstring="[para(2764(a,1),3167(a,1,2))].">
      <j1 rule="para" parents="2764 3167"/>
    </justification>
  </clause>

  <clause id="3183">
    <literal><![CDATA[
      T(x,(y / (1 / z)) * u) = T(x,(y / (z \ 1)) * u)
    ]]></literal>
    <justification jstring="[para(2831(a,1),3168(a,1,2))].">
      <j1 rule="para" parents="2831 3168"/>
    </justification>
  </clause>

  <clause id="3184">
    <literal><![CDATA[
      T(x,T(y,y \ 1) \ z) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(112(a,2),3173(a,1,2,1))].">
      <j1 rule="para" parents="112 3173"/>
    </justification>
  </clause>

  <clause id="3185">
    <literal><![CDATA[
      T(x,R(y \ 1,y,z) \ u) = T(x,(z / (y * z)) \ u)
    ]]></literal>
    <justification jstring="[para(2843(a,2),3173(a,1,2,1))].">
      <j1 rule="para" parents="2843 3173"/>
    </justification>
  </clause>

  <clause id="3186">
    <literal><![CDATA[
      (1 / x) / T(y,y \ (x \ 1)) = y \ (1 / x)
    ]]></literal>
    <justification jstring="[hyper(197,a,3175,a(flip),b,112,a(flip))].">
      <j1 rule="hyper" parents="197 3175 112"/>
    </justification>
  </clause>

  <clause id="3187">
    <literal><![CDATA[
      T(x,y * ((1 / z) * u)) = T(x,y * ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[para(2644(a,1),3164(a,1,2,2))].">
      <j1 rule="para" parents="2644 3164"/>
    </justification>
  </clause>

  <clause id="3188">
    <literal><![CDATA[
      T(x,(y * ((z \ 1) \ 1)) \ u) = T(x,(y * z) \ u)
    ]]></literal>
    <justification jstring="[para(2424(a,1),3177(a,1,2,1))].">
      <j1 rule="para" parents="2424 3177"/>
    </justification>
  </clause>

  <clause id="3189">
    <literal><![CDATA[
      T(x,(((y \ 1) \ 1) \ z) \ u) = T(x,(y \ z) \ u)
    ]]></literal>
    <justification jstring="[para(2683(a,1),3177(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2683 3177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3190">
    <literal><![CDATA[
      T(x,((y \ 1) * y) \ z) = T(x,z)
    ]]></literal>
    <justification jstring="[para(167(a,1),3178(a,1,2)),flip(a)].">
      <j1 rule="para" parents="167 3178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3191">
    <literal><![CDATA[
      T(x,y * ((z / u) * (1 / u))) = T(x,y * (z / (u * u)))
    ]]></literal>
    <justification jstring="[para(818(a,1),3180(a,2,2,2))].">
      <j1 rule="para" parents="818 3180"/>
    </justification>
  </clause>

  <clause id="3192">
    <literal><![CDATA[
      T(x,y * (z * (u \ (1 / u)))) = T(x,y * (z / (u * u)))
    ]]></literal>
    <justification jstring="[para(800(a,1),3191(a,1,2,2))].">
      <j1 rule="para" parents="800 3191"/>
    </justification>
  </clause>

  <clause id="3193">
    <literal><![CDATA[
      (x * (K(y,y \ 1) * (z * u))) \ ((K(y,y \ 1) * (x * z)) * u) = a(x,K(y,y \ 1) * z,u)
    ]]></literal>
    <justification jstring="[para(2762(a,1),2506(a,1,1,2))].">
      <j1 rule="para" parents="2762 2506"/>
    </justification>
  </clause>

  <clause id="3194">
    <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(2815(a,1),2828(a,1,2,1))].">
      <j1 rule="para" parents="2815 2828"/>
    </justification>
  </clause>

  <clause id="3195">
    <literal><![CDATA[
      (x * (K(y,y \ 1) * (z * u))) \ (K(y,y \ 1) * ((x * z) * u)) = a(x,K(y,y \ 1) * z,u)
    ]]></literal>
    <justification jstring="[para(2762(a,1),3193(a,1,2))].">
      <j1 rule="para" parents="2762 3193"/>
    </justification>
  </clause>

  <clause id="3196">
    <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(2796(a,1),3194(a,1,2))].">
      <j1 rule="para" parents="2796 3194"/>
    </justification>
  </clause>

  <clause id="3197">
    <literal><![CDATA[
      ((x * (K(y,y \ 1) * (z * u))) \ ((x * z) * u)) * K(y,y \ 1) = a(x,K(y,y \ 1) * z,u)
    ]]></literal>
    <justification jstring="[hyper(2431,a,3195,a)].">
      <j1 rule="hyper" parents="2431 3195"/>
    </justification>
  </clause>

  <clause id="3198">
    <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(878,a,3196,a)].">
      <j1 rule="hyper" parents="878 3196"/>
    </justification>
  </clause>

  <clause id="3199">
    <literal><![CDATA[
      a(x * K(y \ 1,y),z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(2800,a,3198,a),flip(a)].">
      <j1 rule="hyper" parents="2800 3198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3201">
    <literal><![CDATA[
      a(1 / x,y,z) = a(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(1131(a,1),3199(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1131 3199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3202">
    <literal><![CDATA[
      a((x \ 1) \ 1,y,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(1248(a,1),3199(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1248 3199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3203">
    <literal><![CDATA[
      L(x,y,y \ 1) \ x = a(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,2658,a,b,3201,a)].">
      <j1 rule="hyper" parents="63 2658 3201"/>
    </justification>
  </clause>

  <clause id="3204">
    <literal><![CDATA[
      L(x,y,y \ 1) * a(y \ 1,y,x) = x
    ]]></literal>
    <justification jstring="[hyper(126,a,3201,a(flip),b,2658,a)].">
      <j1 rule="hyper" parents="126 3201 2658"/>
    </justification>
  </clause>

  <clause id="3205">
    <literal><![CDATA[
      a(x \ 1,x,y) * L(y,x,x \ 1) = y
    ]]></literal>
    <justification jstring="[hyper(125,a,3203,a(flip),b,2558,a)].">
      <j1 rule="hyper" parents="125 3203 2558"/>
    </justification>
  </clause>

  <clause id="3206">
    <literal><![CDATA[
      (1 / L(x,y,y \ 1)) \ a(y \ 1,y,x) = x
    ]]></literal>
    <justification jstring="[hyper(121,a,3203,a(flip),b,2556,a)].">
      <j1 rule="hyper" parents="121 3203 2556"/>
    </justification>
  </clause>

  <clause id="3207">
    <literal><![CDATA[
      a(x \ 1,x,y) \ y = L(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[para(3203(a,1),2559(a,1,1))].">
      <j1 rule="para" parents="3203 2559"/>
    </justification>
  </clause>

  <clause id="3208">
    <literal><![CDATA[
      L(x,y,y \ 1) \ x != z
    ]]></literal>
    <literal><![CDATA[
      a(y \ 1,y,x) = z
    ]]></literal>
    <justification jstring="[para(3204(a,1),342(a,1,2))].">
      <j1 rule="para" parents="3204 342"/>
    </justification>
  </clause>

  <clause id="3210">
    <literal><![CDATA[
      (((x * (y * z)) \ ((x * y) * z)) * K(u \ 1,u)) * K(u,u \ 1) = a(x,K(u,u \ 1) * y,z)
    ]]></literal>
    <justification jstring="[para(2850(a,1),3197(a,1,1))].">
      <j1 rule="para" parents="2850 3197"/>
    </justification>
  </clause>

  <clause id="3211">
    <literal><![CDATA[
      (a(x,y,z) * K(u \ 1,u)) * K(u,u \ 1) = a(x,K(u,u \ 1) * y,z)
    ]]></literal>
    <justification jstring="[para(14(a,2),3210(a,1,1,1))].">
      <j1 rule="para" parents="14 3210"/>
    </justification>
  </clause>

  <clause id="3212">
    <literal><![CDATA[
      a(x,K(y,y \ 1) * z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(2152,a,3211,a),flip(a)].">
      <j1 rule="hyper" parents="2152 3211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3214">
    <literal><![CDATA[
      a(x,(y \ 1) \ 1,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(2104(a,1),3212(a,1,2))].">
      <j1 rule="para" parents="2104 3212"/>
    </justification>
  </clause>

  <clause id="3215">
    <literal><![CDATA[
      a(x,1 / y,z) = a(x,y \ 1,z)
    ]]></literal>
    <justification jstring="[para(2128(a,1),3212(a,1,2))].">
      <j1 rule="para" parents="2128 3212"/>
    </justification>
  </clause>

  <clause id="3216">
    <literal><![CDATA[
      a(x,y * K(z,z \ 1),u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[para(2397(a,1),3212(a,1,2))].">
      <j1 rule="para" parents="2397 3212"/>
    </justification>
  </clause>

  <clause id="3217">
    <literal><![CDATA[
      L(a(x,1 / y,z),u,K(w \ 1,w)) = a(x,y \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(2801,a,3215,a)].">
      <j1 rule="hyper" parents="2801 3215"/>
    </justification>
  </clause>

  <clause id="3218">
    <literal><![CDATA[
      a(x,y \ 1,z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,1 / y,z) = u
    ]]></literal>
    <justification jstring="[para(3217(a,1),509(a,1))].">
      <j1 rule="para" parents="3217 509"/>
    </justification>
  </clause>

  <clause id="3219">
    <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(2830,a,2819,a),flip(a)].">
      <j1 rule="hyper" parents="2830 2819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3220">
    <literal><![CDATA[
      L(x,y * K(z \ 1,z),u) = (u * y) \ (u * (y * x))
    ]]></literal>
    <justification jstring="[para(2492(a,1),3219(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2492 3219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3221">
    <literal><![CDATA[
      L(x,y * K(z \ 1,z),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(333,a,18,a,b,3220,a),flip(a)].">
      <j1 rule="hyper" parents="333 18 3220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3223">
    <literal><![CDATA[
      L(x,K(y \ 1,y) * z,u) = L(x,z,u)
    ]]></literal>
    <justification jstring="[para(2412(a,2),3221(a,1,2))].">
      <j1 rule="para" parents="2412 3221"/>
    </justification>
  </clause>

  <clause id="3224">
    <literal><![CDATA[
      L(x,y / ((z \ 1) \ 1),u) = L(x,y / z,u)
    ]]></literal>
    <justification jstring="[para(2456(a,1),3223(a,1,2))].">
      <j1 rule="para" parents="2456 3223"/>
    </justification>
  </clause>

  <clause id="3225">
    <literal><![CDATA[
      ((x \ (x / y)) \ 1) \ R((x \ (x / y)) \ 1,z,u) = ((x * y) \ x) * R(((x * y) \ x) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(2890(a,1),2895(a,1,2,1))].">
      <j1 rule="para" parents="2890 2895"/>
    </justification>
  </clause>

  <clause id="3226">
    <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(1082(a,1),2975(a,2,1))].">
      <j1 rule="para" parents="1082 2975"/>
    </justification>
  </clause>

  <clause id="3227">
    <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(333,a,2961,a(flip),b,3226,a),flip(a)].">
      <j1 rule="hyper" parents="333 2961 3226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3228">
    <literal><![CDATA[
      ((x * y) \ x) * R(((x * y) \ x) \ 1,z,u) = (x \ (x / y)) * R((x \ (x / y)) \ 1,z,u)
    ]]></literal>
    <justification jstring="[hyper(3032,a,3225,a),flip(a)].">
      <j1 rule="hyper" parents="3032 3225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3229">
    <literal><![CDATA[
      (x \ (x / y)) * R((x \ (x / y)) \ 1,z,u) = (x * y) \ (x * R(x \ (x * y),z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,1538,a(flip),b,3228,a),flip(a)].">
      <j1 rule="hyper" parents="63 1538 3228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3230">
    <literal><![CDATA[
      (x \ (x / y)) * R((x \ (x / y)) \ 1,z,u) = (x * y) \ (x * R(y,z,u))
    ]]></literal>
    <justification jstring="[para(9(a,1),3229(a,2,2,2,1))].">
      <j1 rule="para" parents="9 3229"/>
    </justification>
  </clause>

  <clause id="3231">
    <literal><![CDATA[
      x \ ((x / y) * R((x / y) \ x,z,u)) = (x * y) \ (x * R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,1538,a(flip),b,3230,a)].">
      <j1 rule="hyper" parents="63 1538 3230"/>
    </justification>
  </clause>

  <clause id="3232">
    <literal><![CDATA[
      (x * y) \ (x * R(y,z,u)) = x \ ((x / y) * R(y,z,u))
    ]]></literal>
    <justification jstring="[para(79(a,1),3231(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="79 3231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3233">
    <literal><![CDATA[
      ((x * (y * (z * K(u \ 1,u)))) \ ((x * y) * z)) * K(u \ 1,u) = a(x,y,z * K(u \ 1,u))
    ]]></literal>
    <justification jstring="[hyper(2477,a,2493,a),flip(a)].">
      <j1 rule="hyper" parents="2477 2493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3234">
    <literal><![CDATA[
      T(K(x \ 1,x),((y * x) / y) \ x) = K(x \ (((y * x) / y) \ x),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,679,a(flip),b,2525,a)].">
      <j1 rule="hyper" parents="63 679 2525"/>
    </justification>
  </clause>

  <clause id="3235">
    <literal><![CDATA[
      K(x \ (((y * x) / y) \ x),x) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(2443,a,3234,a),flip(a)].">
      <j1 rule="hyper" parents="2443 3234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3238">
    <literal><![CDATA[
      ((x \ (x / y)) \ 1) \ L(1 / ((x * y) \ x),z,u) = (1 * L((x * y) \ x,z,u)) / ((x * y) \ x)
    ]]></literal>
    <justification jstring="[para(65(a,1),2896(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="65 2896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3239">
    <literal><![CDATA[
      ((x \ (x / y)) \ 1) \ L(1 / ((x * y) \ x),z,u) = L((x * y) \ x,z,u) / ((x * y) \ x)
    ]]></literal>
    <justification jstring="[hyper(333,a,157,a(flip),b,3238,a),flip(a)].">
      <j1 rule="hyper" parents="333 157 3238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3240">
    <literal><![CDATA[
      ((x \ (x / y)) \ 1) \ L(1 / ((x * y) \ x),z,u) = ((x * y) \ x) \ L((x * y) \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(333,a,2516,a(flip),b,3239,a),flip(a)].">
      <j1 rule="hyper" parents="333 2516 3239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3241">
    <literal><![CDATA[
      ((x \ (x / y)) \ 1) \ L(1 / ((x * y) \ x),z,u) = (x * y) \ (x * L(x \ (x * y),z,u))
    ]]></literal>
    <justification jstring="[hyper(333,a,2586,a(flip),b,3240,a),flip(a)].">
      <j1 rule="hyper" parents="333 2586 3240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3242">
    <literal><![CDATA[
      ((x \ (x / y)) \ 1) \ L(1 / ((x * y) \ x),z,u) = (x * y) \ (x * L(y,z,u))
    ]]></literal>
    <justification jstring="[para(9(a,1),3241(a,2,2,2,1))].">
      <j1 rule="para" parents="9 3241"/>
    </justification>
  </clause>

  <clause id="3243">
    <literal><![CDATA[
      ((x \ (x / y)) \ 1) \ L((x \ (x / y)) \ 1,z,u) = (x * y) \ (x * L(y,z,u))
    ]]></literal>
    <justification jstring="[para(2890(a,1),3242(a,1,2,1))].">
      <j1 rule="para" parents="2890 3242"/>
    </justification>
  </clause>

  <clause id="3244">
    <literal><![CDATA[
      (x \ (x / y)) \ (1 * L(1 \ (x \ (x / y)),z,u)) = (x * y) \ (x * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,2586,a(flip),b,3243,a)].">
      <j1 rule="hyper" parents="63 2586 3243"/>
    </justification>
  </clause>

  <clause id="3245">
    <literal><![CDATA[
      (x \ (x / y)) \ (1 * L(x \ (x / y),z,u)) = (x * y) \ (x * L(y,z,u))
    ]]></literal>
    <justification jstring="[para(65(a,1),3244(a,1,2,2,1))].">
      <j1 rule="para" parents="65 3244"/>
    </justification>
  </clause>

  <clause id="3246">
    <literal><![CDATA[
      (x \ (x / y)) \ L(x \ (x / y),z,u) = (x * y) \ (x * L(y,z,u))
    ]]></literal>
    <justification jstring="[para(7(a,1),3245(a,1,2))].">
      <j1 rule="para" parents="7 3245"/>
    </justification>
  </clause>

  <clause id="3247">
    <literal><![CDATA[
      x \ ((x / y) * L((x / y) \ x,z,u)) = (x * y) \ (x * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,2586,a(flip),b,3246,a)].">
      <j1 rule="hyper" parents="63 2586 3246"/>
    </justification>
  </clause>

  <clause id="3248">
    <literal><![CDATA[
      (x * y) \ (x * L(y,z,u)) = x \ ((x / y) * L(y,z,u))
    ]]></literal>
    <justification jstring="[para(79(a,1),3247(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="79 3247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3249">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ (((L(x,y,z) \ x) / x) * L(x,y,z)) = ((L(x,y,z) \ x) * x) \ x
    ]]></literal>
    <justification jstring="[para(2550(a,1),3248(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2550 3248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3250">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ (((L(x,y,z) \ x) / x) * L(x,y,z)) = (x * (L(x,y,z) \ x)) \ x
    ]]></literal>
    <justification jstring="[para(2565(a,1),3249(a,2,1))].">
      <j1 rule="para" parents="2565 3249"/>
    </justification>
  </clause>

  <clause id="3251">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ (((L(x,y,z) \ x) / x) * L(x,y,z)) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,3010,a(flip),b,3250,a),flip(a)].">
      <j1 rule="hyper" parents="333 3010 3250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3252">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ ((1 / L(x,y,z)) * L(x,y,z)) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(2562(a,1),3251(a,1,2,1))].">
      <j1 rule="para" parents="2562 3251"/>
    </justification>
  </clause>

  <clause id="3253">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ 1 = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(12(a,1),3252(a,1,2))].">
      <j1 rule="para" parents="12 3252"/>
    </justification>
  </clause>

  <clause id="3254">
    <literal><![CDATA[
      1 / (x \ L(x,y,z)) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[para(3252(a,1),336(a,1,2))].">
      <j1 rule="para" parents="3252 336"/>
    </justification>
  </clause>

  <clause id="3255">
    <literal><![CDATA[
      1 / (x * L(x \ 1,y,z)) = L(1 / x,y,z) \ (1 / x)
    ]]></literal>
    <justification jstring="[hyper(197,a,1030,a(flip),b,3253,a)].">
      <j1 rule="hyper" parents="197 1030 3253"/>
    </justification>
  </clause>

  <clause id="3257">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ 1 = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(39,a,3009,a,b,3253,a)].">
      <j1 rule="hyper" parents="39 3009 3253"/>
    </justification>
  </clause>

  <clause id="3259">
    <literal><![CDATA[
      a(x \ 1,x,y) \ 1 = y \ L(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[para(3203(a,1),3253(a,1,1))].">
      <j1 rule="para" parents="3203 3253"/>
    </justification>
  </clause>

  <clause id="3261">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ (x \ 1) = (x \ 1) * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(3257(a,1),2266(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3257 2266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3262">
    <literal><![CDATA[
      ((L(x,y,z) \ x) \ 1) \ 1 = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[para(3253(a,2),3257(a,1,1))].">
      <j1 rule="para" parents="3253 3257"/>
    </justification>
  </clause>

  <clause id="3263">
    <literal><![CDATA[
      1 / (L(x,y,z) \ x) = (L(x,y,z) \ x) \ 1
    ]]></literal>
    <justification jstring="[hyper(198,a,3262,a)].">
      <j1 rule="hyper" parents="198 3262"/>
    </justification>
  </clause>

  <clause id="3264">
    <literal><![CDATA[
      1 / (x * L(x \ 1,y,z)) = L(x \ 1,y,z) \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(333,a,2863,a(flip),b,3255,a),flip(a)].">
      <j1 rule="hyper" parents="333 2863 3255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3267">
    <literal><![CDATA[
      (x * (y * (z * K(u \ 1,u)))) \ (K(u \ 1,u) * ((x * y) * z)) = L(a(x,y,z),x * (y * z),K(u \ 1,u))
    ]]></literal>
    <justification jstring="[para(1879(a,1),2481(a,1,1,2))].">
      <j1 rule="para" parents="1879 2481"/>
    </justification>
  </clause>

  <clause id="3268">
    <literal><![CDATA[
      ((1 / (1 / x)) * T(y / x,x * x)) * (1 / x) = x * ((x \ 1) * ((x \ (y * (x \ 1))) / (x \ 1)))
    ]]></literal>
    <justification jstring="[para(2976(a,1),2806(a,1,1,2))].">
      <j1 rule="para" parents="2976 2806"/>
    </justification>
  </clause>

  <clause id="3269">
    <literal><![CDATA[
      T(((1 / (1 / x)) * (y / x)) * (1 / x),x * x) = x * ((x \ 1) * ((x \ (y * (x \ 1))) / (x \ 1)))
    ]]></literal>
    <justification jstring="[hyper(1661,a,3268,a)].">
      <j1 rule="hyper" parents="1661 3268"/>
    </justification>
  </clause>

  <clause id="3270">
    <literal><![CDATA[
      x * ((x \ 1) * ((x \ (y * (x \ 1))) / (x \ 1))) = T((x * (y / x)) * (x \ 1),x * x)
    ]]></literal>
    <justification jstring="[para(2767(a,1),3269(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2767 3269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3271">
    <literal><![CDATA[
      x * ((x \ 1) * ((x \ (y * (x \ 1))) / (x \ 1))) = (x * x) \ ((x * (y / x)) * x)
    ]]></literal>
    <justification jstring="[hyper(333,a,977,a(flip),b,3270,a),flip(a)].">
      <j1 rule="hyper" parents="333 977 3270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3272">
    <literal><![CDATA[
      ((x * (y * (z * K(u \ 1,u)))) \ ((x * y) * z)) * K(u \ 1,u) = L(a(x,y,z),x * (y * z),K(u \ 1,u))
    ]]></literal>
    <justification jstring="[hyper(2495,a,3267,a)].">
      <j1 rule="hyper" parents="2495 3267"/>
    </justification>
  </clause>

  <clause id="3273">
    <literal><![CDATA[
      L(a(x,y,z),x * (y * z),K(u \ 1,u)) = a(x,y,z * K(u \ 1,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,3233,a(flip),b,3272,a),flip(a)].">
      <j1 rule="hyper" parents="63 3233 3272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3274">
    <literal><![CDATA[
      a(x,y,z * K(u \ 1,u)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(2800,a,3273,a),flip(a)].">
      <j1 rule="hyper" parents="2800 3273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3276">
    <literal><![CDATA[
      a(x,y,1 / z) = a(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[para(1131(a,1),3274(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1131 3274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3277">
    <literal><![CDATA[
      a(x,y,(z \ 1) \ 1) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(1248(a,1),3274(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1248 3274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3278">
    <literal><![CDATA[
      a(x,y,K(z,z \ 1) * u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[para(2426(a,1),3274(a,1,3)),flip(a)].">
      <j1 rule="para" parents="2426 3274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3279">
    <literal><![CDATA[
      a(x,y,(1 / z) * u) = a(x,y,(z \ 1) * u)
    ]]></literal>
    <justification jstring="[para(2646(a,1),3274(a,1,3)),flip(a)].">
      <j1 rule="para" parents="2646 3274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3280">
    <literal><![CDATA[
      a(x,y,((z * z) \ u) \ 1) = a(x,y,(1 / u) * (z * z))
    ]]></literal>
    <justification jstring="[para(794(a,1),3276(a,1,3)),flip(a)].">
      <j1 rule="para" parents="794 3276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3281">
    <literal><![CDATA[
      x \ R(x,y \ 1,y) = a(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,1868,a(flip),b,3277,a)].">
      <j1 rule="hyper" parents="63 1868 3277"/>
    </justification>
  </clause>

  <clause id="3282">
    <literal><![CDATA[
      ((x * (y * (K(z,z \ 1) * u))) \ ((x * y) * u)) * K(z,z \ 1) = a(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,2536,a,b,3278,a)].">
      <j1 rule="hyper" parents="63 2536 3278"/>
    </justification>
  </clause>

  <clause id="3283">
    <literal><![CDATA[
      a(x,y,((z * z) \ u) \ 1) = a(x,y,(u \ 1) * (z * z))
    ]]></literal>
    <justification jstring="[hyper(333,a,3279,a(flip),b,3280,a),flip(a)].">
      <j1 rule="hyper" parents="333 3279 3280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3284">
    <literal><![CDATA[
      a(x,y,((z * z) \ u) \ 1) = a(x,y,u \ (z * z))
    ]]></literal>
    <justification jstring="[para(443(a,1),3283(a,2,3))].">
      <j1 rule="para" parents="443 3283"/>
    </justification>
  </clause>

  <clause id="3286">
    <literal><![CDATA[
      ((x * (y * (z * K(u,u \ 1)))) \ ((x * y) * z)) * K(u,u \ 1) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(2397(a,1),3282(a,1,1,1,2,2))].">
      <j1 rule="para" parents="2397 3282"/>
    </justification>
  </clause>

  <clause id="3287">
    <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(333,a,1982,a(flip),b,1985,a),flip(a)].">
      <j1 rule="hyper" parents="333 1982 1985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3288">
    <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(3041(a,2),3287(a,1,1))].">
      <j1 rule="para" parents="3041 3287"/>
    </justification>
  </clause>

  <clause id="3289">
    <literal><![CDATA[
      (x * ((y / (z * (u \ y))) / x)) * (z * (u \ y)) != w
    ]]></literal>
    <literal><![CDATA[
      ((x * ((u / z) / x)) * z) * (u \ y) = w
    ]]></literal>
    <justification jstring="[para(3288(a,1),299(a,1))].">
      <j1 rule="para" parents="3288 299"/>
    </justification>
  </clause>

  <clause id="3290">
    <literal><![CDATA[
      ((x * ((x / y) / x)) * y) * (x \ z) = x * ((x \ T(x,y \ 1)) * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(3289,a,3089,a)].">
      <j1 rule="hyper" parents="3289 3089"/>
    </justification>
  </clause>

  <clause id="3291">
    <literal><![CDATA[
      x * ((x \ T(x,y \ 1)) * (x \ z)) = T(x,y \ 1) * (x \ z)
    ]]></literal>
    <justification jstring="[para(3090(a,1),3290(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3090 3290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3292">
    <literal><![CDATA[
      T(x,(y \ 1) \ 1) * (x \ z) = x * ((x \ T(x,y)) * (x \ z))
    ]]></literal>
    <justification jstring="[para(2983(a,1),3291(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="2983 3291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3293">
    <literal><![CDATA[
      x * ((x \ T(x,y)) * (x \ z)) = T(x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[para(2983(a,1),3292(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2983 3292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3294">
    <literal><![CDATA[
      T(x,y) * (x \ (x * z)) = x * ((x \ T(x,y)) * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),3293(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 3293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3295">
    <literal><![CDATA[
      (T(x,y) * z) / ((x \ T(x,y)) * z) = x
    ]]></literal>
    <justification jstring="[hyper(658,a,3294,a)].">
      <j1 rule="hyper" parents="658 3294"/>
    </justification>
  </clause>

  <clause id="3297">
    <literal><![CDATA[
      x * ((x \ T(x,y)) * z) = T(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(575,a,3294,a),flip(a)].">
      <j1 rule="hyper" parents="575 3294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3298">
    <literal><![CDATA[
      (x \ T(x,y)) * (T(x,y) \ x) = 1
    ]]></literal>
    <justification jstring="[hyper(417,a,3294,a),flip(a)].">
      <j1 rule="hyper" parents="417 3294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3299">
    <literal><![CDATA[
      (x \ 1) \ (T(x,y) \ 1) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(1807,a,3298,a)].">
      <j1 rule="hyper" parents="1807 3298"/>
    </justification>
  </clause>

  <clause id="3300">
    <literal><![CDATA[
      (x \ T(x,y)) \ 1 = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(129,a,3298,a)].">
      <j1 rule="hyper" parents="129 3298"/>
    </justification>
  </clause>

  <clause id="3301">
    <literal><![CDATA[
      T(x / y,y) \ (x / y) = ((x / y) \ (y \ x)) \ 1
    ]]></literal>
    <justification jstring="[para(113(a,1),3300(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="113 3300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3302">
    <literal><![CDATA[
      (T(x,y) \ x) \ 1 = x \ T(x,y)
    ]]></literal>
    <justification jstring="[para(3300(a,1),2539(a,1,1))].">
      <j1 rule="para" parents="3300 2539"/>
    </justification>
  </clause>

  <clause id="3303">
    <literal><![CDATA[
      (x \ T(x,y)) * z = T(x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(1073,a,3295,a),flip(a)].">
      <j1 rule="hyper" parents="1073 3295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3304">
    <literal><![CDATA[
      R(x,x \ T(x,y),z) = x
    ]]></literal>
    <justification jstring="[hyper(798,a,3295,a)].">
      <j1 rule="hyper" parents="798 3295"/>
    </justification>
  </clause>

  <clause id="3305">
    <literal><![CDATA[
      R(x,T(y,x) \ y,z) = x
    ]]></literal>
    <justification jstring="[para(3061(a,2),3304(a,1,2))].">
      <j1 rule="para" parents="3061 3304"/>
    </justification>
  </clause>

  <clause id="3306">
    <literal><![CDATA[
      L(x,y \ T(y,z),y) = x
    ]]></literal>
    <justification jstring="[hyper(783,a,3297,a)].">
      <j1 rule="hyper" parents="783 3297"/>
    </justification>
  </clause>

  <clause id="3309">
    <literal><![CDATA[
      (x \ T(x,y)) * x = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(34,a,280,a(flip),b,3297,a),flip(a)].">
      <j1 rule="hyper" parents="34 280 3297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3311">
    <literal><![CDATA[
      T(x,y) * y = x * ((x * y) / x)
    ]]></literal>
    <justification jstring="[para(3063(a,1),3297(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3063 3297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3313">
    <literal><![CDATA[
      T(x,x \ T(x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(356,a,3309,a)].">
      <j1 rule="hyper" parents="356 3309"/>
    </justification>
  </clause>

  <clause id="3314">
    <literal><![CDATA[
      T(x,y) / x = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(138,a,3309,a)].">
      <j1 rule="hyper" parents="138 3309"/>
    </justification>
  </clause>

  <clause id="3315">
    <literal><![CDATA[
      T(x,R(y,y \ 1,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3068,a,b,3309,a)].">
      <j1 rule="hyper" parents="63 3068 3309"/>
    </justification>
  </clause>

  <clause id="3316">
    <literal><![CDATA[
      x \ T(x,R(y,y \ 1,x)) = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(35,a,1529,a,b,3309,a),flip(a)].">
      <j1 rule="hyper" parents="35 1529 3309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3317">
    <literal><![CDATA[
      (1 / x) * T(x,y) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(126,a,3309,a(flip),b,2352,a)].">
      <j1 rule="hyper" parents="126 3309 2352"/>
    </justification>
  </clause>

  <clause id="3318">
    <literal><![CDATA[
      R(x \ T(x,y),x,z) = (T(x,y) * z) / (x * z)
    ]]></literal>
    <justification jstring="[para(3309(a,1),20(a,2,1,1))].">
      <j1 rule="para" parents="3309 20"/>
    </justification>
  </clause>

  <clause id="3319">
    <literal><![CDATA[
      x * (T(x,y) / x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(3309(a,1),75(a,1,2,1))].">
      <j1 rule="para" parents="3309 75"/>
    </justification>
  </clause>

  <clause id="3320">
    <literal><![CDATA[
      R((x / y) \ T(x / y,z),x / y,y) = (T(x / y,z) * y) / x
    ]]></literal>
    <justification jstring="[para(3309(a,1),109(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="3309 109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3321">
    <literal><![CDATA[
      T(x,K(y \ (y / (x \ 1)),y)) = x
    ]]></literal>
    <justification jstring="[para(2062(a,2),3313(a,1,2))].">
      <j1 rule="para" parents="2062 3313"/>
    </justification>
  </clause>

  <clause id="3322">
    <literal><![CDATA[
      T(x,T(y,x) \ y) = x
    ]]></literal>
    <justification jstring="[para(3061(a,2),3313(a,1,2))].">
      <j1 rule="para" parents="3061 3313"/>
    </justification>
  </clause>

  <clause id="3323">
    <literal><![CDATA[
      (T(x,y) \ x) * y = y * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(126,a,3322,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="126 3322 22"/>
    </justification>
  </clause>

  <clause id="3324">
    <literal><![CDATA[
      (1 / x) * T((1 / x) \ 1,y) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(1657,a,3314,a)].">
      <j1 rule="hyper" parents="1657 3314"/>
    </justification>
  </clause>

  <clause id="3325">
    <literal><![CDATA[
      (x \ 1) \ T(x \ 1,y) = x * T(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(975,a,3314,a),flip(a)].">
      <j1 rule="hyper" parents="975 3314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3327">
    <literal><![CDATA[
      K(x,y) = L(T(x,y) / x,x,y)
    ]]></literal>
    <justification jstring="[para(3314(a,2),785(a,2,1))].">
      <j1 rule="para" parents="3314 785"/>
    </justification>
  </clause>

  <clause id="3329">
    <literal><![CDATA[
      x \ T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) / x = z
    ]]></literal>
    <justification jstring="[para(3319(a,1),342(a,1,2))].">
      <j1 rule="para" parents="3319 342"/>
    </justification>
  </clause>

  <clause id="3330">
    <literal><![CDATA[
      K(1 / (1 / x),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,2944,a(flip),b,3327,a)].">
      <j1 rule="hyper" parents="333 2944 3327"/>
    </justification>
  </clause>

  <clause id="3331">
    <literal><![CDATA[
      (x * K(x,y)) / x = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,901,a(flip),b,3327,a)].">
      <j1 rule="hyper" parents="333 901 3327"/>
    </justification>
  </clause>

  <clause id="3332">
    <literal><![CDATA[
      K(x,y) * x = x * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(125,a,3327,a,b,901,a(flip))].">
      <j1 rule="hyper" parents="125 3327 901"/>
    </justification>
  </clause>

  <clause id="3333">
    <literal><![CDATA[
      K(1 / x,y) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(76(a,1),3330(a,1,1,2))].">
      <j1 rule="para" parents="76 3330"/>
    </justification>
  </clause>

  <clause id="3334">
    <literal><![CDATA[
      K((x \ 1) \ 1,y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(193(a,1),3330(a,1,1)),flip(a)].">
      <j1 rule="para" parents="193 3330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3335">
    <literal><![CDATA[
      T(K(x,y),x) = K(x,y)
    ]]></literal>
    <justification jstring="[para(3330(a,1),2946(a,1,1))].">
      <j1 rule="para" parents="3330 2946"/>
    </justification>
  </clause>

  <clause id="3336">
    <literal><![CDATA[
      (((x * y) \ x) \ 1) \ (((x * y) \ x) \ K(y,x)) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(2332,a,3335,a)].">
      <j1 rule="hyper" parents="2332 3335"/>
    </justification>
  </clause>

  <clause id="3337">
    <literal><![CDATA[
      T(x,K(x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(54,a,3335,a)].">
      <j1 rule="hyper" parents="54 3335"/>
    </justification>
  </clause>

  <clause id="3338">
    <literal><![CDATA[
      x * K(x,y) != z * x
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(3335(a,1),256(a,1,2))].">
      <j1 rule="para" parents="3335 256"/>
    </justification>
  </clause>

  <clause id="3339">
    <literal><![CDATA[
      R(K(x,y),z,u) * x = x * R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(3335(a,1),252(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3335 252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3340">
    <literal><![CDATA[
      T(x,K(T(x,y),z)) = x
    ]]></literal>
    <justification jstring="[hyper(147,a,3337,a)].">
      <j1 rule="hyper" parents="147 3337"/>
    </justification>
  </clause>

  <clause id="3341">
    <literal><![CDATA[
      T(R(x,y,z),K(x,u)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(3337(a,1),27(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3337 27"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3342">
    <literal><![CDATA[
      T(x,y) * K(x,z) = K(x,z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(3337(a,1),250(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3337 250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3343">
    <literal><![CDATA[
      T(T(T(x,y),z),K(x,u)) = T(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(3337(a,1),116(a,2,1,1))].">
      <j1 rule="para" parents="3337 116"/>
    </justification>
  </clause>

  <clause id="3344">
    <literal><![CDATA[
      L(x,y,z) * K(x,u) = K(x,u) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(3337(a,1),251(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3337 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3345">
    <literal><![CDATA[
      R(x,y,z) * K(x,u) = K(x,u) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(3337(a,1),252(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3337 252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3346">
    <literal><![CDATA[
      T(x / y,K(y \ x,z)) = x / y
    ]]></literal>
    <justification jstring="[para(113(a,1),3340(a,1,2,1))].">
      <j1 rule="para" parents="113 3340"/>
    </justification>
  </clause>

  <clause id="3347">
    <literal><![CDATA[
      T(K(x,y),x) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(3331(a,1),350(a,1,1)),flip(b)].">
      <j1 rule="para" parents="3331 350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3348">
    <literal><![CDATA[
      K(x \ 1,(1 / x) \ (y / x)) = (T(y,1 / x) / x) \ (y / x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1671,a(flip),b,3333,a),flip(a)].">
      <j1 rule="hyper" parents="63 1671 3333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3349">
    <literal><![CDATA[
      T(K(x,y),x) = K((x \ 1) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,3335,a,b,3334,a)].">
      <j1 rule="hyper" parents="333 3335 3334"/>
    </justification>
  </clause>

  <clause id="3350">
    <literal><![CDATA[
      K(T(x,x \ 1),y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(112(a,2),3334(a,1,1))].">
      <j1 rule="para" parents="112 3334"/>
    </justification>
  </clause>

  <clause id="3351">
    <literal><![CDATA[
      K(T(1 / x,y),z) = K(T(x \ 1,y),z)
    ]]></literal>
    <justification jstring="[para(2383(a,1),3334(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2383 3334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3352">
    <literal><![CDATA[
      T(x,y) * (x \ y) = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(1074,a,3311,a)].">
      <j1 rule="hyper" parents="1074 3311"/>
    </justification>
  </clause>

  <clause id="3353">
    <literal><![CDATA[
      (x * (x * y)) / x = T(x,x * y) * y
    ]]></literal>
    <justification jstring="[hyper(1065,a,3311,a),flip(a)].">
      <j1 rule="hyper" parents="1065 3311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3354">
    <literal><![CDATA[
      T(x,x / (x / y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(35,a,1457,a,b,3311,a)].">
      <j1 rule="hyper" parents="35 1457 3311"/>
    </justification>
  </clause>

  <clause id="3355">
    <literal><![CDATA[
      T(x,x \ y) * (x \ y) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(10(a,1),3311(a,2,2,1))].">
      <j1 rule="para" parents="10 3311"/>
    </justification>
  </clause>

  <clause id="3357">
    <literal><![CDATA[
      ((T(x,y) * y) / x) \ ((x * (x * y)) / x) = L(x,(x * y) / x,x)
    ]]></literal>
    <justification jstring="[para(3311(a,2),1831(a,1,1,1))].">
      <j1 rule="para" parents="3311 1831"/>
    </justification>
  </clause>

  <clause id="3358">
    <literal><![CDATA[
      T(x,x / (1 / y)) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,1462,a(flip),b,3354,a)].">
      <j1 rule="hyper" parents="63 1462 3354"/>
    </justification>
  </clause>

  <clause id="3359">
    <literal><![CDATA[
      (x / T(y,x)) * y = T(x,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,1108,a(flip),b,3354,a)].">
      <j1 rule="hyper" parents="63 1108 3354"/>
    </justification>
  </clause>

  <clause id="3360">
    <literal><![CDATA[
      T(x,y) / ((x * y) / x) = x / y
    ]]></literal>
    <justification jstring="[hyper(123,a,3354,a(flip),b,1095,a)].">
      <j1 rule="hyper" parents="123 3354 1095"/>
    </justification>
  </clause>

  <clause id="3361">
    <literal><![CDATA[
      (x / y) \ T(x,y) = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(121,a,3354,a(flip),b,1095,a)].">
      <j1 rule="hyper" parents="121 3354 1095"/>
    </justification>
  </clause>

  <clause id="3362">
    <literal><![CDATA[
      T(x * y,(x * y) / x) = T(x * y,y)
    ]]></literal>
    <justification jstring="[para(11(a,1),3354(a,1,2,2))].">
      <j1 rule="para" parents="11 3354"/>
    </justification>
  </clause>

  <clause id="3363">
    <literal><![CDATA[
      T(x,x / y) = T(x,y \ x)
    ]]></literal>
    <justification jstring="[para(76(a,1),3354(a,1,2,2))].">
      <j1 rule="para" parents="76 3354"/>
    </justification>
  </clause>

  <clause id="3364">
    <literal><![CDATA[
      T(x,(y \ x) \ x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(193(a,1),3354(a,1,2)),flip(a)].">
      <j1 rule="para" parents="193 3354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3365">
    <literal><![CDATA[
      x * ((y * (x \ y)) / y) = T(y,x \ y)
    ]]></literal>
    <justification jstring="[hyper(1186,a,3363,a)].">
      <j1 rule="hyper" parents="1186 3363"/>
    </justification>
  </clause>

  <clause id="3366">
    <literal><![CDATA[
      T(x,y \ x) / y = (x * (x / y)) / x
    ]]></literal>
    <justification jstring="[hyper(123,a,3363,a(flip),b,1087,a)].">
      <j1 rule="hyper" parents="123 3363 1087"/>
    </justification>
  </clause>

  <clause id="3367">
    <literal><![CDATA[
      T(T(x,y \ x) / y,x) = x / y
    ]]></literal>
    <justification jstring="[para(3363(a,1),1094(a,1,1,1))].">
      <j1 rule="para" parents="3363 1094"/>
    </justification>
  </clause>

  <clause id="3368">
    <literal><![CDATA[
      T(x \ T(y,x \ y),y) = x \ y
    ]]></literal>
    <justification jstring="[para(3363(a,1),1097(a,1,1,2))].">
      <j1 rule="para" parents="3363 1097"/>
    </justification>
  </clause>

  <clause id="3369">
    <literal><![CDATA[
      T(x,T(y,y \ x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(112(a,2),3364(a,1,2))].">
      <j1 rule="para" parents="112 3364"/>
    </justification>
  </clause>

  <clause id="3370">
    <literal><![CDATA[
      T(x * y,T(x,y)) = T(x * y,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),3369(a,1,2,2))].">
      <j1 rule="para" parents="9 3369"/>
    </justification>
  </clause>

  <clause id="3371">
    <literal><![CDATA[
      T(1 / x,T(x,y)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(253,a,3317,a,b,1012,a)].">
      <j1 rule="hyper" parents="253 3317 1012"/>
    </justification>
  </clause>

  <clause id="3372">
    <literal><![CDATA[
      (x \ T(x,y)) * (z * K(x \ 1,x)) = ((x \ 1) * T(x,y)) * z
    ]]></literal>
    <justification jstring="[para(3317(a,1),2920(a,1,1))].">
      <j1 rule="para" parents="3317 2920"/>
    </justification>
  </clause>

  <clause id="3373">
    <literal><![CDATA[
      T(1 / (1 / x),T(1 / x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(333,a,79,a(flip),b,3371,a),flip(a)].">
      <j1 rule="hyper" parents="333 79 3371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3374">
    <literal><![CDATA[
      T(x \ 1,T(x,y)) = T(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(3371(a,1),259(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3371 259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3375">
    <literal><![CDATA[
      T(x / (y * x),T(y,z)) = R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(3371(a,1),401(a,2,1))].">
      <j1 rule="para" parents="3371 401"/>
    </justification>
  </clause>

  <clause id="3376">
    <literal><![CDATA[
      x * T(x \ 1,T(x,y)) = K(x \ 1,T(x,y))
    ]]></literal>
    <justification jstring="[para(3371(a,1),2068(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3371 2068"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3377">
    <literal><![CDATA[
      (((x * y) / x) \ y) \ y = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(63,a,2168,a(flip),b,3321,a)].">
      <j1 rule="hyper" parents="63 2168 3321"/>
    </justification>
  </clause>

  <clause id="3378">
    <literal><![CDATA[
      x / ((y * x) / y) = ((y * x) / y) \ x
    ]]></literal>
    <justification jstring="[hyper(197,a,3321,a(flip),b,2168,a(flip))].">
      <j1 rule="hyper" parents="197 3321 2168"/>
    </justification>
  </clause>

  <clause id="3379">
    <literal><![CDATA[
      (((x * y) / x) \ y) * ((x * y) / x) = y
    ]]></literal>
    <justification jstring="[hyper(126,a,3321,a(flip),b,2168,a(flip))].">
      <j1 rule="hyper" parents="126 3321 2168"/>
    </justification>
  </clause>

  <clause id="3380">
    <literal><![CDATA[
      T(K(x,y),R(x,z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(54,a,3341,a)].">
      <j1 rule="hyper" parents="54 3341"/>
    </justification>
  </clause>

  <clause id="3381">
    <literal><![CDATA[
      T(K(x \ y,z),y / x) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(54,a,3346,a)].">
      <j1 rule="hyper" parents="54 3346"/>
    </justification>
  </clause>

  <clause id="3382">
    <literal><![CDATA[
      K((x \ 1) \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(3349(a,1),3347(a,1))].">
      <j1 rule="para" parents="3349 3347"/>
    </justification>
  </clause>

  <clause id="3383">
    <literal><![CDATA[
      T(x / y,T(y,x)) = y \ x
    ]]></literal>
    <justification jstring="[hyper(253,a,861,a,b,3352,a)].">
      <j1 rule="hyper" parents="253 861 3352"/>
    </justification>
  </clause>

  <clause id="3384">
    <literal><![CDATA[
      T(x,y) \ ((x * y) / x) = x \ y
    ]]></literal>
    <justification jstring="[hyper(129,a,3352,a)].">
      <j1 rule="hyper" parents="129 3352"/>
    </justification>
  </clause>

  <clause id="3385">
    <literal><![CDATA[
      L((x \ y) \ z,x \ y,T(x,y)) = ((x * y) / x) \ (T(x,y) * z)
    ]]></literal>
    <justification jstring="[para(3352(a,1),99(a,2,1))].">
      <j1 rule="para" parents="3352 99"/>
    </justification>
  </clause>

  <clause id="3386">
    <literal><![CDATA[
      L(((x * y) / x) / y,y,x) = K(T(x,y),y)
    ]]></literal>
    <justification jstring="[para(3352(a,1),2741(a,1,1,1))].">
      <j1 rule="para" parents="3352 2741"/>
    </justification>
  </clause>

  <clause id="3387">
    <literal><![CDATA[
      T(x \ y,T(x,y)) = T(x \ y,x)
    ]]></literal>
    <justification jstring="[para(3383(a,1),259(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3383 259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3388">
    <literal><![CDATA[
      x \ (y * T(y \ x,T(y,x))) = K(y \ x,T(y,x))
    ]]></literal>
    <justification jstring="[para(3383(a,1),2201(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3383 2201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3389">
    <literal><![CDATA[
      R(T(x,x * y),y,x) = (x / T(y,x)) * y
    ]]></literal>
    <justification jstring="[para(3358(a,1),1440(a,1,1))].">
      <j1 rule="para" parents="3358 1440"/>
    </justification>
  </clause>

  <clause id="3391">
    <literal><![CDATA[
      ((x * y) * y) / (x * y) = x \ T(x * y,y)
    ]]></literal>
    <justification jstring="[hyper(36,a,184,a(flip),b,3360,a),flip(a)].">
      <j1 rule="hyper" parents="36 184 3360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3392">
    <literal><![CDATA[
      T(x,T(1 / x,y)) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(3373(a,1),1908(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3373 1908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3393">
    <literal><![CDATA[
      K(T(x,y) \ (T(x,y) / T(x,z)),T(x,y)) = T(x * T(x \ 1,x),z)
    ]]></literal>
    <justification jstring="[para(3374(a,1),2058(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3374 2058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3397">
    <literal><![CDATA[
      x \ (y * T(y \ x,T(y,x))) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[para(3387(a,2),434(a,1,2,2))].">
      <j1 rule="para" parents="3387 434"/>
    </justification>
  </clause>

  <clause id="3399">
    <literal><![CDATA[
      T(x,x \ 1) * T(x \ 1,y) = x * T(1 / x,y)
    ]]></literal>
    <justification jstring="[para(3392(a,1),1557(a,1,1))].">
      <j1 rule="para" parents="3392 1557"/>
    </justification>
  </clause>

  <clause id="3400">
    <literal><![CDATA[
      K(x \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(1 / x,y) = z
    ]]></literal>
    <justification jstring="[para(79(a,1),3382(a,1,1,1))].">
      <j1 rule="para" parents="79 3382"/>
    </justification>
  </clause>

  <clause id="3401">
    <literal><![CDATA[
      K(T(x \ y,y \ x),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,z) = u
    ]]></literal>
    <justification jstring="[para(2283(a,2),3382(a,1,1))].">
      <j1 rule="para" parents="2283 3382"/>
    </justification>
  </clause>

  <clause id="3402">
    <literal><![CDATA[
      (x \ 1) * (T(x,y) \ x) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(142,a,3299,a)].">
      <j1 rule="hyper" parents="142 3299"/>
    </justification>
  </clause>

  <clause id="3403">
    <literal><![CDATA[
      (T(x,y) * z) / (x * z) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(123,a,155,a(flip),b,3303,a)].">
      <j1 rule="hyper" parents="123 155 3303"/>
    </justification>
  </clause>

  <clause id="3404">
    <literal><![CDATA[
      (x \ T(x,y)) \ (T(x,y) * z) = x * z
    ]]></literal>
    <justification jstring="[hyper(121,a,155,a(flip),b,3303,a)].">
      <j1 rule="hyper" parents="121 155 3303"/>
    </justification>
  </clause>

  <clause id="3405">
    <literal><![CDATA[
      (x \ T(x,y)) \ z = x * (T(x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(121,a,71,a(flip),b,3303,a)].">
      <j1 rule="hyper" parents="121 71 3303"/>
    </justification>
  </clause>

  <clause id="3406">
    <literal><![CDATA[
      T(x,R(T(y,x),T(y,x) \ 1,x)) = x * (T(y,x) \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,1531,a,b,3323,a)].">
      <j1 rule="hyper" parents="63 1531 3323"/>
    </justification>
  </clause>

  <clause id="3407">
    <literal><![CDATA[
      T(K(x,y),T(x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(254,a,3342,a)].">
      <j1 rule="hyper" parents="254 3342"/>
    </justification>
  </clause>

  <clause id="3410">
    <literal><![CDATA[
      T(K(x,y),T(T(x,z),u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(54,a,3343,a)].">
      <j1 rule="hyper" parents="54 3343"/>
    </justification>
  </clause>

  <clause id="3411">
    <literal><![CDATA[
      T(T(x,x * y) * y,x) = x * y
    ]]></literal>
    <justification jstring="[para(3353(a,1),238(a,1,1))].">
      <j1 rule="para" parents="3353 238"/>
    </justification>
  </clause>

  <clause id="3412">
    <literal><![CDATA[
      ((x \ y) \ y) * (x \ y) = x * (y / x)
    ]]></literal>
    <justification jstring="[hyper(736,a,3355,a)].">
      <j1 rule="hyper" parents="736 3355"/>
    </justification>
  </clause>

  <clause id="3413">
    <literal><![CDATA[
      T(x,x \ (y \ x)) \ (y \ T(x,y \ 1)) = x \ (y \ x)
    ]]></literal>
    <justification jstring="[hyper(121,a,3107,a,b,3355,a)].">
      <j1 rule="hyper" parents="121 3107 3355"/>
    </justification>
  </clause>

  <clause id="3414">
    <literal><![CDATA[
      (x \ T(x,x \ y)) * y = x * (y / x)
    ]]></literal>
    <justification jstring="[hyper(63,a,3303,a,b,3355,a)].">
      <j1 rule="hyper" parents="63 3303 3355"/>
    </justification>
  </clause>

  <clause id="3415">
    <literal><![CDATA[
      (x * (y / x)) \ (T(x,x \ y) * ((x \ y) * z)) = L(z,x \ y,T(x,x \ y))
    ]]></literal>
    <justification jstring="[para(3355(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="3355 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3416">
    <literal><![CDATA[
      T(x,y \ x) != y * z
    ]]></literal>
    <literal><![CDATA[
      (x * (y \ x)) / x = z
    ]]></literal>
    <justification jstring="[para(3365(a,1),43(a,1))].">
      <j1 rule="para" parents="3365 43"/>
    </justification>
  </clause>

  <clause id="3418">
    <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(2661(a,1),3379(a,1,1,1,1))].">
      <j1 rule="para" parents="2661 3379"/>
    </justification>
  </clause>

  <clause id="3420">
    <literal><![CDATA[
      (1 / x) * ((T(x,y) \ 1) * x) = (x \ 1) * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(333,a,2021,a,b,3402,a)].">
      <j1 rule="hyper" parents="333 2021 3402"/>
    </justification>
  </clause>

  <clause id="3421">
    <literal><![CDATA[
      (x \ T(x,y)) \ (T(x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(3403(a,1),345(a,1,1))].">
      <j1 rule="para" parents="3403 345"/>
    </justification>
  </clause>

  <clause id="3423">
    <literal><![CDATA[
      (x \ T(x,y)) \ y = T(y,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(333,a,1075,a(flip),b,3405,a),flip(a)].">
      <j1 rule="hyper" parents="333 1075 3405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3424">
    <literal><![CDATA[
      T(x,T(y,x)) \ x = y \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(39,a,2709,a,b,3423,a)].">
      <j1 rule="hyper" parents="39 2709 3423"/>
    </justification>
  </clause>

  <clause id="3425">
    <literal><![CDATA[
      L(x,T(y,T(z,y)) \ y,z) = x
    ]]></literal>
    <justification jstring="[para(3424(a,2),3306(a,1,2))].">
      <j1 rule="para" parents="3424 3306"/>
    </justification>
  </clause>

  <clause id="3426">
    <literal><![CDATA[
      T(x,R(T(y,x),T(y,x) \ 1,x)) \ x = y \ T(y,x)
    ]]></literal>
    <justification jstring="[para(3315(a,2),3424(a,1,1))].">
      <j1 rule="para" parents="3315 3424"/>
    </justification>
  </clause>

  <clause id="3427">
    <literal><![CDATA[
      L(x,T(y,z) \ y,(y * z) / y) = x
    ]]></literal>
    <justification jstring="[para(238(a,1),3425(a,1,2,1,2))].">
      <j1 rule="para" parents="238 3425"/>
    </justification>
  </clause>

  <clause id="3428">
    <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(3375(a,1),3101(a,2,2,2,1))].">
      <j1 rule="para" parents="3375 3101"/>
    </justification>
  </clause>

  <clause id="3429">
    <literal><![CDATA[
      L(x \ T(x,y),y,x) = K(T(x,y),y)
    ]]></literal>
    <justification jstring="[para(3064(a,1),3386(a,1,1))].">
      <j1 rule="para" parents="3064 3386"/>
    </justification>
  </clause>

  <clause id="3430">
    <literal><![CDATA[
      K(T(x,T(y,x)),T(y,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3080,a,b,3429,a),flip(a)].">
      <j1 rule="hyper" parents="63 3080 3429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3431">
    <literal><![CDATA[
      K(T(x,y),y) = K(x,(x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(63,a,3069,a(flip),b,3429,a),flip(a)].">
      <j1 rule="hyper" parents="63 3069 3429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3432">
    <literal><![CDATA[
      K(T(x,x \ y),x \ y) = K(x,y / x)
    ]]></literal>
    <justification jstring="[para(10(a,1),3431(a,2,2,1))].">
      <j1 rule="para" parents="10 3431"/>
    </justification>
  </clause>

  <clause id="3433">
    <literal><![CDATA[
      R(T(x,x * y),y,x) = T(x,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(333,a,3359,a(flip),b,3389,a),flip(a)].">
      <j1 rule="hyper" parents="333 3359 3389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3434">
    <literal><![CDATA[
      L(R(x,y,x),y,x) * y = y * T(x,T(y,x))
    ]]></literal>
    <justification jstring="[para(3433(a,1),1046(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3433 1046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3435">
    <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(3324(a,1),2979(a,2,1))].">
      <j1 rule="para" parents="3324 2979"/>
    </justification>
  </clause>

  <clause id="3436">
    <literal><![CDATA[
      (x * T(x \ 1,y)) \ 1 = T(x \ 1,y) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(3325(a,1),3300(a,1,1))].">
      <j1 rule="para" parents="3325 3300"/>
    </justification>
  </clause>

  <clause id="3437">
    <literal><![CDATA[
      (x * T(x \ 1,y)) \ y = T(y,T(x \ 1,y))
    ]]></literal>
    <justification jstring="[para(3325(a,1),3423(a,1,1))].">
      <j1 rule="para" parents="3325 3423"/>
    </justification>
  </clause>

  <clause id="3438">
    <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(871,a,3339,a),flip(a)].">
      <j1 rule="hyper" parents="871 3339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3439">
    <literal><![CDATA[
      K(x,R(K(x,y),z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(120,a,3339,a,b,88,a),flip(a)].">
      <j1 rule="hyper" parents="120 3339 88"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3441">
    <literal><![CDATA[
      K(x \ 1,T(x,y)) = x * T(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(3374(a,1),3376(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3374 3376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3442">
    <literal><![CDATA[
      K(x \ 1,T(x,y)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,358,a(flip),b,3441,a),flip(a)].">
      <j1 rule="hyper" parents="333 358 3441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3443">
    <literal><![CDATA[
      K(x \ 1,T(x,y)) = (x \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(333,a,111,a(flip),b,3441,a),flip(a)].">
      <j1 rule="hyper" parents="333 111 3441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3446">
    <literal><![CDATA[
      T(x \ T(x * y,y),x * y) = y
    ]]></literal>
    <justification jstring="[para(3391(a,1),238(a,1,1))].">
      <j1 rule="para" parents="3391 238"/>
    </justification>
  </clause>

  <clause id="3447">
    <literal><![CDATA[
      T(x \ T(x * y,y),x) = R(y,x,y)
    ]]></literal>
    <justification jstring="[para(3391(a,1),830(a,2,1)),flip(a)].">
      <j1 rule="para" parents="3391 830"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3448">
    <literal><![CDATA[
      (x \ T(x * y,y)) * x = x * R(y,x,y)
    ]]></literal>
    <justification jstring="[para(3391(a,1),842(a,1,1))].">
      <j1 rule="para" parents="3391 842"/>
    </justification>
  </clause>

  <clause id="3449">
    <literal><![CDATA[
      x * R(y,x,y) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ T(x * y,y)) * x = z
    ]]></literal>
    <justification jstring="[para(3447(a,1),300(a,1,2))].">
      <j1 rule="para" parents="3447 300"/>
    </justification>
  </clause>

  <clause id="3450">
    <literal><![CDATA[
      (x * R(y,x,y)) \ T(x * y,y) = K(x,x \ T(x * y,y))
    ]]></literal>
    <justification jstring="[para(3448(a,1),90(a,1,1))].">
      <j1 rule="para" parents="3448 90"/>
    </justification>
  </clause>

  <clause id="3451">
    <literal><![CDATA[
      T((x * y) / x,T(x,y)) = L(R(y,x,y),x,y)
    ]]></literal>
    <justification jstring="[hyper(35,a,472,a,b,3434,a)].">
      <j1 rule="hyper" parents="35 472 3434"/>
    </justification>
  </clause>

  <clause id="3452">
    <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(3391(a,1),3451(a,1,1))].">
      <j1 rule="para" parents="3391 3451"/>
    </justification>
  </clause>

  <clause id="3453">
    <literal><![CDATA[
      T(x,R(y,y \ 1,x)) \ x = 1 / (y \ ((x * y) / x))
    ]]></literal>
    <justification jstring="[hyper(197,a,3316,a(flip),b,3302,a),flip(a)].">
      <j1 rule="hyper" parents="197 3316 3302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3454">
    <literal><![CDATA[
      R(x \ T(x,y),x,z) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,3403,a(flip),b,3318,a),flip(a)].">
      <j1 rule="hyper" parents="333 3403 3318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3455">
    <literal><![CDATA[
      R(T(x,y) \ x,y,z) = (T(y,T(x,y)) * z) / (y * z)
    ]]></literal>
    <justification jstring="[para(3061(a,2),3318(a,1,1))].">
      <j1 rule="para" parents="3061 3318"/>
    </justification>
  </clause>

  <clause id="3457">
    <literal><![CDATA[
      (x \ T(x,y)) \ z != u
    ]]></literal>
    <literal><![CDATA[
      x * (T(x,y) \ z) = u
    ]]></literal>
    <justification jstring="[para(10(a,1),3421(a,1,2))].">
      <j1 rule="para" parents="10 3421"/>
    </justification>
  </clause>

  <clause id="3459">
    <literal><![CDATA[
      ((x / y) \ (y \ x)) \ 1 = (y \ x) \ (x / y)
    ]]></literal>
    <justification jstring="[para(113(a,1),3301(a,1,1)),flip(a)].">
      <j1 rule="para" parents="113 3301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3460">
    <literal><![CDATA[
      (x \ (x * y)) \ ((x * y) / x) = (((x * y) / x) \ y) \ 1
    ]]></literal>
    <justification jstring="[para(9(a,1),3459(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 3459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3461">
    <literal><![CDATA[
      K(x \ y,T(x,y)) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,3397,a(flip),b,3388,a),flip(a)].">
      <j1 rule="hyper" parents="63 3397 3388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3462">
    <literal><![CDATA[
      K(x \ (x * y),x) = K(y,T(x,x * y))
    ]]></literal>
    <justification jstring="[hyper(63,a,705,a(flip),b,3461,a),flip(a)].">
      <j1 rule="hyper" parents="63 705 3461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3463">
    <literal><![CDATA[
      K(x,T(y,y * x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,705,a(flip),b,3462,a),flip(a)].">
      <j1 rule="hyper" parents="63 705 3462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3465">
    <literal><![CDATA[
      K(x,x \ 1) * T(x \ 1,y) = T(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(2865,a,3399,a)].">
      <j1 rule="hyper" parents="2865 3399"/>
    </justification>
  </clause>

  <clause id="3466">
    <literal><![CDATA[
      ((x \ 1) \ 1) * T(x \ 1,y) = x * T(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(736,a,3399,a)].">
      <j1 rule="hyper" parents="736 3399"/>
    </justification>
  </clause>

  <clause id="3468">
    <literal><![CDATA[
      T(x \ 1,y) * (K(x,x \ 1) * z) = T(1 / x,y) * z
    ]]></literal>
    <justification jstring="[para(3465(a,1),2682(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3465 2682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3469">
    <literal><![CDATA[
      T(L(x \ 1,x,y) \ 1,y) \ (L(x \ 1,x,y) \ 1) = K(x,y) \ 1
    ]]></literal>
    <justification jstring="[para(1282(a,2),3436(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1282 3436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3470">
    <literal><![CDATA[
      T((x \ y) \ 1,z) \ ((x \ y) \ 1) = (x \ (y * T(y \ x,z))) \ 1
    ]]></literal>
    <justification jstring="[para(1285(a,1),3436(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1285 3436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3471">
    <literal><![CDATA[
      (x * (T(y,x) \ y)) \ x = y \ T(y,x)
    ]]></literal>
    <justification jstring="[para(3406(a,1),3426(a,1,1))].">
      <j1 rule="para" parents="3406 3426"/>
    </justification>
  </clause>

  <clause id="3472">
    <literal><![CDATA[
      x / (y \ T(y,x)) = x * (T(y,x) \ y)
    ]]></literal>
    <justification jstring="[hyper(198,a,3471,a)].">
      <j1 rule="hyper" parents="198 3471"/>
    </justification>
  </clause>

  <clause id="3473">
    <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(1278(a,1),3472(a,1,2,2))].">
      <j1 rule="para" parents="1278 3472"/>
    </justification>
  </clause>

  <clause id="3474">
    <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(3455(a,1),944(a,1,1))].">
      <j1 rule="para" parents="3455 944"/>
    </justification>
  </clause>

  <clause id="3475">
    <literal><![CDATA[
      (T(x,y) \ 1) * ((x \ 1) \ 1) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(2758,a,3420,a(flip))].">
      <j1 rule="hyper" parents="2758 3420"/>
    </justification>
  </clause>

  <clause id="3476">
    <literal><![CDATA[
      ((x \ 1) \ 1) * T(T(x,y) \ 1,x) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,2984,a,b,3475,a)].">
      <j1 rule="hyper" parents="63 2984 3475"/>
    </justification>
  </clause>

  <clause id="3477">
    <literal><![CDATA[
      (((x * y) / x) \ y) \ 1 = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[para(9(a,1),3460(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 3460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3478">
    <literal><![CDATA[
      1 / (x \ ((y * x) / y)) = ((y * x) / y) \ x
    ]]></literal>
    <justification jstring="[hyper(198,a,3477,a)].">
      <j1 rule="hyper" parents="198 3477"/>
    </justification>
  </clause>

  <clause id="3479">
    <literal><![CDATA[
      T(x,R(y,y \ 1,x)) \ x = ((x * y) / x) \ y
    ]]></literal>
    <justification jstring="[hyper(63,a,3453,a,b,3478,a)].">
      <j1 rule="hyper" parents="63 3453 3478"/>
    </justification>
  </clause>

  <clause id="3480">
    <literal><![CDATA[
      ((x * y) / x) \ y = T(x,y) \ x
    ]]></literal>
    <justification jstring="[para(3315(a,1),3479(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3315 3479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3481">
    <literal><![CDATA[
      (T(x,y) \ x) * ((x * y) / x) = y
    ]]></literal>
    <justification jstring="[hyper(125,a,3480,a(flip),b,3378,a)].">
      <j1 rule="hyper" parents="125 3480 3378"/>
    </justification>
  </clause>

  <clause id="3482">
    <literal><![CDATA[
      T(x,x \ y) \ x = (y / x) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),3480(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 3480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3483">
    <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(3480(a,1),1114(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3480 1114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3484">
    <literal><![CDATA[
      ((x * y) / x) * (y \ ((T(x,y) \ x) * z)) = L(z,((x * y) / x) \ y,(x * y) / x)
    ]]></literal>
    <justification jstring="[para(3480(a,1),1300(a,1,2,2,1))].">
      <j1 rule="para" parents="3480 1300"/>
    </justification>
  </clause>

  <clause id="3485">
    <literal><![CDATA[
      T(x,x \ y) \ x = x \ (y / (y / x))
    ]]></literal>
    <justification jstring="[hyper(333,a,3081,a(flip),b,3482,a),flip(a)].">
      <j1 rule="hyper" parents="333 3081 3482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3486">
    <literal><![CDATA[
      x / (x / y) = y * (T(y,y \ x) \ y)
    ]]></literal>
    <justification jstring="[hyper(126,a,3482,a,b,3081,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="126 3482 3081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3487">
    <literal><![CDATA[
      (x * y) / ((x * y) / x) = x * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[para(9(a,1),3486(a,2,2,1,2))].">
      <j1 rule="para" parents="9 3486"/>
    </justification>
  </clause>

  <clause id="3488">
    <literal><![CDATA[
      x / (y \ ((y * x) / y)) = y * (T(y,x) \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,1107,a(flip),b,3487,a)].">
      <j1 rule="hyper" parents="63 1107 3487"/>
    </justification>
  </clause>

  <clause id="3489">
    <literal><![CDATA[
      (x * (T(x,y) \ x)) \ y = x \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(192,a,3488,a)].">
      <j1 rule="hyper" parents="192 3488"/>
    </justification>
  </clause>

  <clause id="3490">
    <literal><![CDATA[
      T(x \ 1,y) * ((x \ 1) \ (K(x,x \ 1) * z)) = T(1 / x,y) * ((x \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(2205(a,2),3468(a,1,2))].">
      <j1 rule="para" parents="2205 3468"/>
    </justification>
  </clause>

  <clause id="3491">
    <literal><![CDATA[
      T(1 / x,y) * ((1 / x) \ z) = T(x \ 1,y) * ((x \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(2665(a,1),3468(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2665 3468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3492">
    <literal><![CDATA[
      K(x \ 1,(1 / x) \ (y / x)) = (T(y,x \ 1) / x) \ (y / x)
    ]]></literal>
    <justification jstring="[para(2986(a,1),3348(a,2,1,1))].">
      <j1 rule="para" parents="2986 3348"/>
    </justification>
  </clause>

  <clause id="3493">
    <literal><![CDATA[
      T(x,y) * (x \ (z * K(x \ 1,x))) = ((x \ 1) * T(x,y)) * z
    ]]></literal>
    <justification jstring="[hyper(63,a,3303,a(flip),b,3372,a)].">
      <j1 rule="hyper" parents="63 3303 3372"/>
    </justification>
  </clause>

  <clause id="3494">
    <literal><![CDATA[
      (1 / x) * (T(x \ 1,y) * ((x \ 1) \ z)) = T(1 / x,y) * z
    ]]></literal>
    <justification jstring="[hyper(126,a,3491,a(flip),b,1053,a)].">
      <j1 rule="hyper" parents="126 3491 1053"/>
    </justification>
  </clause>

  <clause id="3495">
    <literal><![CDATA[
      T(x,y) * (T(x,x \ 1) \ z) = ((x \ 1) * T(x,y)) * z
    ]]></literal>
    <justification jstring="[para(2841(a,1),3493(a,1,2))].">
      <j1 rule="para" parents="2841 3493"/>
    </justification>
  </clause>

  <clause id="3496">
    <literal><![CDATA[
      (T(1 / x,y) * z) / (T(1 / x,y) * ((x \ 1) \ z)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(123,a,3494,a(flip),b,3131,a(flip))].">
      <j1 rule="hyper" parents="123 3494 3131"/>
    </justification>
  </clause>

  <clause id="3497">
    <literal><![CDATA[
      R((x / y) \ T(x / y,z),x / y,y) = (y * T(y \ x,z)) / x
    ]]></literal>
    <justification jstring="[para(471(a,1),3320(a,2,1))].">
      <j1 rule="para" parents="471 3320"/>
    </justification>
  </clause>

  <clause id="3498">
    <literal><![CDATA[
      (x * T(x \ y,z)) / y = (y / x) \ T(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,3454,a(flip),b,3497,a),flip(a)].">
      <j1 rule="hyper" parents="63 3454 3497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3499">
    <literal><![CDATA[
      ((x \ y) / y) \ T((x \ y) / y,z) = x * T(x \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(1153,a,3498,a),flip(a)].">
      <j1 rule="hyper" parents="1153 3498"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3502">
    <literal><![CDATA[
      x \ ((y \ x) / ((y \ x) / x)) = y * T(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,3062,a(flip),b,3499,a)].">
      <j1 rule="hyper" parents="63 3062 3499"/>
    </justification>
  </clause>

  <clause id="3503">
    <literal><![CDATA[
      T(x,T((y \ z) / z,x)) = (y * T(y \ 1,x)) \ x
    ]]></literal>
    <justification jstring="[para(3499(a,1),3423(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3499 3423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3504">
    <literal><![CDATA[
      T(x,T((y \ z) / z,x)) = T(x,T(y \ 1,x))
    ]]></literal>
    <justification jstring="[hyper(333,a,3437,a(flip),b,3503,a),flip(a)].">
      <j1 rule="hyper" parents="333 3437 3503"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3505">
    <literal><![CDATA[
      K(T(1 / T(x,y),T(x,z)),T(x,z)) = T(x * T(x \ 1,x),y)
    ]]></literal>
    <justification jstring="[para(1668(a,1),3393(a,1,1))].">
      <j1 rule="para" parents="1668 3393"/>
    </justification>
  </clause>

  <clause id="3506">
    <literal><![CDATA[
      K(T(1 / T(x,y),T(x,z)),T(x,z)) = T((x \ 1) * x,y)
    ]]></literal>
    <justification jstring="[para(111(a,1),3505(a,2,1))].">
      <j1 rule="para" parents="111 3505"/>
    </justification>
  </clause>

  <clause id="3507">
    <literal><![CDATA[
      K(T(1 / T(x,y),T(x,z)),T(x,z)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,2419,a(flip),b,3506,a),flip(a)].">
      <j1 rule="hyper" parents="333 2419 3506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3509">
    <literal><![CDATA[
      K(T(x,y) \ 1,T(x,y)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(113(a,1),3507(a,1,1))].">
      <j1 rule="para" parents="113 3507"/>
    </justification>
  </clause>

  <clause id="3510">
    <literal><![CDATA[
      K(T(x,y) \ 1,T(x,y)) = (x \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(333,a,276,a(flip),b,3509,a),flip(a)].">
      <j1 rule="hyper" parents="333 276 3509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3511">
    <literal><![CDATA[
      K((x * y) \ y,y \ (x * y)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,2974,a,b,3509,a)].">
      <j1 rule="hyper" parents="63 2974 3509"/>
    </justification>
  </clause>

  <clause id="3512">
    <literal><![CDATA[
      K((x / y) \ 1,x / y) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,3227,a(flip),b,3509,a),flip(a)].">
      <j1 rule="hyper" parents="63 3227 3509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3513">
    <literal><![CDATA[
      (1 / T(x,y)) * K(x \ 1,x) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(126,a,3509,a(flip),b,1132,a)].">
      <j1 rule="hyper" parents="126 3509 1132"/>
    </justification>
  </clause>

  <clause id="3514">
    <literal><![CDATA[
      K(x \ 1,x) * (y * T(x,z)) = y * (1 / (1 / T(x,z)))
    ]]></literal>
    <justification jstring="[para(3509(a,1),2455(a,1,1))].">
      <j1 rule="para" parents="3509 2455"/>
    </justification>
  </clause>

  <clause id="3515">
    <literal><![CDATA[
      ((x \ 1) * x) \ (T(x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      ((T(x,y) \ 1) \ 1) * z = u
    ]]></literal>
    <justification jstring="[para(3510(a,1),2696(a,1,1))].">
      <j1 rule="para" parents="3510 2696"/>
    </justification>
  </clause>

  <clause id="3518">
    <literal><![CDATA[
      ((x * y) * K(x \ 1,x)) \ y = 1 / (1 / ((x * y) \ y))
    ]]></literal>
    <justification jstring="[para(3511(a,1),2941(a,1,1,2))].">
      <j1 rule="para" parents="3511 2941"/>
    </justification>
  </clause>

  <clause id="3523">
    <literal><![CDATA[
      x * ((1 / T(x,y)) * K(x \ 1,x)) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(126,a,3513,a,b,1069,a)].">
      <j1 rule="hyper" parents="126 3513 1069"/>
    </justification>
  </clause>

  <clause id="3526">
    <literal><![CDATA[
      (x * (1 / T(x,y))) * K(x \ 1,x) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(1882,a,3523,a)].">
      <j1 rule="hyper" parents="1882 3523"/>
    </justification>
  </clause>

  <clause id="3528">
    <literal><![CDATA[
      (x \ 1) * (x * (1 / T(x,y))) = (1 / x) * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[para(3526(a,1),2642(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3526 2642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3529">
    <literal><![CDATA[
      K(x \ 1,x) * (y * T(x,z)) = y * T(1 / (1 / x),z)
    ]]></literal>
    <justification jstring="[para(2384(a,1),3514(a,2,2))].">
      <j1 rule="para" parents="2384 3514"/>
    </justification>
  </clause>

  <clause id="3530">
    <literal><![CDATA[
      1 / (1 / ((x * y) \ y)) = ((1 / (1 / x)) * y) \ y
    ]]></literal>
    <justification jstring="[para(2765(a,1),3518(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2765 3518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3531">
    <literal><![CDATA[
      (((1 / (1 / x)) * y) \ y) \ 1 = 1 / ((x * y) \ y)
    ]]></literal>
    <justification jstring="[hyper(192,a,3530,a)].">
      <j1 rule="hyper" parents="192 3530"/>
    </justification>
  </clause>

  <clause id="3532">
    <literal><![CDATA[
      1 / (((x \ 1) * y) \ y) = (((1 / x) * y) \ y) \ 1
    ]]></literal>
    <justification jstring="[para(76(a,1),3531(a,1,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="76 3531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3533">
    <literal><![CDATA[
      ((((1 / x) * y) \ y) \ 1) \ 1 = ((x \ 1) * y) \ y
    ]]></literal>
    <justification jstring="[hyper(192,a,3532,a)].">
      <j1 rule="hyper" parents="192 3532"/>
    </justification>
  </clause>

  <clause id="3534">
    <literal><![CDATA[
      ((L(x,y,y \ 1) \ (y * x)) \ 1) \ 1 = ((y \ 1) * (y * x)) \ (y * x)
    ]]></literal>
    <justification jstring="[para(2652(a,1),3533(a,1,1,1,1))].">
      <j1 rule="para" parents="2652 3533"/>
    </justification>
  </clause>

  <clause id="3535">
    <literal><![CDATA[
      K(((1 / x) * y) \ y,z) = K(((x \ 1) * y) \ y,z)
    ]]></literal>
    <justification jstring="[para(3533(a,1),3334(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3533 3334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3536">
    <literal><![CDATA[
      L((1 / T(x,y)) * x,x \ 1,x) = ((1 / x) * (T(x,y) \ x)) * x
    ]]></literal>
    <justification jstring="[para(3528(a,1),1721(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3528 1721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3537">
    <literal><![CDATA[
      K(x \ 1,x) * (y * ((x \ z) \ z)) = y * T(1 / (1 / x),x \ z)
    ]]></literal>
    <justification jstring="[para(112(a,1),3529(a,1,2,2))].">
      <j1 rule="para" parents="112 3529"/>
    </justification>
  </clause>

  <clause id="3538">
    <literal><![CDATA[
      ((1 / x) * (T(x,y) \ x)) * x = L(T(x,y) \ x,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(2704(a,1),3536(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2704 3536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3539">
    <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(63,a,2770,a,b,3538,a)].">
      <j1 rule="hyper" parents="63 2770 3538"/>
    </justification>
  </clause>

  <clause id="3540">
    <literal><![CDATA[
      R(x,K(y,x) \ 1,z) = x
    ]]></literal>
    <justification jstring="[para(3469(a,1),3305(a,1,2))].">
      <j1 rule="para" parents="3469 3305"/>
    </justification>
  </clause>

  <clause id="3541">
    <literal><![CDATA[
      R(x,K(y,x),z) = x
    ]]></literal>
    <justification jstring="[hyper(1941,a,3540,a)].">
      <j1 rule="hyper" parents="1941 3540"/>
    </justification>
  </clause>

  <clause id="3542">
    <literal><![CDATA[
      (x * K(y,x)) * z = x * (K(y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(125,a,3541,a(flip),b,20,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="125 3541 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3544">
    <literal><![CDATA[
      x \ ((x * K(y,x)) * z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[para(3541(a,1),187(a,1,1))].">
      <j1 rule="para" parents="3541 187"/>
    </justification>
  </clause>

  <clause id="3545">
    <literal><![CDATA[
      (x * (K(y,x) * z)) / z = x * K(y,x)
    ]]></literal>
    <justification jstring="[para(3541(a,1),313(a,1,1,1))].">
      <j1 rule="para" parents="3541 313"/>
    </justification>
  </clause>

  <clause id="3546">
    <literal><![CDATA[
      (T(x,y) * K(z,x)) * u = T(x,y) * (K(z,x) * u)
    ]]></literal>
    <justification jstring="[para(3541(a,1),458(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="3541 458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3547">
    <literal><![CDATA[
      L(x,K(y,z),z) = x
    ]]></literal>
    <justification jstring="[hyper(501,a,3542,a)].">
      <j1 rule="hyper" parents="501 3542"/>
    </justification>
  </clause>

  <clause id="3548">
    <literal><![CDATA[
      (x * (K(y,x) * z)) \ ((x * K(y,x)) * (z * u)) = L(u,z,x * K(y,x))
    ]]></literal>
    <justification jstring="[para(3542(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="3542 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3549">
    <literal><![CDATA[
      L(x,K(y,z),z) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(3547(a,1),50(a,2))].">
      <j1 rule="para" parents="3547 50"/>
    </justification>
  </clause>

  <clause id="3550">
    <literal><![CDATA[
      (x * K(y,x)) * z != u
    ]]></literal>
    <literal><![CDATA[
      x * (K(y,x) * z) = u
    ]]></literal>
    <justification jstring="[para(3547(a,1),306(a,1,2))].">
      <j1 rule="para" parents="3547 306"/>
    </justification>
  </clause>

  <clause id="3552">
    <literal><![CDATA[
      (x * y) * R(K(x * y,z),y,T(x,y)) = (K(y * T(x,y),z) * y) * T(x,y)
    ]]></literal>
    <justification jstring="[para(111(a,2),3438(a,2,1,1,1))].">
      <j1 rule="para" parents="111 3438"/>
    </justification>
  </clause>

  <clause id="3553">
    <literal><![CDATA[
      (x * (K(y,x) * z)) \ (x * (K(y,x) * (z * u))) = L(u,z,x * K(y,x))
    ]]></literal>
    <justification jstring="[para(3542(a,1),3548(a,1,2))].">
      <j1 rule="para" parents="3542 3548"/>
    </justification>
  </clause>

  <clause id="3554">
    <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(16(a,2),3474(a,2,1))].">
      <j1 rule="para" parents="16 3474"/>
    </justification>
  </clause>

  <clause id="3555">
    <literal><![CDATA[
      R(K(x,y),x,z) = L(x \ T(x,T(y,x)),T(y,x),x)
    ]]></literal>
    <justification jstring="[para(3403(a,1),3554(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3403 3554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3556">
    <literal><![CDATA[
      R(K(x,y),x,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,3080,a,b,3555,a),flip(a)].">
      <j1 rule="hyper" parents="333 3080 3555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3557">
    <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(3555(a,1),547(a,1))].">
      <j1 rule="para" parents="3555 547"/>
    </justification>
  </clause>

  <clause id="3559">
    <literal><![CDATA[
      (K(x,y) * x) * z = K(x,y) * (x * z)
    ]]></literal>
    <justification jstring="[hyper(125,a,3556,a(flip),b,20,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="125 3556 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3560">
    <literal><![CDATA[
      K(x,y) * (1 / x) = K(x,y) / x
    ]]></literal>
    <justification jstring="[para(3556(a,1),1188(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3556 1188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3561">
    <literal><![CDATA[
      (1 / x) * K(x,y) = K(x,y) / x
    ]]></literal>
    <justification jstring="[hyper(63,a,1383,a(flip),b,3560,a)].">
      <j1 rule="hyper" parents="63 1383 3560"/>
    </justification>
  </clause>

  <clause id="3562">
    <literal><![CDATA[
      (K(x,y) / x) * L(z,K(x,y),1 / x) = (1 / x) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(125,a,3561,a(flip),b,190,a)].">
      <j1 rule="hyper" parents="125 3561 190"/>
    </justification>
  </clause>

  <clause id="3563">
    <literal><![CDATA[
      L(x,y,K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(501,a,3559,a)].">
      <j1 rule="hyper" parents="501 3559"/>
    </justification>
  </clause>

  <clause id="3564">
    <literal><![CDATA[
      (x * K(x,y)) * z = K(x,y) * (x * z)
    ]]></literal>
    <justification jstring="[para(3332(a,1),3559(a,1,1))].">
      <j1 rule="para" parents="3332 3559"/>
    </justification>
  </clause>

  <clause id="3565">
    <literal><![CDATA[
      L(x,y,K(y \ 1,z)) = x
    ]]></literal>
    <justification jstring="[hyper(2631,a,3563,a)].">
      <j1 rule="hyper" parents="2631 3563"/>
    </justification>
  </clause>

  <clause id="3566">
    <literal><![CDATA[
      L(x,y \ 1,K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(2626,a,3563,a)].">
      <j1 rule="hyper" parents="2626 3563"/>
    </justification>
  </clause>

  <clause id="3567">
    <literal><![CDATA[
      L(x,y,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(3563(a,1),50(a,2))].">
      <j1 rule="para" parents="3563 50"/>
    </justification>
  </clause>

  <clause id="3568">
    <literal><![CDATA[
      R(K(x,y),x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(3555(a,2),3557(a,1))].">
      <j1 rule="para" parents="3555 3557"/>
    </justification>
  </clause>

  <clause id="3570">
    <literal><![CDATA[
      T(x \ 1,y) * ((((x \ 1) \ 1) \ 1) \ z) = T(1 / x,y) * ((x \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(2821(a,1),3490(a,1,2))].">
      <j1 rule="para" parents="2821 3490"/>
    </justification>
  </clause>

  <clause id="3571">
    <literal><![CDATA[
      T(x \ 1,y) * (T(x \ 1,(x \ 1) \ 1) \ z) = T(1 / x,y) * ((x \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(112(a,2),3570(a,1,2,1))].">
      <j1 rule="para" parents="112 3570"/>
    </justification>
  </clause>

  <clause id="3572">
    <literal><![CDATA[
      R(T(x,y) \ x,x \ 1,x) = L(T(x,y) \ x,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(2710(a,1),3539(a,1,1))].">
      <j1 rule="para" parents="2710 3539"/>
    </justification>
  </clause>

  <clause id="3573">
    <literal><![CDATA[
      (((x \ 1) \ 1) * T(x \ 1,y)) * z = T(1 / x,y) * ((x \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,3495,a(flip),b,3571,a)].">
      <j1 rule="hyper" parents="63 3495 3571"/>
    </justification>
  </clause>

  <clause id="3574">
    <literal><![CDATA[
      T(1 / x,y) * ((x \ 1) \ z) = (x * T(1 / x,y)) * z
    ]]></literal>
    <justification jstring="[para(3466(a,1),3573(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3466 3573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3575">
    <literal><![CDATA[
      (T(1 / x,y) * z) / ((x * T(1 / x,y)) * z) = x \ 1
    ]]></literal>
    <justification jstring="[para(3574(a,1),3496(a,1,2))].">
      <j1 rule="para" parents="3574 3496"/>
    </justification>
  </clause>

  <clause id="3576">
    <literal><![CDATA[
      T(1 / x,y) * ((x * T(1 / x,y)) \ z) = (x \ 1) * z
    ]]></literal>
    <justification jstring="[para(3575(a,1),335(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3575 335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3577">
    <literal><![CDATA[
      (x \ 1) \ T(1 / x,y) = x * T(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(413,a,3576,a)].">
      <j1 rule="hyper" parents="413 3576"/>
    </justification>
  </clause>

  <clause id="3578">
    <literal><![CDATA[
      ((x * y) / x) * (y \ ((T(x,y) \ x) * z)) = L(z,T(x,y) \ x,(x * y) / x)
    ]]></literal>
    <justification jstring="[para(3480(a,1),3484(a,2,2))].">
      <j1 rule="para" parents="3480 3484"/>
    </justification>
  </clause>

  <clause id="3579">
    <literal><![CDATA[
      x \ ((T(y,x) \ y) * z) = ((y * x) / y) \ z
    ]]></literal>
    <justification jstring="[hyper(121,a,3427,a(flip),b,3578,a),flip(a)].">
      <j1 rule="hyper" parents="121 3427 3578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3580">
    <literal><![CDATA[
      x * (((y * x) / y) \ z) = (T(y,x) \ y) * z
    ]]></literal>
    <justification jstring="[hyper(142,a,3579,a)].">
      <j1 rule="hyper" parents="142 3579"/>
    </justification>
  </clause>

  <clause id="3581">
    <literal><![CDATA[
      (T(x,y) \ x) * (x * y) = y * x
    ]]></literal>
    <justification jstring="[hyper(126,a,79,a(flip),b,3579,a),flip(a)].">
      <j1 rule="hyper" parents="126 79 3579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3582">
    <literal><![CDATA[
      K(x,y) = T(T(y,x) \ y,y * x)
    ]]></literal>
    <justification jstring="[hyper(253,a,3581,a,b,88,a),flip(a)].">
      <j1 rule="hyper" parents="253 3581 88"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3583">
    <literal><![CDATA[
      (x * y) / (y * x) = T(y,x) \ y
    ]]></literal>
    <justification jstring="[hyper(138,a,3581,a)].">
      <j1 rule="hyper" parents="138 3581"/>
    </justification>
  </clause>

  <clause id="3584">
    <literal><![CDATA[
      T(x / y,y) \ (x / y) = (y * (x / y)) / x
    ]]></literal>
    <justification jstring="[para(12(a,1),3583(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12 3583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3585">
    <literal><![CDATA[
      x \ y != (z * y) / (y * z)
    ]]></literal>
    <literal><![CDATA[
      T(y,z) = x
    ]]></literal>
    <justification jstring="[para(3583(a,2),48(a,1)),flip(a)].">
      <j1 rule="para" parents="3583 48"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3586">
    <literal><![CDATA[
      T(x,y / x) \ x != z
    ]]></literal>
    <literal><![CDATA[
      y / (x * (y / x)) = z
    ]]></literal>
    <justification jstring="[para(3583(a,1),422(a,1))].">
      <j1 rule="para" parents="3583 422"/>
    </justification>
  </clause>

  <clause id="3587">
    <literal><![CDATA[
      R(x \ T(x,y),y,((x * y) / x) \ z) \ z = (T(x,y) \ x) * z
    ]]></literal>
    <justification jstring="[hyper(63,a,3074,a,b,3580,a)].">
      <j1 rule="hyper" parents="63 3074 3580"/>
    </justification>
  </clause>

  <clause id="3588">
    <literal><![CDATA[
      (x * (y / x)) / y = (x \ y) \ (y / x)
    ]]></literal>
    <justification jstring="[para(113(a,1),3584(a,1,1)),flip(a)].">
      <j1 rule="para" parents="113 3584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3589">
    <literal><![CDATA[
      (x * (y / x)) / y = x \ ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[hyper(333,a,3078,a(flip),b,3588,a),flip(a)].">
      <j1 rule="hyper" parents="333 3078 3588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3590">
    <literal><![CDATA[
      x \ ((x \ (y \ x)) \ (y \ x)) = x \ T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,3083,a(flip),b,3589,a),flip(a)].">
      <j1 rule="hyper" parents="63 3083 3589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3591">
    <literal><![CDATA[
      T(x,x \ (y \ x)) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(696,a,3590,a)].">
      <j1 rule="hyper" parents="696 3590"/>
    </justification>
  </clause>

  <clause id="3592">
    <literal><![CDATA[
      (x \ y) / T(y,x \ 1) = y \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(197,a,3591,a(flip),b,112,a(flip))].">
      <j1 rule="hyper" parents="197 3591 112"/>
    </justification>
  </clause>

  <clause id="3593">
    <literal><![CDATA[
      T(x,(x / y) \ 1) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(79(a,1),3591(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="79 3591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3595">
    <literal><![CDATA[
      T(x,y \ 1) \ (y \ T(x,y \ 1)) = x \ (y \ x)
    ]]></literal>
    <justification jstring="[para(3591(a,1),3413(a,1,1))].">
      <j1 rule="para" parents="3591 3413"/>
    </justification>
  </clause>

  <clause id="3596">
    <literal><![CDATA[
      x \ ((y \ x) / ((y \ x) / x)) = T(x,y \ 1) \ x
    ]]></literal>
    <justification jstring="[para(3591(a,1),3485(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3591 3485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3597">
    <literal><![CDATA[
      (x / y) \ T(x,x \ y) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(3593(a,1),3109(a,1,2))].">
      <j1 rule="para" parents="3593 3109"/>
    </justification>
  </clause>

  <clause id="3598">
    <literal><![CDATA[
      ((x \ 1) \ y) / T(y,x) = y \ ((x \ 1) \ y)
    ]]></literal>
    <justification jstring="[para(2983(a,1),3592(a,1,2))].">
      <j1 rule="para" parents="2983 3592"/>
    </justification>
  </clause>

  <clause id="3599">
    <literal><![CDATA[
      (x / (y * x)) \ T(x,x \ (y * x)) = x * y
    ]]></literal>
    <justification jstring="[para(11(a,1),3597(a,2,2))].">
      <j1 rule="para" parents="11 3597"/>
    </justification>
  </clause>

  <clause id="3600">
    <literal><![CDATA[
      (x / (y * x)) \ T(x,T(y,x)) = x * y
    ]]></literal>
    <justification jstring="[para(22(a,2),3599(a,1,2,2))].">
      <j1 rule="para" parents="22 3599"/>
    </justification>
  </clause>

  <clause id="3601">
    <literal><![CDATA[
      T(x,y \ 1) \ z != x \ (y \ x)
    ]]></literal>
    <literal><![CDATA[
      y \ T(x,y \ 1) = z
    ]]></literal>
    <justification jstring="[para(3595(a,1),47(a,1)),flip(a)].">
      <j1 rule="para" parents="3595 47"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3602">
    <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(2656(a,1),3595(a,2,2))].">
      <j1 rule="para" parents="2656 3595"/>
    </justification>
  </clause>

  <clause id="3603">
    <literal><![CDATA[
      T(x,y \ 1) \ x = y * T(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,3502,a(flip),b,3596,a),flip(a)].">
      <j1 rule="hyper" parents="63 3502 3596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3604">
    <literal><![CDATA[
      K(x \ (x / y),x) = T(x,y \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(333,a,2057,a,b,3603,a)].">
      <j1 rule="hyper" parents="333 2057 3603"/>
    </justification>
  </clause>

  <clause id="3605">
    <literal><![CDATA[
      T(x,(y \ 1) \ 1) \ x = y \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,1010,a(flip),b,3603,a),flip(a)].">
      <j1 rule="hyper" parents="333 1010 3603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3607">
    <literal><![CDATA[
      K(x \ (x / y),x) \ x = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(3604(a,2),2709(a,1,1))].">
      <j1 rule="para" parents="3604 2709"/>
    </justification>
  </clause>

  <clause id="3608">
    <literal><![CDATA[
      T(x,y) \ x = y \ T(y,x)
    ]]></literal>
    <justification jstring="[para(2983(a,1),3605(a,1,1))].">
      <j1 rule="para" parents="2983 3605"/>
    </justification>
  </clause>

  <clause id="3609">
    <literal><![CDATA[
      T(x,y / x) \ x = x \ (y / (y / x))
    ]]></literal>
    <justification jstring="[hyper(333,a,3062,a(flip),b,3608,a),flip(a)].">
      <j1 rule="hyper" parents="333 3062 3608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3610">
    <literal><![CDATA[
      T(x,y) * (y \ T(y,x)) = x
    ]]></literal>
    <justification jstring="[hyper(142,a,3608,a)].">
      <j1 rule="hyper" parents="142 3608"/>
    </justification>
  </clause>

  <clause id="3611">
    <literal><![CDATA[
      (x * y) / x = y * (T(y,x) \ y)
    ]]></literal>
    <justification jstring="[hyper(126,a,3608,a,b,3059,a),flip(a)].">
      <j1 rule="hyper" parents="126 3608 3059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3612">
    <literal><![CDATA[
      (T(x,y / z) \ x) * y = z * T(z \ y,x)
    ]]></literal>
    <justification jstring="[hyper(125,a,3608,a,b,3498,a)].">
      <j1 rule="hyper" parents="125 3608 3498"/>
    </justification>
  </clause>

  <clause id="3613">
    <literal><![CDATA[
      T(x,T(y,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(39,a,3424,a,b,3608,a)].">
      <j1 rule="hyper" parents="39 3424 3608"/>
    </justification>
  </clause>

  <clause id="3614">
    <literal><![CDATA[
      x * ((T(y,x) \ y) * z) = T(x,y) * z
    ]]></literal>
    <justification jstring="[para(3608(a,2),3297(a,1,2,1))].">
      <j1 rule="para" parents="3608 3297"/>
    </justification>
  </clause>

  <clause id="3615">
    <literal><![CDATA[
      T(x,y) * (x \ z) = (T(y,x) \ y) * z
    ]]></literal>
    <justification jstring="[para(3608(a,2),3303(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3608 3303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3616">
    <literal><![CDATA[
      K(x,y) = T(x \ T(x,y),y * x)
    ]]></literal>
    <justification jstring="[para(3608(a,1),3582(a,2,1))].">
      <j1 rule="para" parents="3608 3582"/>
    </justification>
  </clause>

  <clause id="3617">
    <literal><![CDATA[
      T((T(x,y) * y) / T(x,y),x) = y
    ]]></literal>
    <justification jstring="[hyper(478,a,3613,a)].">
      <j1 rule="hyper" parents="478 3613"/>
    </justification>
  </clause>

  <clause id="3618">
    <literal><![CDATA[
      R(T(x,x * y),y,x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3433,a,b,3613,a)].">
      <j1 rule="hyper" parents="63 3433 3613"/>
    </justification>
  </clause>

  <clause id="3619">
    <literal><![CDATA[
      (x / T(y,x)) * y = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3359,a,b,3613,a)].">
      <j1 rule="hyper" parents="63 3359 3613"/>
    </justification>
  </clause>

  <clause id="3620">
    <literal><![CDATA[
      T(x,y) \ (x * y) = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,249,a,b,3613,a)].">
      <j1 rule="hyper" parents="63 249 3613"/>
    </justification>
  </clause>

  <clause id="3621">
    <literal><![CDATA[
      T(x,T(y \ 1,x)) = T(x,(y \ z) / z)
    ]]></literal>
    <justification jstring="[hyper(63,a,3504,a(flip),b,3613,a)].">
      <j1 rule="hyper" parents="63 3504 3613"/>
    </justification>
  </clause>

  <clause id="3622">
    <literal><![CDATA[
      T(x / T(y,x),y) = y \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(444,a,3613,a(flip),b,3359,a)].">
      <j1 rule="hyper" parents="444 3613 3359"/>
    </justification>
  </clause>

  <clause id="3623">
    <literal><![CDATA[
      (x * y) / T(y,x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(197,a,3613,a(flip),b,249,a)].">
      <j1 rule="hyper" parents="197 3613 249"/>
    </justification>
  </clause>

  <clause id="3624">
    <literal><![CDATA[
      T(x,y) * T(y,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(126,a,3613,a(flip),b,249,a)].">
      <j1 rule="hyper" parents="126 3613 249"/>
    </justification>
  </clause>

  <clause id="3625">
    <literal><![CDATA[
      T(x,y) / y = x / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(123,a,3613,a(flip),b,3359,a)].">
      <j1 rule="hyper" parents="123 3613 3359"/>
    </justification>
  </clause>

  <clause id="3626">
    <literal><![CDATA[
      T(x,y) / (T(y,x) \ x) = y
    ]]></literal>
    <justification jstring="[hyper(123,a,3613,a(flip),b,1075,a)].">
      <j1 rule="hyper" parents="123 3613 1075"/>
    </justification>
  </clause>

  <clause id="3627">
    <literal><![CDATA[
      (x / T(y,x)) \ T(x,y) = y
    ]]></literal>
    <justification jstring="[hyper(121,a,3613,a(flip),b,3359,a)].">
      <j1 rule="hyper" parents="121 3613 3359"/>
    </justification>
  </clause>

  <clause id="3628">
    <literal><![CDATA[
      T(x,y) \ y = x \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(121,a,3613,a(flip),b,1075,a),flip(a)].">
      <j1 rule="hyper" parents="121 3613 1075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3629">
    <literal><![CDATA[
      T(T(x,y),T(z,x)) = T(T(x,z),y)
    ]]></literal>
    <justification jstring="[para(3613(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3613 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3630">
    <literal><![CDATA[
      T(x,T(T(y,x),z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(23(a,1),3613(a,1,2))].">
      <j1 rule="para" parents="23 3613"/>
    </justification>
  </clause>

  <clause id="3632">
    <literal><![CDATA[
      T(x,L(T(y,x),z,u)) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(25(a,2),3613(a,1,2))].">
      <j1 rule="para" parents="25 3613"/>
    </justification>
  </clause>

  <clause id="3633">
    <literal><![CDATA[
      T(x,y / x) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(113(a,1),3613(a,1,2)),flip(a)].">
      <j1 rule="para" parents="113 3613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3634">
    <literal><![CDATA[
      T(x,(x * y) / x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(238(a,1),3613(a,1,2)),flip(a)].">
      <j1 rule="para" parents="238 3613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3635">
    <literal><![CDATA[
      T(x,y) * T(T(y,x),z) = T(y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(3613(a,1),250(a,1,2,1))].">
      <j1 rule="para" parents="3613 250"/>
    </justification>
  </clause>

  <clause id="3636">
    <literal><![CDATA[
      T(x,T(y,y * x)) = T(x,L(y,x,y))
    ]]></literal>
    <justification jstring="[para(635(a,1),3613(a,1,2))].">
      <j1 rule="para" parents="635 3613"/>
    </justification>
  </clause>

  <clause id="3637">
    <literal><![CDATA[
      T(x,y) * L(T(y,x),z,u) = L(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(3613(a,1),251(a,1,2,1))].">
      <j1 rule="para" parents="3613 251"/>
    </justification>
  </clause>

  <clause id="3638">
    <literal><![CDATA[
      T(x,y) * R(T(y,x),z,u) = R(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(3613(a,1),252(a,1,2,1))].">
      <j1 rule="para" parents="3613 252"/>
    </justification>
  </clause>

  <clause id="3640">
    <literal><![CDATA[
      (x / (y * x)) \ T(x,y) = x * y
    ]]></literal>
    <justification jstring="[para(3613(a,1),3600(a,1,2))].">
      <j1 rule="para" parents="3613 3600"/>
    </justification>
  </clause>

  <clause id="3641">
    <literal><![CDATA[
      T(x,y) \ x != z
    ]]></literal>
    <literal><![CDATA[
      y \ T(y,x) = z
    ]]></literal>
    <justification jstring="[para(3610(a,1),342(a,1,2))].">
      <j1 rule="para" parents="3610 342"/>
    </justification>
  </clause>

  <clause id="3642">
    <literal><![CDATA[
      T(x,y) / T(y,x) = x / T(T(y,x),x)
    ]]></literal>
    <justification jstring="[hyper(123,a,3613,a(flip),b,3619,a)].">
      <j1 rule="hyper" parents="123 3613 3619"/>
    </justification>
  </clause>

  <clause id="3643">
    <literal><![CDATA[
      x / T(y * y,x) = (y * y) \ x
    ]]></literal>
    <justification jstring="[hyper(35,a,680,a,b,3619,a),flip(a)].">
      <j1 rule="hyper" parents="35 680 3619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3644">
    <literal><![CDATA[
      T(x,y) * (y * x) = x * (x * y)
    ]]></literal>
    <justification jstring="[hyper(125,a,3619,a(flip),b,1438,a)].">
      <j1 rule="hyper" parents="125 3619 1438"/>
    </justification>
  </clause>

  <clause id="3645">
    <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(3619(a,1),633(a,1,2))].">
      <j1 rule="para" parents="3619 633"/>
    </justification>
  </clause>

  <clause id="3646">
    <literal><![CDATA[
      (x * R(y,z,u)) / R(T(y,x),z,u) = T(x,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(197,a,27,a,b,3620,a)].">
      <j1 rule="hyper" parents="197 27 3620"/>
    </justification>
  </clause>

  <clause id="3648">
    <literal><![CDATA[
      T(x,x \ y) \ y = T(x \ y,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),3620(a,1,2))].">
      <j1 rule="para" parents="10 3620"/>
    </justification>
  </clause>

  <clause id="3649">
    <literal><![CDATA[
      T(x,y) = (x \ (y * x)) \ (y * x)
    ]]></literal>
    <justification jstring="[para(22(a,1),3620(a,1,1)),flip(a)].">
      <j1 rule="para" parents="22 3620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3650">
    <literal><![CDATA[
      T(x,y) * (x \ T(y,x)) = y
    ]]></literal>
    <justification jstring="[hyper(1074,a,3624,a)].">
      <j1 rule="hyper" parents="1074 3624"/>
    </justification>
  </clause>

  <clause id="3651">
    <literal><![CDATA[
      R(x,T(y,z),T(z,y)) * (y * z) = (x * T(y,z)) * T(z,y)
    ]]></literal>
    <justification jstring="[hyper(126,a,3624,a(flip),b,187,a)].">
      <j1 rule="hyper" parents="126 3624 187"/>
    </justification>
  </clause>

  <clause id="3652">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * T(y,z)) * T(z,y)) = a(x,T(y,z),T(z,y))
    ]]></literal>
    <justification jstring="[para(3624(a,1),14(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="3624 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3653">
    <literal><![CDATA[
      (T(x,y) * (T(y,x) * z)) \ ((x * y) * z) = a(T(x,y),T(y,x),z)
    ]]></literal>
    <justification jstring="[para(3624(a,1),14(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="3624 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3654">
    <literal><![CDATA[
      T(x,y) * (T(y,x) * z) != (x * y) * u
    ]]></literal>
    <literal><![CDATA[
      L(z,T(y,x),T(x,y)) = u
    ]]></literal>
    <justification jstring="[para(3624(a,1),501(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3624 501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3655">
    <literal><![CDATA[
      (T(x,y) / y) \ x = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(192,a,3625,a(flip))].">
      <j1 rule="hyper" parents="192 3625"/>
    </justification>
  </clause>

  <clause id="3656">
    <literal><![CDATA[
      T(x * (y / x),x) = x * (y / T(x,y))
    ]]></literal>
    <justification jstring="[hyper(126,a,3625,a(flip),b,1403,a),flip(a)].">
      <j1 rule="hyper" parents="126 3625 1403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3658">
    <literal><![CDATA[
      T(x,T(y,z)) / (T(T(y,x),z) \ x) = T(y,z)
    ]]></literal>
    <justification jstring="[para(23(a,1),3626(a,1,2,1))].">
      <j1 rule="para" parents="23 3626"/>
    </justification>
  </clause>

  <clause id="3659">
    <literal><![CDATA[
      (T(x,y) \ y) * z = (x \ T(y,x)) * z
    ]]></literal>
    <justification jstring="[para(3626(a,1),195(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="3626 195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3660">
    <literal><![CDATA[
      (x / T(y,x)) \ z != y
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(3627(a,1),47(a,1)),flip(a)].">
      <j1 rule="para" parents="3627 47"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3661">
    <literal><![CDATA[
      T(x,y) \ ((T(y,x) \ x) * y) = K(y \ T(x,y),y)
    ]]></literal>
    <justification jstring="[para(3628(a,2),89(a,1,2,1))].">
      <j1 rule="para" parents="3628 89"/>
    </justification>
  </clause>

  <clause id="3662">
    <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(3628(a,1),85(a,1,1,2,1))].">
      <j1 rule="para" parents="3628 85"/>
    </justification>
  </clause>

  <clause id="3663">
    <literal><![CDATA[
      T(x,y) * L(x \ T(y,x),z,u) = T(x * L(x \ y,z,u),y)
    ]]></literal>
    <justification jstring="[para(3628(a,1),1790(a,1,2,1))].">
      <j1 rule="para" parents="3628 1790"/>
    </justification>
  </clause>

  <clause id="3664">
    <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(3628(a,1),1749(a,1,2,1))].">
      <j1 rule="para" parents="3628 1749"/>
    </justification>
  </clause>

  <clause id="3665">
    <literal><![CDATA[
      T(x,y / x) = (x \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(333,a,112,a(flip),b,3633,a),flip(a)].">
      <j1 rule="hyper" parents="333 112 3633"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3666">
    <literal><![CDATA[
      R(T(x,y),y / x,x) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,851,a,b,3633,a)].">
      <j1 rule="hyper" parents="63 851 3633"/>
    </justification>
  </clause>

  <clause id="3667">
    <literal><![CDATA[
      T(x,y / x) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ y) \ y = z
    ]]></literal>
    <justification jstring="[para(3633(a,2),432(a,1))].">
      <j1 rule="para" parents="3633 432"/>
    </justification>
  </clause>

  <clause id="3669">
    <literal><![CDATA[
      (x * (y / x)) * x = y * T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(3633(a,1),969(a,2,2))].">
      <j1 rule="para" parents="3633 969"/>
    </justification>
  </clause>

  <clause id="3670">
    <literal><![CDATA[
      x \ (T(x,y / x) / (1 / (x \ y))) = (x / (1 / (x \ y))) / x
    ]]></literal>
    <justification jstring="[para(3633(a,2),3100(a,1,2,1))].">
      <j1 rule="para" parents="3633 3100"/>
    </justification>
  </clause>

  <clause id="3671">
    <literal><![CDATA[
      T(x,T(y,x / y)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(3633(a,2),3369(a,1,2))].">
      <j1 rule="para" parents="3633 3369"/>
    </justification>
  </clause>

  <clause id="3672">
    <literal><![CDATA[
      (x / y) * ((y \ x) \ x) = y * (x / y)
    ]]></literal>
    <justification jstring="[hyper(126,a,3665,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="126 3665 22"/>
    </justification>
  </clause>

  <clause id="3673">
    <literal><![CDATA[
      T(T(x,y),z / x) = T((x \ z) \ z,y)
    ]]></literal>
    <justification jstring="[para(3665(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3665 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3674">
    <literal><![CDATA[
      T(x \ y,x) = ((x \ y) \ y) \ y
    ]]></literal>
    <justification jstring="[para(76(a,1),3665(a,1,2))].">
      <j1 rule="para" parents="76 3665"/>
    </justification>
  </clause>

  <clause id="3676">
    <literal><![CDATA[
      T(x * y,T(y,x)) = T(x * y,y)
    ]]></literal>
    <justification jstring="[para(11(a,1),3671(a,1,2,2))].">
      <j1 rule="para" parents="11 3671"/>
    </justification>
  </clause>

  <clause id="3677">
    <literal><![CDATA[
      T(x,x * (y / x)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(852,a,3618,a),flip(a)].">
      <j1 rule="hyper" parents="852 3618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3678">
    <literal><![CDATA[
      T(x,y * x) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(849,a,3618,a)].">
      <j1 rule="hyper" parents="849 3618"/>
    </justification>
  </clause>

  <clause id="3679">
    <literal><![CDATA[
      R(T(x,y),x \ y,x) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),3618(a,1,1,2))].">
      <j1 rule="para" parents="10 3618"/>
    </justification>
  </clause>

  <clause id="3680">
    <literal><![CDATA[
      T(x,y * z) != T(y,z)
    ]]></literal>
    <literal><![CDATA[
      R(y,z,y) = x
    ]]></literal>
    <justification jstring="[para(3618(a,1),149(a,2))].">
      <j1 rule="para" parents="3618 149"/>
    </justification>
  </clause>

  <clause id="3681">
    <literal><![CDATA[
      T(x,(x \ y) * x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(75(a,1),3677(a,1,2)),flip(a)].">
      <j1 rule="para" parents="75 3677"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3683">
    <literal><![CDATA[
      T(L(x,y,x),y) = T(x,y * x)
    ]]></literal>
    <justification jstring="[hyper(333,a,635,a,b,3678,a)].">
      <j1 rule="hyper" parents="333 635 3678"/>
    </justification>
  </clause>

  <clause id="3684">
    <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(63,a,27,a,b,3678,a)].">
      <j1 rule="hyper" parents="63 27 3678"/>
    </justification>
  </clause>

  <clause id="3685">
    <literal><![CDATA[
      T(T(x,x * y),z) = T(T(x,z),y * x)
    ]]></literal>
    <justification jstring="[para(3678(a,1),23(a,1,1))].">
      <j1 rule="para" parents="3678 23"/>
    </justification>
  </clause>

  <clause id="3686">
    <literal><![CDATA[
      x * T(y,x * y) = L(y,x,y) * x
    ]]></literal>
    <justification jstring="[para(3678(a,2),640(a,1,2))].">
      <j1 rule="para" parents="3678 640"/>
    </justification>
  </clause>

  <clause id="3688">
    <literal><![CDATA[
      x * L(T(y,x * y),z,u) = L(L(y,x,y),z,u) * x
    ]]></literal>
    <justification jstring="[para(3678(a,2),671(a,1,2,1))].">
      <j1 rule="para" parents="3678 671"/>
    </justification>
  </clause>

  <clause id="3689">
    <literal><![CDATA[
      K(x,T(y,x * y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(3678(a,2),3463(a,1,2))].">
      <j1 rule="para" parents="3678 3463"/>
    </justification>
  </clause>

  <clause id="3690">
    <literal><![CDATA[
      (x * ((x \ y) * x)) / x = (x \ y) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(126,a,3681,a(flip),b,859,a),flip(a)].">
      <j1 rule="hyper" parents="126 3681 859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3691">
    <literal><![CDATA[
      ((x \ y) * x) * T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      x * ((x \ y) * x) = z
    ]]></literal>
    <justification jstring="[para(3681(a,1),300(a,1,2))].">
      <j1 rule="para" parents="3681 300"/>
    </justification>
  </clause>

  <clause id="3692">
    <literal><![CDATA[
      T((x \ y) * T(x,y),x) = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(3681(a,1),856(a,1,1,2))].">
      <j1 rule="para" parents="3681 856"/>
    </justification>
  </clause>

  <clause id="3693">
    <literal><![CDATA[
      (((x \ y) * x) / T(x,y)) * x = T((x \ y) * x,x)
    ]]></literal>
    <justification jstring="[para(3681(a,1),3619(a,1,1,2))].">
      <j1 rule="para" parents="3681 3619"/>
    </justification>
  </clause>

  <clause id="3694">
    <literal><![CDATA[
      K(x,T(x \ y,y)) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),3689(a,1,2,2))].">
      <j1 rule="para" parents="10 3689"/>
    </justification>
  </clause>

  <clause id="3695">
    <literal><![CDATA[
      T((x * y) / x,x * y) = L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(478,a,3683,a)].">
      <j1 rule="hyper" parents="478 3683"/>
    </justification>
  </clause>

  <clause id="3697">
    <literal><![CDATA[
      ((x \ y) * x) / (x \ y) = y / (y / x)
    ]]></literal>
    <justification jstring="[hyper(333,a,3486,a,b,3611,a),flip(a)].">
      <j1 rule="hyper" parents="333 3486 3611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3698">
    <literal><![CDATA[
      (x / (x / y)) * (y \ x) = (y \ x) * y
    ]]></literal>
    <justification jstring="[hyper(125,a,3486,a,b,3611,a)].">
      <j1 rule="hyper" parents="125 3486 3611"/>
    </justification>
  </clause>

  <clause id="3699">
    <literal><![CDATA[
      T(x * (T(x,y) \ x),y) = x
    ]]></literal>
    <justification jstring="[para(3611(a,1),238(a,1,1))].">
      <j1 rule="para" parents="3611 238"/>
    </justification>
  </clause>

  <clause id="3700">
    <literal><![CDATA[
      ((x * y) / x) \ x = y \ ((y * x) / y)
    ]]></literal>
    <justification jstring="[para(3611(a,2),3489(a,1,1))].">
      <j1 rule="para" parents="3611 3489"/>
    </justification>
  </clause>

  <clause id="3701">
    <literal><![CDATA[
      T(x / (x / y),y \ x) = y
    ]]></literal>
    <justification jstring="[para(3486(a,2),3699(a,1,1))].">
      <j1 rule="para" parents="3486 3699"/>
    </justification>
  </clause>

  <clause id="3703">
    <literal><![CDATA[
      T(x / (x / (x / y)),y) = x / y
    ]]></literal>
    <justification jstring="[para(79(a,1),3701(a,1,2))].">
      <j1 rule="para" parents="79 3701"/>
    </justification>
  </clause>

  <clause id="3704">
    <literal><![CDATA[
      x \ T(x,T(y,(y \ 1) * x) \ 1) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(333,a,3101,a(flip),b,3616,a)].">
      <j1 rule="hyper" parents="333 3101 3616"/>
    </justification>
  </clause>

  <clause id="3705">
    <literal><![CDATA[
      T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      (T(y,z) * z) / T(y,z) = x
    ]]></literal>
    <justification jstring="[para(3617(a,1),49(a,1)),flip(a)].">
      <j1 rule="para" parents="3617 49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3706">
    <literal><![CDATA[
      T(x,T(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(3617(a,1),742(a,1,1))].">
      <j1 rule="para" parents="3617 742"/>
    </justification>
  </clause>

  <clause id="3707">
    <literal><![CDATA[
      T(T(x,y),L(T(z,x),u,w)) = T(T(x,L(z,u,w)),y)
    ]]></literal>
    <justification jstring="[para(25(a,2),3629(a,1,2))].">
      <j1 rule="para" parents="25 3629"/>
    </justification>
  </clause>

  <clause id="3708">
    <literal><![CDATA[
      T(x,T(y,T(z,T(y,x)))) = T(x,T(T(y,x),z))
    ]]></literal>
    <justification jstring="[para(3613(a,1),3630(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3613 3630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3709">
    <literal><![CDATA[
      T(x,x \ y) / y = x / ((x \ y) * x)
    ]]></literal>
    <justification jstring="[hyper(354,a,3640,a)].">
      <j1 rule="hyper" parents="354 3640"/>
    </justification>
  </clause>

  <clause id="3710">
    <literal><![CDATA[
      T(x,y) / (x * y) = x / (y * x)
    ]]></literal>
    <justification jstring="[hyper(198,a,3640,a)].">
      <j1 rule="hyper" parents="198 3640"/>
    </justification>
  </clause>

  <clause id="3711">
    <literal><![CDATA[
      (T(x,y * x) * y) * x = x * (x * y)
    ]]></literal>
    <justification jstring="[hyper(872,a,3644,a)].">
      <j1 rule="hyper" parents="872 3644"/>
    </justification>
  </clause>

  <clause id="3712">
    <literal><![CDATA[
      (T(x,y) * (y * x)) * z = (x * (x * y)) * z
    ]]></literal>
    <justification jstring="[hyper(125,a,3644,a,b,11,a)].">
      <j1 rule="hyper" parents="125 3644 11"/>
    </justification>
  </clause>

  <clause id="3713">
    <literal><![CDATA[
      T(x,x \ (x \ y)) \ y = (x \ (x \ y)) * x
    ]]></literal>
    <justification jstring="[hyper(121,a,72,a(flip),b,3644,a)].">
      <j1 rule="hyper" parents="121 72 3644"/>
    </justification>
  </clause>

  <clause id="3714">
    <literal><![CDATA[
      (x * (x * y)) \ (T(x,y) * ((y * x) * z)) = L(z,y * x,T(x,y))
    ]]></literal>
    <justification jstring="[para(3644(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="3644 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3715">
    <literal><![CDATA[
      ((T(x,y) * y) / x) \ ((x * (x * y)) / x) = L(x,y,T(x,y))
    ]]></literal>
    <justification jstring="[para(3644(a,1),1829(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="3644 1829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3716">
    <literal><![CDATA[
      T(x \ (y \ x),x) = T(x,y \ 1) \ (y \ x)
    ]]></literal>
    <justification jstring="[para(3591(a,1),3648(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3591 3648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3717">
    <literal><![CDATA[
      T(T(x \ y,z),x) = T(((x \ y) \ y) \ y,z)
    ]]></literal>
    <justification jstring="[para(3674(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3674 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3718">
    <literal><![CDATA[
      L((((x \ y) \ z) \ z) \ z,x \ y,x) = T(y \ (x * z),x \ y)
    ]]></literal>
    <justification jstring="[para(3674(a,1),791(a,1,1))].">
      <j1 rule="para" parents="3674 791"/>
    </justification>
  </clause>

  <clause id="3719">
    <literal><![CDATA[
      (x * (y / x)) / x = y / (y / (y / x))
    ]]></literal>
    <justification jstring="[hyper(289,a,3703,a)].">
      <j1 rule="hyper" parents="289 3703"/>
    </justification>
  </clause>

  <clause id="3720">
    <literal><![CDATA[
      T(x,y) / (x * y) = R(1 / y,y,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,230,a,b,3710,a),flip(a)].">
      <j1 rule="hyper" parents="333 230 3710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3721">
    <literal><![CDATA[
      R(T(x,y),x \ y,x) = (x \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(333,a,112,a(flip),b,3679,a),flip(a)].">
      <j1 rule="hyper" parents="333 112 3679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3722">
    <literal><![CDATA[
      (x * (y * x)) / x = L(x,y,x) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,857,a,b,3686,a)].">
      <j1 rule="hyper" parents="63 857 3686"/>
    </justification>
  </clause>

  <clause id="3723">
    <literal><![CDATA[
      (L(x,y,x) * y) * x = x * (y * x)
    ]]></literal>
    <justification jstring="[hyper(125,a,3686,a(flip),b,857,a)].">
      <j1 rule="hyper" parents="125 3686 857"/>
    </justification>
  </clause>

  <clause id="3724">
    <literal><![CDATA[
      L(x,y,(y * x) / y) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,973,a,b,3686,a(flip))].">
      <j1 rule="hyper" parents="35 973 3686"/>
    </justification>
  </clause>

  <clause id="3725">
    <literal><![CDATA[
      T(L(x,y,x) * y,x) = y * x
    ]]></literal>
    <justification jstring="[para(3686(a,1),856(a,1,1))].">
      <j1 rule="para" parents="3686 856"/>
    </justification>
  </clause>

  <clause id="3727">
    <literal><![CDATA[
      T((x * y) * (x \ 1),x * y) = R(L(y,x,y),x,x)
    ]]></literal>
    <justification jstring="[para(3695(a,1),819(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3695 819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3728">
    <literal><![CDATA[
      R(1 / x,x,T(y,x)) = R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[hyper(703,a,3720,a)].">
      <j1 rule="hyper" parents="703 3720"/>
    </justification>
  </clause>

  <clause id="3729">
    <literal><![CDATA[
      T((x * y) / x,L(x,y,x)) = y
    ]]></literal>
    <justification jstring="[hyper(1830,a,3722,a)].">
      <j1 rule="hyper" parents="1830 3722"/>
    </justification>
  </clause>

  <clause id="3731">
    <literal><![CDATA[
      T(x,L(y,x,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(3729(a,1),288(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3729 288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3732">
    <literal><![CDATA[
      T(x,T(y,y * x)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3636,a,b,3731,a)].">
      <j1 rule="hyper" parents="63 3636 3731"/>
    </justification>
  </clause>

  <clause id="3733">
    <literal><![CDATA[
      L(x,y,x) * T(y,x) = y * L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(126,a,3731,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="126 3731 22"/>
    </justification>
  </clause>

  <clause id="3734">
    <literal><![CDATA[
      T(x,x * y) * L(T(y,x),z,u) = L(y,z,u) * T(x,x * y)
    ]]></literal>
    <justification jstring="[para(3732(a,1),251(a,1,2,1))].">
      <j1 rule="para" parents="3732 251"/>
    </justification>
  </clause>

  <clause id="3735">
    <literal><![CDATA[
      T(x,x * y) * R(T(y,x),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      R(y,z,u) * T(x,x * y) = w
    ]]></literal>
    <justification jstring="[para(3732(a,1),421(a,1,2,1))].">
      <j1 rule="para" parents="3732 421"/>
    </justification>
  </clause>

  <clause id="3736">
    <literal><![CDATA[
      L(R(x,y,x),y,x) = x
    ]]></literal>
    <justification jstring="[hyper(1021,a,3723,a)].">
      <j1 rule="hyper" parents="1021 3723"/>
    </justification>
  </clause>

  <clause id="3737">
    <literal><![CDATA[
      R(L(x,y,x),y,x) = x
    ]]></literal>
    <justification jstring="[hyper(543,a,3723,a)].">
      <j1 rule="hyper" parents="543 3723"/>
    </justification>
  </clause>

  <clause id="3738">
    <literal><![CDATA[
      R(x,y,T(x,y)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(1106,a,3736,a)].">
      <j1 rule="hyper" parents="1106 3736"/>
    </justification>
  </clause>

  <clause id="3739">
    <literal><![CDATA[
      x \ T(y * x,y) = R(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(511,a,3736,a)].">
      <j1 rule="hyper" parents="511 3736"/>
    </justification>
  </clause>

  <clause id="3740">
    <literal><![CDATA[
      T(x \ T(x * y,y),T(x * y,y)) = y
    ]]></literal>
    <justification jstring="[hyper(63,a,3452,a,b,3736,a)].">
      <j1 rule="hyper" parents="63 3452 3736"/>
    </justification>
  </clause>

  <clause id="3741">
    <literal><![CDATA[
      L(T(R(x,y,x),z),y,x) = T(x,z)
    ]]></literal>
    <justification jstring="[para(3736(a,1),25(a,2,1))].">
      <j1 rule="para" parents="3736 25"/>
    </justification>
  </clause>

  <clause id="3742">
    <literal><![CDATA[
      L(T(x,y),y,T(x,y)) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(949,a,3737,a),flip(a)].">
      <j1 rule="hyper" parents="949 3737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3743">
    <literal><![CDATA[
      R(x,y,z) != z
    ]]></literal>
    <literal><![CDATA[
      L(z,y,z) = x
    ]]></literal>
    <justification jstring="[para(3737(a,1),51(a,1)),flip(a)].">
      <j1 rule="para" parents="3737 51"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3744">
    <literal><![CDATA[
      x * R(y,x,y) = T(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(126,a,3738,a(flip),b,1104,a)].">
      <j1 rule="hyper" parents="126 3738 1104"/>
    </justification>
  </clause>

  <clause id="3745">
    <literal><![CDATA[
      R(x,T(y,x),T(x,y)) = R(x,T(y,x),x)
    ]]></literal>
    <justification jstring="[para(3613(a,1),3738(a,1,3))].">
      <j1 rule="para" parents="3613 3738"/>
    </justification>
  </clause>

  <clause id="3746">
    <literal><![CDATA[
      R(x,x \ y,x) = (x \ y) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),3739(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 3739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3747">
    <literal><![CDATA[
      R(x / y,y,x / y) = y \ T(x,x / y)
    ]]></literal>
    <justification jstring="[para(12(a,1),3739(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12 3739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3748">
    <literal><![CDATA[
      (x * y) \ (x * T(z * y,z)) = L(R(z,y,z),y,x)
    ]]></literal>
    <justification jstring="[para(3739(a,1),99(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3739 99"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3749">
    <literal><![CDATA[
      (x \ T(x * y,y)) * x = T(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(3449,a,3744,a)].">
      <j1 rule="hyper" parents="3449 3744"/>
    </justification>
  </clause>

  <clause id="3750">
    <literal><![CDATA[
      T(x * y,x) != y * z
    ]]></literal>
    <literal><![CDATA[
      R(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(3744(a,1),43(a,1))].">
      <j1 rule="para" parents="3744 43"/>
    </justification>
  </clause>

  <clause id="3751">
    <literal><![CDATA[
      x \ T(y * x,y) != z
    ]]></literal>
    <literal><![CDATA[
      R(y,x,y) = z
    ]]></literal>
    <justification jstring="[para(3744(a,1),342(a,1,2))].">
      <j1 rule="para" parents="3744 342"/>
    </justification>
  </clause>

  <clause id="3752">
    <literal><![CDATA[
      T(x * y,x) * T(x,y) = (x * y) * R(x,y,x)
    ]]></literal>
    <justification jstring="[para(3744(a,1),1587(a,1,1))].">
      <j1 rule="para" parents="3744 1587"/>
    </justification>
  </clause>

  <clause id="3753">
    <literal><![CDATA[
      L(R(T(x,y),z,x),z,x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(27(a,2),3741(a,1,1))].">
      <j1 rule="para" parents="27 3741"/>
    </justification>
  </clause>

  <clause id="3754">
    <literal><![CDATA[
      T(x,(y \ x) \ 1) = K(x \ y,x) \ x
    ]]></literal>
    <justification jstring="[para(76(a,1),3607(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="76 3607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3755">
    <literal><![CDATA[
      x / (y * (x / y)) = y \ (x / (x / y))
    ]]></literal>
    <justification jstring="[hyper(3586,a,3609,a)].">
      <j1 rule="hyper" parents="3586 3609"/>
    </justification>
  </clause>

  <clause id="3756">
    <literal><![CDATA[
      x * (((y * x) / y) \ z) = T(x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(333,a,3580,a,b,3615,a)].">
      <j1 rule="hyper" parents="333 3580 3615"/>
    </justification>
  </clause>

  <clause id="3757">
    <literal><![CDATA[
      T(x,(y \ z) / z) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(3706,a,3621,a),flip(a)].">
      <j1 rule="hyper" parents="3706 3621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3758">
    <literal><![CDATA[
      T(x,(y \ z) / z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ 1) = u
    ]]></literal>
    <justification jstring="[para(3621(a,1),3706(a,1))].">
      <j1 rule="para" parents="3621 3706"/>
    </justification>
  </clause>

  <clause id="3759">
    <literal><![CDATA[
      T(x,y / (z * y)) = T(x,z \ 1)
    ]]></literal>
    <justification jstring="[para(9(a,1),3757(a,1,2,1))].">
      <j1 rule="para" parents="9 3757"/>
    </justification>
  </clause>

  <clause id="3760">
    <literal><![CDATA[
      T(x,(y / z) \ 1) = T(x,z / y)
    ]]></literal>
    <justification jstring="[para(79(a,1),3757(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="79 3757"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3761">
    <literal><![CDATA[
      ((x \ y) / y) * T(z,x \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      z * ((x \ y) / y) = u
    ]]></literal>
    <justification jstring="[para(3757(a,1),300(a,1,2))].">
      <j1 rule="para" parents="3757 300"/>
    </justification>
  </clause>

  <clause id="3762">
    <literal><![CDATA[
      T(x * y,x \ 1) = ((x * y) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(3667,a,3759,a),flip(a)].">
      <j1 rule="hyper" parents="3667 3759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3763">
    <literal><![CDATA[
      T(x / (y / (z * y)),z \ 1) = (y / (z * y)) \ x
    ]]></literal>
    <justification jstring="[hyper(423,a,3759,a),flip(a)].">
      <j1 rule="hyper" parents="423 3759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3764">
    <literal><![CDATA[
      T(x / (y * x),y \ 1) = x / (y * x)
    ]]></literal>
    <justification jstring="[hyper(346,a,3759,a),flip(a)].">
      <j1 rule="hyper" parents="346 3759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3765">
    <literal><![CDATA[
      x / T(y * x,y \ 1) = (y * x) \ x
    ]]></literal>
    <justification jstring="[hyper(197,a,3759,a(flip),b,3665,a(flip))].">
      <j1 rule="hyper" parents="197 3759 3665"/>
    </justification>
  </clause>

  <clause id="3766">
    <literal><![CDATA[
      (x / (y * x)) * T(z,y \ 1) = z * (x / (y * x))
    ]]></literal>
    <justification jstring="[hyper(126,a,3759,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="126 3759 22"/>
    </justification>
  </clause>

  <clause id="3768">
    <literal><![CDATA[
      T(x,R(1 / y,y,z)) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(230(a,2),3759(a,1,2))].">
      <j1 rule="para" parents="230 3759"/>
    </justification>
  </clause>

  <clause id="3769">
    <literal><![CDATA[
      T(x,x * (y / T(x,y))) = T(x,x * (y / x))
    ]]></literal>
    <justification jstring="[para(3656(a,1),3613(a,1,2))].">
      <j1 rule="para" parents="3656 3613"/>
    </justification>
  </clause>

  <clause id="3770">
    <literal><![CDATA[
      T(T(x,y) \ y,z) = T(x \ T(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(253,a,3659,a,b,111,a)].">
      <j1 rule="hyper" parents="253 3659 111"/>
    </justification>
  </clause>

  <clause id="3771">
    <literal><![CDATA[
      T(x * (y / x),x) = x \ (y * ((x \ y) \ y))
    ]]></literal>
    <justification jstring="[hyper(444,a,328,a(flip),b,3669,a)].">
      <j1 rule="hyper" parents="444 328 3669"/>
    </justification>
  </clause>

  <clause id="3772">
    <literal><![CDATA[
      (x * y) \ (y * T(x,x \ y)) = a(x,y / x,x)
    ]]></literal>
    <justification jstring="[para(3669(a,1),86(a,1,2))].">
      <j1 rule="para" parents="3669 86"/>
    </justification>
  </clause>

  <clause id="3773">
    <literal><![CDATA[
      (x \ y) * T(y,y \ (x \ y)) = (x \ T(y,x \ 1)) * y
    ]]></literal>
    <justification jstring="[para(3107(a,2),3669(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3107 3669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3774">
    <literal><![CDATA[
      (x / (x / y)) * (y \ x) = (x / y) * (x / (x / y))
    ]]></literal>
    <justification jstring="[para(79(a,1),3672(a,1,2,1))].">
      <j1 rule="para" parents="79 3672"/>
    </justification>
  </clause>

  <clause id="3775">
    <literal><![CDATA[
      T(T(x,y),z / x) = T(T(x,y),x \ z)
    ]]></literal>
    <justification jstring="[hyper(333,a,330,a,b,3673,a),flip(a)].">
      <j1 rule="hyper" parents="333 330 3673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3776">
    <literal><![CDATA[
      T(T(x,y),(z \ 1) * x) = T(T(x,z \ x),y)
    ]]></literal>
    <justification jstring="[para(1686(a,1),3685(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1686 3685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3778">
    <literal><![CDATA[
      T(x / (x / y),x) = L(y,y \ x,y)
    ]]></literal>
    <justification jstring="[para(3697(a,1),659(a,1,1))].">
      <j1 rule="para" parents="3697 659"/>
    </justification>
  </clause>

  <clause id="3779">
    <literal><![CDATA[
      x * T(x / (x / y),x) = y * ((y \ x) * y)
    ]]></literal>
    <justification jstring="[hyper(126,a,3778,a,b,98,a)].">
      <j1 rule="hyper" parents="126 3778 98"/>
    </justification>
  </clause>

  <clause id="3780">
    <literal><![CDATA[
      T(T(x / (x / y),x),z) = L(T(y,z),y \ x,y)
    ]]></literal>
    <justification jstring="[para(3778(a,2),25(a,2,1)),flip(a)].">
      <j1 rule="para" parents="3778 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3781">
    <literal><![CDATA[
      L(x \ y,(x \ y) \ y,x \ y) = T(y / x,y)
    ]]></literal>
    <justification jstring="[para(76(a,1),3778(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="76 3778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3782">
    <literal><![CDATA[
      T(T(x,x \ y) / y,x \ y) = R((x \ y) \ 1,x \ y,x)
    ]]></literal>
    <justification jstring="[para(3709(a,2),686(a,1,1))].">
      <j1 rule="para" parents="3709 686"/>
    </justification>
  </clause>

  <clause id="3783">
    <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(3709(a,2),748(a,1,2,1))].">
      <j1 rule="para" parents="3709 748"/>
    </justification>
  </clause>

  <clause id="3784">
    <literal><![CDATA[
      T(x,y \ 1) / (y \ x) = x / ((x \ (y \ x)) * x)
    ]]></literal>
    <justification jstring="[para(3591(a,1),3709(a,1,1))].">
      <j1 rule="para" parents="3591 3709"/>
    </justification>
  </clause>

  <clause id="3785">
    <literal><![CDATA[
      R(1 / x,x,y / x) = R(1 / x,x,x \ y)
    ]]></literal>
    <justification jstring="[para(113(a,1),3728(a,1,3)),flip(a)].">
      <j1 rule="para" parents="113 3728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3787">
    <literal><![CDATA[
      K(x,x \ T(x * y,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(3740(a,1),3694(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3740 3694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3788">
    <literal><![CDATA[
      K(x,y) = (x * R(y,x,y)) \ T(x * y,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3450,a,b,3787,a),flip(a)].">
      <j1 rule="hyper" parents="63 3450 3787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3789">
    <literal><![CDATA[
      K(x \ y,x) \ x = x * K(x,y / x)
    ]]></literal>
    <justification jstring="[hyper(63,a,3086,a(flip),b,3754,a),flip(a)].">
      <j1 rule="hyper" parents="63 3086 3754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3790">
    <literal><![CDATA[
      x * ((x * y) * (y / (x * y))) = ((x * y) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(63,a,3112,a,b,3762,a)].">
      <j1 rule="hyper" parents="63 3112 3762"/>
    </justification>
  </clause>

  <clause id="3791">
    <literal><![CDATA[
      T((x \ 1) * y,x) = (((x \ 1) * y) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(63,a,2983,a(flip),b,3762,a)].">
      <j1 rule="hyper" parents="63 2983 3762"/>
    </justification>
  </clause>

  <clause id="3792">
    <literal><![CDATA[
      (x \ 1) * (((x * y) \ y) \ y) = (x * y) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(126,a,3762,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="126 3762 22"/>
    </justification>
  </clause>

  <clause id="3793">
    <literal><![CDATA[
      T((1 / x) * y,x) = (((1 / x) * y) \ y) \ y
    ]]></literal>
    <justification jstring="[para(79(a,1),3762(a,1,2))].">
      <j1 rule="para" parents="79 3762"/>
    </justification>
  </clause>

  <clause id="3794">
    <literal><![CDATA[
      R(x / y,y,x / y) = y \ T(x,y \ x)
    ]]></literal>
    <justification jstring="[para(3363(a,1),3747(a,2,2))].">
      <j1 rule="para" parents="3363 3747"/>
    </justification>
  </clause>

  <clause id="3795">
    <literal><![CDATA[
      T(x,y / z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,(z / y) \ 1) = u
    ]]></literal>
    <justification jstring="[para(79(a,1),3758(a,1,2,1))].">
      <j1 rule="para" parents="79 3758"/>
    </justification>
  </clause>

  <clause id="3796">
    <literal><![CDATA[
      K(x,y) = T(y * x,y) \ T(x * y,y)
    ]]></literal>
    <justification jstring="[para(3744(a,1),3788(a,2,1))].">
      <j1 rule="para" parents="3744 3788"/>
    </justification>
  </clause>

  <clause id="3797">
    <literal><![CDATA[
      K(x \ T(x * y,x),x) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,1409,a(flip),b,3796,a)].">
      <j1 rule="hyper" parents="333 1409 3796"/>
    </justification>
  </clause>

  <clause id="3798">
    <literal><![CDATA[
      K(x \ T(y,x),x) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),3797(a,1,1,2,1))].">
      <j1 rule="para" parents="10 3797"/>
    </justification>
  </clause>

  <clause id="3799">
    <literal><![CDATA[
      x * K(y \ (y / (x \ z)),y) = (T(y,x / z) \ y) * x
    ]]></literal>
    <justification jstring="[hyper(333,a,2063,a(flip),b,3612,a)].">
      <j1 rule="hyper" parents="333 2063 3612"/>
    </justification>
  </clause>

  <clause id="3800">
    <literal><![CDATA[
      T(x,y) \ (y * x) = T(T(y,x),x)
    ]]></literal>
    <justification jstring="[hyper(121,a,3624,a(flip),b,3635,a)].">
      <j1 rule="hyper" parents="121 3624 3635"/>
    </justification>
  </clause>

  <clause id="3801">
    <literal><![CDATA[
      T(x,y) * T(T(y,z),x) = T(y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(23(a,1),3635(a,1,2))].">
      <j1 rule="para" parents="23 3635"/>
    </justification>
  </clause>

  <clause id="3802">
    <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(25(a,2),3800(a,1,1))].">
      <j1 rule="para" parents="25 3800"/>
    </justification>
  </clause>

  <clause id="3803">
    <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(3613(a,1),3658(a,1,2,1))].">
      <j1 rule="para" parents="3613 3658"/>
    </justification>
  </clause>

  <clause id="3804">
    <literal><![CDATA[
      T(x,T(y,T(z,T(y,x)))) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(333,a,3630,a(flip),b,3708,a),flip(a)].">
      <j1 rule="hyper" parents="333 3630 3708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3805">
    <literal><![CDATA[
      T(x,x * (y / T(x,y))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,3677,a(flip),b,3769,a),flip(a)].">
      <j1 rule="hyper" parents="333 3677 3769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3806">
    <literal><![CDATA[
      ((x / y) \ T((x / y) * y,y)) * (x / y) = y \ (x * ((y \ x) \ x))
    ]]></literal>
    <justification jstring="[hyper(63,a,3749,a,b,3771,a)].">
      <j1 rule="hyper" parents="63 3749 3771"/>
    </justification>
  </clause>

  <clause id="3807">
    <literal><![CDATA[
      x \ (y * ((x \ y) \ y)) = x * (y / T(x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,3656,a(flip),b,3771,a),flip(a)].">
      <j1 rule="hyper" parents="63 3656 3771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3808">
    <literal><![CDATA[
      T(T(x,y),(z \ 1) * x) = T(T(x,y),z \ x)
    ]]></literal>
    <justification jstring="[hyper(333,a,23,a,b,3776,a),flip(a)].">
      <j1 rule="hyper" parents="333 23 3776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3809">
    <literal><![CDATA[
      (x / (x / y)) * x = y * ((y \ x) * y)
    ]]></literal>
    <justification jstring="[hyper(300,a,3779,a)].">
      <j1 rule="hyper" parents="300 3779"/>
    </justification>
  </clause>

  <clause id="3810">
    <literal><![CDATA[
      T(T(x,(y / (y / x)) * y) * ((x \ y) * x),x) = x * ((x \ y) * x)
    ]]></literal>
    <justification jstring="[para(3809(a,2),3411(a,1,1,1,2))].">
      <j1 rule="para" parents="3809 3411"/>
    </justification>
  </clause>

  <clause id="3811">
    <literal><![CDATA[
      T(x,((y / (y / x)) * y) / x) = T(x,(x \ y) * x)
    ]]></literal>
    <justification jstring="[para(3809(a,2),3634(a,1,2,1))].">
      <j1 rule="para" parents="3809 3634"/>
    </justification>
  </clause>

  <clause id="3812">
    <literal><![CDATA[
      ((x / (x / y)) * x) / y = (y \ x) * T(y,x)
    ]]></literal>
    <justification jstring="[para(3809(a,2),3690(a,1,1))].">
      <j1 rule="para" parents="3809 3690"/>
    </justification>
  </clause>

  <clause id="3813">
    <literal><![CDATA[
      R(1 / x,x,y / x) = (x \ y) / y
    ]]></literal>
    <justification jstring="[hyper(333,a,399,a(flip),b,3785,a),flip(a)].">
      <j1 rule="hyper" parents="333 399 3785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3814">
    <literal><![CDATA[
      ((x \ y) / y) * (x * (y / x)) = y / x
    ]]></literal>
    <justification jstring="[hyper(125,a,3813,a(flip),b,230,a(flip))].">
      <j1 rule="hyper" parents="125 3813 230"/>
    </justification>
  </clause>

  <clause id="3815">
    <literal><![CDATA[
      x * (y * (z / y)) != z / y
    ]]></literal>
    <literal><![CDATA[
      (y \ z) / z = x
    ]]></literal>
    <justification jstring="[para(3814(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="3814 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3816">
    <literal><![CDATA[
      ((((x / y) \ 1) * x) \ x) \ x = ((x / y) \ 1) * (y * (x / y))
    ]]></literal>
    <justification jstring="[hyper(63,a,1716,a(flip),b,3791,a),flip(a)].">
      <j1 rule="hyper" parents="63 1716 3791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3817">
    <literal><![CDATA[
      L(T(x,y),T(z,x),z / T(z,x)) * z = (z / T(z,x)) * (T(x,y) * T(z,x))
    ]]></literal>
    <justification jstring="[hyper(126,a,3801,a(flip),b,790,a),flip(a)].">
      <j1 rule="hyper" parents="126 3801 790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3819">
    <literal><![CDATA[
      L(T(x,y),T(y,x),x) = T(x,y * x)
    ]]></literal>
    <justification jstring="[hyper(1035,a,3637,a),flip(a)].">
      <j1 rule="hyper" parents="1035 3637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3820">
    <literal><![CDATA[
      T(x,y) * T(y,y * x) = L(y,x,y) * T(x,y)
    ]]></literal>
    <justification jstring="[para(634(a,1),3637(a,1,2))].">
      <j1 rule="para" parents="634 3637"/>
    </justification>
  </clause>

  <clause id="3821">
    <literal><![CDATA[
      L(x,T(y,x),x) * y = y * T(x,y * x)
    ]]></literal>
    <justification jstring="[para(3819(a,1),251(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3819 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3822">
    <literal><![CDATA[
      ((x * (y * x)) / x) / y = L(x,T(y,x),x)
    ]]></literal>
    <justification jstring="[hyper(123,a,857,a,b,3821,a)].">
      <j1 rule="hyper" parents="123 857 3821"/>
    </justification>
  </clause>

  <clause id="3823">
    <literal><![CDATA[
      L(x,T(y,x),x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,3686,a(flip),b,3821,a),flip(a)].">
      <j1 rule="hyper" parents="35 3686 3821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3824">
    <literal><![CDATA[
      L(x,(x * y) / x,x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(238(a,1),3823(a,1,2)),flip(a)].">
      <j1 rule="para" parents="238 3823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3825">
    <literal><![CDATA[
      T(x,y) * T(y,y * x) = x * L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,3733,a(flip),b,3820,a),flip(a)].">
      <j1 rule="hyper" parents="333 3733 3820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3826">
    <literal><![CDATA[
      T(x,y) * T(y,x * y) = x * L(y,x,y)
    ]]></literal>
    <justification jstring="[para(3678(a,2),3825(a,1,2))].">
      <j1 rule="para" parents="3678 3825"/>
    </justification>
  </clause>

  <clause id="3827">
    <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(3638(a,1),243(a,1,1,2))].">
      <j1 rule="para" parents="3638 243"/>
    </justification>
  </clause>

  <clause id="3828">
    <literal><![CDATA[
      R(x,y,x) * T(x * y,x) = T(x * y,x) * T(x,y)
    ]]></literal>
    <justification jstring="[para(3618(a,1),3638(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3618 3638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3829">
    <literal><![CDATA[
      R(x,y / x,x) * T(y,x) = T(y,x) * T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(3666(a,1),3638(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3666 3638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3830">
    <literal><![CDATA[
      R(x,x \ y,x) * T(y,x) = T(y,x) * T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(3679(a,1),3638(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3679 3638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3831">
    <literal><![CDATA[
      T(x,y) * K(y \ x,y) = (T(y,x) \ x) * y
    ]]></literal>
    <justification jstring="[hyper(126,a,3798,a(flip),b,3661,a)].">
      <j1 rule="hyper" parents="126 3798 3661"/>
    </justification>
  </clause>

  <clause id="3833">
    <literal><![CDATA[
      ((x \ y) * x) / T(x,y) = x \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,1397,a(flip),b,3693,a),flip(a)].">
      <j1 rule="hyper" parents="35 1397 3693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3834">
    <literal><![CDATA[
      (x \ T(y,x)) * T(x,y) = (x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(140,a,3833,a)].">
      <j1 rule="hyper" parents="140 3833"/>
    </justification>
  </clause>

  <clause id="3835">
    <literal><![CDATA[
      R(x,K(x,y \ 1),z) = x
    ]]></literal>
    <justification jstring="[para(3704(a,1),3304(a,1,2))].">
      <j1 rule="para" parents="3704 3304"/>
    </justification>
  </clause>

  <clause id="3836">
    <literal><![CDATA[
      R(x,K(x,y),z) = x
    ]]></literal>
    <justification jstring="[para(79(a,1),3835(a,1,2,2))].">
      <j1 rule="para" parents="79 3835"/>
    </justification>
  </clause>

  <clause id="3837">
    <literal><![CDATA[
      (x * K(x,y)) * y = x * (y * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(125,a,3836,a(flip),b,2743,a),flip(a)].">
      <j1 rule="hyper" parents="125 3836 2743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3838">
    <literal><![CDATA[
      R(T(x,y),K(x,z),u) = T(x,y)
    ]]></literal>
    <justification jstring="[para(3836(a,1),27(a,2,1))].">
      <j1 rule="para" parents="3836 27"/>
    </justification>
  </clause>

  <clause id="3839">
    <literal><![CDATA[
      (L(x,y,z) * K(x,u)) * w = L(x,y,z) * (K(x,u) * w)
    ]]></literal>
    <justification jstring="[para(3836(a,1),457(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="3836 457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3840">
    <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(3838(a,1),453(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="3838 453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3841">
    <literal><![CDATA[
      T((x * y) * (x \ 1),x * y) = L(R(y,x,x),x,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,29,a(flip),b,3727,a),flip(a)].">
      <j1 rule="hyper" parents="333 29 3727"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3842">
    <literal><![CDATA[
      (x / (y * x)) * T(z,y \ 1) = z * R(1 / y,y,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,397,a,b,3766,a),flip(a)].">
      <j1 rule="hyper" parents="333 397 3766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3843">
    <literal><![CDATA[
      (x / y) * (x / (x / y)) = (y \ x) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,3698,a(flip),b,3774,a),flip(a)].">
      <j1 rule="hyper" parents="63 3698 3774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3844">
    <literal><![CDATA[
      ((x \ y) * x) * x = y * (y / (y / x))
    ]]></literal>
    <justification jstring="[para(3843(a,1),1448(a,1,1))].">
      <j1 rule="para" parents="3843 1448"/>
    </justification>
  </clause>

  <clause id="3845">
    <literal><![CDATA[
      ((x \ T(y,x)) * T(x,y)) * T(x,y) = y * (y / (y / T(x,y)))
    ]]></literal>
    <justification jstring="[para(3628(a,1),3844(a,1,1,1))].">
      <j1 rule="para" parents="3628 3844"/>
    </justification>
  </clause>

  <clause id="3846">
    <literal><![CDATA[
      T(x,y) / ((y \ 1) \ x) = x / ((x \ ((y \ 1) \ x)) * x)
    ]]></literal>
    <justification jstring="[para(2983(a,1),3784(a,1,1))].">
      <j1 rule="para" parents="2983 3784"/>
    </justification>
  </clause>

  <clause id="3847">
    <literal><![CDATA[
      T(x,((y / (y / x)) * y) / x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,3681,a(flip),b,3811,a),flip(a)].">
      <j1 rule="hyper" parents="333 3681 3811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3848">
    <literal><![CDATA[
      T(x,(x \ y) * T(x,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(3812(a,1),3847(a,1,2))].">
      <j1 rule="para" parents="3812 3847"/>
    </justification>
  </clause>

  <clause id="3849">
    <literal><![CDATA[
      R(T(x,y),x \ y,T(x,y)) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(3848(a,1),1433(a,1,1))].">
      <j1 rule="para" parents="3848 1433"/>
    </justification>
  </clause>

  <clause id="3850">
    <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(1284(a,1),3646(a,1,2,1))].">
      <j1 rule="para" parents="1284 3646"/>
    </justification>
  </clause>

  <clause id="3851">
    <literal><![CDATA[
      T(L(L(x,y,x),z,u) * y,x) = L(x,z,u) * T(y,x)
    ]]></literal>
    <justification jstring="[para(3688(a,1),1840(a,1,1))].">
      <j1 rule="para" parents="3688 1840"/>
    </justification>
  </clause>

  <clause id="3852">
    <literal><![CDATA[
      R(x,y,x) * T(x * y,x) = (x * y) * R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,3752,a(flip),b,3828,a),flip(a)].">
      <j1 rule="hyper" parents="333 3752 3828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3853">
    <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(3852(a,1),3748(a,1,2))].">
      <j1 rule="para" parents="3852 3748"/>
    </justification>
  </clause>

  <clause id="3854">
    <literal><![CDATA[
      R(x,y / x,x) = R(x,x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,3829,a,b,3830,a)].">
      <j1 rule="hyper" parents="35 3829 3830"/>
    </justification>
  </clause>

  <clause id="3855">
    <literal><![CDATA[
      R(x,y / x,x) = (x \ y) \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,3746,a(flip),b,3854,a),flip(a)].">
      <j1 rule="hyper" parents="333 3746 3854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3856">
    <literal><![CDATA[
      R(x,x \ (y \ x),x) = ((y \ T(x,y \ 1)) * x) / (y \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,3110,a(flip),b,3854,a),flip(a)].">
      <j1 rule="hyper" parents="63 3110 3854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3857">
    <literal><![CDATA[
      R(x,(x * y) / x,x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),3854(a,2,2))].">
      <j1 rule="para" parents="9 3854"/>
    </justification>
  </clause>

  <clause id="3858">
    <literal><![CDATA[
      R(x,T(y,x),x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(239(a,1),3857(a,1,2)),flip(a)].">
      <j1 rule="para" parents="239 3857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3859">
    <literal><![CDATA[
      R(x,T(y,x),T(x,y)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,3745,a,b,3858,a)].">
      <j1 rule="hyper" parents="63 3745 3858"/>
    </justification>
  </clause>

  <clause id="3860">
    <literal><![CDATA[
      R(R(x,y,z),T(u,x),T(x,u)) = R(R(x,u,x),y,z)
    ]]></literal>
    <justification jstring="[para(3859(a,1),31(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3859 31"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3861">
    <literal><![CDATA[
      (x \ (y * x)) \ T(y * x,x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(11(a,1),3855(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11 3855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3862">
    <literal><![CDATA[
      (x \ T(y,x \ 1)) * y = (x \ y) * T(y,x \ 1)
    ]]></literal>
    <justification jstring="[para(3591(a,1),3773(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3591 3773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3863">
    <literal><![CDATA[
      (T(x,(y / z) / (1 / z)) \ x) * (y / z) = T(y,x) / z
    ]]></literal>
    <justification jstring="[hyper(63,a,2170,a(flip),b,3799,a),flip(a)].">
      <j1 rule="hyper" parents="63 2170 3799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3864">
    <literal><![CDATA[
      L(x,K(y,z),L(y,u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(501,a,3839,a)].">
      <j1 rule="hyper" parents="501 3839"/>
    </justification>
  </clause>

  <clause id="3865">
    <literal><![CDATA[
      (K(x,y) * L(x,z,u)) * w = L(x,z,u) * (K(x,y) * w)
    ]]></literal>
    <justification jstring="[para(3344(a,1),3839(a,1,1))].">
      <j1 rule="para" parents="3344 3839"/>
    </justification>
  </clause>

  <clause id="3866">
    <literal><![CDATA[
      L(x,K(y,z),L(y,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      x = v5
    ]]></literal>
    <justification jstring="[para(3864(a,1),50(a,2))].">
      <j1 rule="para" parents="3864 50"/>
    </justification>
  </clause>

  <clause id="3867">
    <literal><![CDATA[
      L(x,K(y,z),y) = x
    ]]></literal>
    <justification jstring="[para(371(a,1),3864(a,1,3))].">
      <j1 rule="para" parents="371 3864"/>
    </justification>
  </clause>

  <clause id="3869">
    <literal><![CDATA[
      (T(x,y) / ((y \ 1) \ x)) \ x = (x \ ((y \ 1) \ x)) * x
    ]]></literal>
    <justification jstring="[hyper(192,a,3846,a(flip))].">
      <j1 rule="hyper" parents="192 3846"/>
    </justification>
  </clause>

  <clause id="3870">
    <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(3860(a,1),3651(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3860 3651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3871">
    <literal><![CDATA[
      L(x,(x * y) / x,x) = L(x,y,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,3357,a(flip),b,3715,a)].">
      <j1 rule="hyper" parents="63 3357 3715"/>
    </justification>
  </clause>

  <clause id="3872">
    <literal><![CDATA[
      L(x,y,T(x,y)) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,3824,a(flip),b,3871,a),flip(a)].">
      <j1 rule="hyper" parents="63 3824 3871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3873">
    <literal><![CDATA[
      R(x,x \ (y \ x),x) = ((y \ x) * T(x,y \ 1)) / (y \ x)
    ]]></literal>
    <justification jstring="[para(3862(a,1),3856(a,2,1))].">
      <j1 rule="para" parents="3862 3856"/>
    </justification>
  </clause>

  <clause id="3875">
    <literal><![CDATA[
      ((x \ y) * x) * T(x,y) = y * (y / (y / T(x,y)))
    ]]></literal>
    <justification jstring="[para(3834(a,1),3845(a,1,1))].">
      <j1 rule="para" parents="3834 3845"/>
    </justification>
  </clause>

  <clause id="3876">
    <literal><![CDATA[
      x * (x / (x / T(y,x))) = y * ((y \ x) * y)
    ]]></literal>
    <justification jstring="[hyper(3691,a,3875,a),flip(a)].">
      <j1 rule="hyper" parents="3691 3875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3877">
    <literal><![CDATA[
      x / (x / T(y,x)) = T(x / (x / y),x)
    ]]></literal>
    <justification jstring="[hyper(253,a,3809,a,b,3876,a),flip(a)].">
      <j1 rule="hyper" parents="253 3809 3876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3878">
    <literal><![CDATA[
      T(x / (x / y),x) \ x = x / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(192,a,3877,a)].">
      <j1 rule="hyper" parents="192 3877"/>
    </justification>
  </clause>

  <clause id="3879">
    <literal><![CDATA[
      x / T(y \ x,x) = T(x / y,x) \ x
    ]]></literal>
    <justification jstring="[para(76(a,1),3878(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="76 3878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3880">
    <literal><![CDATA[
      L(x,x \ y,x) \ y = y / T(x,y)
    ]]></literal>
    <justification jstring="[para(3778(a,1),3878(a,1,1))].">
      <j1 rule="para" parents="3778 3878"/>
    </justification>
  </clause>

  <clause id="3881">
    <literal><![CDATA[
      L(x,x \ y,x) \ y = T(y,x) / x
    ]]></literal>
    <justification jstring="[hyper(333,a,3625,a,b,3880,a),flip(a)].">
      <j1 rule="hyper" parents="333 3625 3880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3882">
    <literal><![CDATA[
      L(x,x \ y,x) = y / (T(y,x) / x)
    ]]></literal>
    <justification jstring="[hyper(197,a,3625,a,b,3880,a),flip(a)].">
      <j1 rule="hyper" parents="197 3625 3880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3885">
    <literal><![CDATA[
      (R(x,y,z) * T(u,x)) * T(x,u) = (R(x,y,z) * u) * x
    ]]></literal>
    <justification jstring="[hyper(333,a,453,a(flip),b,3870,a),flip(a)].">
      <j1 rule="hyper" parents="333 453 3870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3886">
    <literal><![CDATA[
      T(x * y,x) * T(x,y) = (R(x,y,x) * y) * x
    ]]></literal>
    <justification jstring="[para(1524(a,1),3885(a,1,1))].">
      <j1 rule="para" parents="1524 3885"/>
    </justification>
  </clause>

  <clause id="3887">
    <literal><![CDATA[
      (R(x,y,x) * y) * x = (x * y) * R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,3752,a(flip),b,3886,a),flip(a)].">
      <j1 rule="hyper" parents="63 3752 3886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3888">
    <literal><![CDATA[
      (R(x,y,x) * y) \ ((x * y) * R(x,y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(3887(a,1),342(a,1,2))].">
      <j1 rule="para" parents="3887 342"/>
    </justification>
  </clause>

  <clause id="3890">
    <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(3802(a,2),437(a,1))].">
      <j1 rule="para" parents="3802 437"/>
    </justification>
  </clause>

  <clause id="3891">
    <literal><![CDATA[
      T(x,T(y,z)) / (T(T(y,x),z) \ x) = T(y,T(z,T(y,x)))
    ]]></literal>
    <justification jstring="[para(3804(a,1),3803(a,1,1))].">
      <j1 rule="para" parents="3804 3803"/>
    </justification>
  </clause>

  <clause id="3892">
    <literal><![CDATA[
      T(x,T(y,T(x,z))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3658,a(flip),b,3891,a),flip(a)].">
      <j1 rule="hyper" parents="63 3658 3891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3894">
    <literal><![CDATA[
      T(x,T(y,z)) * T(y,x) = y * T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(126,a,3892,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="126 3892 22"/>
    </justification>
  </clause>

  <clause id="3898">
    <literal><![CDATA[
      T(x,y) \ (x * T(y,T(x,z))) = T(T(y,x),T(x,z))
    ]]></literal>
    <justification jstring="[hyper(121,a,3894,a(flip),b,3635,a)].">
      <j1 rule="hyper" parents="121 3894 3635"/>
    </justification>
  </clause>

  <clause id="3899">
    <literal><![CDATA[
      ((x / y) \ T(x,y)) * (x / y) = y \ (x * ((y \ x) \ x))
    ]]></literal>
    <justification jstring="[para(12(a,1),3806(a,1,1,2,1))].">
      <j1 rule="para" parents="12 3806"/>
    </justification>
  </clause>

  <clause id="3900">
    <literal><![CDATA[
      x \ (y * ((x \ y) \ y)) = ((y * x) / y) * (y / x)
    ]]></literal>
    <justification jstring="[para(3361(a,1),3899(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3361 3899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3901">
    <literal><![CDATA[
      ((x * y) / x) * (x / y) = y * (x / T(y,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,3807,a(flip),b,3900,a),flip(a)].">
      <j1 rule="hyper" parents="63 3807 3900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3902">
    <literal><![CDATA[
      ((x * y) / x) * (x / y) != y * z
    ]]></literal>
    <literal><![CDATA[
      x / T(y,x) = z
    ]]></literal>
    <justification jstring="[para(3901(a,2),43(a,1))].">
      <j1 rule="para" parents="3901 43"/>
    </justification>
  </clause>

  <clause id="3903">
    <literal><![CDATA[
      (x \ y) * (y / T(x \ y,y)) = ((y * (x \ y)) / y) * x
    ]]></literal>
    <justification jstring="[para(76(a,1),3901(a,1,2)),flip(a)].">
      <j1 rule="para" parents="76 3901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3904">
    <literal><![CDATA[
      ((x \ y) \ y) * (y / T(T(x,x \ y),y)) = ((y * ((x \ y) \ y)) / y) * (x \ y)
    ]]></literal>
    <justification jstring="[para(112(a,2),3903(a,1,2,2,1))].">
      <j1 rule="para" parents="112 3903"/>
    </justification>
  </clause>

  <clause id="3905">
    <literal><![CDATA[
      L(R(x,y,x),y,R(x,y,x)) = x
    ]]></literal>
    <justification jstring="[hyper(3888,a,3853,a),flip(a)].">
      <j1 rule="hyper" parents="3888 3853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3906">
    <literal><![CDATA[
      ((x \ y) \ y) * (y / T(T(x,x \ y),y)) = x \ (y * ((x \ y) \ y))
    ]]></literal>
    <justification jstring="[hyper(333,a,1744,a(flip),b,3904,a),flip(a)].">
      <j1 rule="hyper" parents="333 1744 3904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3907">
    <literal><![CDATA[
      ((x \ y) \ y) * (y / T(T(x,x \ y),y)) = x * (y / T(x,y))
    ]]></literal>
    <justification jstring="[hyper(333,a,3807,a(flip),b,3906,a),flip(a)].">
      <j1 rule="hyper" parents="333 3807 3906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3908">
    <literal><![CDATA[
      T(x,R(x * K(y,x),z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(269,a,3850,a),flip(a)].">
      <j1 rule="hyper" parents="269 3850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3912">
    <literal><![CDATA[
      (x \ T(x,(x \ 1) * y)) * y = y * K(((1 / x) * y) \ y,(x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(2861(a,1),3435(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2861 3435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3913">
    <literal><![CDATA[
      (x \ T(x,(x \ 1) * y)) * y = y * K(((x \ 1) * y) \ y,(x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(3535(a,1),3912(a,2,2))].">
      <j1 rule="para" parents="3535 3912"/>
    </justification>
  </clause>

  <clause id="3914">
    <literal><![CDATA[
      (((x \ 1) * y) \ y) * ((x \ 1) * y) = (x \ T(x,(x \ 1) * y)) * y
    ]]></literal>
    <justification jstring="[hyper(333,a,317,a(flip),b,3913,a)].">
      <j1 rule="hyper" parents="333 317 3913"/>
    </justification>
  </clause>

  <clause id="3915">
    <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(1513(a,1),3827(a,1,1))].">
      <j1 rule="para" parents="1513 3827"/>
    </justification>
  </clause>

  <clause id="3916">
    <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(1169(a,1),3915(a,1,2))].">
      <j1 rule="para" parents="1169 3915"/>
    </justification>
  </clause>

  <clause id="3917">
    <literal><![CDATA[
      a(x,T(y,x),R(T(x,y),z,u)) = a(R(x,z,u),y,x)
    ]]></literal>
    <justification jstring="[hyper(752,a,3916,a),flip(a)].">
      <j1 rule="hyper" parents="752 3916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3918">
    <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(2262(a,1),3483(a,1,1))].">
      <j1 rule="para" parents="2262 3483"/>
    </justification>
  </clause>

  <clause id="3919">
    <literal><![CDATA[
      ((x * ((y \ T(z,x)) * y)) / x) * (((x * y) / x) \ y) = (y \ (z * (T(x,y) \ x))) * y
    ]]></literal>
    <justification jstring="[para(111(a,1),3918(a,1,1,1,2))].">
      <j1 rule="para" parents="111 3918"/>
    </justification>
  </clause>

  <clause id="3920">
    <literal><![CDATA[
      ((x * ((y \ T(z,x)) * y)) / x) * (T(x,y) \ x) = (y \ (z * (T(x,y) \ x))) * y
    ]]></literal>
    <justification jstring="[para(3480(a,1),3919(a,1,2))].">
      <j1 rule="para" parents="3480 3919"/>
    </justification>
  </clause>

  <clause id="3921">
    <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(11(a,1),3418(a,1,1,1))].">
      <j1 rule="para" parents="11 3418"/>
    </justification>
  </clause>

  <clause id="3922">
    <literal><![CDATA[
      L(x,y,y \ 1) \ ((1 / y) * (x * y)) = T(y,(1 / y) * (x * y)) \ y
    ]]></literal>
    <justification jstring="[hyper(35,a,3481,a,b,3921,a),flip(a)].">
      <j1 rule="hyper" parents="35 3481 3921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3925">
    <literal><![CDATA[
      L(K(x,y),y * x,y \ 1) = T(y,(1 / y) * (x * y)) \ y
    ]]></literal>
    <justification jstring="[hyper(3152,a,3922,a)].">
      <j1 rule="hyper" parents="3152 3922"/>
    </justification>
  </clause>

  <clause id="3926">
    <literal><![CDATA[
      L(K(x,y),y * x,y \ 1) = T(y,(y \ 1) * (x * y)) \ y
    ]]></literal>
    <justification jstring="[para(2648(a,1),3925(a,2,1))].">
      <j1 rule="para" parents="2648 3925"/>
    </justification>
  </clause>

  <clause id="3927">
    <literal><![CDATA[
      T(x,(x \ 1) * (y * x)) \ x = (y * x) / (x * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3123,a(flip),b,3926,a),flip(a)].">
      <j1 rule="hyper" parents="63 3123 3926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3928">
    <literal><![CDATA[
      T(x,(x \ 1) * (y * x)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(3585,a,3927,a),flip(a)].">
      <j1 rule="hyper" parents="3585 3927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3929">
    <literal><![CDATA[
      T(x,T((x \ 1) * y,x)) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(1714(a,1),3928(a,1,2))].">
      <j1 rule="para" parents="1714 3928"/>
    </justification>
  </clause>

  <clause id="3930">
    <literal><![CDATA[
      T(x,(x \ 1) * y) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(3706,a,3929,a)].">
      <j1 rule="hyper" parents="3706 3929"/>
    </justification>
  </clause>

  <clause id="3931">
    <literal><![CDATA[
      T(x,(1 / x) * y) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3169,a,b,3930,a)].">
      <j1 rule="hyper" parents="63 3169 3930"/>
    </justification>
  </clause>

  <clause id="3932">
    <literal><![CDATA[
      (((x \ 1) * y) \ y) * ((x \ 1) * y) = (x \ T(x,x \ y)) * y
    ]]></literal>
    <justification jstring="[para(3930(a,1),3914(a,2,1,2))].">
      <j1 rule="para" parents="3930 3914"/>
    </justification>
  </clause>

  <clause id="3933">
    <literal><![CDATA[
      x / T(y,(1 / y) * x) = y \ x
    ]]></literal>
    <justification jstring="[hyper(197,a,3931,a,b,112,a(flip))].">
      <j1 rule="hyper" parents="197 3931 112"/>
    </justification>
  </clause>

  <clause id="3934">
    <literal><![CDATA[
      x / T(y \ 1,y * x) = (y \ 1) \ x
    ]]></literal>
    <justification jstring="[para(76(a,1),3933(a,1,2,2,1))].">
      <j1 rule="para" parents="76 3933"/>
    </justification>
  </clause>

  <clause id="3935">
    <literal><![CDATA[
      T(x \ 1,x * y) = ((x \ 1) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(192,a,3934,a),flip(a)].">
      <j1 rule="hyper" parents="192 3934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3936">
    <literal><![CDATA[
      (x \ y) / T(x \ 1,y) = (x \ 1) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),3934(a,1,2,2))].">
      <j1 rule="para" parents="10 3934"/>
    </justification>
  </clause>

  <clause id="3937">
    <literal><![CDATA[
      T((x / y) \ 1,x) = (((x / y) \ 1) \ y) \ y
    ]]></literal>
    <justification jstring="[para(12(a,1),3935(a,1,2))].">
      <j1 rule="para" parents="12 3935"/>
    </justification>
  </clause>

  <clause id="3938">
    <literal><![CDATA[
      ((x \ 1) \ y) \ (y * R(y \ ((x \ 1) \ y),z,u)) = T(x \ 1,x * y) * R((((x \ 1) \ y) \ y) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(3935(a,2),1538(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3935 1538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3939">
    <literal><![CDATA[
      (((x \ 1) * y) \ y) * ((x \ 1) * y) = x * (y / x)
    ]]></literal>
    <justification jstring="[hyper(333,a,3414,a(flip),b,3932,a),flip(a)].">
      <j1 rule="hyper" parents="333 3414 3932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3942">
    <literal><![CDATA[
      x * (T(((x * y) \ x) \ 1,x) \ (((x * y) \ x) \ 1)) = x / K(y,x)
    ]]></literal>
    <justification jstring="[para(3336(a,1),3473(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3336 3473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3943">
    <literal><![CDATA[
      x * (((x * y) \ (x * T(x \ (x * y),x))) \ 1) = x / K(y,x)
    ]]></literal>
    <justification jstring="[para(3470(a,1),3942(a,1,2))].">
      <j1 rule="para" parents="3470 3942"/>
    </justification>
  </clause>

  <clause id="3944">
    <literal><![CDATA[
      x * (((x * y) \ (x * T(y,x))) \ 1) = x / K(y,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),3943(a,1,2,1,2,2,1))].">
      <j1 rule="para" parents="9 3943"/>
    </justification>
  </clause>

  <clause id="3945">
    <literal><![CDATA[
      x * (((x * y) \ (y * x)) \ 1) = x / K(y,x)
    ]]></literal>
    <justification jstring="[para(111(a,1),3944(a,1,2,1,2))].">
      <j1 rule="para" parents="111 3944"/>
    </justification>
  </clause>

  <clause id="3946">
    <literal><![CDATA[
      x * (K(y,x) \ 1) = x / K(y,x)
    ]]></literal>
    <justification jstring="[para(16(a,2),3945(a,1,2,1))].">
      <j1 rule="para" parents="16 3945"/>
    </justification>
  </clause>

  <clause id="3947">
    <literal><![CDATA[
      (K(x,y) \ y) / (K(x,y) \ 1) = y
    ]]></literal>
    <justification jstring="[hyper(123,a,2773,a(flip),b,3946,a)].">
      <j1 rule="hyper" parents="123 2773 3946"/>
    </justification>
  </clause>

  <clause id="3948">
    <literal><![CDATA[
      K(x,y) \ y != y * z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) \ 1 = z
    ]]></literal>
    <justification jstring="[para(3947(a,1),131(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3947 131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3949">
    <literal><![CDATA[
      K(x \ y,x) \ 1 = K(x,y / x)
    ]]></literal>
    <justification jstring="[hyper(3948,a,3789,a)].">
      <j1 rule="hyper" parents="3948 3789"/>
    </justification>
  </clause>

  <clause id="3950">
    <literal><![CDATA[
      K(x,(x * y) / x) = K(y,x) \ 1
    ]]></literal>
    <justification jstring="[para(9(a,1),3949(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 3949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3951">
    <literal><![CDATA[
      K(T(x,y),y) = K(y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,3431,a,b,3950,a)].">
      <j1 rule="hyper" parents="63 3431 3950"/>
    </justification>
  </clause>

  <clause id="3953">
    <literal><![CDATA[
      K(T(x,y),y) * K(y,x) = 1
    ]]></literal>
    <justification jstring="[hyper(126,a,3430,a(flip),b,3951,a(flip))].">
      <j1 rule="hyper" parents="126 3430 3951"/>
    </justification>
  </clause>

  <clause id="3954">
    <literal><![CDATA[
      (K(x,y) \ 1) * (K(T(y,x),x) \ z) = z
    ]]></literal>
    <justification jstring="[hyper(125,a,3951,a(flip),b,76,a)].">
      <j1 rule="hyper" parents="125 3951 76"/>
    </justification>
  </clause>

  <clause id="3955">
    <literal><![CDATA[
      K(T(x,y),y) * z != 1
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(3953(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="3953 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3956">
    <literal><![CDATA[
      K(T(x,y),y) \ 1 != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(3953(a,1),342(a,1,2))].">
      <j1 rule="para" parents="3953 342"/>
    </justification>
  </clause>

  <clause id="3957">
    <literal><![CDATA[
      K(T(x,y),y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) \ 1 = z
    ]]></literal>
    <justification jstring="[para(3954(a,1),209(a,1))].">
      <j1 rule="para" parents="3954 209"/>
    </justification>
  </clause>

  <clause id="3958">
    <literal><![CDATA[
      T(x \ 1,x) \ R(y,T(x,x \ 1),T(x,x \ 1) \ 1) = T(((x \ 1) \ 1) * T(y,x),T(x,x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(1205(a,1),2996(a,1,1))].">
      <j1 rule="para" parents="1205 2996"/>
    </justification>
  </clause>

  <clause id="3959">
    <literal><![CDATA[
      T(x \ 1,x) \ R(y,T(x,x \ 1),T(x \ 1,x)) = T(((x \ 1) \ 1) * T(y,x),T(x,x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(1205(a,1),3958(a,1,2,3))].">
      <j1 rule="para" parents="1205 3958"/>
    </justification>
  </clause>

  <clause id="3960">
    <literal><![CDATA[
      T(((x \ 1) \ 1) * T(y,x),T(x,x \ 1) \ 1) = T(x \ 1,x) \ R(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[para(1958(a,1),3959(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1958 3959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3961">
    <literal><![CDATA[
      T(x * T(y,y \ 1),T(y,y \ 1) \ 1) = T(y \ 1,y) \ R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(2994(a,1),3960(a,1,1))].">
      <j1 rule="para" parents="2994 3960"/>
    </justification>
  </clause>

  <clause id="3962">
    <literal><![CDATA[
      T(x \ 1,x) \ R(T(x,y) \ 1,x,x \ 1) = T(T(x,y) \ x,T(x,x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(3476(a,1),3960(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3476 3960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3963">
    <literal><![CDATA[
      T(x \ 1,x) \ R(y,x,x \ 1) = T(y * T(x,x \ 1),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,3184,a(flip),b,3961,a),flip(a)].">
      <j1 rule="hyper" parents="63 3184 3961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3965">
    <literal><![CDATA[
      T(x \ 1,x) \ R(y,x,x \ 1) = R((x \ 1) \ y,1 / x,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,3000,a(flip),b,3963,a),flip(a)].">
      <j1 rule="hyper" parents="333 3000 3963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3966">
    <literal><![CDATA[
      T(x \ 1,x) \ R(y,x,x \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      R((x \ 1) \ y,x \ 1,x) = z
    ]]></literal>
    <justification jstring="[para(3965(a,2),1946(a,1))].">
      <j1 rule="para" parents="3965 1946"/>
    </justification>
  </clause>

  <clause id="3967">
    <literal><![CDATA[
      R((x \ 1) \ (T(x,y) \ 1),x \ 1,x) = T(T(x,y) \ x,T(x,x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(3966,a,3962,a)].">
      <j1 rule="hyper" parents="3966 3962"/>
    </justification>
  </clause>

  <clause id="3968">
    <literal><![CDATA[
      R((x \ 1) \ (T(x,y) \ 1),x \ 1,x) = T(T(x,y) \ x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(333,a,3184,a(flip),b,3967,a),flip(a)].">
      <j1 rule="hyper" parents="333 3184 3967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3969">
    <literal><![CDATA[
      R((x \ 1) \ (T(x,y) \ 1),x \ 1,x) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(333,a,2771,a(flip),b,3968,a),flip(a)].">
      <j1 rule="hyper" parents="333 2771 3968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3970">
    <literal><![CDATA[
      R(T(x,y) \ x,x \ 1,x) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[para(3299(a,1),3969(a,1,1))].">
      <j1 rule="para" parents="3299 3969"/>
    </justification>
  </clause>

  <clause id="3971">
    <literal><![CDATA[
      L(T(x,y) \ x,x \ 1,x) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,3572,a(flip),b,3970,a)].">
      <j1 rule="hyper" parents="63 3572 3970"/>
    </justification>
  </clause>

  <clause id="3972">
    <literal><![CDATA[
      L(T(x,y) \ x,T(x,y),y) = L((x * y) \ (y * x),x \ 1,x)
    ]]></literal>
    <justification jstring="[para(3971(a,1),945(a,1,1))].">
      <j1 rule="para" parents="3971 945"/>
    </justification>
  </clause>

  <clause id="3973">
    <literal><![CDATA[
      L((x * y) \ (y * x),x \ 1,x) = (x * y) \ (y * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,520,a(flip),b,3972,a),flip(a)].">
      <j1 rule="hyper" parents="63 520 3972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3974">
    <literal><![CDATA[
      K(x,y) = L((y * x) \ (x * y),y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,16,a,b,3973,a)].">
      <j1 rule="hyper" parents="333 16 3973"/>
    </justification>
  </clause>

  <clause id="3975">
    <literal><![CDATA[
      L(K(x,y),y \ 1,y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(16(a,2),3974(a,2,1)),flip(a)].">
      <j1 rule="para" parents="16 3974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3976">
    <literal><![CDATA[
      (x \ 1) * K(y,x) = x \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(121,a,3975,a(flip),b,275,a),flip(a)].">
      <j1 rule="hyper" parents="121 3975 275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3977">
    <literal><![CDATA[
      ((x * (y \ 1)) * K(z,y)) / (y \ K(z,y)) = R(x,y \ 1,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(197,a,3976,a(flip),b,187,a)].">
      <j1 rule="hyper" parents="197 3976 187"/>
    </justification>
  </clause>

  <clause id="3978">
    <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(79(a,1),3049(a,1,1,3))].">
      <j1 rule="para" parents="79 3049"/>
    </justification>
  </clause>

  <clause id="3979">
    <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(1937(a,1),3978(a,1,1))].">
      <j1 rule="para" parents="1937 3978"/>
    </justification>
  </clause>

  <clause id="3980">
    <literal><![CDATA[
      (x * K(y \ (1 / (1 / x)),y)) * (x \ 1) = ((y \ (1 * x)) * y) / ((1 / x) \ 1)
    ]]></literal>
    <justification jstring="[para(3018(a,1),3979(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3018 3979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3981">
    <literal><![CDATA[
      (x * K(y \ (1 / (1 / x)),y)) * (x \ 1) = ((y \ x) * y) / ((1 / x) \ 1)
    ]]></literal>
    <justification jstring="[para(7(a,1),3980(a,2,1,1,2))].">
      <j1 rule="para" parents="7 3980"/>
    </justification>
  </clause>

  <clause id="3982">
    <literal><![CDATA[
      (x * K(y \ (1 / (1 / x)),y)) * (x \ 1) = ((y \ x) * y) / x
    ]]></literal>
    <justification jstring="[para(79(a,1),3981(a,2,2))].">
      <j1 rule="para" parents="79 3981"/>
    </justification>
  </clause>

  <clause id="3983">
    <literal><![CDATA[
      ((x \ y) * x) * (y \ 1) = ((x \ y) * x) / y
    ]]></literal>
    <justification jstring="[para(3007(a,1),3982(a,1,1))].">
      <j1 rule="para" parents="3007 3982"/>
    </justification>
  </clause>

  <clause id="3984">
    <literal><![CDATA[
      ((x \ y) * x) / y != ((x \ y) * x) * z
    ]]></literal>
    <literal><![CDATA[
      y \ 1 = z
    ]]></literal>
    <justification jstring="[para(3983(a,1),43(a,1))].">
      <j1 rule="para" parents="3983 43"/>
    </justification>
  </clause>

  <clause id="3985">
    <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(79(a,1),3602(a,1,1,2))].">
      <j1 rule="para" parents="79 3602"/>
    </justification>
  </clause>

  <clause id="3986">
    <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(25(a,2),3985(a,1,1))].">
      <j1 rule="para" parents="25 3985"/>
    </justification>
  </clause>

  <clause id="3987">
    <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(2654(a,1),3986(a,1,1))].">
      <j1 rule="para" parents="2654 3986"/>
    </justification>
  </clause>

  <clause id="3988">
    <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(79(a,1),3987(a,1,2,2,2))].">
      <j1 rule="para" parents="79 3987"/>
    </justification>
  </clause>

  <clause id="3989">
    <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(25(a,2),3988(a,1,2,2))].">
      <j1 rule="para" parents="25 3988"/>
    </justification>
  </clause>

  <clause id="3990">
    <literal><![CDATA[
      ((1 / x) * (y * x)) \ ((1 / x) \ ((1 / x) * (y * x))) = L(y,x,x \ 1) \ (x * y)
    ]]></literal>
    <justification jstring="[para(2654(a,1),3989(a,1,2,2))].">
      <j1 rule="para" parents="2654 3989"/>
    </justification>
  </clause>

  <clause id="3991">
    <literal><![CDATA[
      ((1 / x) * (y * x)) \ (y * x) = L(y,x,x \ 1) \ (x * y)
    ]]></literal>
    <justification jstring="[para(9(a,1),3990(a,1,2))].">
      <j1 rule="para" parents="9 3990"/>
    </justification>
  </clause>

  <clause id="3993">
    <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(18(a,2),1642(a,1,2,2,2))].">
      <j1 rule="para" parents="18 1642"/>
    </justification>
  </clause>

  <clause id="3994">
    <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(18(a,2),3993(a,2,2))].">
      <j1 rule="para" parents="18 3993"/>
    </justification>
  </clause>

  <clause id="3995">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * z) = T(a(x,y,z),L(z,y,x))
    ]]></literal>
    <justification jstring="[para(2550(a,1),3994(a,1,2,2))].">
      <j1 rule="para" parents="2550 3994"/>
    </justification>
  </clause>

  <clause id="3996">
    <literal><![CDATA[
      T(a(x,y,z),L(z,y,x)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(752,a,3995,a),flip(a)].">
      <j1 rule="hyper" parents="752 3995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3997">
    <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(1205(a,1),2321(a,1,1,2,1))].">
      <j1 rule="para" parents="1205 2321"/>
    </justification>
  </clause>

  <clause id="3998">
    <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(1354(a,1),3997(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1354 3997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4000">
    <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(2995(a,1),3998(a,2,1))].">
      <j1 rule="para" parents="2995 3998"/>
    </justification>
  </clause>

  <clause id="4001">
    <literal><![CDATA[
      K((x \ R(x,y,z)) \ (x \ 1),x \ R(x,y,z)) = R(1,y,z)
    ]]></literal>
    <justification jstring="[para(234(a,1),4000(a,2,1))].">
      <j1 rule="para" parents="234 4000"/>
    </justification>
  </clause>

  <clause id="4002">
    <literal><![CDATA[
      K((x \ R(x,y,z)) \ (x \ 1),x \ R(x,y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(333,a,382,a(flip),b,4001,a),flip(a)].">
      <j1 rule="hyper" parents="333 382 4001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4005">
    <literal><![CDATA[
      ((x \ R(x,y,z)) \ (x \ 1)) * (x \ R(x,y,z)) = (x \ 1) * 1
    ]]></literal>
    <justification jstring="[hyper(126,a,4002,a(flip),b,89,a),flip(a)].">
      <j1 rule="hyper" parents="126 4002 89"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4006">
    <literal><![CDATA[
      (x \ 1) / (x \ R(x,y,z)) = (x \ R(x,y,z)) \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(123,a,8,a(flip),b,4005,a)].">
      <j1 rule="hyper" parents="123 8 4005"/>
    </justification>
  </clause>

  <clause id="4007">
    <literal><![CDATA[
      (x \ (x \ 1)) * ((y * (z * ((x \ 1) \ 1))) * K(x \ 1,x)) = T(y * (z * (x \ 1)),(x \ 1) \ ((x \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(820(a,1),2924(a,1,1))].">
      <j1 rule="para" parents="820 2924"/>
    </justification>
  </clause>

  <clause id="4008">
    <literal><![CDATA[
      (x \ (x \ 1)) * (y * ((z * ((x \ 1) \ 1)) * K(x \ 1,x))) = T(y * (z * (x \ 1)),(x \ 1) \ ((x \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(1879(a,1),4007(a,1,2))].">
      <j1 rule="para" parents="1879 4007"/>
    </justification>
  </clause>

  <clause id="4009">
    <literal><![CDATA[
      T(x * (y * (z \ 1)),(z \ 1) \ ((z \ 1) \ 1)) = (z \ (z \ 1)) * (x * (y * z))
    ]]></literal>
    <justification jstring="[para(1896(a,1),4008(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1896 4008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4010">
    <literal><![CDATA[
      T(x * (y * (z \ 1)),(z \ 1) \ ((z \ 1) \ 1)) = (z * z) \ (x * (y * z))
    ]]></literal>
    <justification jstring="[hyper(333,a,728,a(flip),b,4009,a),flip(a)].">
      <j1 rule="hyper" parents="333 728 4009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4011">
    <literal><![CDATA[
      (x * y) \ ((x * (y * z)) * R((x * (y * z)) \ (x * y),u,w)) = L(z,y,x) * R(L(z,y,x) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(18(a,2),1539(a,2,2,1,1))].">
      <j1 rule="para" parents="18 1539"/>
    </justification>
  </clause>

  <clause id="4012">
    <literal><![CDATA[
      (x * y) \ (x * ((y * z) * R((y * z) \ y,u,w))) = L(z,y,x) * R(L(z,y,x) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(1027(a,1),4011(a,1,2))].">
      <j1 rule="para" parents="1027 4011"/>
    </justification>
  </clause>

  <clause id="4013">
    <literal><![CDATA[
      (x * y) \ (x * (y * (z * R(z \ 1,u,w)))) = L(z,y,x) * R(L(z,y,x) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(1026(a,1),4012(a,1,2,2))].">
      <j1 rule="para" parents="1026 4012"/>
    </justification>
  </clause>

  <clause id="4014">
    <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(504,a,4013,a),flip(a)].">
      <j1 rule="hyper" parents="504 4013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4016">
    <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(63,a,1265,a(flip),b,4014,a),flip(a)].">
      <j1 rule="hyper" parents="63 1265 4014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4017">
    <literal><![CDATA[
      L(x,y,z) * R(L(x,y,z) \ 1,x,x \ 1) = L(T((x \ 1) * x,x \ 1),y,z)
    ]]></literal>
    <justification jstring="[para(3744(a,1),4014(a,2,1))].">
      <j1 rule="para" parents="3744 4014"/>
    </justification>
  </clause>

  <clause id="4018">
    <literal><![CDATA[
      L(T((x \ 1) * x,x \ 1),y,z) = a(1 / L(x,y,z),x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(1327,a,4017,a),flip(a)].">
      <j1 rule="hyper" parents="1327 4017"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4019">
    <literal><![CDATA[
      a(1 / L(x,y,z),x,x \ 1) = L(K(x \ 1,x),y,z)
    ]]></literal>
    <justification jstring="[para(2419(a,1),4018(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2419 4018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4020">
    <literal><![CDATA[
      L(K(x \ 1,x),y,z) / R(L(x,y,z) \ 1,x,x \ 1) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(123,a,4019,a(flip),b,1324,a)].">
      <j1 rule="hyper" parents="123 4019 1324"/>
    </justification>
  </clause>

  <clause id="4022">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,x) / R(L(x,y,z) \ 1,x,x \ 1) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(2421(a,1),4020(a,1,1))].">
      <j1 rule="para" parents="2421 4020"/>
    </justification>
  </clause>

  <clause id="4023">
    <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(1611(a,1),4016(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1611 4016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4024">
    <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(333,a,2328,a(flip),b,4023,a),flip(a)].">
      <j1 rule="hyper" parents="333 2328 4023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4025">
    <literal><![CDATA[
      (x \ 1) / (x \ L(x,y,z)) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(35,a,276,a(flip),b,4024,a),flip(a)].">
      <j1 rule="hyper" parents="35 276 4024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4026">
    <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(18(a,2),1542(a,2,2,1,1))].">
      <j1 rule="para" parents="18 1542"/>
    </justification>
  </clause>

  <clause id="4027">
    <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(1024(a,1),4026(a,1,2))].">
      <j1 rule="para" parents="1024 4026"/>
    </justification>
  </clause>

  <clause id="4028">
    <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(9(a,1),4027(a,1,2,2,2,1,2))].">
      <j1 rule="para" parents="9 4027"/>
    </justification>
  </clause>

  <clause id="4029">
    <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(929(a,1),4028(a,1,2,2))].">
      <j1 rule="para" parents="929 4028"/>
    </justification>
  </clause>

  <clause id="4030">
    <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(504,a,4029,a),flip(a)].">
      <j1 rule="hyper" parents="504 4029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4031">
    <literal><![CDATA[
      (x * y) \ (x * (y * (z * L(z \ 1,u,w)))) = L(z,y,x) \ L(L(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(333,a,2582,a(flip),b,4029,a),flip(a)].">
      <j1 rule="hyper" parents="333 2582 4029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4032">
    <literal><![CDATA[
      (x * y) \ (x * (y * (z \ L(z,u,w)))) = L(z,y,x) \ L(L(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[para(2582(a,1),4031(a,1,2,2,2))].">
      <j1 rule="para" parents="2582 4031"/>
    </justification>
  </clause>

  <clause id="4033">
    <literal><![CDATA[
      L(x,y,z) \ L(L(x,y,z),u,w) = L(x \ L(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(504,a,4032,a),flip(a)].">
      <j1 rule="hyper" parents="504 4032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4034">
    <literal><![CDATA[
      L(x,y,z) \ L(L(x,y,z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x \ L(x,u,w),y,z) = v5
    ]]></literal>
    <justification jstring="[para(4032(a,1),504(a,1))].">
      <j1 rule="para" parents="4032 504"/>
    </justification>
  </clause>

  <clause id="4035">
    <literal><![CDATA[
      L(L(x,y,z),u,w) \ L(x,y,z) = L(x \ L(x,u,w),y,z) \ 1
    ]]></literal>
    <justification jstring="[para(4033(a,1),3257(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4033 3257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4036">
    <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(20(a,2),1547(a,2,2,1,1))].">
      <j1 rule="para" parents="20 1547"/>
    </justification>
  </clause>

  <clause id="4037">
    <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(1553(a,1),4036(a,1,1))].">
      <j1 rule="para" parents="1553 4036"/>
    </justification>
  </clause>

  <clause id="4038">
    <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(1338(a,1),4037(a,1,1,1))].">
      <j1 rule="para" parents="1338 4037"/>
    </justification>
  </clause>

  <clause id="4039">
    <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(544,a,4038,a),flip(a)].">
      <j1 rule="hyper" parents="544 4038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4040">
    <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(63,a,1319,a(flip),b,4039,a),flip(a)].">
      <j1 rule="hyper" parents="63 1319 4039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4041">
    <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(691(a,1),4039(a,2,1,2))].">
      <j1 rule="para" parents="691 4039"/>
    </justification>
  </clause>

  <clause id="4042">
    <literal><![CDATA[
      R(x * T(1 * (x \ 1),x),y,z) = a(1 / R(x,y,z),x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(1327,a,4041,a),flip(a)].">
      <j1 rule="hyper" parents="1327 4041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4043">
    <literal><![CDATA[
      a(1 / R(x,y,z),x,x \ 1) = R(x * T(x \ 1,x),y,z)
    ]]></literal>
    <justification jstring="[para(7(a,1),4042(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7 4042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4044">
    <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(1356(a,1),4040(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1356 4040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4045">
    <literal><![CDATA[
      (x \ 1) / (x \ R(x,y,z)) = R(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(2322,a,4044,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="2322 4044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4046">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ (x \ 1) = R(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,4006,a(flip),b,4045,a)].">
      <j1 rule="hyper" parents="63 4006 4045"/>
    </justification>
  </clause>

  <clause id="4047">
    <literal><![CDATA[
      (x \ 1) \ (R(x,y,z) \ 1) = (x \ R(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[hyper(121,a,4046,a(flip),b,2264,a)].">
      <j1 rule="hyper" parents="121 4046 2264"/>
    </justification>
  </clause>

  <clause id="4051">
    <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(107(a,1),1643(a,1,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="107 1643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4052">
    <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(333,a,906,a(flip),b,4051,a),flip(a)].">
      <j1 rule="hyper" parents="333 906 4051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4053">
    <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(333,a,1979,a(flip),b,4052,a),flip(a)].">
      <j1 rule="hyper" parents="333 1979 4052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4054">
    <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(906(a,1),4053(a,1,1))].">
      <j1 rule="para" parents="906 4053"/>
    </justification>
  </clause>

  <clause id="4055">
    <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(1990(a,1),4054(a,2,1))].">
      <j1 rule="para" parents="1990 4054"/>
    </justification>
  </clause>

  <clause id="4056">
    <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(35,a,107,a,b,4055,a),flip(a)].">
      <j1 rule="hyper" parents="35 107 4055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4057">
    <literal><![CDATA[
      R(x * ((y * (x \ 1)) / y),z,u) = K(y,(y / R(x,z,u)) / y)
    ]]></literal>
    <justification jstring="[hyper(1561,a,4056,a),flip(a)].">
      <j1 rule="hyper" parents="1561 4056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4058">
    <literal><![CDATA[
      R(x \ T(x,y \ 1),z,u) = K(x,(x / R(y,z,u)) / x)
    ]]></literal>
    <justification jstring="[para(3071(a,1),4057(a,1,1))].">
      <j1 rule="para" parents="3071 4057"/>
    </justification>
  </clause>

  <clause id="4059">
    <literal><![CDATA[
      R(x \ T(x,y \ 1),z,u) = x \ T(x,R(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(333,a,3082,a(flip),b,4058,a),flip(a)].">
      <j1 rule="hyper" parents="333 3082 4058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4060">
    <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(333,a,3428,a,b,4059,a)].">
      <j1 rule="hyper" parents="333 3428 4059"/>
    </justification>
  </clause>

  <clause id="4061">
    <literal><![CDATA[
      T(x \ T(x,(y / (z * y)) \ 1),T(z,u)) = R(x \ T(x,z),z,y)
    ]]></literal>
    <justification jstring="[para(2983(a,1),4060(a,2,1,2))].">
      <j1 rule="para" parents="2983 4060"/>
    </justification>
  </clause>

  <clause id="4062">
    <literal><![CDATA[
      T(x \ T(x,(y * z) / z),T(y,u)) = R(x \ T(x,y),y,z)
    ]]></literal>
    <justification jstring="[para(3760(a,1),4061(a,1,1,2))].">
      <j1 rule="para" parents="3760 4061"/>
    </justification>
  </clause>

  <clause id="4063">
    <literal><![CDATA[
      T(x \ T(x,y),T(y,z)) = R(x \ T(x,y),y,u)
    ]]></literal>
    <justification jstring="[para(11(a,1),4062(a,1,1,2,2))].">
      <j1 rule="para" parents="11 4062"/>
    </justification>
  </clause>

  <clause id="4064">
    <literal><![CDATA[
      R(x \ T(x,y),y,z) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,2750,a(flip),b,4063,a),flip(a)].">
      <j1 rule="hyper" parents="63 2750 4063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4065">
    <literal><![CDATA[
      (x \ T(x,y)) \ (((x * y) / x) * z) = y * z
    ]]></literal>
    <justification jstring="[para(4064(a,1),3070(a,1,1))].">
      <j1 rule="para" parents="4064 3070"/>
    </justification>
  </clause>

  <clause id="4066">
    <literal><![CDATA[
      (x \ T(x,y)) \ z = (T(x,y) \ x) * z
    ]]></literal>
    <justification jstring="[para(4064(a,1),3587(a,1,1))].">
      <j1 rule="para" parents="4064 3587"/>
    </justification>
  </clause>

  <clause id="4067">
    <literal><![CDATA[
      (T(x,y) \ x) * z != u
    ]]></literal>
    <literal><![CDATA[
      x * (T(x,y) \ z) = u
    ]]></literal>
    <justification jstring="[para(4066(a,1),3457(a,1))].">
      <j1 rule="para" parents="4066 3457"/>
    </justification>
  </clause>

  <clause id="4069">
    <literal><![CDATA[
      L(x,y \ 1,(z * y) / z) = y * ((y \ 1) * x)
    ]]></literal>
    <justification jstring="[hyper(3077,a,4065,a)].">
      <j1 rule="hyper" parents="3077 4065"/>
    </justification>
  </clause>

  <clause id="4070">
    <literal><![CDATA[
      (x \ T(x,x \ y)) \ y = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(81(a,1),4065(a,1,2))].">
      <j1 rule="para" parents="81 4065"/>
    </justification>
  </clause>

  <clause id="4072">
    <literal><![CDATA[
      (x \ ((x \ y) \ y)) \ y = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(112(a,1),4070(a,1,1,2))].">
      <j1 rule="para" parents="112 4070"/>
    </justification>
  </clause>

  <clause id="4073">
    <literal><![CDATA[
      x / ((y \ x) * y) = y \ ((y \ x) \ x)
    ]]></literal>
    <justification jstring="[hyper(198,a,4072,a)].">
      <j1 rule="hyper" parents="198 4072"/>
    </justification>
  </clause>

  <clause id="4074">
    <literal><![CDATA[
      (x * (y / x)) / y = y / ((x \ y) * x)
    ]]></literal>
    <justification jstring="[hyper(333,a,3589,a,b,4073,a)].">
      <j1 rule="hyper" parents="333 3589 4073"/>
    </justification>
  </clause>

  <clause id="4075">
    <literal><![CDATA[
      x * (T(x,(y / z) / (1 / z)) \ (y / z)) = T(y,x) / z
    ]]></literal>
    <justification jstring="[hyper(4067,a,3863,a)].">
      <j1 rule="hyper" parents="4067 3863"/>
    </justification>
  </clause>

  <clause id="4076">
    <literal><![CDATA[
      x * T(x \ y,z) = z * (T(z,y / x) \ y)
    ]]></literal>
    <justification jstring="[hyper(4067,a,3612,a),flip(a)].">
      <j1 rule="hyper" parents="4067 3612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4077">
    <literal><![CDATA[
      x * (T(x,y / (z \ 1)) \ y) != u
    ]]></literal>
    <literal><![CDATA[
      z \ T(z * y,x) = u
    ]]></literal>
    <justification jstring="[para(4076(a,1),1017(a,1))].">
      <j1 rule="para" parents="4076 1017"/>
    </justification>
  </clause>

  <clause id="4078">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ 1) * z) = L(z,T(x,y) \ 1,x)
    ]]></literal>
    <justification jstring="[para(239(a,1),4069(a,1,3)),flip(a)].">
      <j1 rule="para" parents="239 4069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4079">
    <literal><![CDATA[
      L(x,T(y,z) \ 1,T(y,z)) = L(x,T(y,z) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(505,a,4078,a)].">
      <j1 rule="hyper" parents="505 4078"/>
    </justification>
  </clause>

  <clause id="4080">
    <literal><![CDATA[
      L(x,1 / T(y,y \ z),(y \ z) \ z) = L(x,T(y,y \ z) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,2621,a(flip),b,4079,a)].">
      <j1 rule="hyper" parents="63 2621 4079"/>
    </justification>
  </clause>

  <clause id="4081">
    <literal><![CDATA[
      x * (T(x,(y / z) / (z \ 1)) \ (y / z)) = T(y,x) / z
    ]]></literal>
    <justification jstring="[para(3174(a,1),4075(a,1,2,1))].">
      <j1 rule="para" parents="3174 4075"/>
    </justification>
  </clause>

  <clause id="4082">
    <literal><![CDATA[
      x \ T(x * (y / x),z) = T(y,z) / x
    ]]></literal>
    <justification jstring="[hyper(4077,a,4081,a)].">
      <j1 rule="hyper" parents="4077 4081"/>
    </justification>
  </clause>

  <clause id="4083">
    <literal><![CDATA[
      T(x * (y / x),z) = x * (T(y,z) / x)
    ]]></literal>
    <justification jstring="[hyper(142,a,4082,a),flip(a)].">
      <j1 rule="hyper" parents="142 4082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4084">
    <literal><![CDATA[
      (x \ T(x * (y / x),z)) * x = T(y,z)
    ]]></literal>
    <justification jstring="[hyper(125,a,4082,a,b,xx)].">
      <j1 rule="hyper" parents="125 4082"/>
    </justification>
  </clause>

  <clause id="4085">
    <literal><![CDATA[
      T(x * y,z) / y = y \ T(y * x,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),4082(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="11 4082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4086">
    <literal><![CDATA[
      (x \ y) \ T((x \ y) * x,z) = T(y,z) / (x \ y)
    ]]></literal>
    <justification jstring="[para(76(a,1),4082(a,1,2,1,2))].">
      <j1 rule="para" parents="76 4082"/>
    </justification>
  </clause>

  <clause id="4087">
    <literal><![CDATA[
      T((x \ y) * x,z) / x = x \ T(y,z)
    ]]></literal>
    <justification jstring="[para(75(a,1),4082(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="75 4082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4088">
    <literal><![CDATA[
      x * (y * (T(z,x) / y)) = (y * (z / y)) * x
    ]]></literal>
    <justification jstring="[para(4082(a,1),241(a,1,2,2))].">
      <j1 rule="para" parents="4082 241"/>
    </justification>
  </clause>

  <clause id="4092">
    <literal><![CDATA[
      x * (T(y * x,z) / x) = T(x * y,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),4083(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="11 4083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4093">
    <literal><![CDATA[
      T(x * (y / x),z) != x * u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) / x = u
    ]]></literal>
    <justification jstring="[para(4083(a,2),43(a,1))].">
      <j1 rule="para" parents="4083 43"/>
    </justification>
  </clause>

  <clause id="4094">
    <literal><![CDATA[
      T(x * (y / x),y) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(110(a,1),4083(a,2,2,1))].">
      <j1 rule="para" parents="110 4083"/>
    </justification>
  </clause>

  <clause id="4095">
    <literal><![CDATA[
      T(x * ((y / z) / x),z) = x * ((z \ y) / x)
    ]]></literal>
    <justification jstring="[para(113(a,1),4083(a,2,2,1))].">
      <j1 rule="para" parents="113 4083"/>
    </justification>
  </clause>

  <clause id="4098">
    <literal><![CDATA[
      T(x * (y / x),K(z,y)) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(2716(a,1),4083(a,2,2,1))].">
      <j1 rule="para" parents="2716 4083"/>
    </justification>
  </clause>

  <clause id="4099">
    <literal><![CDATA[
      T(x,y * (x / y)) = x
    ]]></literal>
    <justification jstring="[hyper(54,a,4094,a)].">
      <j1 rule="hyper" parents="54 4094"/>
    </justification>
  </clause>

  <clause id="4100">
    <literal><![CDATA[
      T(x * (y / x),y) / y = y / ((x \ y) * x)
    ]]></literal>
    <justification jstring="[para(4094(a,2),4074(a,1,1))].">
      <j1 rule="para" parents="4094 4074"/>
    </justification>
  </clause>

  <clause id="4102">
    <literal><![CDATA[
      T((x \ y) * x,y) = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(75(a,1),4099(a,1,2))].">
      <j1 rule="para" parents="75 4099"/>
    </justification>
  </clause>

  <clause id="4103">
    <literal><![CDATA[
      K(x \ 1,x) * T(K(x,x \ 1) * y,z) = T(y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,2462,a,b,4084,a)].">
      <j1 rule="hyper" parents="63 2462 4084"/>
    </justification>
  </clause>

  <clause id="4104">
    <literal><![CDATA[
      (x \ T(x * y,z)) * x = T(y * x,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),4084(a,1,1,2,1,2))].">
      <j1 rule="para" parents="11 4084"/>
    </justification>
  </clause>

  <clause id="4105">
    <literal><![CDATA[
      T((x \ y) * x,z) = (x \ T(y,z)) * x
    ]]></literal>
    <justification jstring="[para(75(a,1),4084(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="75 4084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4107">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ y,z) = T(y * x,z) / x
    ]]></literal>
    <justification jstring="[hyper(333,a,953,a,b,4085,a)].">
      <j1 rule="hyper" parents="333 953 4085"/>
    </justification>
  </clause>

  <clause id="4109">
    <literal><![CDATA[
      (((x \ 1) \ y) * (x \ 1)) * x = T(y * x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(125,a,963,a(flip),b,4085,a)].">
      <j1 rule="hyper" parents="125 963 4085"/>
    </justification>
  </clause>

  <clause id="4110">
    <literal><![CDATA[
      (1 / x) * T((1 / x) \ y,z) = x \ T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,1648,a,b,4085,a)].">
      <j1 rule="hyper" parents="63 1648 4085"/>
    </justification>
  </clause>

  <clause id="4112">
    <literal><![CDATA[
      T(x \ T(x * y,z),x) = x \ T(y * x,z)
    ]]></literal>
    <justification jstring="[para(4085(a,1),113(a,1,1))].">
      <j1 rule="para" parents="4085 113"/>
    </justification>
  </clause>

  <clause id="4113">
    <literal><![CDATA[
      x * (T(y * x,z) / x) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ T(x * y,z) = w
    ]]></literal>
    <justification jstring="[para(4085(a,2),416(a,1,2))].">
      <j1 rule="para" parents="4085 416"/>
    </justification>
  </clause>

  <clause id="4114">
    <literal><![CDATA[
      x * (y \ T(y * (x \ z),x)) = ((x \ (z * y)) * x) / y
    ]]></literal>
    <justification jstring="[para(4085(a,1),3047(a,1,2))].">
      <j1 rule="para" parents="4085 3047"/>
    </justification>
  </clause>

  <clause id="4116">
    <literal><![CDATA[
      (x \ T(y,z)) * x != u
    ]]></literal>
    <literal><![CDATA[
      T((x \ y) * x,z) = u
    ]]></literal>
    <justification jstring="[para(4087(a,1),264(a,1,1)),flip(b)].">
      <j1 rule="para" parents="4087 264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4118">
    <literal><![CDATA[
      T(x,y) / R(x,z,u) = R(x,z,u) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(3014(a,1),4087(a,1,1,1))].">
      <j1 rule="para" parents="3014 4087"/>
    </justification>
  </clause>

  <clause id="4119">
    <literal><![CDATA[
      T(x * y,z) != x * u
    ]]></literal>
    <literal><![CDATA[
      T(y * x,z) / x = u
    ]]></literal>
    <justification jstring="[para(4092(a,1),43(a,1))].">
      <j1 rule="para" parents="4092 43"/>
    </justification>
  </clause>

  <clause id="4120">
    <literal><![CDATA[
      T(x,T(y * x,z)) = T(x,T(x * y,z))
    ]]></literal>
    <justification jstring="[para(4092(a,1),3677(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4092 3677"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4122">
    <literal><![CDATA[
      ((1 / x) \ T(L(y,x,x \ 1),z)) * (1 / x) = T((x * y) * (1 / x),z)
    ]]></literal>
    <justification jstring="[para(2652(a,1),4104(a,1,1,2,1))].">
      <j1 rule="para" parents="2652 4104"/>
    </justification>
  </clause>

  <clause id="4124">
    <literal><![CDATA[
      x * ((y \ T(z,x)) * y) = ((y \ z) * y) * x
    ]]></literal>
    <justification jstring="[hyper(126,a,4105,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="126 4105 22"/>
    </justification>
  </clause>

  <clause id="4125">
    <literal><![CDATA[
      T((x \ (y / z)) * x,z) = (x \ (z \ y)) * x
    ]]></literal>
    <justification jstring="[para(113(a,1),4105(a,2,1,2))].">
      <j1 rule="para" parents="113 4105"/>
    </justification>
  </clause>

  <clause id="4126">
    <literal><![CDATA[
      ((x * T((y \ z) * y,x)) / x) * (T(x,y) \ x) = (y \ (z * (T(x,y) \ x))) * y
    ]]></literal>
    <justification jstring="[para(4105(a,2),3920(a,1,1,1,2))].">
      <j1 rule="para" parents="4105 3920"/>
    </justification>
  </clause>

  <clause id="4127">
    <literal><![CDATA[
      (x * ((y / z) / x)) * z = z * (x * ((z \ y) / x))
    ]]></literal>
    <justification jstring="[para(113(a,1),4088(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="113 4088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4128">
    <literal><![CDATA[
      (x * (((y * z) / y) / x)) * y = y * (x * (z / x))
    ]]></literal>
    <justification jstring="[para(238(a,1),4088(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="238 4088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4129">
    <literal><![CDATA[
      T((x * x) * (y / ((x * x) * z)),z) = (x * x) * ((z \ y) / (x * x))
    ]]></literal>
    <justification jstring="[para(447(a,1),4095(a,1,1,2))].">
      <j1 rule="para" parents="447 4095"/>
    </justification>
  </clause>

  <clause id="4130">
    <literal><![CDATA[
      x / ((((y \ 1) * x) \ x) * ((y \ 1) * x)) = T((y \ x) * y,x) / x
    ]]></literal>
    <justification jstring="[para(3117(a,1),4100(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="3117 4100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4131">
    <literal><![CDATA[
      (R(x,y,z) \ T(x,u)) \ T(x,u) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(192,a,4118,a)].">
      <j1 rule="hyper" parents="192 4118"/>
    </justification>
  </clause>

  <clause id="4132">
    <literal><![CDATA[
      ((x \ (y / z)) * x) * z = z * ((x \ (z \ y)) * x)
    ]]></literal>
    <justification jstring="[para(113(a,1),4124(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="113 4124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4133">
    <literal><![CDATA[
      (x \ y) * ((z \ ((x \ y) \ y)) * z) = ((z \ x) * z) * (x \ y)
    ]]></literal>
    <justification jstring="[para(112(a,1),4124(a,1,2,1,2))].">
      <j1 rule="para" parents="112 4124"/>
    </justification>
  </clause>

  <clause id="4134">
    <literal><![CDATA[
      (x * ((y \ (x \ z)) * y)) / x = (y \ (z / x)) * y
    ]]></literal>
    <justification jstring="[hyper(289,a,4125,a)].">
      <j1 rule="hyper" parents="289 4125"/>
    </justification>
  </clause>

  <clause id="4135">
    <literal><![CDATA[
      T((x \ L(y,y \ z,y)) * x,T(z,y) / y) = (x \ ((T(z,y) / y) \ z)) * x
    ]]></literal>
    <justification jstring="[para(3882(a,2),4125(a,1,1,1,2))].">
      <j1 rule="para" parents="3882 4125"/>
    </justification>
  </clause>

  <clause id="4136">
    <literal><![CDATA[
      (x \ y) \ T((x \ y) * x,x) = (y * x) / y
    ]]></literal>
    <justification jstring="[hyper(333,a,1086,a(flip),b,4086,a),flip(a)].">
      <j1 rule="hyper" parents="333 1086 4086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4137">
    <literal><![CDATA[
      T(K(x,x \ 1) * y,z) = K(x,x \ 1) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(2460,a,4103,a),flip(a)].">
      <j1 rule="hyper" parents="2460 4103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4138">
    <literal><![CDATA[
      T(K(x,x \ 1) * y,z) = T(y,z) * K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(2442,a,4103,a),flip(a)].">
      <j1 rule="hyper" parents="2442 4103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4140">
    <literal><![CDATA[
      T(K(x \ 1,x) * y,z) = K(x \ 1,x) * T(y,z)
    ]]></literal>
    <justification jstring="[para(2450(a,1),4103(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2450 4103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4141">
    <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(1484(a,1),4107(a,2,1,1))].">
      <j1 rule="para" parents="1484 4107"/>
    </justification>
  </clause>

  <clause id="4142">
    <literal><![CDATA[
      ((1 / x) / y) * T(((1 / x) / y) \ z,u) = (x \ T(x * (z * y),u)) / y
    ]]></literal>
    <justification jstring="[hyper(123,a,4110,a(flip),b,1730,a),flip(a)].">
      <j1 rule="hyper" parents="123 4110 1730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4143">
    <literal><![CDATA[
      (x * (y \ z)) * (u * (((x * (y \ z)) \ z) / u)) = ((u * ((y / x) / u)) * x) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(3289,a,4127,a),flip(a)].">
      <j1 rule="hyper" parents="3289 4127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4144">
    <literal><![CDATA[
      (x * ((y / (y * z)) / x)) * (y * z) = (y * z) * (x * (L(z \ 1,z,y) / x))
    ]]></literal>
    <justification jstring="[para(227(a,2),4127(a,2,2,2,1))].">
      <j1 rule="para" parents="227 4127"/>
    </justification>
  </clause>

  <clause id="4145">
    <literal><![CDATA[
      ((x \ (y * (z \ 1))) * x) / (z \ 1) = z * ((x \ (z \ y)) * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,3044,a,b,4132,a)].">
      <j1 rule="hyper" parents="63 3044 4132"/>
    </justification>
  </clause>

  <clause id="4146">
    <literal><![CDATA[
      ((x \ R(1 / y,y,z)) * x) * (y * z) = (y * z) * ((x \ ((y * z) \ z)) * x)
    ]]></literal>
    <justification jstring="[para(230(a,2),4132(a,1,1,1,2))].">
      <j1 rule="para" parents="230 4132"/>
    </justification>
  </clause>

  <clause id="4147">
    <literal><![CDATA[
      (x * ((y \ z) * y)) / x = (y \ ((x * z) / x)) * y
    ]]></literal>
    <justification jstring="[para(9(a,1),4134(a,1,1,2,1,2))].">
      <j1 rule="para" parents="9 4134"/>
    </justification>
  </clause>

  <clause id="4148">
    <literal><![CDATA[
      ((x \ (y / z)) * x) * z != u
    ]]></literal>
    <literal><![CDATA[
      z * ((x \ (z \ y)) * x) = u
    ]]></literal>
    <justification jstring="[para(4134(a,1),264(a,1,1)),flip(b)].">
      <j1 rule="para" parents="4134 264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4150">
    <literal><![CDATA[
      T(x * K(y,y \ 1),z) = K(y,y \ 1) * T(x,z)
    ]]></literal>
    <justification jstring="[para(2397(a,1),4137(a,1,1))].">
      <j1 rule="para" parents="2397 4137"/>
    </justification>
  </clause>

  <clause id="4151">
    <literal><![CDATA[
      T(((x \ 1) \ 1) \ y,z) * K(x,x \ 1) = T(x \ y,z)
    ]]></literal>
    <justification jstring="[para(2683(a,1),4138(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2683 4138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4152">
    <literal><![CDATA[
      T(K(x \ 1,x) * y,z) = T(y,z) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,2412,a(flip),b,4140,a),flip(a)].">
      <j1 rule="hyper" parents="333 2412 4140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4154">
    <literal><![CDATA[
      (x \ ((y * (x * z)) / y)) * x = (y * (z * x)) / y
    ]]></literal>
    <justification jstring="[para(9(a,1),4147(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 4147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4155">
    <literal><![CDATA[
      T(x * K(y \ 1,y),z) = T(x,z) * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(2412(a,1),4152(a,1,1))].">
      <j1 rule="para" parents="2412 4152"/>
    </justification>
  </clause>

  <clause id="4156">
    <literal><![CDATA[
      x \ T(y * K(z \ 1,z),u) = (x \ T(y,u)) * K(z \ 1,z)
    ]]></literal>
    <justification jstring="[para(4155(a,2),1881(a,1,2))].">
      <j1 rule="para" parents="4155 1881"/>
    </justification>
  </clause>

  <clause id="4157">
    <literal><![CDATA[
      ((x \ (y / (z \ 1))) * x) * (z \ 1) = ((x \ (y * z)) * x) / z
    ]]></literal>
    <justification jstring="[hyper(63,a,1236,a,b,4114,a)].">
      <j1 rule="hyper" parents="63 1236 4114"/>
    </justification>
  </clause>

  <clause id="4158">
    <literal><![CDATA[
      T(x,T(((y \ 1) \ 1) \ z,u)) = T(x,T(y \ z,u))
    ]]></literal>
    <justification jstring="[para(4151(a,1),3160(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4151 3160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4159">
    <literal><![CDATA[
      ((x \ y) * x) * (y \ 1) = (1 / y) * ((x \ y) * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,2918,a(flip),b,4133,a),flip(a)].">
      <j1 rule="hyper" parents="63 2918 4133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4160">
    <literal><![CDATA[
      (1 / x) * ((y \ x) * y) = ((y \ x) * y) / x
    ]]></literal>
    <justification jstring="[hyper(63,a,3983,a(flip),b,4159,a),flip(a)].">
      <j1 rule="hyper" parents="63 3983 4159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4161">
    <literal><![CDATA[
      (x \ 1) * ((y \ ((x \ 1) \ z)) * y) = ((y \ (z * x)) * y) / x
    ]]></literal>
    <justification jstring="[hyper(4148,a,4157,a)].">
      <j1 rule="hyper" parents="4148 4157"/>
    </justification>
  </clause>

  <clause id="4162">
    <literal><![CDATA[
      ((x \ (y * z)) * x) / z = z \ ((x \ (z * y)) * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,2573,a(flip),b,4161,a),flip(a)].">
      <j1 rule="hyper" parents="63 2573 4161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4163">
    <literal><![CDATA[
      L(x,T(y,y \ z) \ 1,y) = L(x,((y \ z) \ z) \ 1,(y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,2622,a,b,4080,a),flip(a)].">
      <j1 rule="hyper" parents="63 2622 4080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4164">
    <literal><![CDATA[
      T((x * x) * (y / ((x * x) * z)),z) = T(z \ y,x \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(333,a,995,a(flip),b,4129,a),flip(a)].">
      <j1 rule="hyper" parents="333 995 4129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4165">
    <literal><![CDATA[
      ((x \ 1) \ y) / (x * x) = T(x \ y,x \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,1337,a(flip),b,4164,a)].">
      <j1 rule="hyper" parents="63 1337 4164"/>
    </justification>
  </clause>

  <clause id="4166">
    <literal><![CDATA[
      T(x \ y,x \ (x \ 1)) = (x \ 1) \ (y / (x * x))
    ]]></literal>
    <justification jstring="[hyper(746,a,4165,a),flip(a)].">
      <j1 rule="hyper" parents="746 4165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4167">
    <literal><![CDATA[
      T(x \ y,x \ (x \ 1)) != z
    ]]></literal>
    <literal><![CDATA[
      T(y / x,x \ 1) = z
    ]]></literal>
    <justification jstring="[para(4166(a,2),821(a,1))].">
      <j1 rule="para" parents="4166 821"/>
    </justification>
  </clause>

  <clause id="4168">
    <literal><![CDATA[
      T((x \ y) * x,y) / y = y / (x * (y / x))
    ]]></literal>
    <justification jstring="[para(3939(a,1),4130(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3939 4130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4169">
    <literal><![CDATA[
      ((x \ y) * x) / y = y / (x * (y / x))
    ]]></literal>
    <justification jstring="[para(4102(a,1),4168(a,1,1))].">
      <j1 rule="para" parents="4102 4168"/>
    </justification>
  </clause>

  <clause id="4170">
    <literal><![CDATA[
      ((x \ y) * x) / y = x \ (y / (y / x))
    ]]></literal>
    <justification jstring="[hyper(333,a,3755,a(flip),b,4169,a),flip(a)].">
      <j1 rule="hyper" parents="333 3755 4169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4171">
    <literal><![CDATA[
      (1 / x) * ((y \ x) * y) = y \ (x / (x / y))
    ]]></literal>
    <justification jstring="[hyper(63,a,4160,a,b,4170,a)].">
      <j1 rule="hyper" parents="63 4160 4170"/>
    </justification>
  </clause>

  <clause id="4172">
    <literal><![CDATA[
      L((x \ ((y \ 1) \ 1)) * x,y \ 1,y) = y * (x \ (y / (y / x)))
    ]]></literal>
    <justification jstring="[para(4171(a,1),2919(a,2,2))].">
      <j1 rule="para" parents="4171 2919"/>
    </justification>
  </clause>

  <clause id="4173">
    <literal><![CDATA[
      (x \ (1 \ (y * 1))) * x = y * (x \ (y / (y / x)))
    ]]></literal>
    <justification jstring="[hyper(63,a,2555,a(flip),b,4172,a)].">
      <j1 rule="hyper" parents="63 2555 4172"/>
    </justification>
  </clause>

  <clause id="4174">
    <literal><![CDATA[
      x * (y \ (x / (x / y))) = (y \ x) * y
    ]]></literal>
    <justification jstring="[para(165(a,1),4173(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="165 4173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4175">
    <literal><![CDATA[
      x \ (y / (y / x)) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(34,a,317,a,b,4174,a),flip(a)].">
      <j1 rule="hyper" parents="34 317 4174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4176">
    <literal><![CDATA[
      x / (x / y) = y * K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(142,a,4175,a),flip(a)].">
      <j1 rule="hyper" parents="142 4175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4177">
    <literal><![CDATA[
      (1 / x) * ((y \ x) * y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,4171,a,b,4175,a)].">
      <j1 rule="hyper" parents="63 4171 4175"/>
    </justification>
  </clause>

  <clause id="4178">
    <literal><![CDATA[
      ((x \ y) * x) / y = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,4170,a,b,4175,a)].">
      <j1 rule="hyper" parents="63 4170 4175"/>
    </justification>
  </clause>

  <clause id="4179">
    <literal><![CDATA[
      x / (y * (x / y)) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3755,a,b,4175,a)].">
      <j1 rule="hyper" parents="63 3755 4175"/>
    </justification>
  </clause>

  <clause id="4184">
    <literal><![CDATA[
      K(x \ y,x) * y = (x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(125,a,4175,a(flip),b,4170,a)].">
      <j1 rule="hyper" parents="125 4175 4170"/>
    </justification>
  </clause>

  <clause id="4185">
    <literal><![CDATA[
      K(x \ y,x) * (x * (y / x)) = y
    ]]></literal>
    <justification jstring="[hyper(125,a,4175,a(flip),b,3755,a)].">
      <j1 rule="hyper" parents="125 4175 3755"/>
    </justification>
  </clause>

  <clause id="4187">
    <literal><![CDATA[
      (x / (x / y)) * z = y * (K(y \ x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(125,a,4176,a,b,3545,a)].">
      <j1 rule="hyper" parents="125 4176 3545"/>
    </justification>
  </clause>

  <clause id="4188">
    <literal><![CDATA[
      L(x,y \ 1,y) / (L(x,y \ 1,y) / y) = y * K((y \ 1) * x,y)
    ]]></literal>
    <justification jstring="[para(439(a,1),4176(a,2,2,1))].">
      <j1 rule="para" parents="439 4176"/>
    </justification>
  </clause>

  <clause id="4189">
    <literal><![CDATA[
      x \ ((y / (y / x)) * z) = K(x \ y,x) * z
    ]]></literal>
    <justification jstring="[para(4176(a,2),3544(a,1,2,1))].">
      <j1 rule="para" parents="4176 3544"/>
    </justification>
  </clause>

  <clause id="4190">
    <literal><![CDATA[
      T(x * K(x \ y,x),y) = L(x,x \ y,x)
    ]]></literal>
    <justification jstring="[para(4176(a,1),3778(a,1,1))].">
      <j1 rule="para" parents="4176 3778"/>
    </justification>
  </clause>

  <clause id="4191">
    <literal><![CDATA[
      ((x \ y) * x) * (y \ 1) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,3983,a,b,4178,a)].">
      <j1 rule="hyper" parents="63 3983 4178"/>
    </justification>
  </clause>

  <clause id="4192">
    <literal><![CDATA[
      K(x \ y,x) \ y = x * (y / x)
    ]]></literal>
    <justification jstring="[hyper(192,a,4179,a)].">
      <j1 rule="hyper" parents="192 4179"/>
    </justification>
  </clause>

  <clause id="4193">
    <literal><![CDATA[
      x \ y != K(z \ u,z) * (z * (u / z))
    ]]></literal>
    <literal><![CDATA[
      x * u = y
    ]]></literal>
    <justification jstring="[para(4179(a,1),591(a,2,1))].">
      <j1 rule="para" parents="4179 591"/>
    </justification>
  </clause>

  <clause id="4194">
    <literal><![CDATA[
      ((x * (y / x)) \ T((x * (y / x)) * K(x \ y,x),z)) * (x * (y / x)) = T(y,z)
    ]]></literal>
    <justification jstring="[para(4179(a,1),4084(a,1,1,2,1,2))].">
      <j1 rule="para" parents="4179 4084"/>
    </justification>
  </clause>

  <clause id="4195">
    <literal><![CDATA[
      T(x,K(y \ x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(482,a,4184,a)].">
      <j1 rule="hyper" parents="482 4184"/>
    </justification>
  </clause>

  <clause id="4196">
    <literal><![CDATA[
      (x * K(y \ z,y)) * z != u * ((y \ z) * y)
    ]]></literal>
    <literal><![CDATA[
      R(x,K(y \ z,y),z) = u
    ]]></literal>
    <justification jstring="[para(4184(a,1),543(a,2,2))].">
      <j1 rule="para" parents="4184 543"/>
    </justification>
  </clause>

  <clause id="4197">
    <literal><![CDATA[
      T((x \ 1) * ((y \ x) * y),x) = (x \ 1) * ((y \ x) * y)
    ]]></literal>
    <justification jstring="[para(4184(a,1),1718(a,2,2))].">
      <j1 rule="para" parents="4184 1718"/>
    </justification>
  </clause>

  <clause id="4198">
    <literal><![CDATA[
      T(x * y,K(y,x)) = x * y
    ]]></literal>
    <justification jstring="[para(9(a,1),4195(a,1,2,1))].">
      <j1 rule="para" parents="9 4195"/>
    </justification>
  </clause>

  <clause id="4199">
    <literal><![CDATA[
      K(x,y) \ (x * y) = y * x
    ]]></literal>
    <justification jstring="[hyper(63,a,321,a(flip),b,4198,a)].">
      <j1 rule="hyper" parents="63 321 4198"/>
    </justification>
  </clause>

  <clause id="4200">
    <literal><![CDATA[
      K(x,y) = (x * y) / (y * x)
    ]]></literal>
    <justification jstring="[hyper(197,a,4198,a(flip),b,321,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="197 4198 321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4201">
    <literal><![CDATA[
      K(x,y) * (y * x) = x * y
    ]]></literal>
    <justification jstring="[hyper(126,a,4198,a(flip),b,321,a(flip))].">
      <j1 rule="hyper" parents="126 4198 321"/>
    </justification>
  </clause>

  <clause id="4202">
    <literal><![CDATA[
      K(L(x,y,z),z * y) * (z * (y * x)) = L(x,y,z) * (z * y)
    ]]></literal>
    <justification jstring="[hyper(126,a,97,a(flip),b,4199,a)].">
      <j1 rule="hyper" parents="126 97 4199"/>
    </justification>
  </clause>

  <clause id="4203">
    <literal><![CDATA[
      K(x,x \ y) \ y = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(10(a,1),4199(a,1,2))].">
      <j1 rule="para" parents="10 4199"/>
    </justification>
  </clause>

  <clause id="4204">
    <literal><![CDATA[
      (x * (y * z)) / L(z * y,K(y,z),x) = x * K(y,z)
    ]]></literal>
    <justification jstring="[para(4199(a,1),488(a,1,2,1))].">
      <j1 rule="para" parents="4199 488"/>
    </justification>
  </clause>

  <clause id="4205">
    <literal><![CDATA[
      K(x,y) = T(y,x) \ y
    ]]></literal>
    <justification jstring="[hyper(333,a,3583,a(flip),b,4200,a),flip(a)].">
      <j1 rule="hyper" parents="333 3583 4200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4206">
    <literal><![CDATA[
      T(x,y) = x / K(y,x)
    ]]></literal>
    <justification jstring="[hyper(197,a,4200,a,b,3583,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="197 4200 3583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4207">
    <literal><![CDATA[
      T(x,y) * K(y,x) = x
    ]]></literal>
    <justification jstring="[hyper(126,a,4200,a,b,3583,a(flip))].">
      <j1 rule="hyper" parents="126 4200 3583"/>
    </justification>
  </clause>

  <clause id="4208">
    <literal><![CDATA[
      K(x,x \ y) * ((x \ y) * x) = y
    ]]></literal>
    <justification jstring="[para(4200(a,2),81(a,1,1))].">
      <j1 rule="para" parents="4200 81"/>
    </justification>
  </clause>

  <clause id="4209">
    <literal><![CDATA[
      K(x,y) != z \ y
    ]]></literal>
    <literal><![CDATA[
      T(y,x) = z
    ]]></literal>
    <justification jstring="[para(4200(a,2),3585(a,2)),flip(a)].">
      <j1 rule="para" parents="4200 3585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4210">
    <literal><![CDATA[
      K(x \ (x / y),x) = K(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,3604,a,b,4205,a)].">
      <j1 rule="hyper" parents="333 3604 4205"/>
    </justification>
  </clause>

  <clause id="4211">
    <literal><![CDATA[
      K(x,y) = ((y * x) / y) \ x
    ]]></literal>
    <justification jstring="[hyper(333,a,3480,a,b,4205,a),flip(a)].">
      <j1 rule="hyper" parents="333 3480 4205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4212">
    <literal><![CDATA[
      K(x,y) = y / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,2705,a,b,4205,a),flip(a)].">
      <j1 rule="hyper" parents="333 2705 4205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4213">
    <literal><![CDATA[
      K(x,y) = (1 / T(y,x)) * y
    ]]></literal>
    <justification jstring="[hyper(333,a,2704,a,b,4205,a),flip(a)].">
      <j1 rule="hyper" parents="333 2704 4205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4214">
    <literal><![CDATA[
      K(x,y) = y * (T(y,x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(333,a,1063,a,b,4205,a),flip(a)].">
      <j1 rule="hyper" parents="333 1063 4205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4215">
    <literal><![CDATA[
      K(x,y) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,3608,a(flip),b,4205,a),flip(a)].">
      <j1 rule="hyper" parents="333 3608 4205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4216">
    <literal><![CDATA[
      x * T(x \ 1,y) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,3603,a(flip),b,4205,a)].">
      <j1 rule="hyper" parents="333 3603 4205"/>
    </justification>
  </clause>

  <clause id="4217">
    <literal><![CDATA[
      K(T(x,y),y) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,3424,a(flip),b,4205,a),flip(a)].">
      <j1 rule="hyper" parents="333 3424 4205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4218">
    <literal><![CDATA[
      (T(x,y) \ 1) / K(y,x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(197,a,4205,a,b,3299,a)].">
      <j1 rule="hyper" parents="197 4205 3299"/>
    </justification>
  </clause>

  <clause id="4219">
    <literal><![CDATA[
      (x \ 1) * K(y,x) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(126,a,4205,a,b,3299,a)].">
      <j1 rule="hyper" parents="126 4205 3299"/>
    </justification>
  </clause>

  <clause id="4220">
    <literal><![CDATA[
      (1 / x) * K(y,x) = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(126,a,4205,a,b,2866,a)].">
      <j1 rule="hyper" parents="126 4205 2866"/>
    </justification>
  </clause>

  <clause id="4221">
    <literal><![CDATA[
      x / (x / y) = y * K(x / y,y)
    ]]></literal>
    <justification jstring="[hyper(126,a,4205,a,b,3609,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="126 4205 3609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4222">
    <literal><![CDATA[
      T(x,y) = x * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(126,a,4205,a,b,3608,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="126 4205 3608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4223">
    <literal><![CDATA[
      ((x \ y) \ y) * K(x \ y,x) = x
    ]]></literal>
    <justification jstring="[hyper(126,a,4205,a,b,326,a(flip))].">
      <j1 rule="hyper" parents="126 4205 326"/>
    </justification>
  </clause>

  <clause id="4224">
    <literal><![CDATA[
      K(x,y) * T(y,x) = y
    ]]></literal>
    <justification jstring="[hyper(125,a,4205,a,b,2705,a)].">
      <j1 rule="hyper" parents="125 4205 2705"/>
    </justification>
  </clause>

  <clause id="4225">
    <literal><![CDATA[
      K(x,y) / y = 1 / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(123,a,4205,a,b,2704,a)].">
      <j1 rule="hyper" parents="123 4205 2704"/>
    </justification>
  </clause>

  <clause id="4226">
    <literal><![CDATA[
      T(x,y) \ 1 = x \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(121,a,4205,a,b,1063,a),flip(a)].">
      <j1 rule="hyper" parents="121 4205 1063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4227">
    <literal><![CDATA[
      x \ K(x \ 1,y) = T(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(121,a,4205,a,b,3603,a(flip))].">
      <j1 rule="hyper" parents="121 4205 3603"/>
    </justification>
  </clause>

  <clause id="4228">
    <literal><![CDATA[
      T(T(x,y),z) \ T(x,z) = K(y,T(x,z))
    ]]></literal>
    <justification jstring="[para(23(a,1),4205(a,2,1)),flip(a)].">
      <j1 rule="para" parents="23 4205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4230">
    <literal><![CDATA[
      R(T(x,y),z,u) \ R(x,z,u) = K(y,R(x,z,u))
    ]]></literal>
    <justification jstring="[para(27(a,2),4205(a,2,1)),flip(a)].">
      <j1 rule="para" parents="27 4205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4233">
    <literal><![CDATA[
      T(x,y) = K(y,x) \ x
    ]]></literal>
    <justification jstring="[para(4205(a,2),2709(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4205 2709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4234">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      y / T(y,x) = z
    ]]></literal>
    <justification jstring="[para(4205(a,2),2708(a,1))].">
      <j1 rule="para" parents="4205 2708"/>
    </justification>
  </clause>

  <clause id="4235">
    <literal><![CDATA[
      K(x,y) * ((y * x) / y) = x
    ]]></literal>
    <justification jstring="[para(4205(a,2),3481(a,1,1))].">
      <j1 rule="para" parents="4205 3481"/>
    </justification>
  </clause>

  <clause id="4236">
    <literal><![CDATA[
      x * (((y * x) / y) \ z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(4205(a,2),3580(a,2,1))].">
      <j1 rule="para" parents="4205 3580"/>
    </justification>
  </clause>

  <clause id="4237">
    <literal><![CDATA[
      K(x,y) = T(y,T(x,y)) \ y
    ]]></literal>
    <justification jstring="[para(3613(a,2),4205(a,2,1))].">
      <j1 rule="para" parents="3613 4205"/>
    </justification>
  </clause>

  <clause id="4238">
    <literal><![CDATA[
      (x * y) / x = y * K(x,y)
    ]]></literal>
    <justification jstring="[para(4205(a,2),3611(a,2,2))].">
      <j1 rule="para" parents="4205 3611"/>
    </justification>
  </clause>

  <clause id="4239">
    <literal><![CDATA[
      T(x * K(y,x),y) = x
    ]]></literal>
    <justification jstring="[para(4205(a,2),3699(a,1,1,2))].">
      <j1 rule="para" parents="4205 3699"/>
    </justification>
  </clause>

  <clause id="4240">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      x \ T(x,y) = z
    ]]></literal>
    <justification jstring="[para(4205(a,2),3641(a,1))].">
      <j1 rule="para" parents="4205 3641"/>
    </justification>
  </clause>

  <clause id="4241">
    <literal><![CDATA[
      x * (K(x,y) * z) = T(x,y) * z
    ]]></literal>
    <justification jstring="[para(4205(a,2),3614(a,1,2,1))].">
      <j1 rule="para" parents="4205 3614"/>
    </justification>
  </clause>

  <clause id="4242">
    <literal><![CDATA[
      T(x,y) * (x \ z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(4205(a,2),3615(a,2,1))].">
      <j1 rule="para" parents="4205 3615"/>
    </justification>
  </clause>

  <clause id="4243">
    <literal><![CDATA[
      K(x / y,z) * x = y * T(y \ x,z)
    ]]></literal>
    <justification jstring="[para(4205(a,2),3612(a,1,1))].">
      <j1 rule="para" parents="4205 3612"/>
    </justification>
  </clause>

  <clause id="4244">
    <literal><![CDATA[
      T(x,x * y) * K(y * x,x) = x
    ]]></literal>
    <justification jstring="[hyper(125,a,3678,a(flip),b,4206,a(flip))].">
      <j1 rule="hyper" parents="125 3678 4206"/>
    </justification>
  </clause>

  <clause id="4246">
    <literal><![CDATA[
      (x \ y) * K(x,y / x) = y / x
    ]]></literal>
    <justification jstring="[hyper(125,a,113,a(flip),b,4206,a(flip))].">
      <j1 rule="hyper" parents="125 113 4206"/>
    </justification>
  </clause>

  <clause id="4247">
    <literal><![CDATA[
      T(x,y) != x / z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(4206(a,2),45(a,1))].">
      <j1 rule="para" parents="4206 45"/>
    </justification>
  </clause>

  <clause id="4248">
    <literal><![CDATA[
      T(x,y) * z != x
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(4206(a,2),131(a,1,1))].">
      <j1 rule="para" parents="4206 131"/>
    </justification>
  </clause>

  <clause id="4249">
    <literal><![CDATA[
      T(x,y) \ x != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(4206(a,2),345(a,1,1))].">
      <j1 rule="para" parents="4206 345"/>
    </justification>
  </clause>

  <clause id="4250">
    <literal><![CDATA[
      T(x,y) * (K(y,x) * z) = x * z
    ]]></literal>
    <justification jstring="[para(4207(a,1),3546(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4207 3546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4253">
    <literal><![CDATA[
      K(x,y) != y / z
    ]]></literal>
    <literal><![CDATA[
      T(y,x) = z
    ]]></literal>
    <justification jstring="[para(4212(a,2),45(a,1))].">
      <j1 rule="para" parents="4212 45"/>
    </justification>
  </clause>

  <clause id="4254">
    <literal><![CDATA[
      K(x,y) \ y != z
    ]]></literal>
    <literal><![CDATA[
      T(y,x) = z
    ]]></literal>
    <justification jstring="[para(4212(a,2),345(a,1,1))].">
      <j1 rule="para" parents="4212 345"/>
    </justification>
  </clause>

  <clause id="4255">
    <literal><![CDATA[
      x \ y != K(z,u) * T(u,z)
    ]]></literal>
    <literal><![CDATA[
      x * u = y
    ]]></literal>
    <justification jstring="[para(4212(a,2),591(a,2,1))].">
      <j1 rule="para" parents="4212 591"/>
    </justification>
  </clause>

  <clause id="4256">
    <literal><![CDATA[
      K(x * K(y,y \ 1),z) = z / T(z,x)
    ]]></literal>
    <justification jstring="[para(3160(a,1),4212(a,2,2))].">
      <j1 rule="para" parents="3160 4212"/>
    </justification>
  </clause>

  <clause id="4257">
    <literal><![CDATA[
      L(T(x,y),T(z,x),z / T(z,x)) * z = K(x,z) * (T(x,y) * T(z,x))
    ]]></literal>
    <justification jstring="[para(4212(a,2),3817(a,2,1))].">
      <j1 rule="para" parents="4212 3817"/>
    </justification>
  </clause>

  <clause id="4258">
    <literal><![CDATA[
      T(T(x,y),x \ 1) = (x \ 1) \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(444,a,4215,a,b,1012,a)].">
      <j1 rule="hyper" parents="444 4215 1012"/>
    </justification>
  </clause>

  <clause id="4259">
    <literal><![CDATA[
      (T(x,y) * z) / (x * z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,3403,a,b,4215,a)].">
      <j1 rule="hyper" parents="333 3403 4215"/>
    </justification>
  </clause>

  <clause id="4260">
    <literal><![CDATA[
      K(x,y) = (1 / x) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,3317,a,b,4215,a),flip(a)].">
      <j1 rule="hyper" parents="333 3317 4215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4261">
    <literal><![CDATA[
      K(x,y) = T(x,y) / x
    ]]></literal>
    <justification jstring="[hyper(333,a,3314,a,b,4215,a),flip(a)].">
      <j1 rule="hyper" parents="333 3314 4215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4262">
    <literal><![CDATA[
      T(x \ T(x,y \ 1),z) = K(x,T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(333,a,3101,a,b,4215,a)].">
      <j1 rule="hyper" parents="333 3101 4215"/>
    </justification>
  </clause>

  <clause id="4263">
    <literal><![CDATA[
      x * ((y * (x \ 1)) / y) = K(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(333,a,3071,a,b,4215,a)].">
      <j1 rule="hyper" parents="333 3071 4215"/>
    </justification>
  </clause>

  <clause id="4264">
    <literal><![CDATA[
      K(x,y) = ((x * y) / x) * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(333,a,3067,a,b,4215,a),flip(a)].">
      <j1 rule="hyper" parents="333 3067 4215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4265">
    <literal><![CDATA[
      K(x,y) = ((x * y) / x) / y
    ]]></literal>
    <justification jstring="[hyper(333,a,3064,a,b,4215,a),flip(a)].">
      <j1 rule="hyper" parents="333 3064 4215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4266">
    <literal><![CDATA[
      K(x,y) = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(333,a,3059,a,b,4215,a),flip(a)].">
      <j1 rule="hyper" parents="333 3059 4215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4267">
    <literal><![CDATA[
      K(x,y) = T(x,y) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(333,a,1012,a,b,4215,a),flip(a)].">
      <j1 rule="hyper" parents="333 1012 4215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4268">
    <literal><![CDATA[
      x * T(x \ 1,y) = K(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,1110,a(flip),b,4215,a)].">
      <j1 rule="hyper" parents="333 1110 4215"/>
    </justification>
  </clause>

  <clause id="4270">
    <literal><![CDATA[
      x * K(y,(x \ z) \ 1) = z * ((y * (z \ x)) / y)
    ]]></literal>
    <justification jstring="[hyper(126,a,4215,a,b,3084,a)].">
      <j1 rule="hyper" parents="126 4215 3084"/>
    </justification>
  </clause>

  <clause id="4271">
    <literal><![CDATA[
      T(x,y) * K(y,T(x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(126,a,4215,a,b,3061,a)].">
      <j1 rule="hyper" parents="126 4215 3061"/>
    </justification>
  </clause>

  <clause id="4272">
    <literal><![CDATA[
      (x \ y) \ y = x * K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(126,a,4215,a,b,325,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="126 4215 325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4273">
    <literal><![CDATA[
      K(x,y) * (x * z) = T(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(125,a,4215,a,b,3403,a)].">
      <j1 rule="hyper" parents="125 4215 3403"/>
    </justification>
  </clause>

  <clause id="4274">
    <literal><![CDATA[
      T(x,y) = K(x,y) * x
    ]]></literal>
    <justification jstring="[hyper(125,a,4215,a,b,3314,a),flip(a)].">
      <j1 rule="hyper" parents="125 4215 3314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4275">
    <literal><![CDATA[
      (x * y) / x = K(x,y) * y
    ]]></literal>
    <justification jstring="[hyper(125,a,4215,a,b,3064,a),flip(a)].">
      <j1 rule="hyper" parents="125 4215 3064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4276">
    <literal><![CDATA[
      K((x \ 1) * y,x) * y = (x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(125,a,4215,a,b,3120,a(flip))].">
      <j1 rule="hyper" parents="125 4215 3120"/>
    </justification>
  </clause>

  <clause id="4277">
    <literal><![CDATA[
      K(x,y) / T(x,y) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(123,a,4215,a,b,3317,a)].">
      <j1 rule="hyper" parents="123 4215 3317"/>
    </justification>
  </clause>

  <clause id="4278">
    <literal><![CDATA[
      T(x,y) = (1 / x) \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(121,a,4215,a,b,3317,a),flip(a)].">
      <j1 rule="hyper" parents="121 4215 3317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4279">
    <literal><![CDATA[
      x \ K(y,x \ 1) = (y * (x \ 1)) / y
    ]]></literal>
    <justification jstring="[hyper(121,a,4215,a,b,3071,a)].">
      <j1 rule="hyper" parents="121 4215 3071"/>
    </justification>
  </clause>

  <clause id="4281">
    <literal><![CDATA[
      K(x \ (x * y),z) = y \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,705,a,b,4215,a)].">
      <j1 rule="hyper" parents="63 705 4215"/>
    </justification>
  </clause>

  <clause id="4282">
    <literal><![CDATA[
      (1 / x) * K(x \ 1,y) = T(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(126,a,3333,a(flip),b,4215,a(flip))].">
      <j1 rule="hyper" parents="126 3333 4215"/>
    </justification>
  </clause>

  <clause id="4283">
    <literal><![CDATA[
      L(x,y,z) \ L(T(x,u),y,z) = K(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(25(a,2),4215(a,2,2)),flip(a)].">
      <j1 rule="para" parents="25 4215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4284">
    <literal><![CDATA[
      R(x,y,z) \ R(T(x,u),y,z) = K(R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(27(a,2),4215(a,2,2)),flip(a)].">
      <j1 rule="para" parents="27 4215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4285">
    <literal><![CDATA[
      x * K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(4215(a,2),273(a,1,2)),flip(b)].">
      <j1 rule="para" parents="4215 273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4286">
    <literal><![CDATA[
      x * (y * K(y,x)) = y * x
    ]]></literal>
    <justification jstring="[para(4215(a,2),241(a,1,2,2))].">
      <j1 rule="para" parents="4215 241"/>
    </justification>
  </clause>

  <clause id="4287">
    <literal><![CDATA[
      x * K(x,y) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ T(x,y) = u
    ]]></literal>
    <justification jstring="[para(4215(a,2),416(a,1,2))].">
      <j1 rule="para" parents="4215 416"/>
    </justification>
  </clause>

  <clause id="4288">
    <literal><![CDATA[
      K(x,y) * ((x \ 1) \ z) = z * T(z \ ((x \ 1) \ z),y)
    ]]></literal>
    <justification jstring="[para(4215(a,2),1155(a,1,1))].">
      <j1 rule="para" parents="4215 1155"/>
    </justification>
  </clause>

  <clause id="4289">
    <literal><![CDATA[
      K(x,x * (y \ 1)) = x \ T(x,y \ x)
    ]]></literal>
    <justification jstring="[para(1686(a,1),4215(a,2,2))].">
      <j1 rule="para" parents="1686 4215"/>
    </justification>
  </clause>

  <clause id="4290">
    <literal><![CDATA[
      x \ T(x,y \ 1) = K(x,1 / y)
    ]]></literal>
    <justification jstring="[para(2986(a,1),4215(a,2,2)),flip(a)].">
      <j1 rule="para" parents="2986 4215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4291">
    <literal><![CDATA[
      (x * K(y,x)) * y = y * x
    ]]></literal>
    <justification jstring="[para(4215(a,2),3056(a,1,1,2))].">
      <j1 rule="para" parents="4215 3056"/>
    </justification>
  </clause>

  <clause id="4292">
    <literal><![CDATA[
      (x \ y) * K(x,x \ y) = y / x
    ]]></literal>
    <justification jstring="[para(4215(a,2),3058(a,1,2))].">
      <j1 rule="para" parents="4215 3058"/>
    </justification>
  </clause>

  <clause id="4293">
    <literal><![CDATA[
      K(x,y * K(z,z \ 1)) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[para(3160(a,1),4215(a,2,2))].">
      <j1 rule="para" parents="3160 4215"/>
    </justification>
  </clause>

  <clause id="4294">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) / x = z
    ]]></literal>
    <justification jstring="[para(4215(a,2),3329(a,1))].">
      <j1 rule="para" parents="4215 3329"/>
    </justification>
  </clause>

  <clause id="4295">
    <literal><![CDATA[
      K(x,y) \ (T(x,y) * z) = x * z
    ]]></literal>
    <justification jstring="[para(4215(a,2),3404(a,1,1))].">
      <j1 rule="para" parents="4215 3404"/>
    </justification>
  </clause>

  <clause id="4296">
    <literal><![CDATA[
      x * (T(x,y) \ z) = K(x,y) \ z
    ]]></literal>
    <justification jstring="[para(4215(a,2),3405(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4215 3405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4297">
    <literal><![CDATA[
      K(x,x \ y) * y = x * (y / x)
    ]]></literal>
    <justification jstring="[para(4215(a,2),3414(a,1,1))].">
      <j1 rule="para" parents="4215 3414"/>
    </justification>
  </clause>

  <clause id="4300">
    <literal><![CDATA[
      x \ T(x,x * y) = K(x,y * x)
    ]]></literal>
    <justification jstring="[para(3678(a,1),4215(a,2,2)),flip(a)].">
      <j1 rule="para" parents="3678 4215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4301">
    <literal><![CDATA[
      T(x * y,z) / a(x,y,K(x * y,z)) = x * (y * K(x * y,z))
    ]]></literal>
    <justification jstring="[hyper(123,a,4222,a,b,84,a)].">
      <j1 rule="hyper" parents="123 4222 84"/>
    </justification>
  </clause>

  <clause id="4302">
    <literal><![CDATA[
      T(x,T(y,T(x,z))) = x * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3892,a,b,4222,a)].">
      <j1 rule="hyper" parents="63 3892 4222"/>
    </justification>
  </clause>

  <clause id="4303">
    <literal><![CDATA[
      T(x,T(y,x / y)) = x * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3671,a,b,4222,a)].">
      <j1 rule="hyper" parents="63 3671 4222"/>
    </justification>
  </clause>

  <clause id="4304">
    <literal><![CDATA[
      x * K(x,y * (z \ 1)) = T(x,y * (1 / z))
    ]]></literal>
    <justification jstring="[hyper(63,a,3165,a,b,4222,a),flip(a)].">
      <j1 rule="hyper" parents="63 3165 4222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4305">
    <literal><![CDATA[
      T(x,y) != x * z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(4222(a,2),43(a,1))].">
      <j1 rule="para" parents="4222 43"/>
    </justification>
  </clause>

  <clause id="4306">
    <literal><![CDATA[
      x \ T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(4222(a,2),342(a,1,2))].">
      <j1 rule="para" parents="4222 342"/>
    </justification>
  </clause>

  <clause id="4307">
    <literal><![CDATA[
      T(x,y) != T(z,y) * K(T(z,y),u)
    ]]></literal>
    <literal><![CDATA[
      T(z,u) = x
    ]]></literal>
    <justification jstring="[para(4222(a,1),147(a,1)),flip(a)].">
      <j1 rule="para" parents="4222 147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4310">
    <literal><![CDATA[
      T(x,y) != z * x
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(4222(a,2),3338(a,1))].">
      <j1 rule="para" parents="4222 3338"/>
    </justification>
  </clause>

  <clause id="4311">
    <literal><![CDATA[
      x * (y * K(x,y)) = T(x,y) * y
    ]]></literal>
    <justification jstring="[para(4222(a,2),3837(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4222 3837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4312">
    <literal><![CDATA[
      K(x,y / x) * (x \ y) = y / x
    ]]></literal>
    <justification jstring="[para(113(a,1),4224(a,1,2))].">
      <j1 rule="para" parents="113 4224"/>
    </justification>
  </clause>

  <clause id="4313">
    <literal><![CDATA[
      x / T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(4224(a,1),268(a,1,1)),flip(b)].">
      <j1 rule="para" parents="4224 268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4314">
    <literal><![CDATA[
      K(x,y) * z != y * L(u,T(y,x),K(x,y))
    ]]></literal>
    <literal><![CDATA[
      T(y,x) * u = z
    ]]></literal>
    <justification jstring="[para(4224(a,1),502(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4224 502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4315">
    <literal><![CDATA[
      K(x,y / x) \ (y / x) = x \ y
    ]]></literal>
    <justification jstring="[hyper(423,a,4233,a),flip(a)].">
      <j1 rule="hyper" parents="423 4233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4316">
    <literal><![CDATA[
      T(x,(y \ x) \ 1) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(333,a,3754,a,b,4233,a)].">
      <j1 rule="hyper" parents="333 3754 4233"/>
    </justification>
  </clause>

  <clause id="4317">
    <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(4233(a,2),2336(a,1,2,1))].">
      <j1 rule="para" parents="4233 2336"/>
    </justification>
  </clause>

  <clause id="4318">
    <literal><![CDATA[
      (T(x,y) * y) / T(x,y) = y * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(3705,a,4239,a)].">
      <j1 rule="hyper" parents="3705 4239"/>
    </justification>
  </clause>

  <clause id="4319">
    <literal><![CDATA[
      T((x * y) / x,z) = T(y,z) * K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(478,a,4239,a)].">
      <j1 rule="hyper" parents="478 4239"/>
    </justification>
  </clause>

  <clause id="4320">
    <literal><![CDATA[
      T(T(x * K(y,x),z),y) = T(x,z)
    ]]></literal>
    <justification jstring="[para(4239(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4239 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4321">
    <literal><![CDATA[
      T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      z * K(y,z) = x
    ]]></literal>
    <justification jstring="[para(4239(a,1),49(a,1)),flip(a)].">
      <j1 rule="para" parents="4239 49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4322">
    <literal><![CDATA[
      T(x * K(y,x),z) * y = y * T(x,z)
    ]]></literal>
    <justification jstring="[para(4239(a,1),250(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4239 250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4323">
    <literal><![CDATA[
      T(x * K(y,x),z) = (y * T(x,z)) / y
    ]]></literal>
    <justification jstring="[para(4239(a,1),287(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4239 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4324">
    <literal><![CDATA[
      T(x * K(y,x),(x * K(y,x)) * y) = L(x,y,x * K(y,x))
    ]]></literal>
    <justification jstring="[para(4239(a,1),634(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4239 634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4325">
    <literal><![CDATA[
      L(x * K(y,x),z,u) * y = y * L(x,z,u)
    ]]></literal>
    <justification jstring="[para(4239(a,1),251(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4239 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4326">
    <literal><![CDATA[
      T(1 / (1 / (x * K(y,x))),y) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[para(4239(a,1),2384(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4239 2384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4327">
    <literal><![CDATA[
      T(K(x,y) * y,x) = y
    ]]></literal>
    <justification jstring="[para(2717(a,2),4239(a,1,1))].">
      <j1 rule="para" parents="2717 4239"/>
    </justification>
  </clause>

  <clause id="4328">
    <literal><![CDATA[
      T(x,y * K(x,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(4239(a,1),3613(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4239 3613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4329">
    <literal><![CDATA[
      T(x,L(y * K(x,y),z,u)) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(4239(a,1),3632(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4239 3632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4330">
    <literal><![CDATA[
      L(x * K(y,x),y,x * K(y,x)) = L(x * K(y,x),y,x)
    ]]></literal>
    <justification jstring="[para(4239(a,1),3872(a,1,3)),flip(a)].">
      <j1 rule="para" parents="4239 3872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4331">
    <literal><![CDATA[
      ((x \ (y * K(z,y))) * x) * z = z * ((x \ y) * x)
    ]]></literal>
    <justification jstring="[para(4239(a,1),4124(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="4239 4124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4332">
    <literal><![CDATA[
      T(1 / x,y) * x = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,957,a(flip),b,4261,a)].">
      <j1 rule="hyper" parents="333 957 4261"/>
    </justification>
  </clause>

  <clause id="4333">
    <literal><![CDATA[
      K(x \ (x * y),z) * y = T(y,z)
    ]]></literal>
    <justification jstring="[hyper(125,a,705,a,b,4261,a(flip))].">
      <j1 rule="hyper" parents="125 705 4261"/>
    </justification>
  </clause>

  <clause id="4334">
    <literal><![CDATA[
      R(T(x,y),z,u) / R(x,z,u) = K(R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(27(a,2),4261(a,2,1)),flip(a)].">
      <j1 rule="para" parents="27 4261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4335">
    <literal><![CDATA[
      K(x,y) * x != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(4261(a,2),264(a,1,1)),flip(b)].">
      <j1 rule="para" parents="4261 264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4341">
    <literal><![CDATA[
      K(L(x,y,z),u) * L(x,y,z) = L(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,25,a,b,4274,a),flip(a)].">
      <j1 rule="hyper" parents="63 25 4274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4342">
    <literal><![CDATA[
      x * (K(y,x) * y) = y * x
    ]]></literal>
    <justification jstring="[hyper(126,a,4274,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="126 4274 22"/>
    </justification>
  </clause>

  <clause id="4345">
    <literal><![CDATA[
      T(x,y) / x != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(4274(a,2),268(a,1,1)),flip(b)].">
      <j1 rule="para" parents="4274 268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4346">
    <literal><![CDATA[
      L(x \ y,x,K(y,z)) = (K(y,z) * x) \ T(y,z)
    ]]></literal>
    <justification jstring="[para(4274(a,2),99(a,2,2))].">
      <j1 rule="para" parents="4274 99"/>
    </justification>
  </clause>

  <clause id="4347">
    <literal><![CDATA[
      T(x,y) \ (K(x,y) * (z * x)) = L(T(z,x),x,K(x,y))
    ]]></literal>
    <justification jstring="[para(4274(a,2),246(a,1,1))].">
      <j1 rule="para" parents="4274 246"/>
    </justification>
  </clause>

  <clause id="4348">
    <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(4274(a,2),543(a,2,2))].">
      <j1 rule="para" parents="4274 543"/>
    </justification>
  </clause>

  <clause id="4349">
    <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(4274(a,2),633(a,1,2))].">
      <j1 rule="para" parents="4274 633"/>
    </justification>
  </clause>

  <clause id="4350">
    <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(4274(a,2),751(a,1,1))].">
      <j1 rule="para" parents="4274 751"/>
    </justification>
  </clause>

  <clause id="4351">
    <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(4274(a,2),980(a,1,2,1))].">
      <j1 rule="para" parents="4274 980"/>
    </justification>
  </clause>

  <clause id="4352">
    <literal><![CDATA[
      K(x,x \ y) * (x \ y) = y / x
    ]]></literal>
    <justification jstring="[hyper(262,a,4327,a),flip(a)].">
      <j1 rule="hyper" parents="262 4327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4353">
    <literal><![CDATA[
      (x * y) * L(z,y * x,K(x,y)) = K(x,y) * ((y * x) * z)
    ]]></literal>
    <justification jstring="[hyper(125,a,4201,a(flip),b,190,a)].">
      <j1 rule="hyper" parents="125 4201 190"/>
    </justification>
  </clause>

  <clause id="4354">
    <literal><![CDATA[
      K(x,y) = x / ((y * x) / y)
    ]]></literal>
    <justification jstring="[hyper(333,a,3378,a,b,4211,a),flip(a)].">
      <j1 rule="hyper" parents="333 3378 4211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4355">
    <literal><![CDATA[
      ((x * y) / x) \ 1 = y \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(121,a,4211,a,b,1298,a),flip(a)].">
      <j1 rule="hyper" parents="121 4211 1298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4356">
    <literal><![CDATA[
      L(x / (x / y),z,u) \ L(y,z,u) = K(L(y,z,u),x / y)
    ]]></literal>
    <justification jstring="[para(894(a,1),4211(a,2,1)),flip(a)].">
      <j1 rule="para" parents="894 4211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4357">
    <literal><![CDATA[
      K(x \ K(x,y),x) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(4211(a,2),3235(a,1,1,2))].">
      <j1 rule="para" parents="4211 3235"/>
    </justification>
  </clause>

  <clause id="4358">
    <literal><![CDATA[
      K(x,y) \ x = (y * x) / y
    ]]></literal>
    <justification jstring="[para(4211(a,2),3377(a,1,1))].">
      <j1 rule="para" parents="4211 3377"/>
    </justification>
  </clause>

  <clause id="4359">
    <literal><![CDATA[
      K(x,x \ 1) / ((y * x) \ y) = 1 / T((y * x) \ y,x)
    ]]></literal>
    <justification jstring="[hyper(123,a,2925,a(flip),b,4213,a(flip))].">
      <j1 rule="hyper" parents="123 2925 4213"/>
    </justification>
  </clause>

  <clause id="4360">
    <literal><![CDATA[
      K(x,y) / y != z
    ]]></literal>
    <literal><![CDATA[
      1 / T(y,x) = z
    ]]></literal>
    <justification jstring="[para(4213(a,2),268(a,1,1)),flip(b)].">
      <j1 rule="para" parents="4213 268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4361">
    <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(4213(a,2),544(a,1,2))].">
      <j1 rule="para" parents="4213 544"/>
    </justification>
  </clause>

  <clause id="4362">
    <literal><![CDATA[
      T(x,x * x) \ 1 = x \ a(x,x,x)
    ]]></literal>
    <justification jstring="[hyper(121,a,93,a(flip),b,4214,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="121 93 4214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4363">
    <literal><![CDATA[
      (x * y) \ (x * K(z,y)) = L(T(y,z) \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(4214(a,2),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4214 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4364">
    <literal><![CDATA[
      L(T(x \ y,z) \ 1,x \ y,x) = y \ (x * K(z,x \ y))
    ]]></literal>
    <justification jstring="[para(4214(a,2),98(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4214 98"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4365">
    <literal><![CDATA[
      K(T(x,y),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,4215,a,b,4217,a),flip(a)].">
      <j1 rule="hyper" parents="333 4215 4217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4367">
    <literal><![CDATA[
      K(x,y) \ 1 = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(3957,a,4365,a)].">
      <j1 rule="hyper" parents="3957 4365"/>
    </justification>
  </clause>

  <clause id="4368">
    <literal><![CDATA[
      K(x,y / x) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3432,a(flip),b,4365,a)].">
      <j1 rule="hyper" parents="63 3432 4365"/>
    </justification>
  </clause>

  <clause id="4369">
    <literal><![CDATA[
      K(x,(x * y) / x) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3431,a(flip),b,4365,a)].">
      <j1 rule="hyper" parents="63 3431 4365"/>
    </justification>
  </clause>

  <clause id="4370">
    <literal><![CDATA[
      K(x,T(y,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3430,a(flip),b,4365,a),flip(a)].">
      <j1 rule="hyper" parents="63 3430 4365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4371">
    <literal><![CDATA[
      1 / K(x,y) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(197,a,4365,a(flip),b,3951,a(flip))].">
      <j1 rule="hyper" parents="197 4365 3951"/>
    </justification>
  </clause>

  <clause id="4372">
    <literal><![CDATA[
      (x * y) * K(x,y) = T(x,y) * y
    ]]></literal>
    <justification jstring="[hyper(126,a,4365,a(flip),b,244,a)].">
      <j1 rule="hyper" parents="126 4365 244"/>
    </justification>
  </clause>

  <clause id="4373">
    <literal><![CDATA[
      K(x,y) * K(y,x) = 1
    ]]></literal>
    <justification jstring="[hyper(126,a,4365,a(flip),b,3951,a(flip))].">
      <j1 rule="hyper" parents="126 4365 3951"/>
    </justification>
  </clause>

  <clause id="4374">
    <literal><![CDATA[
      K(x \ (y * x),x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(22(a,1),4365(a,1,1))].">
      <j1 rule="para" parents="22 4365"/>
    </justification>
  </clause>

  <clause id="4375">
    <literal><![CDATA[
      K(x / y,y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[para(113(a,1),4365(a,1,1)),flip(a)].">
      <j1 rule="para" parents="113 4365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4376">
    <literal><![CDATA[
      K((x * y) / x,x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(238(a,1),4365(a,1,1)),flip(a)].">
      <j1 rule="para" parents="238 4365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4377">
    <literal><![CDATA[
      K((x \ y) \ y,x \ y) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(112(a,1),4365(a,1,1))].">
      <j1 rule="para" parents="112 4365"/>
    </justification>
  </clause>

  <clause id="4378">
    <literal><![CDATA[
      K(T(x,x * y),y) = K(L(x,y,x),y)
    ]]></literal>
    <justification jstring="[para(635(a,1),4365(a,1,1))].">
      <j1 rule="para" parents="635 4365"/>
    </justification>
  </clause>

  <clause id="4379">
    <literal><![CDATA[
      K(R(x \ y,x,z),x) = K((y * z) / (x * z),x)
    ]]></literal>
    <justification jstring="[para(688(a,1),4365(a,1,1))].">
      <j1 rule="para" parents="688 4365"/>
    </justification>
  </clause>

  <clause id="4380">
    <literal><![CDATA[
      K(R(x,y,x),y * x) = K(T(x,y),y * x)
    ]]></literal>
    <justification jstring="[para(844(a,1),4365(a,1,1)),flip(a)].">
      <j1 rule="para" parents="844 4365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4381">
    <literal><![CDATA[
      K(x,y) * z != 1
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(4365(a,1),3955(a,1,1))].">
      <j1 rule="para" parents="4365 3955"/>
    </justification>
  </clause>

  <clause id="4382">
    <literal><![CDATA[
      K(x,y) \ 1 != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(4365(a,1),3956(a,1,1))].">
      <j1 rule="para" parents="4365 3956"/>
    </justification>
  </clause>

  <clause id="4383">
    <literal><![CDATA[
      T(x * K(y,x),T(y,x)) = x
    ]]></literal>
    <justification jstring="[para(4365(a,1),4239(a,1,1,2))].">
      <j1 rule="para" parents="4365 4239"/>
    </justification>
  </clause>

  <clause id="4384">
    <literal><![CDATA[
      K(x * K(y,x),y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(4239(a,1),4365(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4239 4365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4387">
    <literal><![CDATA[
      x * (K(y,z) * K(z,y)) = x
    ]]></literal>
    <justification jstring="[para(4367(a,1),69(a,1,2,2))].">
      <j1 rule="para" parents="4367 69"/>
    </justification>
  </clause>

  <clause id="4388">
    <literal><![CDATA[
      1 / K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(4367(a,1),301(a,1,2)),flip(b)].">
      <j1 rule="para" parents="4367 301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4389">
    <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(4367(a,1),1795(a,2,1,2,1))].">
      <j1 rule="para" parents="4367 1795"/>
    </justification>
  </clause>

  <clause id="4390">
    <literal><![CDATA[
      L(x,K(y,z),u) = L(x,K(z,y),u)
    ]]></literal>
    <justification jstring="[para(4367(a,1),2596(a,1,2))].">
      <j1 rule="para" parents="4367 2596"/>
    </justification>
  </clause>

  <clause id="4391">
    <literal><![CDATA[
      L(x,K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,K(z,y),u) = w
    ]]></literal>
    <justification jstring="[para(4367(a,1),2631(a,1,2))].">
      <j1 rule="para" parents="4367 2631"/>
    </justification>
  </clause>

  <clause id="4393">
    <literal><![CDATA[
      K(x,T(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(4367(a,1),3956(a,1))].">
      <j1 rule="para" parents="4367 3956"/>
    </justification>
  </clause>

  <clause id="4394">
    <literal><![CDATA[
      K(x,x \ (y * x)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(22(a,1),4370(a,1,2))].">
      <j1 rule="para" parents="22 4370"/>
    </justification>
  </clause>

  <clause id="4397">
    <literal><![CDATA[
      K(x,L(y / x,z,u)) = K(x,L(x \ y,z,u))
    ]]></literal>
    <justification jstring="[para(260(a,1),4370(a,1,2)),flip(a)].">
      <j1 rule="para" parents="260 4370"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4398">
    <literal><![CDATA[
      K(x,R(y / x,z,u)) = K(x,R(x \ y,z,u))
    ]]></literal>
    <justification jstring="[para(261(a,1),4370(a,1,2)),flip(a)].">
      <j1 rule="para" parents="261 4370"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4400">
    <literal><![CDATA[
      K(x,y) \ T(y,x) = T(T(y,x),x)
    ]]></literal>
    <justification jstring="[para(4370(a,1),4233(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4370 4233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4401">
    <literal><![CDATA[
      K(x,y) != 1 / z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(4371(a,1),45(a,1))].">
      <j1 rule="para" parents="4371 45"/>
    </justification>
  </clause>

  <clause id="4402">
    <literal><![CDATA[
      x * (K(y,z) / z) = x * (1 / T(z,y))
    ]]></literal>
    <justification jstring="[hyper(126,a,4225,a,b,9,a)].">
      <j1 rule="hyper" parents="126 4225 9"/>
    </justification>
  </clause>

  <clause id="4403">
    <literal><![CDATA[
      T(x,y) = 1 / (x \ K(y,x))
    ]]></literal>
    <justification jstring="[hyper(198,a,4226,a),flip(a)].">
      <j1 rule="hyper" parents="198 4226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4404">
    <literal><![CDATA[
      1 / (x \ K(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(4226(a,1),301(a,1,2)),flip(b)].">
      <j1 rule="para" parents="4226 301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4405">
    <literal><![CDATA[
      T(x,y) * L(x \ K(y,x),z,u) = T(x * L(x \ 1,z,u),y)
    ]]></literal>
    <justification jstring="[para(4226(a,1),1965(a,1,2,1))].">
      <j1 rule="para" parents="4226 1965"/>
    </justification>
  </clause>

  <clause id="4406">
    <literal><![CDATA[
      T(T(x,x \ 1),y) = (x \ K(y,x)) \ 1
    ]]></literal>
    <justification jstring="[para(4226(a,1),2378(a,2,1))].">
      <j1 rule="para" parents="4226 2378"/>
    </justification>
  </clause>

  <clause id="4407">
    <literal><![CDATA[
      K(x \ y,x) * (y / x) = x \ y
    ]]></literal>
    <justification jstring="[para(10(a,1),4235(a,1,2,1))].">
      <j1 rule="para" parents="10 4235"/>
    </justification>
  </clause>

  <clause id="4409">
    <literal><![CDATA[
      K(a(x,y,z),x * (y * z)) * (((x * y) * z) / (x * (y * z))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(84(a,1),4235(a,1,2,1))].">
      <j1 rule="para" parents="84 4235"/>
    </justification>
  </clause>

  <clause id="4410">
    <literal><![CDATA[
      ((x * y) / x) * L(((x * y) / x) \ y,z,u) = L(K(y,x),z,u) * ((x * y) / x)
    ]]></literal>
    <justification jstring="[para(4235(a,1),666(a,1,2,1,2))].">
      <j1 rule="para" parents="4235 666"/>
    </justification>
  </clause>

  <clause id="4412">
    <literal><![CDATA[
      T(x,y) * (K(x,y) * z) = T(T(x,y),y) * z
    ]]></literal>
    <justification jstring="[para(4237(a,2),3614(a,1,2,1))].">
      <j1 rule="para" parents="4237 3614"/>
    </justification>
  </clause>

  <clause id="4413">
    <literal><![CDATA[
      x * ((y * z) / y) = x * (z * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(126,a,4238,a,b,9,a)].">
      <j1 rule="hyper" parents="126 4238 9"/>
    </justification>
  </clause>

  <clause id="4414">
    <literal><![CDATA[
      ((x * y) / x) * z = y * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(125,a,4238,a,b,3545,a)].">
      <j1 rule="hyper" parents="125 4238 3545"/>
    </justification>
  </clause>

  <clause id="4415">
    <literal><![CDATA[
      (x * y) \ ((x * y) / x) = L(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(121,a,4238,a,b,1310,a)].">
      <j1 rule="hyper" parents="121 4238 1310"/>
    </justification>
  </clause>

  <clause id="4416">
    <literal><![CDATA[
      T(x,y) * K(y,T(x,y)) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(4238(a,1),302(a,1))].">
      <j1 rule="para" parents="4238 302"/>
    </justification>
  </clause>

  <clause id="4417">
    <literal><![CDATA[
      T(x,y) * K(y,T(x,y)) != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(4238(a,1),305(a,1))].">
      <j1 rule="para" parents="4238 305"/>
    </justification>
  </clause>

  <clause id="4418">
    <literal><![CDATA[
      ((x * y) * z) / R(x,y,z) = (y * z) * K(R(x,y,z),y * z)
    ]]></literal>
    <justification jstring="[para(107(a,1),4238(a,1,1))].">
      <j1 rule="para" parents="107 4238"/>
    </justification>
  </clause>

  <clause id="4419">
    <literal><![CDATA[
      R(x * K(y,x),y,z) = ((y * x) * z) / (y * z)
    ]]></literal>
    <justification jstring="[para(4238(a,1),108(a,1,1))].">
      <j1 rule="para" parents="4238 108"/>
    </justification>
  </clause>

  <clause id="4420">
    <literal><![CDATA[
      (x \ y) * K(x,x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      y / x = z
    ]]></literal>
    <justification jstring="[para(4238(a,1),363(a,1))].">
      <j1 rule="para" parents="4238 363"/>
    </justification>
  </clause>

  <clause id="4421">
    <literal><![CDATA[
      R(x / y,y,K(z,x)) \ ((z * x) / z) = y * K(z,x)
    ]]></literal>
    <justification jstring="[para(4238(a,2),530(a,1,2))].">
      <j1 rule="para" parents="4238 530"/>
    </justification>
  </clause>

  <clause id="4422">
    <literal><![CDATA[
      R(x * K(y,x),y,y \ 1) = (y * x) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(4238(a,1),554(a,1,1))].">
      <j1 rule="para" parents="4238 554"/>
    </justification>
  </clause>

  <clause id="4423">
    <literal><![CDATA[
      a(x,y,z) * K(x * (y * z),a(x,y,z)) = ((x * y) * z) / (x * (y * z))
    ]]></literal>
    <justification jstring="[para(84(a,1),4238(a,1,1)),flip(a)].">
      <j1 rule="para" parents="84 4238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4424">
    <literal><![CDATA[
      T(T(x * K(y,x),z),y) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z) = u
    ]]></literal>
    <justification jstring="[para(4238(a,1),742(a,1,1,1))].">
      <j1 rule="para" parents="4238 742"/>
    </justification>
  </clause>

  <clause id="4425">
    <literal><![CDATA[
      T(x * K(y * x,x),y) = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(4238(a,1),830(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4238 830"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4426">
    <literal><![CDATA[
      L(x * K(y,x),z,u) = (y * L(x,z,u)) / y
    ]]></literal>
    <justification jstring="[para(4238(a,1),891(a,1,1))].">
      <j1 rule="para" parents="4238 891"/>
    </justification>
  </clause>

  <clause id="4427">
    <literal><![CDATA[
      R(x * K(y,x),z,u) = (y * R(x,z,u)) / y
    ]]></literal>
    <justification jstring="[para(4238(a,1),902(a,1,1))].">
      <j1 rule="para" parents="4238 902"/>
    </justification>
  </clause>

  <clause id="4428">
    <literal><![CDATA[
      ((x / y) * (y * K(z,x))) \ ((z * x) / z) = a(x / y,y,K(z,x))
    ]]></literal>
    <justification jstring="[para(4238(a,2),87(a,1,2))].">
      <j1 rule="para" parents="4238 87"/>
    </justification>
  </clause>

  <clause id="4429">
    <literal><![CDATA[
      L(x * K(y * z,x),z,y) = (y * (z * x)) / (y * z)
    ]]></literal>
    <justification jstring="[para(4238(a,1),892(a,1,1))].">
      <j1 rule="para" parents="4238 892"/>
    </justification>
  </clause>

  <clause id="4431">
    <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(1575(a,1),4238(a,1,1))].">
      <j1 rule="para" parents="1575 4238"/>
    </justification>
  </clause>

  <clause id="4432">
    <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(1817(a,1),4238(a,1,1))].">
      <j1 rule="para" parents="1817 4238"/>
    </justification>
  </clause>

  <clause id="4433">
    <literal><![CDATA[
      T(x * y,y * K(x,y)) = T(x * y,y)
    ]]></literal>
    <justification jstring="[para(4238(a,1),3362(a,1,2))].">
      <j1 rule="para" parents="4238 3362"/>
    </justification>
  </clause>

  <clause id="4434">
    <literal><![CDATA[
      x \ (((y * x) / y) * z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[para(4238(a,2),3544(a,1,2,1))].">
      <j1 rule="para" parents="4238 3544"/>
    </justification>
  </clause>

  <clause id="4435">
    <literal><![CDATA[
      ((x * y) / x) * z != u
    ]]></literal>
    <literal><![CDATA[
      y * (K(x,y) * z) = u
    ]]></literal>
    <justification jstring="[para(4238(a,2),3550(a,1,1))].">
      <j1 rule="para" parents="4238 3550"/>
    </justification>
  </clause>

  <clause id="4436">
    <literal><![CDATA[
      L(x,y,x * K(y,x)) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(4238(a,1),3724(a,1,3))].">
      <j1 rule="para" parents="4238 3724"/>
    </justification>
  </clause>

  <clause id="4438">
    <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(3254(a,1),4260(a,2,1)),flip(a)].">
      <j1 rule="para" parents="3254 4260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4439">
    <literal><![CDATA[
      K(x,y) = (1 / y) * ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(333,a,1346,a,b,4265,a),flip(a)].">
      <j1 rule="hyper" parents="333 1346 4265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4440">
    <literal><![CDATA[
      R(K(x,y / z),y / z,z) = (((x * (y / z)) / x) * z) / y
    ]]></literal>
    <justification jstring="[para(4265(a,2),556(a,1,1))].">
      <j1 rule="para" parents="4265 556"/>
    </justification>
  </clause>

  <clause id="4441">
    <literal><![CDATA[
      ((x * ((y * z) / y)) / x) / ((x * z) / x) = K(y,(x * z) / x)
    ]]></literal>
    <justification jstring="[para(998(a,1),4265(a,2,1)),flip(a)].">
      <j1 rule="para" parents="998 4265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4442">
    <literal><![CDATA[
      (x \ T(x * y,y)) / y = K(x * y,y)
    ]]></literal>
    <justification jstring="[para(3391(a,1),4265(a,2,1)),flip(a)].">
      <j1 rule="para" parents="3391 4265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4444">
    <literal><![CDATA[
      x \ K(y,1 / x) = (y * (x \ 1)) / y
    ]]></literal>
    <justification jstring="[hyper(121,a,4266,a,b,1333,a(flip))].">
      <j1 rule="hyper" parents="121 4266 1333"/>
    </justification>
  </clause>

  <clause id="4445">
    <literal><![CDATA[
      (x \ y) \ (y / x) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),4266(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10 4266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4446">
    <literal><![CDATA[
      x * K(y,x) != z
    ]]></literal>
    <literal><![CDATA[
      (y * x) / y = z
    ]]></literal>
    <justification jstring="[para(4266(a,2),273(a,1,2)),flip(b)].">
      <j1 rule="para" parents="4266 273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4447">
    <literal><![CDATA[
      K(1 / x,y) / x = T(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(466,a,4267,a(flip))].">
      <j1 rule="hyper" parents="466 4267"/>
    </justification>
  </clause>

  <clause id="4448">
    <literal><![CDATA[
      (x * T(y,z)) \ (x * K(y,z)) = L(y \ 1,T(y,z),x)
    ]]></literal>
    <justification jstring="[para(4267(a,2),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4267 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4449">
    <literal><![CDATA[
      T(K(x,y),z) * K(y,x) = K(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(4367(a,1),4267(a,2,2)),flip(a)].">
      <j1 rule="para" parents="4367 4267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4450">
    <literal><![CDATA[
      R(x / K(y,z),K(y,z),z) = (x * z) / ((y * z) / y)
    ]]></literal>
    <justification jstring="[hyper(197,a,4275,a,b,530,a),flip(a)].">
      <j1 rule="hyper" parents="197 4275 530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4451">
    <literal><![CDATA[
      K(x,y) / (x * K(x,y)) = 1 / x
    ]]></literal>
    <justification jstring="[para(4222(a,1),4277(a,1,2))].">
      <j1 rule="para" parents="4222 4277"/>
    </justification>
  </clause>

  <clause id="4452">
    <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(4328(a,1),3851(a,2,2))].">
      <j1 rule="para" parents="4328 3851"/>
    </justification>
  </clause>

  <clause id="4453">
    <literal><![CDATA[
      (x * y) \ (y * (K(x,y) * (x * z))) = L(z,x,y * K(x,y))
    ]]></literal>
    <justification jstring="[para(4342(a,1),3553(a,1,1))].">
      <j1 rule="para" parents="4342 3553"/>
    </justification>
  </clause>

  <clause id="4454">
    <literal><![CDATA[
      K(x,y) / x = 1 / ((y * x) / y)
    ]]></literal>
    <justification jstring="[hyper(123,a,4354,a,b,1454,a)].">
      <j1 rule="hyper" parents="123 4354 1454"/>
    </justification>
  </clause>

  <clause id="4458">
    <literal><![CDATA[
      K(x,y) \ x = x * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,4238,a(flip),b,4358,a),flip(a)].">
      <j1 rule="hyper" parents="333 4238 4358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4459">
    <literal><![CDATA[
      R(K(x,y) \ x,y,z) = ((y * x) * z) / (y * z)
    ]]></literal>
    <justification jstring="[para(4358(a,2),108(a,1,1))].">
      <j1 rule="para" parents="4358 108"/>
    </justification>
  </clause>

  <clause id="4460">
    <literal><![CDATA[
      x \ (y * (x / y)) = K(y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,91,a,b,4368,a)].">
      <j1 rule="hyper" parents="63 91 4368"/>
    </justification>
  </clause>

  <clause id="4461">
    <literal><![CDATA[
      x * K(y,y \ x) = y * (x / y)
    ]]></literal>
    <justification jstring="[hyper(126,a,4368,a(flip),b,91,a)].">
      <j1 rule="hyper" parents="126 4368 91"/>
    </justification>
  </clause>

  <clause id="4463">
    <literal><![CDATA[
      T(x * y,K(x,y)) = x * y
    ]]></literal>
    <justification jstring="[para(4374(a,1),4195(a,1,2))].">
      <j1 rule="para" parents="4374 4195"/>
    </justification>
  </clause>

  <clause id="4464">
    <literal><![CDATA[
      x * K(x / y,y) = (y \ x) * y
    ]]></literal>
    <justification jstring="[hyper(126,a,4375,a,b,89,a)].">
      <j1 rule="hyper" parents="126 4375 89"/>
    </justification>
  </clause>

  <clause id="4465">
    <literal><![CDATA[
      (x * (y / x)) \ y = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,92,a,b,4375,a)].">
      <j1 rule="hyper" parents="63 92 4375"/>
    </justification>
  </clause>

  <clause id="4466">
    <literal><![CDATA[
      (x * (y / x)) * K(x \ y,x) = y
    ]]></literal>
    <justification jstring="[hyper(126,a,4375,a(flip),b,92,a)].">
      <j1 rule="hyper" parents="126 4375 92"/>
    </justification>
  </clause>

  <clause id="4467">
    <literal><![CDATA[
      L(x * K(y,x),z,u) * T(y,x) = T(y,x) * L(x,z,u)
    ]]></literal>
    <justification jstring="[para(4383(a,1),251(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4383 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4468">
    <literal><![CDATA[
      x * K(T(y,x),x) = K(x,y) \ x
    ]]></literal>
    <justification jstring="[para(4365(a,2),4458(a,2,2)),flip(a)].">
      <j1 rule="para" parents="4365 4458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4469">
    <literal><![CDATA[
      T(T(x,y),z) \ T(x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(x,z)) = u
    ]]></literal>
    <justification jstring="[para(23(a,1),4249(a,1,1))].">
      <j1 rule="para" parents="23 4249"/>
    </justification>
  </clause>

  <clause id="4471">
    <literal><![CDATA[
      x * T(x \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,y) = z
    ]]></literal>
    <justification jstring="[para(3603(a,1),4249(a,1))].">
      <j1 rule="para" parents="3603 4249"/>
    </justification>
  </clause>

  <clause id="4472">
    <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(25(a,2),4306(a,1,2))].">
      <j1 rule="para" parents="25 4306"/>
    </justification>
  </clause>

  <clause id="4473">
    <literal><![CDATA[
      x \ L(T(x,y),y,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,x * y) = z
    ]]></literal>
    <justification jstring="[para(634(a,2),4306(a,1,2))].">
      <j1 rule="para" parents="634 4306"/>
    </justification>
  </clause>

  <clause id="4474">
    <literal><![CDATA[
      (x * T(x \ y,z)) / y != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(3498(a,2),4306(a,1))].">
      <j1 rule="para" parents="3498 4306"/>
    </justification>
  </clause>

  <clause id="4475">
    <literal><![CDATA[
      T(T(x,y),z) != u * T(x,z)
    ]]></literal>
    <literal><![CDATA[
      K(T(x,z),y) = u
    ]]></literal>
    <justification jstring="[para(23(a,1),4310(a,1))].">
      <j1 rule="para" parents="23 4310"/>
    </justification>
  </clause>

  <clause id="4478">
    <literal><![CDATA[
      K(x,y / x) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ y) = z
    ]]></literal>
    <justification jstring="[para(3949(a,1),4382(a,1))].">
      <j1 rule="para" parents="3949 4382"/>
    </justification>
  </clause>

  <clause id="4479">
    <literal><![CDATA[
      K(x,x \ (y * x)) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(22(a,1),4393(a,1,2))].">
      <j1 rule="para" parents="22 4393"/>
    </justification>
  </clause>

  <clause id="4480">
    <literal><![CDATA[
      (x * (1 / x)) \ 1 = (x \ 1) * x
    ]]></literal>
    <justification jstring="[para(2098(a,1),4203(a,1,1))].">
      <j1 rule="para" parents="2098 4203"/>
    </justification>
  </clause>

  <clause id="4482">
    <literal><![CDATA[
      R(x * T(x \ 1,y),z,u) = K(R(x,z,u) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,2319,a,b,4210,a)].">
      <j1 rule="hyper" parents="63 2319 4210"/>
    </justification>
  </clause>

  <clause id="4483">
    <literal><![CDATA[
      x \ (y * T(y \ x,z)) = K((x \ y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,2061,a(flip),b,4210,a)].">
      <j1 rule="hyper" parents="63 2061 4210"/>
    </justification>
  </clause>

  <clause id="4484">
    <literal><![CDATA[
      (x * T(x \ y,z)) / y = K((x / y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,2059,a(flip),b,4210,a)].">
      <j1 rule="hyper" parents="63 2059 4210"/>
    </justification>
  </clause>

  <clause id="4486">
    <literal><![CDATA[
      x * T(x \ y,z) = y * K((y \ x) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(126,a,4210,a(flip),b,2061,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="126 4210 2061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4487">
    <literal><![CDATA[
      K((x / y) \ 1,z) * y = x * T(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(125,a,4210,a(flip),b,2059,a(flip))].">
      <j1 rule="hyper" parents="125 4210 2059"/>
    </justification>
  </clause>

  <clause id="4489">
    <literal><![CDATA[
      (x \ y) * K(((x \ y) \ (x \ 1)) \ 1,z) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[para(4210(a,1),2086(a,1,2))].">
      <j1 rule="para" parents="4210 2086"/>
    </justification>
  </clause>

  <clause id="4490">
    <literal><![CDATA[
      (x / y) * K(((x / y) \ (1 / y)) \ 1,z) = T(x,z) / y
    ]]></literal>
    <justification jstring="[para(4210(a,1),2170(a,1,2))].">
      <j1 rule="para" parents="4210 2170"/>
    </justification>
  </clause>

  <clause id="4491">
    <literal><![CDATA[
      (x * y) * K(L(z,y,x) \ 1,u) = x * (y * (z * T(z \ 1,u)))
    ]]></literal>
    <justification jstring="[para(4210(a,1),2324(a,1,2))].">
      <j1 rule="para" parents="4210 2324"/>
    </justification>
  </clause>

  <clause id="4493">
    <literal><![CDATA[
      x * (y * T(y \ (x \ 1),z)) = K((x * y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(954,a,4216,a)].">
      <j1 rule="hyper" parents="954 4216"/>
    </justification>
  </clause>

  <clause id="4494">
    <literal><![CDATA[
      ((x \ (1 / y)) * x) * y = K((x * y) \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1112,a(flip),b,4216,a)].">
      <j1 rule="hyper" parents="63 1112 4216"/>
    </justification>
  </clause>

  <clause id="4495">
    <literal><![CDATA[
      x \ K((x * y) \ 1,z) = y * T(y \ (x \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(121,a,4216,a(flip),b,940,a(flip))].">
      <j1 rule="hyper" parents="121 4216 940"/>
    </justification>
  </clause>

  <clause id="4496">
    <literal><![CDATA[
      ((x * y) \ x) * (x * y) = x * K(y \ 1,x * y)
    ]]></literal>
    <justification jstring="[para(4216(a,1),966(a,2,2))].">
      <j1 rule="para" parents="4216 966"/>
    </justification>
  </clause>

  <clause id="4497">
    <literal><![CDATA[
      K(x \ 1,y) * (x \ z) = z * T(z \ (x \ z),y)
    ]]></literal>
    <justification jstring="[para(4216(a,1),1138(a,1,1))].">
      <j1 rule="para" parents="4216 1138"/>
    </justification>
  </clause>

  <clause id="4498">
    <literal><![CDATA[
      x * (y * T(y \ (x \ y),z)) = K(x \ 1,z) * y
    ]]></literal>
    <justification jstring="[para(4216(a,1),1359(a,2,1))].">
      <j1 rule="para" parents="4216 1359"/>
    </justification>
  </clause>

  <clause id="4501">
    <literal><![CDATA[
      T(1 / x,y) \ 1 = K(x \ 1,y) \ x
    ]]></literal>
    <justification jstring="[para(4216(a,1),1808(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4216 1808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4503">
    <literal><![CDATA[
      (x * y) * (z * T(z \ L(y \ z,y,x),u)) = (x * K(y \ 1,u)) * z
    ]]></literal>
    <justification jstring="[para(4216(a,1),2250(a,2,1,2))].">
      <j1 rule="para" parents="4216 2250"/>
    </justification>
  </clause>

  <clause id="4504">
    <literal><![CDATA[
      (x * y) * ((z \ L(y \ z,y,x)) * z) = (x * K(y \ 1,z)) * z
    ]]></literal>
    <justification jstring="[para(4216(a,1),2251(a,2,1,2))].">
      <j1 rule="para" parents="4216 2251"/>
    </justification>
  </clause>

  <clause id="4506">
    <literal><![CDATA[
      x / y != (z \ 1) * K(u,z)
    ]]></literal>
    <literal><![CDATA[
      (T(z,u) \ 1) * y = x
    ]]></literal>
    <justification jstring="[para(4218(a,1),338(a,2,1))].">
      <j1 rule="para" parents="4218 338"/>
    </justification>
  </clause>

  <clause id="4507">
    <literal><![CDATA[
      K(x,y) * (1 / y) = 1 / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,2034,a,b,4220,a)].">
      <j1 rule="hyper" parents="63 2034 4220"/>
    </justification>
  </clause>

  <clause id="4508">
    <literal><![CDATA[
      (x * (y / x)) \ x = y \ (y / (y / x))
    ]]></literal>
    <justification jstring="[para(4221(a,2),1309(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4221 1309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4510">
    <literal><![CDATA[
      T(x,y) \ (x * z) = K(x,y) \ z
    ]]></literal>
    <justification jstring="[hyper(631,a,4241,a)].">
      <j1 rule="hyper" parents="631 4241"/>
    </justification>
  </clause>

  <clause id="4511">
    <literal><![CDATA[
      K(x,y) \ (x \ z) = T(x,y) \ z
    ]]></literal>
    <justification jstring="[hyper(629,a,4241,a),flip(a)].">
      <j1 rule="hyper" parents="629 4241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4512">
    <literal><![CDATA[
      T(x,y) * T(z,K(x,y)) = x * (z * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(595,a,4241,a),flip(a)].">
      <j1 rule="hyper" parents="595 4241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4513">
    <literal><![CDATA[
      T(x,y) * (K(x,y) \ z) = x * z
    ]]></literal>
    <justification jstring="[hyper(343,a,4241,a),flip(a)].">
      <j1 rule="hyper" parents="343 4241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4515">
    <literal><![CDATA[
      x \ (T(x,y) * z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(129,a,4241,a)].">
      <j1 rule="hyper" parents="129 4241"/>
    </justification>
  </clause>

  <clause id="4516">
    <literal><![CDATA[
      K(x,y) * (x \ 1) = x \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(121,a,4267,a,b,4241,a),flip(a)].">
      <j1 rule="hyper" parents="121 4267 4241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4517">
    <literal><![CDATA[
      x \ ((x * y) / x) = K(x,y) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(121,a,3352,a(flip),b,4241,a)].">
      <j1 rule="hyper" parents="121 3352 4241"/>
    </justification>
  </clause>

  <clause id="4518">
    <literal><![CDATA[
      K(x,y) * (T(x,y) \ z) = x \ z
    ]]></literal>
    <justification jstring="[hyper(121,a,10,a(flip),b,4241,a),flip(a)].">
      <j1 rule="hyper" parents="121 10 4241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4519">
    <literal><![CDATA[
      ((x * y) / x) \ z = K(y,x) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(34,a,3756,a,b,4241,a)].">
      <j1 rule="hyper" parents="34 3756 4241"/>
    </justification>
  </clause>

  <clause id="4520">
    <literal><![CDATA[
      K(x,y) * (z * x) = T(x,y) * T(z,x)
    ]]></literal>
    <justification jstring="[hyper(34,a,1055,a,b,4241,a),flip(a)].">
      <j1 rule="hyper" parents="34 1055 4241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4521">
    <literal><![CDATA[
      K(x,y) * T(y,x * y) = L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(34,a,3826,a(flip),b,4241,a),flip(a)].">
      <j1 rule="hyper" parents="34 3826 4241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4522">
    <literal><![CDATA[
      K(x,y) * T(y,y * x) = L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(34,a,3825,a(flip),b,4241,a),flip(a)].">
      <j1 rule="hyper" parents="34 3825 4241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4523">
    <literal><![CDATA[
      K(x * y,x) * T(x,y) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(34,a,3752,a(flip),b,4241,a),flip(a)].">
      <j1 rule="hyper" parents="34 3752 4241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4524">
    <literal><![CDATA[
      (x * ((K(x,y) * z) * u)) \ ((T(x,y) * z) * u) = a(x,K(x,y) * z,u)
    ]]></literal>
    <justification jstring="[para(4241(a,1),14(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4241 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4525">
    <literal><![CDATA[
      T(x,y) * z != x * u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * z = u
    ]]></literal>
    <justification jstring="[para(4241(a,1),43(a,1))].">
      <j1 rule="para" parents="4241 43"/>
    </justification>
  </clause>

  <clause id="4526">
    <literal><![CDATA[
      (x * y) \ (x * (T(y,z) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(y,z) * u,y,x) = w
    ]]></literal>
    <justification jstring="[para(4241(a,1),504(a,1,2,2))].">
      <j1 rule="para" parents="4241 504"/>
    </justification>
  </clause>

  <clause id="4527">
    <literal><![CDATA[
      T(x,y * ((z \ 1) * (K(1 / z,u) * w))) = T(x,y * (T(1 / z,u) * w))
    ]]></literal>
    <justification jstring="[para(4241(a,1),3187(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4241 3187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4528">
    <literal><![CDATA[
      x * (T(K(x,y),z) * (z * K(x,y))) = T(x,y) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(3644(a,2),4241(a,1,2))].">
      <j1 rule="para" parents="3644 4241"/>
    </justification>
  </clause>

  <clause id="4529">
    <literal><![CDATA[
      T(x,y) * (x \ R(x,z,u)) = R(x,z,u) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,3345,a,b,4242,a),flip(a)].">
      <j1 rule="hyper" parents="333 3345 4242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4530">
    <literal><![CDATA[
      T(x,y) \ (K(x,y) * z) = x \ z
    ]]></literal>
    <justification jstring="[hyper(129,a,4242,a)].">
      <j1 rule="hyper" parents="129 4242"/>
    </justification>
  </clause>

  <clause id="4531">
    <literal><![CDATA[
      x \ (K(x,y) \ z) = T(x,y) \ z
    ]]></literal>
    <justification jstring="[hyper(121,a,10,a(flip),b,4242,a),flip(a)].">
      <j1 rule="hyper" parents="121 10 4242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4532">
    <literal><![CDATA[
      x * (K(x,y) * (x \ z)) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(63,a,4241,a,b,4242,a)].">
      <j1 rule="hyper" parents="63 4241 4242"/>
    </justification>
  </clause>

  <clause id="4533">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ y,z) = K(x,z) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,473,a,b,4242,a)].">
      <j1 rule="hyper" parents="63 473 4242"/>
    </justification>
  </clause>

  <clause id="4534">
    <literal><![CDATA[
      (x \ L(x,y,z)) * T(x,u) = K(x,u) * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,2524,a(flip),b,4242,a)].">
      <j1 rule="hyper" parents="63 2524 4242"/>
    </justification>
  </clause>

  <clause id="4535">
    <literal><![CDATA[
      (x * (y / x)) / y = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(123,a,3355,a(flip),b,4242,a(flip))].">
      <j1 rule="hyper" parents="123 3355 4242"/>
    </justification>
  </clause>

  <clause id="4536">
    <literal><![CDATA[
      K(x * y,z) * (x * (y * u)) = T(x * y,z) * L(u,y,x)
    ]]></literal>
    <justification jstring="[para(18(a,2),4242(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18 4242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4537">
    <literal><![CDATA[
      L(T(x,y),z,u) * (L(x,z,u) \ w) = K(L(x,z,u),y) * w
    ]]></literal>
    <justification jstring="[para(25(a,2),4242(a,1,1))].">
      <j1 rule="para" parents="25 4242"/>
    </justification>
  </clause>

  <clause id="4538">
    <literal><![CDATA[
      K(x,y) * ((z \ x) * z) = T(x,y) * K(z \ x,z)
    ]]></literal>
    <justification jstring="[para(89(a,1),4242(a,1,2)),flip(a)].">
      <j1 rule="para" parents="89 4242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4539">
    <literal><![CDATA[
      K(x,y) * (x * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * z = u
    ]]></literal>
    <justification jstring="[para(4242(a,1),575(a,1))].">
      <j1 rule="para" parents="4242 575"/>
    </justification>
  </clause>

  <clause id="4540">
    <literal><![CDATA[
      T(x,y) * (x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      y * K(x,y) = z
    ]]></literal>
    <justification jstring="[para(4242(a,2),2726(a,1))].">
      <j1 rule="para" parents="4242 2726"/>
    </justification>
  </clause>

  <clause id="4541">
    <literal><![CDATA[
      K(x,y) * T(x,z) = T(x,y) * K(x,z)
    ]]></literal>
    <justification jstring="[para(4215(a,2),4242(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4215 4242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4542">
    <literal><![CDATA[
      K(x,y) * ((z * x) / z) = T(x,y) * K(z,x)
    ]]></literal>
    <justification jstring="[para(4266(a,2),4242(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4266 4242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4543">
    <literal><![CDATA[
      K(x * y,y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(4248,a,4244,a),flip(a)].">
      <j1 rule="hyper" parents="4248 4244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4544">
    <literal><![CDATA[
      K(x * (y / x),x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(12(a,1),4543(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12 4543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4546">
    <literal><![CDATA[
      K(x,y / z) * (z * T(z \ y,x)) = y
    ]]></literal>
    <justification jstring="[hyper(1111,a,4250,a)].">
      <j1 rule="hyper" parents="1111 4250"/>
    </justification>
  </clause>

  <clause id="4547">
    <literal><![CDATA[
      x \ (T(x,y) * z) = K(y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(631,a,4250,a)].">
      <j1 rule="hyper" parents="631 4250"/>
    </justification>
  </clause>

  <clause id="4548">
    <literal><![CDATA[
      K(x,y) \ (T(y,x) \ z) = y \ z
    ]]></literal>
    <justification jstring="[hyper(629,a,4250,a),flip(a)].">
      <j1 rule="hyper" parents="629 4250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4549">
    <literal><![CDATA[
      (x * y) / (K(z,x) * y) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(138,a,4250,a)].">
      <j1 rule="hyper" parents="138 4250"/>
    </justification>
  </clause>

  <clause id="4550">
    <literal><![CDATA[
      T(x,y) \ (x * z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(129,a,4250,a)].">
      <j1 rule="hyper" parents="129 4250"/>
    </justification>
  </clause>

  <clause id="4551">
    <literal><![CDATA[
      T(x,y) / (K(z,x) * K(x,y)) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(123,a,4222,a,b,4250,a)].">
      <j1 rule="hyper" parents="123 4222 4250"/>
    </justification>
  </clause>

  <clause id="4552">
    <literal><![CDATA[
      T(x,y) \ T(x,z) = K(y,x) * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(121,a,4222,a,b,4250,a)].">
      <j1 rule="hyper" parents="121 4222 4250"/>
    </justification>
  </clause>

  <clause id="4553">
    <literal><![CDATA[
      K(x,T(y,z)) * K(z,y) = T(T(y,z),x) \ y
    ]]></literal>
    <justification jstring="[hyper(121,a,4207,a(flip),b,4250,a),flip(a)].">
      <j1 rule="hyper" parents="121 4207 4250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4554">
    <literal><![CDATA[
      T(x,y) \ (z * x) = K(y,x) * T(z,x)
    ]]></literal>
    <justification jstring="[hyper(121,a,111,a(flip),b,4250,a)].">
      <j1 rule="hyper" parents="121 111 4250"/>
    </justification>
  </clause>

  <clause id="4555">
    <literal><![CDATA[
      K(x,y) * (y \ z) = T(y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(121,a,10,a(flip),b,4250,a),flip(a)].">
      <j1 rule="hyper" parents="121 10 4250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4556">
    <literal><![CDATA[
      x * (T(x,y) \ z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(34,a,1058,a,b,4250,a)].">
      <j1 rule="hyper" parents="34 1058 4250"/>
    </justification>
  </clause>

  <clause id="4557">
    <literal><![CDATA[
      K(x,y) * (T(y,x) * z) = y * z
    ]]></literal>
    <justification jstring="[hyper(34,a,1052,a,b,4250,a),flip(a)].">
      <j1 rule="hyper" parents="34 1052 4250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4558">
    <literal><![CDATA[
      K(x,y) * (K(y,x) * z) = z
    ]]></literal>
    <justification jstring="[hyper(34,a,4241,a(flip),b,4250,a),flip(a)].">
      <j1 rule="hyper" parents="34 4241 4250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4560">
    <literal><![CDATA[
      R(x,y,z * K(u,z)) = R(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[para(4250(a,1),1854(a,1,3))].">
      <j1 rule="para" parents="4250 1854"/>
    </justification>
  </clause>

  <clause id="4561">
    <literal><![CDATA[
      R(x,y,z * K(u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y,T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(4250(a,1),1855(a,1,3))].">
      <j1 rule="para" parents="4250 1855"/>
    </justification>
  </clause>

  <clause id="4562">
    <literal><![CDATA[
      L(x,y * K(z,y),u) = L(x,T(y,z),u)
    ]]></literal>
    <justification jstring="[para(4250(a,1),2592(a,1,2))].">
      <j1 rule="para" parents="4250 2592"/>
    </justification>
  </clause>

  <clause id="4563">
    <literal><![CDATA[
      L(x,y * K(z,y),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,T(y,z),u) = w
    ]]></literal>
    <justification jstring="[para(4250(a,1),2593(a,1,2))].">
      <j1 rule="para" parents="4250 2593"/>
    </justification>
  </clause>

  <clause id="4564">
    <literal><![CDATA[
      (K(x,y) \ z) / z = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(3815,a,4558,a)].">
      <j1 rule="hyper" parents="3815 4558"/>
    </justification>
  </clause>

  <clause id="4565">
    <literal><![CDATA[
      K(x,y) * (z * K(y,x)) = T(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(595,a,4558,a)].">
      <j1 rule="hyper" parents="595 4558"/>
    </justification>
  </clause>

  <clause id="4566">
    <literal><![CDATA[
      x \ (K(y,z) \ x) = T(K(z,y),x)
    ]]></literal>
    <justification jstring="[hyper(418,a,4558,a),flip(a)].">
      <j1 rule="hyper" parents="418 4558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4567">
    <literal><![CDATA[
      K(x,y) \ z = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(343,a,4558,a),flip(a)].">
      <j1 rule="hyper" parents="343 4558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4568">
    <literal><![CDATA[
      K(x,y) \ (K(y,x) \ z) = z
    ]]></literal>
    <justification jstring="[hyper(308,a,4558,a),flip(a)].">
      <j1 rule="hyper" parents="308 4558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4569">
    <literal><![CDATA[
      x / (K(y,z) * x) = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(138,a,4558,a)].">
      <j1 rule="hyper" parents="138 4558"/>
    </justification>
  </clause>

  <clause id="4570">
    <literal><![CDATA[
      K(x,1 / x) * (y / x) = y / (1 / (1 / x))
    ]]></literal>
    <justification jstring="[hyper(34,a,2811,a,b,4558,a),flip(a)].">
      <j1 rule="hyper" parents="34 2811 4558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4571">
    <literal><![CDATA[
      K(x,y) * R(K(y,x),z,z \ 1) = a(K(y,x),z,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(34,a,768,a,b,4558,a),flip(a)].">
      <j1 rule="hyper" parents="34 768 4558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4572">
    <literal><![CDATA[
      K(x,y) * (R(x,z,u) * K(y,x)) = R(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(34,a,2729,a(flip),b,4558,a),flip(a)].">
      <j1 rule="hyper" parents="34 2729 4558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4573">
    <literal><![CDATA[
      K(x,y) * (K(x,z) * K(y,x)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(34,a,2005,a(flip),b,4558,a),flip(a)].">
      <j1 rule="hyper" parents="34 2005 4558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4574">
    <literal><![CDATA[
      R(x,K(y,z),K(z,y) * u) * u = (x * K(y,z)) * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(126,a,4558,a(flip),b,187,a)].">
      <j1 rule="hyper" parents="126 4558 187"/>
    </justification>
  </clause>

  <clause id="4575">
    <literal><![CDATA[
      x * L(y,K(z,u) * x,K(u,z)) = K(u,z) * ((K(z,u) * x) * y)
    ]]></literal>
    <justification jstring="[hyper(125,a,4558,a(flip),b,190,a)].">
      <j1 rule="hyper" parents="125 4558 190"/>
    </justification>
  </clause>

  <clause id="4576">
    <literal><![CDATA[
      x \ (K(y,x) * z) = T(x,y) \ z
    ]]></literal>
    <justification jstring="[hyper(121,a,4558,a(flip),b,4242,a),flip(a)].">
      <j1 rule="hyper" parents="121 4558 4242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4577">
    <literal><![CDATA[
      K(x,y) * z != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * u = z
    ]]></literal>
    <justification jstring="[para(4558(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="4558 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4578">
    <literal><![CDATA[
      x * (K(y,z) * u) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) = x
    ]]></literal>
    <justification jstring="[para(4558(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="4558 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4579">
    <literal><![CDATA[
      x / (K(y,z) * x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) = u
    ]]></literal>
    <justification jstring="[para(4558(a,1),268(a,1,1)),flip(b)].">
      <j1 rule="para" parents="4558 268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4580">
    <literal><![CDATA[
      K(x,y) \ z != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * z = u
    ]]></literal>
    <justification jstring="[para(4558(a,1),342(a,1,2))].">
      <j1 rule="para" parents="4558 342"/>
    </justification>
  </clause>

  <clause id="4581">
    <literal><![CDATA[
      L(x \ (K(y,z) * u),x,K(z,y)) = (K(z,y) * x) \ u
    ]]></literal>
    <justification jstring="[para(4558(a,1),99(a,2,2))].">
      <j1 rule="para" parents="4558 99"/>
    </justification>
  </clause>

  <clause id="4582">
    <literal><![CDATA[
      T(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) * (x * K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(4558(a,1),595(a,1))].">
      <j1 rule="para" parents="4558 595"/>
    </justification>
  </clause>

  <clause id="4583">
    <literal><![CDATA[
      (x * y) \ ((x * K(z,u)) * (K(u,z) * y)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,K(z,u),K(u,z) * y) = w
    ]]></literal>
    <justification jstring="[para(4558(a,1),752(a,1,1,2))].">
      <j1 rule="para" parents="4558 752"/>
    </justification>
  </clause>

  <clause id="4584">
    <literal><![CDATA[
      K(x,y) != z / u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) \ u = z
    ]]></literal>
    <justification jstring="[para(4564(a,1),46(a,1))].">
      <j1 rule="para" parents="4564 46"/>
    </justification>
  </clause>

  <clause id="4585">
    <literal><![CDATA[
      K(x,y) * z != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) \ z = u
    ]]></literal>
    <justification jstring="[para(4564(a,1),264(a,1,1)),flip(b)].">
      <j1 rule="para" parents="4564 264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4586">
    <literal><![CDATA[
      x / y != K(z,u) * w
    ]]></literal>
    <literal><![CDATA[
      (K(u,z) \ w) * y = x
    ]]></literal>
    <justification jstring="[para(4564(a,1),338(a,2,1))].">
      <j1 rule="para" parents="4564 338"/>
    </justification>
  </clause>

  <clause id="4587">
    <literal><![CDATA[
      K(x,y) \ T(T(x,z),u) = T(T(x,z),u) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,2732,a,b,4567,a),flip(a)].">
      <j1 rule="hyper" parents="333 2732 4567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4588">
    <literal><![CDATA[
      (K(x,y) \ z) * L(u,z,K(y,x)) = K(y,x) * (z * u)
    ]]></literal>
    <justification jstring="[hyper(125,a,4567,a,b,190,a)].">
      <j1 rule="hyper" parents="125 4567 190"/>
    </justification>
  </clause>

  <clause id="4589">
    <literal><![CDATA[
      K(x,y) * R(K(y,x),z \ 1,z) = a(K(y,x),z \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,3281,a(flip),b,4567,a),flip(a)].">
      <j1 rule="hyper" parents="63 3281 4567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4590">
    <literal><![CDATA[
      K(x,y) * (K(y,x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      z = u
    ]]></literal>
    <justification jstring="[para(4567(a,1),274(a,1,2))].">
      <j1 rule="para" parents="4567 274"/>
    </justification>
  </clause>

  <clause id="4591">
    <literal><![CDATA[
      L(K(x,y) * (z \ u),K(y,x),z) = (z * K(y,x)) \ u
    ]]></literal>
    <justification jstring="[para(4567(a,1),311(a,1,1))].">
      <j1 rule="para" parents="4567 311"/>
    </justification>
  </clause>

  <clause id="4592">
    <literal><![CDATA[
      x \ y != K(z,u) * (K(u,z) * w)
    ]]></literal>
    <literal><![CDATA[
      x * w = y
    ]]></literal>
    <justification jstring="[para(4567(a,1),341(a,2,2))].">
      <j1 rule="para" parents="4567 341"/>
    </justification>
  </clause>

  <clause id="4593">
    <literal><![CDATA[
      T((x \ K(y,z)) \ 1,K(z,y) * x) = (x \ K(y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(4567(a,1),614(a,1,2))].">
      <j1 rule="para" parents="4567 614"/>
    </justification>
  </clause>

  <clause id="4594">
    <literal><![CDATA[
      R(x,K(y,z),K(z,y) * u) * u = (x * K(y,z)) * (K(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(4567(a,1),367(a,1,1,3))].">
      <j1 rule="para" parents="4567 367"/>
    </justification>
  </clause>

  <clause id="4595">
    <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(4567(a,1),3033(a,1,1))].">
      <j1 rule="para" parents="4567 3033"/>
    </justification>
  </clause>

  <clause id="4596">
    <literal><![CDATA[
      x / y != K(z,u) * (K(u,z) * w)
    ]]></literal>
    <literal><![CDATA[
      w * y = x
    ]]></literal>
    <justification jstring="[para(4569(a,1),338(a,2,1))].">
      <j1 rule="para" parents="4569 338"/>
    </justification>
  </clause>

  <clause id="4598">
    <literal><![CDATA[
      K(x,y) \ (y * z) = T(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(37,a,4564,a,b,4259,a)].">
      <j1 rule="hyper" parents="37 4564 4259"/>
    </justification>
  </clause>

  <clause id="4599">
    <literal><![CDATA[
      (T(x,y) * R(x \ 1,x,z)) / ((z / (x * z)) * x) = K(x,y)
    ]]></literal>
    <justification jstring="[para(692(a,2),4259(a,1,2))].">
      <j1 rule="para" parents="692 4259"/>
    </justification>
  </clause>

  <clause id="4600">
    <literal><![CDATA[
      (x * T(x \ y,y)) * (y \ 1) = K(x \ y,y)
    ]]></literal>
    <justification jstring="[para(863(a,1),4264(a,2,1)),flip(a)].">
      <j1 rule="para" parents="863 4264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4601">
    <literal><![CDATA[
      (x * T(x \ y,z)) / y = K(1 / (x / y),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,1735,a(flip),b,4268,a)].">
      <j1 rule="hyper" parents="63 1735 4268"/>
    </justification>
  </clause>

  <clause id="4602">
    <literal><![CDATA[
      K(1 / x,y) / x != z
    ]]></literal>
    <literal><![CDATA[
      T(1 / x,y) = z
    ]]></literal>
    <justification jstring="[para(4268(a,1),475(a,1,1))].">
      <j1 rule="para" parents="4268 475"/>
    </justification>
  </clause>

  <clause id="4603">
    <literal><![CDATA[
      (x * y) * K(1 / L(z,y,x),u) = x * (y * (z * T(z \ 1,u)))
    ]]></literal>
    <justification jstring="[para(4268(a,1),2326(a,1,2))].">
      <j1 rule="para" parents="4268 2326"/>
    </justification>
  </clause>

  <clause id="4605">
    <literal><![CDATA[
      K(x,x \ y) * (x * z) = ((x \ y) \ y) * z
    ]]></literal>
    <justification jstring="[para(4272(a,2),3564(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4272 3564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4606">
    <literal><![CDATA[
      K(x,y) \ (z * T(x,y)) = x * T(z,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(121,a,111,a(flip),b,4273,a)].">
      <j1 rule="hyper" parents="121 111 4273"/>
    </justification>
  </clause>

  <clause id="4607">
    <literal><![CDATA[
      (x * y) / (T(x,z) * y) = K(z,x)
    ]]></literal>
    <justification jstring="[hyper(197,a,4273,a(flip),b,4567,a)].">
      <j1 rule="hyper" parents="197 4273 4567"/>
    </justification>
  </clause>

  <clause id="4608">
    <literal><![CDATA[
      T(x,y) * (x \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * z = u
    ]]></literal>
    <justification jstring="[para(4273(a,1),343(a,1))].">
      <j1 rule="para" parents="4273 343"/>
    </justification>
  </clause>

  <clause id="4609">
    <literal><![CDATA[
      K(x,y) * (R(z,u,w) * x) = T(x,y) * R(T(z,x),u,w)
    ]]></literal>
    <justification jstring="[para(252(a,1),4273(a,1,2))].">
      <j1 rule="para" parents="252 4273"/>
    </justification>
  </clause>

  <clause id="4610">
    <literal><![CDATA[
      T(x,y) * T(z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * (z * x) = u
    ]]></literal>
    <justification jstring="[para(4273(a,1),595(a,1))].">
      <j1 rule="para" parents="4273 595"/>
    </justification>
  </clause>

  <clause id="4611">
    <literal><![CDATA[
      L(T(x,K(x,y) \ z),K(x,y) \ z,K(x,y)) = z \ (T(x,y) * (K(x,y) \ z))
    ]]></literal>
    <justification jstring="[para(4273(a,1),754(a,2,2))].">
      <j1 rule="para" parents="4273 754"/>
    </justification>
  </clause>

  <clause id="4612">
    <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(4273(a,1),498(a,1,1))].">
      <j1 rule="para" parents="4273 498"/>
    </justification>
  </clause>

  <clause id="4613">
    <literal><![CDATA[
      T(x,y) * (T(y,x) * z) = x * (y * z)
    ]]></literal>
    <justification jstring="[para(4273(a,1),4250(a,1,2))].">
      <j1 rule="para" parents="4273 4250"/>
    </justification>
  </clause>

  <clause id="4614">
    <literal><![CDATA[
      K(x \ (x * y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) = u
    ]]></literal>
    <justification jstring="[para(4281(a,2),4306(a,1))].">
      <j1 rule="para" parents="4281 4306"/>
    </justification>
  </clause>

  <clause id="4615">
    <literal><![CDATA[
      K(x,1 / y) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(4306,a,4290,a),flip(a)].">
      <j1 rule="hyper" parents="4306 4290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4616">
    <literal><![CDATA[
      K(x,(x / y) / x) = K(x,1 / y)
    ]]></literal>
    <justification jstring="[hyper(3087,a,4290,a)].">
      <j1 rule="hyper" parents="3087 4290"/>
    </justification>
  </clause>

  <clause id="4618">
    <literal><![CDATA[
      K(x,1 / y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ 1) = z
    ]]></literal>
    <justification jstring="[para(4290(a,1),4306(a,1))].">
      <j1 rule="para" parents="4290 4306"/>
    </justification>
  </clause>

  <clause id="4621">
    <literal><![CDATA[
      K(x,(y \ 1) \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[para(76(a,1),4615(a,1,2)),flip(a)].">
      <j1 rule="para" parents="76 4615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4622">
    <literal><![CDATA[
      K(x,T(y,1 / y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(1196(a,2),4621(a,1,2))].">
      <j1 rule="para" parents="1196 4621"/>
    </justification>
  </clause>

  <clause id="4623">
    <literal><![CDATA[
      K(x,T(y / z,y \ z)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(2496(a,2),4621(a,1,2))].">
      <j1 rule="para" parents="2496 4621"/>
    </justification>
  </clause>

  <clause id="4624">
    <literal><![CDATA[
      (x \ y) * (K(x,x \ y) * z) = (y / x) * z
    ]]></literal>
    <justification jstring="[hyper(125,a,4292,a(flip),b,3545,a),flip(a)].">
      <j1 rule="hyper" parents="125 4292 3545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4625">
    <literal><![CDATA[
      (x \ y) * z != y / x
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ y) = z
    ]]></literal>
    <justification jstring="[para(4292(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="4292 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4626">
    <literal><![CDATA[
      (x \ y) * K((x \ 1) \ 1,x \ y) = y / x
    ]]></literal>
    <justification jstring="[para(3334(a,2),4292(a,1,2))].">
      <j1 rule="para" parents="3334 4292"/>
    </justification>
  </clause>

  <clause id="4628">
    <literal><![CDATA[
      T(x \ y,R(y / x,z,u)) = x \ y
    ]]></literal>
    <justification jstring="[para(4292(a,1),3908(a,1,2,1))].">
      <j1 rule="para" parents="4292 3908"/>
    </justification>
  </clause>

  <clause id="4629">
    <literal><![CDATA[
      K(x,y / z) \ y = z * T(z \ y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,4076,a,b,4296,a),flip(a)].">
      <j1 rule="hyper" parents="63 4076 4296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4630">
    <literal><![CDATA[
      x / (y * T(y \ x,z)) = K(z,x / y)
    ]]></literal>
    <justification jstring="[hyper(197,a,4076,a,b,4296,a(flip))].">
      <j1 rule="hyper" parents="197 4076 4296"/>
    </justification>
  </clause>

  <clause id="4631">
    <literal><![CDATA[
      (x \ y) / (T(x,z) \ y) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(197,a,1062,a(flip),b,4296,a(flip))].">
      <j1 rule="hyper" parents="197 1062 4296"/>
    </justification>
  </clause>

  <clause id="4632">
    <literal><![CDATA[
      T(x * (y / x),z) / T(y,z) = K(x,x \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(123,a,4083,a,b,4297,a)].">
      <j1 rule="hyper" parents="123 4083 4297"/>
    </justification>
  </clause>

  <clause id="4633">
    <literal><![CDATA[
      R(x,K(y,y \ z),z) * (y * (z / y)) = (x * K(y,y \ z)) * z
    ]]></literal>
    <justification jstring="[hyper(126,a,4297,a(flip),b,187,a)].">
      <j1 rule="hyper" parents="126 4297 187"/>
    </justification>
  </clause>

  <clause id="4634">
    <literal><![CDATA[
      (x * (y / x)) \ (K(x,x \ y) * (y * z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(z,y,K(x,x \ y)) = u
    ]]></literal>
    <justification jstring="[para(4297(a,1),504(a,1,1))].">
      <j1 rule="para" parents="4297 504"/>
    </justification>
  </clause>

  <clause id="4635">
    <literal><![CDATA[
      (x * K(y,y \ z)) \ (x * (y * (z / y))) != u
    ]]></literal>
    <literal><![CDATA[
      L(z,K(y,y \ z),x) = u
    ]]></literal>
    <justification jstring="[para(4297(a,1),504(a,1,2,2))].">
      <j1 rule="para" parents="4297 504"/>
    </justification>
  </clause>

  <clause id="4636">
    <literal><![CDATA[
      K(x,y * x) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(4306,a,4300,a),flip(a)].">
      <j1 rule="hyper" parents="4306 4300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4637">
    <literal><![CDATA[
      K(x,y * x) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,x * y) = z
    ]]></literal>
    <justification jstring="[para(4300(a,1),4306(a,1))].">
      <j1 rule="para" parents="4300 4306"/>
    </justification>
  </clause>

  <clause id="4638">
    <literal><![CDATA[
      K(x * (y * z),a(x,y,z) * (x * (y * z))) = K(x * (y * z),(x * y) * z)
    ]]></literal>
    <justification jstring="[para(84(a,1),4636(a,2,2))].">
      <j1 rule="para" parents="84 4636"/>
    </justification>
  </clause>

  <clause id="4639">
    <literal><![CDATA[
      K(x,T(y,T(x,z))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(4305,a,4302,a)].">
      <j1 rule="hyper" parents="4305 4302"/>
    </justification>
  </clause>

  <clause id="4640">
    <literal><![CDATA[
      K(x,y / T(x,z)) = K(x,T(x,z) \ y)
    ]]></literal>
    <justification jstring="[para(113(a,1),4639(a,1,2)),flip(a)].">
      <j1 rule="para" parents="113 4639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4641">
    <literal><![CDATA[
      K(x,T(y,x / y)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(4305,a,4303,a)].">
      <j1 rule="hyper" parents="4305 4303"/>
    </justification>
  </clause>

  <clause id="4642">
    <literal><![CDATA[
      K(x,T(y,y \ x)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(3633(a,1),4641(a,1,2))].">
      <j1 rule="para" parents="3633 4641"/>
    </justification>
  </clause>

  <clause id="4643">
    <literal><![CDATA[
      K(x,(y \ x) \ x) = K(x,y)
    ]]></literal>
    <justification jstring="[para(3665(a,1),4641(a,1,2))].">
      <j1 rule="para" parents="3665 4641"/>
    </justification>
  </clause>

  <clause id="4644">
    <literal><![CDATA[
      K(x,x / y) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[para(332(a,1),4642(a,1,2)),flip(a)].">
      <j1 rule="para" parents="332 4642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4645">
    <literal><![CDATA[
      T(x,y * K(x,y)) / (T(x,y) * y) = x / ((y * K(x,y)) * x)
    ]]></literal>
    <justification jstring="[hyper(197,a,4311,a(flip),b,3640,a)].">
      <j1 rule="hyper" parents="197 4311 3640"/>
    </justification>
  </clause>

  <clause id="4646">
    <literal><![CDATA[
      ((x * y) * (z * K(y,z))) / (T(y,z) * z) = R(x,y,z * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(197,a,4311,a(flip),b,187,a)].">
      <j1 rule="hyper" parents="197 4311 187"/>
    </justification>
  </clause>

  <clause id="4648">
    <literal><![CDATA[
      T(x,x \ y) / (y \ x) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(4316(a,1),3096(a,1,1))].">
      <j1 rule="para" parents="4316 3096"/>
    </justification>
  </clause>

  <clause id="4649">
    <literal><![CDATA[
      T(x,y) * K(z,T(x,y)) = T(x * K(z,x),y)
    ]]></literal>
    <justification jstring="[hyper(4321,a,4320,a)].">
      <j1 rule="hyper" parents="4321 4320"/>
    </justification>
  </clause>

  <clause id="4650">
    <literal><![CDATA[
      T(x * K(x * y,x),y) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(3680,a,4320,a),flip(a)].">
      <j1 rule="hyper" parents="3680 4320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4651">
    <literal><![CDATA[
      K(x,T(y,z)) * T(y,z) = T(y * K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(40,a,4327,a,b,4320,a)].">
      <j1 rule="hyper" parents="40 4327 4320"/>
    </justification>
  </clause>

  <clause id="4652">
    <literal><![CDATA[
      T(x,y) != T(z,u)
    ]]></literal>
    <literal><![CDATA[
      T(z * K(y,z),u) = x
    ]]></literal>
    <justification jstring="[para(4320(a,1),49(a,2)),flip(b)].">
      <j1 rule="para" parents="4320 49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4653">
    <literal><![CDATA[
      T(1 / ((x * y) \ x),y) = 1 / ((x * y) \ x)
    ]]></literal>
    <justification jstring="[hyper(123,a,616,a(flip),b,4332,a),flip(a)].">
      <j1 rule="hyper" parents="123 616 4332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4655">
    <literal><![CDATA[
      T(x,x * y) \ K(T(x,x * y),y) = L(x,y,x) \ 1
    ]]></literal>
    <justification jstring="[para(638(a,1),4355(a,1,1)),flip(a)].">
      <j1 rule="para" parents="638 4355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4656">
    <literal><![CDATA[
      (x * y) \ K(x * y,y) = (L(y,x,y) * x) \ 1
    ]]></literal>
    <justification jstring="[para(3722(a,1),4355(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3722 4355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4657">
    <literal><![CDATA[
      (x * K(y,x)) \ 1 = x \ K(x,y)
    ]]></literal>
    <justification jstring="[para(4238(a,1),4355(a,1,1))].">
      <j1 rule="para" parents="4238 4355"/>
    </justification>
  </clause>

  <clause id="4658">
    <literal><![CDATA[
      K(x,y) / (K(x,y) / x) = x * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(126,a,4357,a(flip),b,4175,a),flip(a)].">
      <j1 rule="hyper" parents="126 4357 4175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4661">
    <literal><![CDATA[
      (1 / x) * (x * K(y,x)) = K(y,x)
    ]]></literal>
    <justification jstring="[para(4238(a,1),4439(a,2,2)),flip(a)].">
      <j1 rule="para" parents="4238 4439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4663">
    <literal><![CDATA[
      L(K(x,y),x,1 / x) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(37,a,445,a,b,4451,a)].">
      <j1 rule="hyper" parents="37 445 4451"/>
    </justification>
  </clause>

  <clause id="4664">
    <literal><![CDATA[
      (1 / x) \ L(K(x,y),z,u) = x * L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(4663(a,1),573(a,1,2,1))].">
      <j1 rule="para" parents="4663 573"/>
    </justification>
  </clause>

  <clause id="4665">
    <literal><![CDATA[
      K(R(x,y,y \ 1),y) / R(x,y,y \ 1) = 1 / ((y * x) * (y \ 1))
    ]]></literal>
    <justification jstring="[para(866(a,1),4454(a,2,2))].">
      <j1 rule="para" parents="866 4454"/>
    </justification>
  </clause>

  <clause id="4666">
    <literal><![CDATA[
      1 / (x * K(y,x)) = K(x,y) / x
    ]]></literal>
    <justification jstring="[para(4238(a,1),4454(a,2,2)),flip(a)].">
      <j1 rule="para" parents="4238 4454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4667">
    <literal><![CDATA[
      K(((x / y) \ 1) \ y,(x / y) \ 1) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3116,a,b,4460,a)].">
      <j1 rule="hyper" parents="63 3116 4460"/>
    </justification>
  </clause>

  <clause id="4668">
    <literal><![CDATA[
      L(L(K(x,x \ y),y,z),z * y,u) = (u * (z * y)) \ (u * (z * (x * (y / x))))
    ]]></literal>
    <justification jstring="[para(4460(a,1),526(a,1,1,1))].">
      <j1 rule="para" parents="4460 526"/>
    </justification>
  </clause>

  <clause id="4669">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * (u * (L(z,y,x) / u))) = L(K(u,u \ L(z,y,x)),L(z,y,x),x * y)
    ]]></literal>
    <justification jstring="[para(4460(a,1),524(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4460 524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4670">
    <literal><![CDATA[
      T(x,K(y,y \ x)) = x
    ]]></literal>
    <justification jstring="[hyper(253,a,4461,a,b,4297,a)].">
      <j1 rule="hyper" parents="253 4461 4297"/>
    </justification>
  </clause>

  <clause id="4671">
    <literal><![CDATA[
      (x * (y / x)) \ (y * (K(x,x \ y) * z)) = L(z,K(x,x \ y),y)
    ]]></literal>
    <justification jstring="[para(4461(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4461 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4672">
    <literal><![CDATA[
      R(x,x \ y,K(z,z \ y)) \ (z * (y / z)) = (x \ y) * K(z,z \ y)
    ]]></literal>
    <justification jstring="[para(4461(a,1),529(a,1,2))].">
      <j1 rule="para" parents="4461 529"/>
    </justification>
  </clause>

  <clause id="4673">
    <literal><![CDATA[
      R(x,y,z * (K(u,u \ z) \ 1)) = R(x,y,u * (z / u))
    ]]></literal>
    <justification jstring="[para(4461(a,1),1873(a,2,3))].">
      <j1 rule="para" parents="4461 1873"/>
    </justification>
  </clause>

  <clause id="4674">
    <literal><![CDATA[
      T(x,y) * K(x * y,(x * y) \ T(x,y)) = (x * y) * (x / (y * x))
    ]]></literal>
    <justification jstring="[para(3710(a,1),4461(a,2,2))].">
      <j1 rule="para" parents="3710 4461"/>
    </justification>
  </clause>

  <clause id="4676">
    <literal><![CDATA[
      T(x * (y / x),z) \ T(y,z) = K(x \ T(y,z),x)
    ]]></literal>
    <justification jstring="[para(4083(a,2),4465(a,1,1))].">
      <j1 rule="para" parents="4083 4465"/>
    </justification>
  </clause>

  <clause id="4677">
    <literal><![CDATA[
      T(x,y) * (1 / y) = x * (1 / T(y,x))
    ]]></literal>
    <justification jstring="[para(4507(a,1),4241(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4507 4241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4678">
    <literal><![CDATA[
      (T(x,y) * T(K(x,y) \ z,u)) / T(x,y) = T((x * z) / T(x,y),u)
    ]]></literal>
    <justification jstring="[para(4510(a,1),474(a,1,1,2,1))].">
      <j1 rule="para" parents="4510 474"/>
    </justification>
  </clause>

  <clause id="4680">
    <literal><![CDATA[
      K(x,y) * (T(x,y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      x \ z = u
    ]]></literal>
    <justification jstring="[para(4511(a,1),273(a,1,2)),flip(b)].">
      <j1 rule="para" parents="4511 273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4681">
    <literal><![CDATA[
      L(x \ (T(y,z) \ u),x,K(y,z)) = (K(y,z) * x) \ (y \ u)
    ]]></literal>
    <justification jstring="[para(4511(a,1),311(a,1,1,2))].">
      <j1 rule="para" parents="4511 311"/>
    </justification>
  </clause>

  <clause id="4682">
    <literal><![CDATA[
      (x * (1 / x)) \ (x \ y) = T(x,x \ 1) \ y
    ]]></literal>
    <justification jstring="[para(2098(a,1),4511(a,1,1))].">
      <j1 rule="para" parents="2098 4511"/>
    </justification>
  </clause>

  <clause id="4684">
    <literal><![CDATA[
      x * (K(x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * z = u
    ]]></literal>
    <justification jstring="[para(4513(a,1),575(a,1))].">
      <j1 rule="para" parents="4513 575"/>
    </justification>
  </clause>

  <clause id="4685">
    <literal><![CDATA[
      K(T(x,y) \ (x * z),u) = K(K(x,y) \ z,u)
    ]]></literal>
    <justification jstring="[para(4513(a,1),705(a,1,1,2))].">
      <j1 rule="para" parents="4513 705"/>
    </justification>
  </clause>

  <clause id="4686">
    <literal><![CDATA[
      (x \ 1) * K(x,y) = x \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(1376,a,4516,a)].">
      <j1 rule="hyper" parents="1376 4516"/>
    </justification>
  </clause>

  <clause id="4687">
    <literal><![CDATA[
      K(x,y) * (y \ K(y,x)) = y \ 1
    ]]></literal>
    <justification jstring="[hyper(34,a,4558,a,b,4516,a)].">
      <j1 rule="hyper" parents="34 4558 4516"/>
    </justification>
  </clause>

  <clause id="4688">
    <literal><![CDATA[
      (x \ 1) / (x \ K(x,y)) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(197,a,4516,a(flip),b,4567,a)].">
      <j1 rule="hyper" parents="197 4516 4567"/>
    </justification>
  </clause>

  <clause id="4689">
    <literal><![CDATA[
      x \ y != K(x,z) * u
    ]]></literal>
    <literal><![CDATA[
      T(x,z) \ y = u
    ]]></literal>
    <justification jstring="[para(4518(a,1),43(a,1))].">
      <j1 rule="para" parents="4518 43"/>
    </justification>
  </clause>

  <clause id="4690">
    <literal><![CDATA[
      K(x,y) \ (x \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) \ z = u
    ]]></literal>
    <justification jstring="[para(4518(a,1),342(a,1,2))].">
      <j1 rule="para" parents="4518 342"/>
    </justification>
  </clause>

  <clause id="4692">
    <literal><![CDATA[
      K(x,y \ 1) * (y \ x) = y \ T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(3601,a,4530,a),flip(a)].">
      <j1 rule="hyper" parents="3601 4530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4694">
    <literal><![CDATA[
      K(x,y) * (y * L(y \ z,u,w)) = T(y,x) \ L(y * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(126,a,2576,a(flip),b,4548,a)].">
      <j1 rule="hyper" parents="126 2576 4548"/>
    </justification>
  </clause>

  <clause id="4695">
    <literal><![CDATA[
      K(x,R(y,y \ z,u)) * ((y \ z) * u) = T(R(y,y \ z,u),x) \ (z * u)
    ]]></literal>
    <justification jstring="[hyper(126,a,529,a(flip),b,4548,a)].">
      <j1 rule="hyper" parents="126 529 4548"/>
    </justification>
  </clause>

  <clause id="4696">
    <literal><![CDATA[
      T(x,y) \ (T(y,x) \ z) = x \ (y \ z)
    ]]></literal>
    <justification jstring="[hyper(121,a,4548,a(flip),b,4296,a),flip(a)].">
      <j1 rule="hyper" parents="121 4548 4296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4697">
    <literal><![CDATA[
      K(x,y) * (y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,x) \ z = u
    ]]></literal>
    <justification jstring="[para(4548(a,1),273(a,1,2)),flip(b)].">
      <j1 rule="para" parents="4548 273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4698">
    <literal><![CDATA[
      T(x,y) * (K(y,x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(4549(a,1),264(a,1,1)),flip(b)].">
      <j1 rule="para" parents="4549 264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4699">
    <literal><![CDATA[
      T(x,y) \ (x * L(K(y,x) \ 1,z,u)) = K(y,x) \ L(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(333,a,2582,a(flip),b,4550,a),flip(a)].">
      <j1 rule="hyper" parents="333 2582 4550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4700">
    <literal><![CDATA[
      K(x,y) * T(x,T(y,z)) = T(T(x,y),T(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,3898,a(flip),b,4550,a),flip(a)].">
      <j1 rule="hyper" parents="63 3898 4550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4701">
    <literal><![CDATA[
      x * (K(x * y,x) * y) = T(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(126,a,4550,a(flip),b,3628,a(flip))].">
      <j1 rule="hyper" parents="126 4550 3628"/>
    </justification>
  </clause>

  <clause id="4702">
    <literal><![CDATA[
      L(T(x,y),z,u) \ (L(x,z,u) * w) = K(y,L(x,z,u)) * w
    ]]></literal>
    <justification jstring="[para(25(a,2),4550(a,1,1))].">
      <j1 rule="para" parents="25 4550"/>
    </justification>
  </clause>

  <clause id="4703">
    <literal><![CDATA[
      ((x \ y) \ y) \ z = K(x \ y,x) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(333,a,326,a(flip),b,4555,a)].">
      <j1 rule="hyper" parents="333 326 4555"/>
    </justification>
  </clause>

  <clause id="4704">
    <literal><![CDATA[
      K(x,y) * (T(y,x) \ z) = T(T(y,x),x) \ z
    ]]></literal>
    <justification jstring="[para(4370(a,1),4555(a,1,1))].">
      <j1 rule="para" parents="4370 4555"/>
    </justification>
  </clause>

  <clause id="4705">
    <literal><![CDATA[
      x \ (T(y,x) * (y \ z)) = T(x,y) \ z
    ]]></literal>
    <justification jstring="[hyper(121,a,4242,a,b,4556,a)].">
      <j1 rule="hyper" parents="121 4242 4556"/>
    </justification>
  </clause>

  <clause id="4706">
    <literal><![CDATA[
      T(x,y) \ (y * z) = x \ (T(y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(121,a,4273,a(flip),b,4556,a),flip(a)].">
      <j1 rule="hyper" parents="121 4273 4556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4707">
    <literal><![CDATA[
      K((x / y) / (y \ 1),z) = (T(x,z) / y) / (x / y)
    ]]></literal>
    <justification jstring="[hyper(123,a,4081,a(flip),b,4556,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="123 4081 4556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4709">
    <literal><![CDATA[
      x \ (y * (K(z,y \ x) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(T(y \ x,z) \ u,y \ x,y) = w
    ]]></literal>
    <justification jstring="[para(4556(a,1),784(a,1,2,2))].">
      <j1 rule="para" parents="4556 784"/>
    </justification>
  </clause>

  <clause id="4710">
    <literal><![CDATA[
      (x / T(y,x)) * ((y \ T(x,y)) \ z) = K(y,x / T(y,x)) * z
    ]]></literal>
    <justification jstring="[para(3622(a,1),4556(a,1,2,1))].">
      <j1 rule="para" parents="3622 4556"/>
    </justification>
  </clause>

  <clause id="4711">
    <literal><![CDATA[
      K(x,y) * T(T(y,x),z) = y * K(T(y,x),z)
    ]]></literal>
    <justification jstring="[para(4215(a,2),4556(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4215 4556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4712">
    <literal><![CDATA[
      K(x,y) * (y * z) = y * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(4550(a,1),4556(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4550 4556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4714">
    <literal><![CDATA[
      T(x \ y,z) * T(x,x \ y) = K(z,x \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(121,a,234,a(flip),b,4557,a),flip(a)].">
      <j1 rule="hyper" parents="121 234 4557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4715">
    <literal><![CDATA[
      K(x,y) \ (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,x) * z = u
    ]]></literal>
    <justification jstring="[para(4557(a,1),342(a,1,2))].">
      <j1 rule="para" parents="4557 342"/>
    </justification>
  </clause>

  <clause id="4716">
    <literal><![CDATA[
      x * (T(x,y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * z = u
    ]]></literal>
    <justification jstring="[para(4557(a,1),343(a,1))].">
      <j1 rule="para" parents="4557 343"/>
    </justification>
  </clause>

  <clause id="4717">
    <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(4566(a,1),1505(a,1,2,2,1))].">
      <j1 rule="para" parents="4566 1505"/>
    </justification>
  </clause>

  <clause id="4718">
    <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(4566(a,1),1602(a,1,2,2,1))].">
      <j1 rule="para" parents="4566 1602"/>
    </justification>
  </clause>

  <clause id="4720">
    <literal><![CDATA[
      ((x \ 1) * x) \ (x * y) = T(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[para(276(a,1),4598(a,1,1))].">
      <j1 rule="para" parents="276 4598"/>
    </justification>
  </clause>

  <clause id="4722">
    <literal><![CDATA[
      (R(x,y,z) * u) / (R(T(x,w),y,z) * u) = K(w,R(x,y,z))
    ]]></literal>
    <justification jstring="[para(27(a,2),4607(a,1,2,1))].">
      <j1 rule="para" parents="27 4607"/>
    </justification>
  </clause>

  <clause id="4723">
    <literal><![CDATA[
      (x / y) * K(x,1 / y) = x * ((x / y) / x)
    ]]></literal>
    <justification jstring="[hyper(126,a,4616,a(flip),b,91,a)].">
      <j1 rule="hyper" parents="126 4616 91"/>
    </justification>
  </clause>

  <clause id="4724">
    <literal><![CDATA[
      K(x,1 / (y \ x)) = K(x,y / x)
    ]]></literal>
    <justification jstring="[para(76(a,1),4616(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="76 4616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4725">
    <literal><![CDATA[
      (L(x,y,z) \ u) / (L(T(x,w),y,z) \ u) = K(L(x,y,z),w)
    ]]></literal>
    <justification jstring="[para(25(a,2),4631(a,1,2,1))].">
      <j1 rule="para" parents="25 4631"/>
    </justification>
  </clause>

  <clause id="4726">
    <literal><![CDATA[
      (x \ 1) * K(y,x \ 1) = x \ K(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(121,a,4661,a(flip),b,186,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="121 4661 186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4727">
    <literal><![CDATA[
      (K(x,y) / x) \ 1 = x * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(192,a,4666,a)].">
      <j1 rule="hyper" parents="192 4666"/>
    </justification>
  </clause>

  <clause id="4728">
    <literal><![CDATA[
      1 / ((x \ 1) * K(y,x \ 1)) = K(1 / x,y) / (x \ 1)
    ]]></literal>
    <justification jstring="[para(3333(a,2),4666(a,2,1))].">
      <j1 rule="para" parents="3333 4666"/>
    </justification>
  </clause>

  <clause id="4729">
    <literal><![CDATA[
      x \ K(x,y) != z * K(x,y)
    ]]></literal>
    <literal><![CDATA[
      x \ 1 = z
    ]]></literal>
    <justification jstring="[para(4686(a,1),44(a,1))].">
      <j1 rule="para" parents="4686 44"/>
    </justification>
  </clause>

  <clause id="4730">
    <literal><![CDATA[
      (x \ 1) / (x \ K(x,y)) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(4687(a,1),268(a,1,1)),flip(b)].">
      <j1 rule="para" parents="4687 268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4731">
    <literal><![CDATA[
      L(x,x,x) \ 1 = x \ a(x,x,x)
    ]]></literal>
    <justification jstring="[para(114(a,1),4362(a,1,1))].">
      <j1 rule="para" parents="114 4362"/>
    </justification>
  </clause>

  <clause id="4732">
    <literal><![CDATA[
      K(x,y) \ T(x,y * x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,4567,a,b,4521,a)].">
      <j1 rule="hyper" parents="63 4567 4521"/>
    </justification>
  </clause>

  <clause id="4733">
    <literal><![CDATA[
      T(x,x * y) * K(y,x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(2730,a,4522,a)].">
      <j1 rule="hyper" parents="2730 4522"/>
    </justification>
  </clause>

  <clause id="4734">
    <literal><![CDATA[
      K(x,y) \ T(x,x * y) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,4567,a,b,4522,a)].">
      <j1 rule="hyper" parents="63 4567 4522"/>
    </justification>
  </clause>

  <clause id="4735">
    <literal><![CDATA[
      K(x,y) = T(y,y * x) \ L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(121,a,4522,a(flip),b,2727,a),flip(a)].">
      <j1 rule="hyper" parents="121 4522 2727"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4736">
    <literal><![CDATA[
      T(x,y) * K(x * y,x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(2730,a,4523,a)].">
      <j1 rule="hyper" parents="2730 4523"/>
    </justification>
  </clause>

  <clause id="4737">
    <literal><![CDATA[
      K(x,x * y) \ T(x,y) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,4567,a,b,4523,a)].">
      <j1 rule="hyper" parents="63 4567 4523"/>
    </justification>
  </clause>

  <clause id="4738">
    <literal><![CDATA[
      T(T(x,y),z) * K(u,x) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u) \ T(T(x,y),z) = w
    ]]></literal>
    <justification jstring="[para(2732(a,2),4585(a,1))].">
      <j1 rule="para" parents="2732 4585"/>
    </justification>
  </clause>

  <clause id="4739">
    <literal><![CDATA[
      K((x / y) \ x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) = u
    ]]></literal>
    <justification jstring="[para(12(a,1),4614(a,1,1,2))].">
      <j1 rule="para" parents="12 4614"/>
    </justification>
  </clause>

  <clause id="4740">
    <literal><![CDATA[
      K(T(x,y) \ (x * z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(x,y) \ z,u) = w
    ]]></literal>
    <justification jstring="[para(4513(a,1),4614(a,1,1,2))].">
      <j1 rule="para" parents="4513 4614"/>
    </justification>
  </clause>

  <clause id="4741">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,(y \ 1) \ 1) = z
    ]]></literal>
    <justification jstring="[para(76(a,1),4618(a,1,2))].">
      <j1 rule="para" parents="76 4618"/>
    </justification>
  </clause>

  <clause id="4742">
    <literal><![CDATA[
      T(T(x * K(x * y,x),z),y) = T(R(x,y,x),z)
    ]]></literal>
    <justification jstring="[para(4650(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4650 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4743">
    <literal><![CDATA[
      K(x,x * y) * K(y,x) = x \ L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(121,a,4733,a(flip),b,4241,a),flip(a)].">
      <j1 rule="hyper" parents="121 4733 4241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4746">
    <literal><![CDATA[
      K(x,y) * K(x * y,x) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(121,a,4736,a(flip),b,4241,a),flip(a)].">
      <j1 rule="hyper" parents="121 4736 4241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4747">
    <literal><![CDATA[
      (x * T(y,z)) \ (x * R(y,z,y)) = L(K(y * z,y),T(y,z),x)
    ]]></literal>
    <justification jstring="[para(4736(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4736 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4748">
    <literal><![CDATA[
      R(x,y,x) \ T(x,y) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(39,a,4131,a,b,4737,a)].">
      <j1 rule="hyper" parents="39 4131 4737"/>
    </justification>
  </clause>

  <clause id="4749">
    <literal><![CDATA[
      R(x * x,x \ y,x * x) \ T(x * x,x \ y) = K(x * x,(x \ 1) \ y)
    ]]></literal>
    <justification jstring="[para(708(a,1),4748(a,2,2))].">
      <j1 rule="para" parents="708 4748"/>
    </justification>
  </clause>

  <clause id="4750">
    <literal><![CDATA[
      K(x \ (x * y),x) = (y * x) * ((x * y) \ 1)
    ]]></literal>
    <justification jstring="[para(9(a,1),4191(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 4191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4751">
    <literal><![CDATA[
      ((x * y) / x) \ (T(x,y) * z) = y \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(121,a,4557,a(flip),b,4236,a),flip(a)].">
      <j1 rule="hyper" parents="121 4557 4236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4752">
    <literal><![CDATA[
      x * ((y / (y / x)) \ z) = K(x,x \ y) * z
    ]]></literal>
    <justification jstring="[para(3697(a,1),4236(a,1,2,1))].">
      <j1 rule="para" parents="3697 4236"/>
    </justification>
  </clause>

  <clause id="4753">
    <literal><![CDATA[
      (x * (y * T(y \ z,u))) / (x * z) = K((x * z) / (x * y),u)
    ]]></literal>
    <justification jstring="[hyper(123,a,939,a(flip),b,4243,a)].">
      <j1 rule="hyper" parents="123 939 4243"/>
    </justification>
  </clause>

  <clause id="4755">
    <literal><![CDATA[
      K(x * K(y,y \ 1),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,4212,a,b,4256,a),flip(a)].">
      <j1 rule="hyper" parents="333 4212 4256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4756">
    <literal><![CDATA[
      K(x * K(y \ 1,y),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(2100(a,1),4755(a,1,1,2))].">
      <j1 rule="para" parents="2100 4755"/>
    </justification>
  </clause>

  <clause id="4757">
    <literal><![CDATA[
      K(x * (1 / y),z) = K(x * (y \ 1),z)
    ]]></literal>
    <justification jstring="[para(2141(a,1),4755(a,1,1))].">
      <j1 rule="para" parents="2141 4755"/>
    </justification>
  </clause>

  <clause id="4758">
    <literal><![CDATA[
      K(x * ((y \ 1) \ 1),z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(2142(a,1),4755(a,1,1))].">
      <j1 rule="para" parents="2142 4755"/>
    </justification>
  </clause>

  <clause id="4759">
    <literal><![CDATA[
      K(x * (1 / (1 / y)),z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(2143(a,1),4755(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2143 4755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4760">
    <literal><![CDATA[
      K(K(x,x \ 1) * y,z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(2397(a,2),4755(a,1,1))].">
      <j1 rule="para" parents="2397 4755"/>
    </justification>
  </clause>

  <clause id="4761">
    <literal><![CDATA[
      K(x \ (K(y,y \ 1) * z),u) = K(x \ z,u)
    ]]></literal>
    <justification jstring="[para(2427(a,2),4755(a,1,1))].">
      <j1 rule="para" parents="2427 4755"/>
    </justification>
  </clause>

  <clause id="4762">
    <literal><![CDATA[
      K((1 / x) * y,z) = K((x \ 1) * y,z)
    ]]></literal>
    <justification jstring="[para(2644(a,1),4755(a,1,1))].">
      <j1 rule="para" parents="2644 4755"/>
    </justification>
  </clause>

  <clause id="4763">
    <literal><![CDATA[
      K((1 / x) \ y,z) = K((x \ 1) \ y,z)
    ]]></literal>
    <justification jstring="[para(2669(a,1),4755(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2669 4755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4764">
    <literal><![CDATA[
      K(((x \ 1) \ 1) \ y,z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(2674(a,1),4755(a,1,1))].">
      <j1 rule="para" parents="2674 4755"/>
    </justification>
  </clause>

  <clause id="4765">
    <literal><![CDATA[
      K(x / (1 / y),z) = K(x / (y \ 1),z)
    ]]></literal>
    <justification jstring="[para(1903(a,1),4756(a,1,1))].">
      <j1 rule="para" parents="1903 4756"/>
    </justification>
  </clause>

  <clause id="4766">
    <literal><![CDATA[
      K(x \ (1 / y),z) = K(x \ (y \ 1),z)
    ]]></literal>
    <justification jstring="[para(1918(a,1),4756(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1918 4756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4767">
    <literal><![CDATA[
      K((1 / (1 / x)) * y,z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(2765(a,1),4756(a,1,1))].">
      <j1 rule="para" parents="2765 4756"/>
    </justification>
  </clause>

  <clause id="4768">
    <literal><![CDATA[
      K((K(x,x \ 1) * y) \ z,u) = K(y \ z,u)
    ]]></literal>
    <justification jstring="[para(2847(a,2),4756(a,1,1))].">
      <j1 rule="para" parents="2847 4756"/>
    </justification>
  </clause>

  <clause id="4769">
    <literal><![CDATA[
      K(((1 / x) * y) \ z,u) = K(((x \ 1) * y) \ z,u)
    ]]></literal>
    <justification jstring="[para(2851(a,1),4756(a,1,1))].">
      <j1 rule="para" parents="2851 4756"/>
    </justification>
  </clause>

  <clause id="4770">
    <literal><![CDATA[
      K((x * (K(y,y \ 1) * z)) \ u,w) = K((x * z) \ u,w)
    ]]></literal>
    <justification jstring="[para(2850(a,2),4756(a,1,1))].">
      <j1 rule="para" parents="2850 4756"/>
    </justification>
  </clause>

  <clause id="4771">
    <literal><![CDATA[
      x * (y * ((z * (y \ (x \ 1))) / z)) = K(z,(x * y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(1172,a,4263,a)].">
      <j1 rule="hyper" parents="1172 4263"/>
    </justification>
  </clause>

  <clause id="4772">
    <literal><![CDATA[
      (x * ((y * (x \ z)) / y)) / z = K(y,(x / z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,2269,a(flip),b,4263,a)].">
      <j1 rule="hyper" parents="63 2269 4263"/>
    </justification>
  </clause>

  <clause id="4773">
    <literal><![CDATA[
      K(x,y \ 1) / y = (x * (1 / y)) / x
    ]]></literal>
    <justification jstring="[hyper(123,a,4263,a(flip),b,906,a)].">
      <j1 rule="hyper" parents="123 4263 906"/>
    </justification>
  </clause>

  <clause id="4774">
    <literal><![CDATA[
      (x \ K(y,x \ 1)) * y = y * (x \ 1)
    ]]></literal>
    <justification jstring="[para(4263(a,1),80(a,1,1,2))].">
      <j1 rule="para" parents="4263 80"/>
    </justification>
  </clause>

  <clause id="4776">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ x)) / z) = x * K(z,y \ 1)
    ]]></literal>
    <justification jstring="[para(4263(a,1),1697(a,2,2))].">
      <j1 rule="para" parents="4263 1697"/>
    </justification>
  </clause>

  <clause id="4777">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ y)) / z) = K(z,x \ 1) * y
    ]]></literal>
    <justification jstring="[para(4263(a,1),1990(a,2,1))].">
      <j1 rule="para" parents="4263 1990"/>
    </justification>
  </clause>

  <clause id="4778">
    <literal><![CDATA[
      K(x,R(y,z,u) \ 1) * (z * u) = ((y * z) * ((x * ((y * z) \ z)) / x)) * u
    ]]></literal>
    <justification jstring="[para(4263(a,1),4054(a,1,1))].">
      <j1 rule="para" parents="4263 4054"/>
    </justification>
  </clause>

  <clause id="4779">
    <literal><![CDATA[
      K((x \ 1) * y,x) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,4184,a,b,4276,a),flip(a)].">
      <j1 rule="hyper" parents="35 4184 4276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4780">
    <literal><![CDATA[
      T(x \ K(y,x \ 1),y) = x \ 1
    ]]></literal>
    <justification jstring="[para(4279(a,2),238(a,1,1))].">
      <j1 rule="para" parents="4279 238"/>
    </justification>
  </clause>

  <clause id="4781">
    <literal><![CDATA[
      K(x,x * (y \ 1)) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(333,a,4215,a,b,4289,a),flip(a)].">
      <j1 rule="hyper" parents="333 4215 4289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4782">
    <literal><![CDATA[
      K(x,y * K(z,z \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,4215,a,b,4293,a),flip(a)].">
      <j1 rule="hyper" parents="333 4215 4293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4783">
    <literal><![CDATA[
      K(x,y * K(z,1 / z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(2094(a,2),4782(a,1,2,2))].">
      <j1 rule="para" parents="2094 4782"/>
    </justification>
  </clause>

  <clause id="4784">
    <literal><![CDATA[
      K(x,y * K(z \ 1,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(2100(a,1),4782(a,1,2,2))].">
      <j1 rule="para" parents="2100 4782"/>
    </justification>
  </clause>

  <clause id="4785">
    <literal><![CDATA[
      K(x,y * (1 / z)) = K(x,y * (z \ 1))
    ]]></literal>
    <justification jstring="[para(2141(a,1),4782(a,1,2))].">
      <j1 rule="para" parents="2141 4782"/>
    </justification>
  </clause>

  <clause id="4786">
    <literal><![CDATA[
      K(x,y * ((z \ 1) \ 1)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(2142(a,1),4782(a,1,2))].">
      <j1 rule="para" parents="2142 4782"/>
    </justification>
  </clause>

  <clause id="4787">
    <literal><![CDATA[
      K(x,K(y,y \ 1) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(2397(a,2),4782(a,1,2))].">
      <j1 rule="para" parents="2397 4782"/>
    </justification>
  </clause>

  <clause id="4788">
    <literal><![CDATA[
      K(x,K(y \ 1,y) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(2439(a,1),4782(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2439 4782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4789">
    <literal><![CDATA[
      K(x,y \ (K(z,z \ 1) * u)) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(2427(a,2),4782(a,1,2))].">
      <j1 rule="para" parents="2427 4782"/>
    </justification>
  </clause>

  <clause id="4790">
    <literal><![CDATA[
      K(x,(y \ 1) * (y * z)) = K(x,L(z,y,y \ 1))
    ]]></literal>
    <justification jstring="[para(2454(a,1),4782(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2454 4782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4791">
    <literal><![CDATA[
      K(x,(1 / y) * z) = K(x,(y \ 1) * z)
    ]]></literal>
    <justification jstring="[para(2644(a,1),4782(a,1,2))].">
      <j1 rule="para" parents="2644 4782"/>
    </justification>
  </clause>

  <clause id="4792">
    <literal><![CDATA[
      K(x,(1 / y) \ z) = K(x,(y \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(2669(a,1),4782(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2669 4782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4793">
    <literal><![CDATA[
      K(x,((y \ 1) \ 1) * z) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(2690(a,1),4782(a,1,2))].">
      <j1 rule="para" parents="2690 4782"/>
    </justification>
  </clause>

  <clause id="4794">
    <literal><![CDATA[
      K(x,(1 / y) / z) = K(x,(y \ 1) / z)
    ]]></literal>
    <justification jstring="[para(2862(a,1),4782(a,1,2))].">
      <j1 rule="para" parents="2862 4782"/>
    </justification>
  </clause>

  <clause id="4795">
    <literal><![CDATA[
      K(x,((y \ 1) \ 1) \ z) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(2674(a,1),4782(a,1,2))].">
      <j1 rule="para" parents="2674 4782"/>
    </justification>
  </clause>

  <clause id="4796">
    <literal><![CDATA[
      K(x,y * (z * K(u,1 / u))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(1883(a,1),4783(a,1,2))].">
      <j1 rule="para" parents="1883 4783"/>
    </justification>
  </clause>

  <clause id="4797">
    <literal><![CDATA[
      K(x,K(y,1 / y) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(2408(a,2),4783(a,1,2))].">
      <j1 rule="para" parents="2408 4783"/>
    </justification>
  </clause>

  <clause id="4798">
    <literal><![CDATA[
      K(x,y * (z * K(u \ 1,u))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(1879(a,1),4784(a,1,2))].">
      <j1 rule="para" parents="1879 4784"/>
    </justification>
  </clause>

  <clause id="4799">
    <literal><![CDATA[
      K(x,y / (1 / z)) = K(x,y / (z \ 1))
    ]]></literal>
    <justification jstring="[para(1903(a,1),4784(a,1,2))].">
      <j1 rule="para" parents="1903 4784"/>
    </justification>
  </clause>

  <clause id="4800">
    <literal><![CDATA[
      K(x,y \ (1 / z)) = K(x,y \ (z \ 1))
    ]]></literal>
    <justification jstring="[para(1918(a,1),4784(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1918 4784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4801">
    <literal><![CDATA[
      K(x,(K(y,y \ 1) * z) \ u) = K(x,z \ u)
    ]]></literal>
    <justification jstring="[para(2847(a,2),4784(a,1,2))].">
      <j1 rule="para" parents="2847 4784"/>
    </justification>
  </clause>

  <clause id="4802">
    <literal><![CDATA[
      K(x,((1 / y) * z) \ u) = K(x,((y \ 1) * z) \ u)
    ]]></literal>
    <justification jstring="[para(2851(a,1),4784(a,1,2))].">
      <j1 rule="para" parents="2851 4784"/>
    </justification>
  </clause>

  <clause id="4803">
    <literal><![CDATA[
      K(x,y * (z * (1 / u))) = K(x,y * (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[para(2504(a,1),4787(a,1,2))].">
      <j1 rule="para" parents="2504 4787"/>
    </justification>
  </clause>

  <clause id="4804">
    <literal><![CDATA[
      K(x,y * (z / (1 / u))) = K(x,y * (z / (u \ 1)))
    ]]></literal>
    <justification jstring="[para(2507(a,1),4787(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2507 4787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4805">
    <literal><![CDATA[
      K(x,y * ((1 / z) \ u)) = K(x,y * ((z \ 1) \ u))
    ]]></literal>
    <justification jstring="[para(2673(a,1),4787(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2673 4787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4806">
    <literal><![CDATA[
      K(x,T(y * K(z,z \ 1),u)) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[para(4150(a,2),4787(a,1,2))].">
      <j1 rule="para" parents="4150 4787"/>
    </justification>
  </clause>

  <clause id="4807">
    <literal><![CDATA[
      K(x,(K(y \ 1,y) * z) / u) = K(x,z / u)
    ]]></literal>
    <justification jstring="[para(2799(a,2),4788(a,1,2))].">
      <j1 rule="para" parents="2799 4788"/>
    </justification>
  </clause>

  <clause id="4808">
    <literal><![CDATA[
      K(x,y / (K(z,z \ 1) * u)) = K(x,y / u)
    ]]></literal>
    <justification jstring="[para(2962(a,2),4788(a,1,2))].">
      <j1 rule="para" parents="2962 4788"/>
    </justification>
  </clause>

  <clause id="4809">
    <literal><![CDATA[
      K(x,K(y,1 / y) / z) = K(x,1 / z)
    ]]></literal>
    <justification jstring="[para(2792(a,1),4797(a,1,2))].">
      <j1 rule="para" parents="2792 4797"/>
    </justification>
  </clause>

  <clause id="4810">
    <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(4318(a,1),1334(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4318 1334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4811">
    <literal><![CDATA[
      T(x * K(y \ x,x),y \ 1) = R(x,x \ (y \ x),x)
    ]]></literal>
    <justification jstring="[hyper(333,a,3873,a,b,4323,a),flip(a)].">
      <j1 rule="hyper" parents="333 3873 4323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4812">
    <literal><![CDATA[
      T(x,y) \ T(x * K(z,x),y) = K(z,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(121,a,4323,a,b,4238,a(flip))].">
      <j1 rule="hyper" parents="121 4323 4238"/>
    </justification>
  </clause>

  <clause id="4813">
    <literal><![CDATA[
      K(x,y) * (x / y) = x / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(3902,a,4414,a),flip(a)].">
      <j1 rule="hyper" parents="3902 4414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4814">
    <literal><![CDATA[
      ((x * y) / x) * z = (y * (K(x,y) * z)) * 1
    ]]></literal>
    <justification jstring="[hyper(333,a,8,a,b,4414,a),flip(a)].">
      <j1 rule="hyper" parents="333 8 4414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4815">
    <literal><![CDATA[
      (x * (K(y * z,x) * y)) * z = (y * z) * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(125,a,4414,a(flip),b,1175,a)].">
      <j1 rule="hyper" parents="125 4414 1175"/>
    </justification>
  </clause>

  <clause id="4816">
    <literal><![CDATA[
      K(x,y) * (K((x * y) / x,z) * u) = y \ (T((x * y) / x,z) * u)
    ]]></literal>
    <justification jstring="[hyper(121,a,4241,a(flip),b,4414,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="121 4241 4414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4817">
    <literal><![CDATA[
      K(x,y) * (y * z) = ((x * y) / x) * z
    ]]></literal>
    <justification jstring="[hyper(34,a,1295,a(flip),b,4414,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="34 1295 4414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4818">
    <literal><![CDATA[
      (x / y) * (K(y,y \ x) * z) = ((y * (x / y)) / y) * z
    ]]></literal>
    <justification jstring="[para(4368(a,1),4414(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4368 4414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4819">
    <literal><![CDATA[
      ((x * y) / x) * (x * z) = y * (T(x,y) * z)
    ]]></literal>
    <justification jstring="[para(4273(a,1),4414(a,2,2))].">
      <j1 rule="para" parents="4273 4414"/>
    </justification>
  </clause>

  <clause id="4820">
    <literal><![CDATA[
      K(x,y) * (x / y) = T(x,y) / y
    ]]></literal>
    <justification jstring="[hyper(333,a,3625,a,b,4813,a),flip(a)].">
      <j1 rule="hyper" parents="333 3625 4813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4821">
    <literal><![CDATA[
      T(x,y) * (y / T(x,y)) = x * (y / x)
    ]]></literal>
    <justification jstring="[hyper(126,a,4813,a(flip),b,4550,a)].">
      <j1 rule="hyper" parents="126 4813 4550"/>
    </justification>
  </clause>

  <clause id="4822">
    <literal><![CDATA[
      (x / T(y,x)) * L(z,x / y,K(x,y)) = K(x,y) * ((x / y) * z)
    ]]></literal>
    <justification jstring="[hyper(125,a,4813,a(flip),b,190,a)].">
      <j1 rule="hyper" parents="125 4813 190"/>
    </justification>
  </clause>

  <clause id="4823">
    <literal><![CDATA[
      R(K(x,y),x / y,z) \ ((x / T(y,x)) * z) = (x / y) * z
    ]]></literal>
    <justification jstring="[para(4813(a,1),187(a,1,2,1))].">
      <j1 rule="para" parents="4813 187"/>
    </justification>
  </clause>

  <clause id="4824">
    <literal><![CDATA[
      ((x * y) / x) * (y \ z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(63,a,1296,a(flip),b,4434,a)].">
      <j1 rule="hyper" parents="63 1296 4434"/>
    </justification>
  </clause>

  <clause id="4825">
    <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(4442(a,1),805(a,1,1))].">
      <j1 rule="para" parents="4442 805"/>
    </justification>
  </clause>

  <clause id="4826">
    <literal><![CDATA[
      (x \ 1) * K(y,x \ 1) = x \ K(y,1 / x)
    ]]></literal>
    <justification jstring="[hyper(333,a,4238,a(flip),b,4444,a)].">
      <j1 rule="hyper" parents="333 4238 4444"/>
    </justification>
  </clause>

  <clause id="4827">
    <literal><![CDATA[
      x * ((y * (x / y)) \ y) = x / (x / y)
    ]]></literal>
    <justification jstring="[hyper(126,a,4508,a,b,xx)].">
      <j1 rule="hyper" parents="126 4508"/>
    </justification>
  </clause>

  <clause id="4828">
    <literal><![CDATA[
      x \ (y \ ((y * z) / y)) = x \ (K(y,z) * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(121,a,4517,a,b,10,a)].">
      <j1 rule="hyper" parents="121 4517 10"/>
    </justification>
  </clause>

  <clause id="4829">
    <literal><![CDATA[
      L(x \ (y \ z),x,K(y,z)) = (K(y,z) * x) \ (y \ ((y * z) / y))
    ]]></literal>
    <justification jstring="[para(4517(a,2),99(a,2,2))].">
      <j1 rule="para" parents="4517 99"/>
    </justification>
  </clause>

  <clause id="4830">
    <literal><![CDATA[
      K(x \ y,x) * ((x \ y) \ z) = (y / x) \ z
    ]]></literal>
    <justification jstring="[para(10(a,1),4519(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 4519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4832">
    <literal><![CDATA[
      (x / (x / y)) \ z = K(y,y \ x) * (y \ z)
    ]]></literal>
    <justification jstring="[para(3697(a,1),4519(a,1,1))].">
      <j1 rule="para" parents="3697 4519"/>
    </justification>
  </clause>

  <clause id="4833">
    <literal><![CDATA[
      (x * K(y,x)) \ z = K(x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[para(4238(a,1),4519(a,1,1))].">
      <j1 rule="para" parents="4238 4519"/>
    </justification>
  </clause>

  <clause id="4834">
    <literal><![CDATA[
      K(x \ 1,y) * ((x \ 1) \ z) = (x \ K(y,x \ 1)) \ z
    ]]></literal>
    <justification jstring="[para(4279(a,2),4519(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4279 4519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4836">
    <literal><![CDATA[
      K(x,y) * (x \ (y \ z)) = x \ (T(y,x) \ z)
    ]]></literal>
    <justification jstring="[hyper(121,a,4555,a(flip),b,4532,a),flip(a)].">
      <j1 rule="hyper" parents="121 4555 4532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4837">
    <literal><![CDATA[
      (K(x,y) * T(x,z)) / T(x,y) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(123,a,3342,a(flip),b,4541,a)].">
      <j1 rule="hyper" parents="123 3342 4541"/>
    </justification>
  </clause>

  <clause id="4839">
    <literal><![CDATA[
      K(x,y / (z \ 1)) * (z \ T(z * y,x)) = y
    ]]></literal>
    <justification jstring="[para(953(a,1),4546(a,1,2))].">
      <j1 rule="para" parents="953 4546"/>
    </justification>
  </clause>

  <clause id="4840">
    <literal><![CDATA[
      K(x,(y \ z) / (y \ 1)) * (y \ T(z,x)) = y \ z
    ]]></literal>
    <justification jstring="[para(1011(a,1),4546(a,1,2))].">
      <j1 rule="para" parents="1011 4546"/>
    </justification>
  </clause>

  <clause id="4841">
    <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(4239(a,1),4551(a,1,1))].">
      <j1 rule="para" parents="4239 4551"/>
    </justification>
  </clause>

  <clause id="4842">
    <literal><![CDATA[
      T(x,y) \ T(x,z) = K(x,z) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,2005,a,b,4552,a),flip(a)].">
      <j1 rule="hyper" parents="333 2005 4552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4844">
    <literal><![CDATA[
      L(x,T(T(y,z),z),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(4271(a,1),4562(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4271 4562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4845">
    <literal><![CDATA[
      L(x,T(y \ z,y),u) = L(x,z / y,u)
    ]]></literal>
    <justification jstring="[para(4292(a,1),4562(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4292 4562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4846">
    <literal><![CDATA[
      T(x,y) * (T(y,x) * z) = (x * y) * L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,97,a,b,4613,a),flip(a)].">
      <j1 rule="hyper" parents="333 97 4613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4847">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * z) = a(T(x,y),T(y,x),z)
    ]]></literal>
    <justification jstring="[para(4613(a,1),3653(a,1,1))].">
      <j1 rule="para" parents="4613 3653"/>
    </justification>
  </clause>

  <clause id="4848">
    <literal><![CDATA[
      x * (y * (K(x,y) * z)) = T(x,y) * (y * z)
    ]]></literal>
    <justification jstring="[para(4250(a,1),4613(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4250 4613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4849">
    <literal><![CDATA[
      x / (((y \ (x * z)) * y) / z) = K(y,x / (y / z))
    ]]></literal>
    <justification jstring="[hyper(197,a,1733,a(flip),b,4629,a)].">
      <j1 rule="hyper" parents="197 1733 4629"/>
    </justification>
  </clause>

  <clause id="4850">
    <literal><![CDATA[
      x / (((y \ (x / z)) * y) * z) = K(y,x / (y * z))
    ]]></literal>
    <justification jstring="[hyper(197,a,1112,a(flip),b,4629,a)].">
      <j1 rule="hyper" parents="197 1112 4629"/>
    </justification>
  </clause>

  <clause id="4851">
    <literal><![CDATA[
      x * T(x \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) * y = u
    ]]></literal>
    <justification jstring="[para(4629(a,1),4580(a,1))].">
      <j1 rule="para" parents="4629 4580"/>
    </justification>
  </clause>

  <clause id="4852">
    <literal><![CDATA[
      T(x,x \ (y * x)) / ((y * x) \ x) = x * y
    ]]></literal>
    <justification jstring="[para(11(a,1),4648(a,2,2))].">
      <j1 rule="para" parents="11 4648"/>
    </justification>
  </clause>

  <clause id="4853">
    <literal><![CDATA[
      (x * (y / x)) * (y \ x) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ T(x,x \ y) = u
    ]]></literal>
    <justification jstring="[para(4648(a,1),414(a,1,1))].">
      <j1 rule="para" parents="4648 414"/>
    </justification>
  </clause>

  <clause id="4854">
    <literal><![CDATA[
      T(x,y / x) / (y \ x) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(3633(a,2),4648(a,1,1))].">
      <j1 rule="para" parents="3633 4648"/>
    </justification>
  </clause>

  <clause id="4855">
    <literal><![CDATA[
      L(x,y,x) \ (T(x * y,(y * x) / y) \ z) = ((y * x) / y) \ ((x * y) \ z)
    ]]></literal>
    <justification jstring="[para(639(a,1),4696(a,1,1))].">
      <j1 rule="para" parents="639 4696"/>
    </justification>
  </clause>

  <clause id="4856">
    <literal><![CDATA[
      T(x,y) * ((x \ T(y,x)) * z) = y * L(z,x \ T(y,x),x)
    ]]></literal>
    <justification jstring="[hyper(126,a,495,a(flip),b,4706,a)].">
      <j1 rule="hyper" parents="126 495 4706"/>
    </justification>
  </clause>

  <clause id="4857">
    <literal><![CDATA[
      (x * K(y,x)) * z = K(y,x) * (x * z)
    ]]></literal>
    <justification jstring="[hyper(333,a,3542,a,b,4712,a)].">
      <j1 rule="hyper" parents="333 3542 4712"/>
    </justification>
  </clause>

  <clause id="4858">
    <literal><![CDATA[
      K(x,y) \ (y * z) = y * (K(x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(121,a,154,a(flip),b,4712,a)].">
      <j1 rule="hyper" parents="121 154 4712"/>
    </justification>
  </clause>

  <clause id="4859">
    <literal><![CDATA[
      R(K(x,y),y * z,u) * ((y * z) * u) = (y * (K(x,y) * z)) * u
    ]]></literal>
    <justification jstring="[hyper(125,a,4712,a(flip),b,313,a),flip(a)].">
      <j1 rule="hyper" parents="125 4712 313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4860">
    <literal><![CDATA[
      R(x,y,z) * (K(u,R(x,y,z)) * (y * z)) = K(u,R(x,y,z)) * ((x * y) * z)
    ]]></literal>
    <justification jstring="[para(107(a,1),4712(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 4712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4861">
    <literal><![CDATA[
      x * (K(y,x) * (x \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * z = u
    ]]></literal>
    <justification jstring="[para(4712(a,1),343(a,1))].">
      <j1 rule="para" parents="4712 343"/>
    </justification>
  </clause>

  <clause id="4862">
    <literal><![CDATA[
      (x * (K(y,x) * z)) \ (K(y,x) * (x * (z * u))) = L(L(u,z,x),x * z,K(y,x))
    ]]></literal>
    <justification jstring="[para(4712(a,1),498(a,1,1))].">
      <j1 rule="para" parents="4712 498"/>
    </justification>
  </clause>

  <clause id="4865">
    <literal><![CDATA[
      K(x * T((y * z) \ z,y),u) = K(x * ((y * z) \ z),u)
    ]]></literal>
    <justification jstring="[para(2501(a,2),4758(a,1,1,2))].">
      <j1 rule="para" parents="2501 4758"/>
    </justification>
  </clause>

  <clause id="4866">
    <literal><![CDATA[
      K((1 / x) * y,x) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,4779,a(flip),b,4762,a),flip(a)].">
      <j1 rule="hyper" parents="333 4779 4762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4867">
    <literal><![CDATA[
      K((x \ 1) \ y,x \ 1) = K(x * y,x \ 1)
    ]]></literal>
    <justification jstring="[para(76(a,1),4866(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="76 4866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4869">
    <literal><![CDATA[
      (1 / x) * K(y,1 / x) = K(y,x \ 1) / x
    ]]></literal>
    <justification jstring="[hyper(333,a,4238,a(flip),b,4773,a)].">
      <j1 rule="hyper" parents="333 4238 4773"/>
    </justification>
  </clause>

  <clause id="4870">
    <literal><![CDATA[
      T(K(x,y \ 1) / y,x) = 1 / y
    ]]></literal>
    <justification jstring="[para(4773(a,2),238(a,1,1))].">
      <j1 rule="para" parents="4773 238"/>
    </justification>
  </clause>

  <clause id="4871">
    <literal><![CDATA[
      T(K(x * (1 / y),y \ 1) / y,x) = R(1 / y,x,1 / y)
    ]]></literal>
    <justification jstring="[para(4773(a,2),830(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4773 830"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4873">
    <literal><![CDATA[
      K(x,((y * z) \ y) * u) = K(x,(y \ (y / z)) * u)
    ]]></literal>
    <justification jstring="[para(2889(a,1),4793(a,1,2,1))].">
      <j1 rule="para" parents="2889 4793"/>
    </justification>
  </clause>

  <clause id="4874">
    <literal><![CDATA[
      K(x,R(y \ 1,y,z) \ u) = K(x,(z / (y * z)) \ u)
    ]]></literal>
    <justification jstring="[para(2843(a,2),4795(a,1,2,1))].">
      <j1 rule="para" parents="2843 4795"/>
    </justification>
  </clause>

  <clause id="4875">
    <literal><![CDATA[
      K(x,x \ y) * ((x \ y) * z) = (y / x) * z
    ]]></literal>
    <justification jstring="[para(10(a,1),4817(a,2,1,1))].">
      <j1 rule="para" parents="10 4817"/>
    </justification>
  </clause>

  <clause id="4876">
    <literal><![CDATA[
      K(x \ y,x) * (x * z) = (y / (y / x)) * z
    ]]></literal>
    <justification jstring="[para(3697(a,1),4817(a,2,1))].">
      <j1 rule="para" parents="3697 4817"/>
    </justification>
  </clause>

  <clause id="4877">
    <literal><![CDATA[
      (K(x,y) * y) * z = K(x,y) * (y * z)
    ]]></literal>
    <justification jstring="[para(4275(a,1),4817(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4275 4817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4878">
    <literal><![CDATA[
      T((x / (y * y)) * (y * y),x / (y * y)) = T(y * y,x) * (x / T(y * y,x))
    ]]></literal>
    <justification jstring="[hyper(333,a,237,a,b,4821,a)].">
      <j1 rule="hyper" parents="333 237 4821"/>
    </justification>
  </clause>

  <clause id="4880">
    <literal><![CDATA[
      T(x,1 / (y \ x)) = T(x,y / x)
    ]]></literal>
    <justification jstring="[hyper(124,a,4724,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 4724 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4881">
    <literal><![CDATA[
      T(x,(x / y) / x) = T(x,1 / y)
    ]]></literal>
    <justification jstring="[hyper(124,a,4616,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 4616 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4883">
    <literal><![CDATA[
      T(x,1 / (y \ x)) = x / K(y / x,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,4206,a(flip),b,4880,a),flip(a)].">
      <j1 rule="hyper" parents="333 4206 4880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4884">
    <literal><![CDATA[
      L(x,((y \ z) \ z) \ z,u) = L(x,z / y,u)
    ]]></literal>
    <justification jstring="[para(3674(a,1),4845(a,1,2))].">
      <j1 rule="para" parents="3674 4845"/>
    </justification>
  </clause>

  <clause id="4885">
    <literal><![CDATA[
      (1 / x) * K(y,1 / x) = K(y,1 / x) / x
    ]]></literal>
    <justification jstring="[hyper(123,a,78,a(flip),b,4857,a),flip(a)].">
      <j1 rule="hyper" parents="123 78 4857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4886">
    <literal><![CDATA[
      (x * K(y,x)) \ z = x \ (K(y,x) \ z)
    ]]></literal>
    <justification jstring="[hyper(121,a,72,a(flip),b,4857,a)].">
      <j1 rule="hyper" parents="121 72 4857"/>
    </justification>
  </clause>

  <clause id="4887">
    <literal><![CDATA[
      K(x,y) * (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      y * (K(x,y) * z) = u
    ]]></literal>
    <justification jstring="[para(4857(a,1),3550(a,1))].">
      <j1 rule="para" parents="4857 3550"/>
    </justification>
  </clause>

  <clause id="4888">
    <literal><![CDATA[
      (x * K(y,x)) * K(x,z) = K(y,x) * T(x,z)
    ]]></literal>
    <justification jstring="[para(4222(a,2),4857(a,2,2))].">
      <j1 rule="para" parents="4222 4857"/>
    </justification>
  </clause>

  <clause id="4889">
    <literal><![CDATA[
      R(K(x,y),y,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(1924,a,4877,a)].">
      <j1 rule="hyper" parents="1924 4877"/>
    </justification>
  </clause>

  <clause id="4890">
    <literal><![CDATA[
      L(x,y,K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(501,a,4877,a)].">
      <j1 rule="hyper" parents="501 4877"/>
    </justification>
  </clause>

  <clause id="4891">
    <literal><![CDATA[
      a(K(x,y),y,z) = 1
    ]]></literal>
    <justification jstring="[hyper(120,a,4877,a(flip),b,84,a),flip(a)].">
      <j1 rule="hyper" parents="120 4877 84"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4892">
    <literal><![CDATA[
      L(x,y,K(z,y \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(2631,a,4890,a)].">
      <j1 rule="hyper" parents="2631 4890"/>
    </justification>
  </clause>

  <clause id="4893">
    <literal><![CDATA[
      L(x,y,K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(4890(a,1),50(a,2))].">
      <j1 rule="para" parents="4890 50"/>
    </justification>
  </clause>

  <clause id="4894">
    <literal><![CDATA[
      a(K(x,y),y,z) = u \ u
    ]]></literal>
    <justification jstring="[hyper(333,a,66,a,b,4891,a),flip(a)].">
      <j1 rule="hyper" parents="333 66 4891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4895">
    <literal><![CDATA[
      R(K(x,y),y \ 1,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(1928,a,4889,a)].">
      <j1 rule="hyper" parents="1928 4889"/>
    </justification>
  </clause>

  <clause id="4896">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      R(K(x,y),y,u) = z
    ]]></literal>
    <justification jstring="[para(4889(a,1),1855(a,1))].">
      <j1 rule="para" parents="4889 1855"/>
    </justification>
  </clause>

  <clause id="4897">
    <literal><![CDATA[
      (K(x,y \ 1) * y) * z = K(x,y \ 1) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(1170,a,4892,a),flip(a)].">
      <j1 rule="hyper" parents="1170 4892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4898">
    <literal><![CDATA[
      a(K(x,y),y,z) != u
    ]]></literal>
    <literal><![CDATA[
      1 = u
    ]]></literal>
    <justification jstring="[para(4894(a,2),168(a,1)),flip(b)].">
      <j1 rule="para" parents="4894 168"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4899">
    <literal><![CDATA[
      K(1 / (x \ y),y) = K(x / y,y)
    ]]></literal>
    <justification jstring="[hyper(4247,a,4883,a)].">
      <j1 rule="hyper" parents="4247 4883"/>
    </justification>
  </clause>

  <clause id="4900">
    <literal><![CDATA[
      K((x / y) / x,x) = K(1 / y,x)
    ]]></literal>
    <justification jstring="[para(79(a,1),4899(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="79 4899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4901">
    <literal><![CDATA[
      (x \ (x / y)) * x = (x / y) * K(1 / y,x)
    ]]></literal>
    <justification jstring="[para(4900(a,1),4464(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4900 4464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4902">
    <literal><![CDATA[
      (x * K(y,x)) \ y = x \ (y * K(x,y))
    ]]></literal>
    <justification jstring="[para(4458(a,1),4886(a,2,2))].">
      <j1 rule="para" parents="4458 4886"/>
    </justification>
  </clause>

  <clause id="4903">
    <literal><![CDATA[
      (K(x,y) \ x) \ z = x \ (K(y,x) \ z)
    ]]></literal>
    <justification jstring="[para(4458(a,2),4886(a,1,1))].">
      <j1 rule="para" parents="4458 4886"/>
    </justification>
  </clause>

  <clause id="4904">
    <literal><![CDATA[
      x \ (x \ (T(x,y) * z)) = (K(x,y) \ x) \ z
    ]]></literal>
    <justification jstring="[para(4547(a,2),4903(a,2,2)),flip(a)].">
      <j1 rule="para" parents="4547 4903"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4907">
    <literal><![CDATA[
      L(x \ 1,T(x,y),y) = L(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3066,a(flip),b,4415,a)].">
      <j1 rule="hyper" parents="63 3066 4415"/>
    </justification>
  </clause>

  <clause id="4908">
    <literal><![CDATA[
      T(x * L(x \ 1,x,y),y) = T(x,y) * ((x * y) \ y)
    ]]></literal>
    <justification jstring="[para(4907(a,1),1614(a,1,1,2))].">
      <j1 rule="para" parents="4907 1614"/>
    </justification>
  </clause>

  <clause id="4909">
    <literal><![CDATA[
      x \ (y * T(y \ x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K((x \ y) \ 1,z) = u
    ]]></literal>
    <justification jstring="[para(1285(a,1),4471(a,1))].">
      <j1 rule="para" parents="1285 4471"/>
    </justification>
  </clause>

  <clause id="4911">
    <literal><![CDATA[
      K(x,y) * T(x,z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * K(x,z) = u
    ]]></literal>
    <justification jstring="[para(4222(a,2),4539(a,1,2))].">
      <j1 rule="para" parents="4222 4539"/>
    </justification>
  </clause>

  <clause id="4913">
    <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(4576(a,1),4608(a,1,2))].">
      <j1 rule="para" parents="4576 4608"/>
    </justification>
  </clause>

  <clause id="4914">
    <literal><![CDATA[
      K(x / y,z) \ y != u
    ]]></literal>
    <literal><![CDATA[
      T(x / y,z) \ x = u
    ]]></literal>
    <justification jstring="[para(79(a,1),4690(a,1,2))].">
      <j1 rule="para" parents="79 4690"/>
    </justification>
  </clause>

  <clause id="4916">
    <literal><![CDATA[
      K(x,y) * z != u
    ]]></literal>
    <literal><![CDATA[
      T(y,x) \ (y * z) = u
    ]]></literal>
    <justification jstring="[para(9(a,1),4697(a,1,2))].">
      <j1 rule="para" parents="9 4697"/>
    </justification>
  </clause>

  <clause id="4917">
    <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(2049(a,1),4698(a,1,2))].">
      <j1 rule="para" parents="2049 4698"/>
    </justification>
  </clause>

  <clause id="4918">
    <literal><![CDATA[
      x * (K(y,x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * (x * z) = u
    ]]></literal>
    <justification jstring="[para(4550(a,1),4716(a,1,2))].">
      <j1 rule="para" parents="4550 4716"/>
    </justification>
  </clause>

  <clause id="4919">
    <literal><![CDATA[
      K(x,y) * K(y,y * x) = y \ L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(2006,a,4743,a)].">
      <j1 rule="hyper" parents="2006 4743"/>
    </justification>
  </clause>

  <clause id="4920">
    <literal><![CDATA[
      K(x * y,x) * K(x,y) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(2006,a,4746,a)].">
      <j1 rule="hyper" parents="2006 4746"/>
    </justification>
  </clause>

  <clause id="4921">
    <literal><![CDATA[
      x \ y != K(x,z) * K(x * z,x)
    ]]></literal>
    <literal><![CDATA[
      R(x,z,x) = y
    ]]></literal>
    <justification jstring="[para(4746(a,2),47(a,1)),flip(a)].">
      <j1 rule="para" parents="4746 47"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4922">
    <literal><![CDATA[
      x \ R(x,y,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(x * y,x) * K(x,y) = z
    ]]></literal>
    <justification jstring="[para(4746(a,1),2006(a,1))].">
      <j1 rule="para" parents="4746 2006"/>
    </justification>
  </clause>

  <clause id="4923">
    <literal><![CDATA[
      K(x,y) * K(y * x,x) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[para(4543(a,2),4746(a,1,2))].">
      <j1 rule="para" parents="4543 4746"/>
    </justification>
  </clause>

  <clause id="4924">
    <literal><![CDATA[
      K(x,y) * K(y,x * y) = y \ L(y,x,y)
    ]]></literal>
    <justification jstring="[para(4636(a,2),4919(a,1,2))].">
      <j1 rule="para" parents="4636 4919"/>
    </justification>
  </clause>

  <clause id="4925">
    <literal><![CDATA[
      T(x,x * y) \ K(x,y) = x \ (x \ R(x,y,x))
    ]]></literal>
    <justification jstring="[hyper(121,a,4920,a(flip),b,4556,a),flip(a)].">
      <j1 rule="hyper" parents="121 4920 4556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4926">
    <literal><![CDATA[
      x \ R(x,x \ y,x) = K(y,x) * K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),4920(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 4920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4927">
    <literal><![CDATA[
      x \ R(x,y,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * K(x * y,x) = z
    ]]></literal>
    <justification jstring="[para(4920(a,1),2011(a,1))].">
      <j1 rule="para" parents="4920 2011"/>
    </justification>
  </clause>

  <clause id="4928">
    <literal><![CDATA[
      K(x * y,y) * K(y,x) = y \ R(y,x,y)
    ]]></literal>
    <justification jstring="[para(4543(a,2),4920(a,1,1))].">
      <j1 rule="para" parents="4543 4920"/>
    </justification>
  </clause>

  <clause id="4929">
    <literal><![CDATA[
      K(x \ y,x) * ((y / (y / x)) \ z) = x \ z
    ]]></literal>
    <justification jstring="[hyper(416,a,4187,a),flip(a)].">
      <j1 rule="hyper" parents="416 4187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4931">
    <literal><![CDATA[
      x \ (y * (K(y \ x,y) * ((x / y) * z))) = L(z,x / y,x / (x / y))
    ]]></literal>
    <justification jstring="[hyper(121,a,4187,a(flip),b,490,a)].">
      <j1 rule="hyper" parents="121 4187 490"/>
    </justification>
  </clause>

  <clause id="4932">
    <literal><![CDATA[
      K(x,T(y,z) \ 1) = T(K(x,y \ 1),z)
    ]]></literal>
    <justification jstring="[para(4215(a,2),4262(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4215 4262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4934">
    <literal><![CDATA[
      x * K(y,T(z,x) \ 1) = K(y,z \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(126,a,4932,a,b,22,a(flip))].">
      <j1 rule="hyper" parents="126 4932 22"/>
    </justification>
  </clause>

  <clause id="4936">
    <literal><![CDATA[
      K(x,T(1 / y,z) \ 1) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(79(a,1),4932(a,2,1,2))].">
      <j1 rule="para" parents="79 4932"/>
    </justification>
  </clause>

  <clause id="4937">
    <literal><![CDATA[
      K(x,T(y \ 1,z) \ 1) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(4621(a,1),4932(a,2,1))].">
      <j1 rule="para" parents="4621 4932"/>
    </justification>
  </clause>

  <clause id="4939">
    <literal><![CDATA[
      K(x,1 / T(y,z)) = T(K(x,1 / y),z)
    ]]></literal>
    <justification jstring="[para(2381(a,1),4936(a,1,2))].">
      <j1 rule="para" parents="2381 4936"/>
    </justification>
  </clause>

  <clause id="4940">
    <literal><![CDATA[
      K(x,R(T(K(x,y),z),u,w)) = 1
    ]]></literal>
    <justification jstring="[para(4936(a,1),3439(a,1,2,1))].">
      <j1 rule="para" parents="4936 3439"/>
    </justification>
  </clause>

  <clause id="4941">
    <literal><![CDATA[
      L(x,y,z) * K(u,L(x,y,z)) = L(x * K(u,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(35,a,4291,a,b,4325,a)].">
      <j1 rule="hyper" parents="35 4291 4325"/>
    </justification>
  </clause>

  <clause id="4942">
    <literal><![CDATA[
      L((x * y) / x,z,u) = L(y * K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(35,a,669,a,b,4325,a)].">
      <j1 rule="hyper" parents="35 669 4325"/>
    </justification>
  </clause>

  <clause id="4943">
    <literal><![CDATA[
      L(L(x,y,z) * K(u,L(x,y,z)),w,v5) * u = u * L(L(x,w,v5),y,z)
    ]]></literal>
    <justification jstring="[para(30(a,1),4325(a,2,2))].">
      <j1 rule="para" parents="30 4325"/>
    </justification>
  </clause>

  <clause id="4944">
    <literal><![CDATA[
      T(1 / (K(x,y) / x),y) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[para(4666(a,1),4326(a,1,1,2))].">
      <j1 rule="para" parents="4666 4326"/>
    </justification>
  </clause>

  <clause id="4945">
    <literal><![CDATA[
      (1 / (K(x,y) / x)) * y = y * (1 / (1 / x))
    ]]></literal>
    <justification jstring="[hyper(126,a,4944,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="126 4944 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4946">
    <literal><![CDATA[
      L(x,y,z) / L(x * K(u,x),y,z) = K(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(197,a,4426,a,b,4358,a)].">
      <j1 rule="hyper" parents="197 4426 4358"/>
    </justification>
  </clause>

  <clause id="4947">
    <literal><![CDATA[
      L(x * K(y,x),z,u) / L(x,z,u) = K(y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(123,a,4426,a,b,4275,a(flip))].">
      <j1 rule="hyper" parents="123 4426 4275"/>
    </justification>
  </clause>

  <clause id="4948">
    <literal><![CDATA[
      L(x * K(y,x),z,u) \ L(x,z,u) = K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(4426(a,2),4211(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4426 4211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4949">
    <literal><![CDATA[
      R(x,y,z) * K(u,R(x,y,z)) = R(x * K(u,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,4238,a(flip),b,4427,a)].">
      <j1 rule="hyper" parents="333 4238 4427"/>
    </justification>
  </clause>

  <clause id="4950">
    <literal><![CDATA[
      R(x,y,z) \ R(x * K(u,x),y,z) = K(u,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(121,a,4427,a,b,4238,a(flip))].">
      <j1 rule="hyper" parents="121 4427 4238"/>
    </justification>
  </clause>

  <clause id="4951">
    <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(4427(a,2),3700(a,1,1))].">
      <j1 rule="para" parents="4427 3700"/>
    </justification>
  </clause>

  <clause id="4952">
    <literal><![CDATA[
      R(x * K(y,x),z,u) \ R(x,z,u) = K(R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(4427(a,2),4211(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4427 4211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4953">
    <literal><![CDATA[
      (T(x,y) * R(y,z,u)) / T(x,y) = R(K(y,x) \ y,z,u)
    ]]></literal>
    <justification jstring="[para(4468(a,1),4427(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4468 4427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4955">
    <literal><![CDATA[
      x \ (y * (z * T(z \ (y \ x),u))) = K((x \ (y * z)) \ 1,u)
    ]]></literal>
    <justification jstring="[para(940(a,1),4483(a,1,2))].">
      <j1 rule="para" parents="940 4483"/>
    </justification>
  </clause>

  <clause id="4956">
    <literal><![CDATA[
      x \ (((y \ (x * z)) * y) / z) = K((x \ (y / z)) \ 1,y)
    ]]></literal>
    <justification jstring="[para(1733(a,1),4483(a,1,2))].">
      <j1 rule="para" parents="1733 4483"/>
    </justification>
  </clause>

  <clause id="4957">
    <literal><![CDATA[
      (x * (y * T(y \ (x \ z),u))) / z = K(((x * y) / z) \ 1,u)
    ]]></literal>
    <justification jstring="[para(940(a,1),4484(a,1,1))].">
      <j1 rule="para" parents="940 4484"/>
    </justification>
  </clause>

  <clause id="4958">
    <literal><![CDATA[
      x * K((x \ (y * z)) \ 1,u) = y * (z * T(z \ (y \ x),u))
    ]]></literal>
    <justification jstring="[hyper(954,a,4486,a),flip(a)].">
      <j1 rule="hyper" parents="954 4486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4959">
    <literal><![CDATA[
      (x * y) * K(((x * y) \ y) \ 1,z) = T(x,z) * y
    ]]></literal>
    <justification jstring="[hyper(781,a,4486,a),flip(a)].">
      <j1 rule="hyper" parents="781 4486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4960">
    <literal><![CDATA[
      ((x \ (y / z)) * x) * z = y * K((y \ (x * z)) \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1112,a(flip),b,4486,a)].">
      <j1 rule="hyper" parents="63 1112 4486"/>
    </justification>
  </clause>

  <clause id="4961">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ y,z) = y * K((T(y,x) \ x) \ 1,z)
    ]]></literal>
    <justification jstring="[para(3628(a,2),4486(a,2,2,1,1))].">
      <j1 rule="para" parents="3628 4486"/>
    </justification>
  </clause>

  <clause id="4962">
    <literal><![CDATA[
      K(x,y) * T(K(y,x) * z,u) = z * K((z \ K(x,y)) \ 1,u)
    ]]></literal>
    <justification jstring="[para(4567(a,1),4486(a,1,2,1))].">
      <j1 rule="para" parents="4567 4486"/>
    </justification>
  </clause>

  <clause id="4963">
    <literal><![CDATA[
      K(((x \ 1) / (x \ y)) \ 1,z) * (x \ y) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,1011,a(flip),b,4487,a),flip(a)].">
      <j1 rule="hyper" parents="333 1011 4487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4965">
    <literal><![CDATA[
      K((x / y) \ 1,z) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(35,a,4243,a,b,4487,a),flip(a)].">
      <j1 rule="hyper" parents="35 4243 4487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4966">
    <literal><![CDATA[
      x / (y * T(y \ x,z)) = K(z,(y / x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(197,a,4487,a(flip),b,4567,a)].">
      <j1 rule="hyper" parents="197 4487 4567"/>
    </justification>
  </clause>

  <clause id="4967">
    <literal><![CDATA[
      K((x / (x * y)) \ 1,z) * (x * y) = x * T(y,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),4487(a,2,2,1))].">
      <j1 rule="para" parents="9 4487"/>
    </justification>
  </clause>

  <clause id="4968">
    <literal><![CDATA[
      K(1 / (x / y),z) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(3400,a,4965,a)].">
      <j1 rule="hyper" parents="3400 4965"/>
    </justification>
  </clause>

  <clause id="4969">
    <literal><![CDATA[
      K((x / y) \ 1,x) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,4375,a(flip),b,4965,a),flip(a)].">
      <j1 rule="hyper" parents="333 4375 4965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4970">
    <literal><![CDATA[
      K(x / (y * x),z) = K(y \ 1,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),4965(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11 4965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4972">
    <literal><![CDATA[
      K((x \ y) / y,z) = K(x \ 1,z)
    ]]></literal>
    <justification jstring="[para(76(a,1),4965(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="76 4965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4974">
    <literal><![CDATA[
      K(x \ (y \ x),x) = K(y \ 1,x)
    ]]></literal>
    <justification jstring="[para(76(a,1),4969(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="76 4969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4975">
    <literal><![CDATA[
      K(x \ 1,y) * (z / (x * z)) = T(z / (x * z),y)
    ]]></literal>
    <justification jstring="[hyper(125,a,4970,a(flip),b,4261,a(flip))].">
      <j1 rule="hyper" parents="125 4970 4261"/>
    </justification>
  </clause>

  <clause id="4976">
    <literal><![CDATA[
      K(x / (y * x),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(1 / y,z) = u
    ]]></literal>
    <justification jstring="[para(4970(a,2),3400(a,1))].">
      <j1 rule="para" parents="4970 3400"/>
    </justification>
  </clause>

  <clause id="4977">
    <literal><![CDATA[
      ((x * y) \ y) * (x * y) = y * K(x \ 1,x * y)
    ]]></literal>
    <justification jstring="[para(4970(a,1),4464(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4970 4464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4978">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ y,z) != y * u
    ]]></literal>
    <literal><![CDATA[
      T(K(x,z),y) = u
    ]]></literal>
    <justification jstring="[para(4533(a,2),254(a,2)),flip(a)].">
      <j1 rule="para" parents="4533 254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4979">
    <literal><![CDATA[
      (x / y) * (z * K(y,1 / y)) = (x / (1 / (1 / y))) * z
    ]]></literal>
    <justification jstring="[para(4570(a,1),2812(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4570 2812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4980">
    <literal><![CDATA[
      K(1 / ((1 / x) / y),z) = (T(y * x,z) / x) / y
    ]]></literal>
    <justification jstring="[para(1648(a,1),4601(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1648 4601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4981">
    <literal><![CDATA[
      K(x,x \ y) * ((y / x) \ z) = (x \ y) \ z
    ]]></literal>
    <justification jstring="[hyper(121,a,10,a(flip),b,4624,a),flip(a)].">
      <j1 rule="hyper" parents="121 10 4624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4982">
    <literal><![CDATA[
      (x \ y) * (T(x,x \ y) * z) = (y / x) * (x * z)
    ]]></literal>
    <justification jstring="[para(4273(a,1),4624(a,1,2))].">
      <j1 rule="para" parents="4273 4624"/>
    </justification>
  </clause>

  <clause id="4984">
    <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(4649(a,1),342(a,1,2))].">
      <j1 rule="para" parents="4649 342"/>
    </justification>
  </clause>

  <clause id="4985">
    <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(4651(a,1),2726(a,1))].">
      <j1 rule="para" parents="4651 2726"/>
    </justification>
  </clause>

  <clause id="4986">
    <literal><![CDATA[
      T(T(1 / ((x * y) \ x),z),y) = T(1 / ((x * y) \ x),z)
    ]]></literal>
    <justification jstring="[para(4653(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4653 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4987">
    <literal><![CDATA[
      K(x,y) / (K(x,y) / x) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(333,a,4176,a,b,4658,a),flip(a)].">
      <j1 rule="hyper" parents="333 4176 4658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4988">
    <literal><![CDATA[
      (1 / (1 / x)) \ K(x,y) = K(x,y) / x
    ]]></literal>
    <justification jstring="[hyper(192,a,4987,a)].">
      <j1 rule="hyper" parents="192 4987"/>
    </justification>
  </clause>

  <clause id="4989">
    <literal><![CDATA[
      T(x,K(y,z) / y) = T(x,y \ K(y,z))
    ]]></literal>
    <justification jstring="[para(4988(a,1),3172(a,1,2))].">
      <j1 rule="para" parents="4988 3172"/>
    </justification>
  </clause>

  <clause id="4990">
    <literal><![CDATA[
      (x \ T(y,x \ 1)) / (x \ y) = K(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(138,a,4692,a)].">
      <j1 rule="hyper" parents="138 4692"/>
    </justification>
  </clause>

  <clause id="4991">
    <literal><![CDATA[
      (x \ y) / (x \ T(y,x \ 1)) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(197,a,4692,a(flip),b,4567,a)].">
      <j1 rule="hyper" parents="197 4692 4567"/>
    </justification>
  </clause>

  <clause id="4992">
    <literal><![CDATA[
      K(x,y) * (y * (T(y,x) \ z)) = y * (T(T(y,x),x) \ z)
    ]]></literal>
    <justification jstring="[para(4704(a,1),4712(a,2,2))].">
      <j1 rule="para" parents="4704 4712"/>
    </justification>
  </clause>

  <clause id="4993">
    <literal><![CDATA[
      T(T(x,y),z) * K(y,x) = x * K(T(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(2746,a,4711,a)].">
      <j1 rule="hyper" parents="2746 4711"/>
    </justification>
  </clause>

  <clause id="4994">
    <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(4711(a,1),2746(a,1))].">
      <j1 rule="para" parents="4711 2746"/>
    </justification>
  </clause>

  <clause id="4995">
    <literal><![CDATA[
      T(x,(x / y) / x) / ((x / y) \ x) = (x / y) * K(x,1 / y)
    ]]></literal>
    <justification jstring="[hyper(333,a,4854,a,b,4723,a)].">
      <j1 rule="hyper" parents="333 4854 4723"/>
    </justification>
  </clause>

  <clause id="4997">
    <literal><![CDATA[
      K(x,y) = (x * y) * ((y * x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(4614,a,4750,a)].">
      <j1 rule="hyper" parents="4614 4750"/>
    </justification>
  </clause>

  <clause id="4998">
    <literal><![CDATA[
      (x * y) \ K(x,y) = (y * x) \ 1
    ]]></literal>
    <justification jstring="[hyper(121,a,705,a(flip),b,4750,a(flip))].">
      <j1 rule="hyper" parents="121 705 4750"/>
    </justification>
  </clause>

  <clause id="5002">
    <literal><![CDATA[
      K(x \ (y * ((z \ 1) \ 1)),u) = K(x \ (y * z),u)
    ]]></literal>
    <justification jstring="[para(2424(a,1),4761(a,1,1,2))].">
      <j1 rule="para" parents="2424 4761"/>
    </justification>
  </clause>

  <clause id="5003">
    <literal><![CDATA[
      K(x \ (y * (1 / z)),u) = K(x \ (y * (z \ 1)),u)
    ]]></literal>
    <justification jstring="[para(2425(a,1),4761(a,1,1,2))].">
      <j1 rule="para" parents="2425 4761"/>
    </justification>
  </clause>

  <clause id="5004">
    <literal><![CDATA[
      K(x \ (y \ (1 / z)),u) = K(x \ (y \ (z \ 1)),u)
    ]]></literal>
    <justification jstring="[para(2449(a,1),4761(a,1,1,2))].">
      <j1 rule="para" parents="2449 4761"/>
    </justification>
  </clause>

  <clause id="5005">
    <literal><![CDATA[
      K(x \ ((1 / y) \ z),u) = K(x \ ((y \ 1) \ z),u)
    ]]></literal>
    <justification jstring="[para(2665(a,1),4761(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2665 4761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5006">
    <literal><![CDATA[
      K((((x \ 1) \ 1) \ y) \ z,u) = K((x \ y) \ z,u)
    ]]></literal>
    <justification jstring="[para(2821(a,1),4761(a,1,1))].">
      <j1 rule="para" parents="2821 4761"/>
    </justification>
  </clause>

  <clause id="5007">
    <literal><![CDATA[
      K(x \ R(1 / y,z,u),w) = K(x \ R(y \ 1,z,u),w)
    ]]></literal>
    <justification jstring="[para(3006(a,1),4761(a,1,1,2))].">
      <j1 rule="para" parents="3006 4761"/>
    </justification>
  </clause>

  <clause id="5008">
    <literal><![CDATA[
      K(x \ ((y \ 1) * y),z) = K(x \ 1,z)
    ]]></literal>
    <justification jstring="[para(4208(a,1),4761(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4208 4761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5009">
    <literal><![CDATA[
      K((x * ((y \ 1) \ 1)) \ z,u) = K((x * y) \ z,u)
    ]]></literal>
    <justification jstring="[para(2424(a,1),4768(a,1,1,1))].">
      <j1 rule="para" parents="2424 4768"/>
    </justification>
  </clause>

  <clause id="5010">
    <literal><![CDATA[
      K(((1 / x) / y) \ z,u) = K(((x \ 1) / y) \ z,u)
    ]]></literal>
    <justification jstring="[para(2864(a,1),4768(a,1,1,1))].">
      <j1 rule="para" parents="2864 4768"/>
    </justification>
  </clause>

  <clause id="5011">
    <literal><![CDATA[
      K((((1 / x) \ y) \ z) \ u,w) = K((((x \ 1) \ y) \ z) \ u,w)
    ]]></literal>
    <justification jstring="[para(2921(a,1),4768(a,1,1,1))].">
      <j1 rule="para" parents="2921 4768"/>
    </justification>
  </clause>

  <clause id="5012">
    <literal><![CDATA[
      K(x,y \ (z * (1 / u))) = K(x,y \ (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[para(2425(a,1),4789(a,1,2,2))].">
      <j1 rule="para" parents="2425 4789"/>
    </justification>
  </clause>

  <clause id="5013">
    <literal><![CDATA[
      K(x,y \ ((1 / z) * u)) = K(x,y \ ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[para(2624(a,1),4789(a,1,2,2))].">
      <j1 rule="para" parents="2624 4789"/>
    </justification>
  </clause>

  <clause id="5014">
    <literal><![CDATA[
      K(x,y \ (((z \ 1) \ 1) * u)) = K(x,y \ (z * u))
    ]]></literal>
    <justification jstring="[para(2684(a,1),4789(a,1,2,2))].">
      <j1 rule="para" parents="2684 4789"/>
    </justification>
  </clause>

  <clause id="5015">
    <literal><![CDATA[
      K(x,(K(y \ 1,y) * z) \ u) = K(x,z \ u)
    ]]></literal>
    <justification jstring="[para(2804(a,2),4789(a,1,2))].">
      <j1 rule="para" parents="2804 4789"/>
    </justification>
  </clause>

  <clause id="5016">
    <literal><![CDATA[
      K(x,y \ (z * ((1 / u) \ w))) = K(x,y \ (z * ((u \ 1) \ w)))
    ]]></literal>
    <justification jstring="[para(2673(a,1),4789(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2673 4789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5017">
    <literal><![CDATA[
      K(x,y * (K(z,1 / z) * u)) = K(x,y * u)
    ]]></literal>
    <justification jstring="[para(2408(a,2),4796(a,1,2,2))].">
      <j1 rule="para" parents="2408 4796"/>
    </justification>
  </clause>

  <clause id="5018">
    <literal><![CDATA[
      K(x,y * (z * ((u \ 1) \ 1))) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(1896(a,1),4798(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1896 4798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5019">
    <literal><![CDATA[
      K(x,y * (z \ (1 / u))) = K(x,y * (z \ (u \ 1)))
    ]]></literal>
    <justification jstring="[para(1918(a,1),4798(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1918 4798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5020">
    <literal><![CDATA[
      K(x,y * (((z \ 1) \ 1) \ u)) = K(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[para(2688(a,1),4798(a,1,2,2))].">
      <j1 rule="para" parents="2688 4798"/>
    </justification>
  </clause>

  <clause id="5021">
    <literal><![CDATA[
      K(x,(y * (1 / z)) \ u) = K(x,(y * (z \ 1)) \ u)
    ]]></literal>
    <justification jstring="[para(2425(a,1),4801(a,1,2,1))].">
      <j1 rule="para" parents="2425 4801"/>
    </justification>
  </clause>

  <clause id="5022">
    <literal><![CDATA[
      K(x,(y * (z / (1 / u))) \ w) = K(x,(y * (z / (u \ 1))) \ w)
    ]]></literal>
    <justification jstring="[para(2507(a,1),4801(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2507 4801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5023">
    <literal><![CDATA[
      K(x,T((1 / y) * z,u)) = K(x,T((y \ 1) * z,u))
    ]]></literal>
    <justification jstring="[para(2644(a,1),4806(a,1,2,1))].">
      <j1 rule="para" parents="2644 4806"/>
    </justification>
  </clause>

  <clause id="5024">
    <literal><![CDATA[
      K(x,((1 / y) * z) / u) = K(x,((y \ 1) * z) / u)
    ]]></literal>
    <justification jstring="[para(2643(a,1),4807(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2643 4807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5025">
    <literal><![CDATA[
      K(x,y / (z * (1 / u))) = K(x,y / (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[para(2425(a,1),4808(a,1,2,2))].">
      <j1 rule="para" parents="2425 4808"/>
    </justification>
  </clause>

  <clause id="5026">
    <literal><![CDATA[
      K(x,y / (z * (u / (1 / w)))) = K(x,y / (z * (u / (w \ 1))))
    ]]></literal>
    <justification jstring="[para(2507(a,1),4808(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2507 4808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5027">
    <literal><![CDATA[
      K(x,y / (((z \ 1) \ 1) * u)) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[para(2684(a,1),4808(a,1,2,2))].">
      <j1 rule="para" parents="2684 4808"/>
    </justification>
  </clause>

  <clause id="5028">
    <literal><![CDATA[
      T(x,y) \ T(x * K(x * z,x),y) = K(z * x,T(x,y))
    ]]></literal>
    <justification jstring="[para(4543(a,1),4812(a,1,2,1,2))].">
      <j1 rule="para" parents="4543 4812"/>
    </justification>
  </clause>

  <clause id="5029">
    <literal><![CDATA[
      T(x,y) \ T(z * T(z \ x,x),y) = K((x \ z) \ 1,T(x,y))
    ]]></literal>
    <justification jstring="[para(4486(a,2),4812(a,1,2,1))].">
      <j1 rule="para" parents="4486 4812"/>
    </justification>
  </clause>

  <clause id="5031">
    <literal><![CDATA[
      ((x * y) / x) * R(x,z,z \ 1) = y * (T(x,y) * a(x,z,z \ 1))
    ]]></literal>
    <justification jstring="[para(768(a,1),4819(a,1,2))].">
      <j1 rule="para" parents="768 4819"/>
    </justification>
  </clause>

  <clause id="5032">
    <literal><![CDATA[
      a((x * y) / x,x,z) = (y * (T(x,y) * z)) \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[para(4819(a,1),87(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4819 87"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5033">
    <literal><![CDATA[
      T(x,x \ y) \ ((x \ y) \ z) = x \ ((y / x) \ z)
    ]]></literal>
    <justification jstring="[hyper(121,a,4830,a(flip),b,4556,a),flip(a)].">
      <j1 rule="hyper" parents="121 4830 4556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5034">
    <literal><![CDATA[
      K(x \ y,x) * T(z,x \ y) = (y / x) \ (z * (x \ y))
    ]]></literal>
    <justification jstring="[para(22(a,2),4830(a,1,2))].">
      <j1 rule="para" parents="22 4830"/>
    </justification>
  </clause>

  <clause id="5035">
    <literal><![CDATA[
      (T(x,y) * (y * z)) \ ((x * y) * (K(x,y) * z)) = a(x,y,K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(4848(a,1),14(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4848 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5036">
    <literal><![CDATA[
      T(x,x \ y) * ((x \ y) * z) = x * ((y / x) * z)
    ]]></literal>
    <justification jstring="[para(4624(a,1),4848(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4624 4848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5037">
    <literal><![CDATA[
      T(x,T(y,x)) / ((y * x) \ x) = x * y
    ]]></literal>
    <justification jstring="[para(22(a,2),4852(a,1,1,2))].">
      <j1 rule="para" parents="22 4852"/>
    </justification>
  </clause>

  <clause id="5038">
    <literal><![CDATA[
      T(x,y) / ((y * x) \ x) = x * y
    ]]></literal>
    <justification jstring="[para(3613(a,1),5037(a,1,1))].">
      <j1 rule="para" parents="3613 5037"/>
    </justification>
  </clause>

  <clause id="5039">
    <literal><![CDATA[
      (x * (y / x)) \ (y / x) = y \ T(y / x,x)
    ]]></literal>
    <justification jstring="[hyper(366,a,5038,a),flip(a)].">
      <j1 rule="hyper" parents="366 5038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5040">
    <literal><![CDATA[
      ((x \ y) * x) \ x = y \ T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(352,a,5038,a),flip(a)].">
      <j1 rule="hyper" parents="352 5038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5041">
    <literal><![CDATA[
      (x * y) \ T(x,y) = (y * x) \ x
    ]]></literal>
    <justification jstring="[hyper(192,a,5038,a)].">
      <j1 rule="hyper" parents="192 5038"/>
    </justification>
  </clause>

  <clause id="5042">
    <literal><![CDATA[
      T(x,y) = (x * y) * ((y * x) \ x)
    ]]></literal>
    <justification jstring="[hyper(140,a,5038,a),flip(a)].">
      <j1 rule="hyper" parents="140 5038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5043">
    <literal><![CDATA[
      T(x * y,(y * x) \ x) = ((y * x) \ x) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(5038(a,1),113(a,1,1))].">
      <j1 rule="para" parents="5038 113"/>
    </justification>
  </clause>

  <clause id="5044">
    <literal><![CDATA[
      (x * y) \ T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      (y * x) \ x = z
    ]]></literal>
    <justification jstring="[para(5038(a,1),345(a,1,1))].">
      <j1 rule="para" parents="5038 345"/>
    </justification>
  </clause>

  <clause id="5045">
    <literal><![CDATA[
      T(x * y,z) * ((y * x) \ x) = K(x * y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(126,a,5041,a(flip),b,4530,a)].">
      <j1 rule="hyper" parents="126 5041 4530"/>
    </justification>
  </clause>

  <clause id="5046">
    <literal><![CDATA[
      (x * y) \ (y \ (x * y)) = (y * x) \ x
    ]]></literal>
    <justification jstring="[para(22(a,1),5041(a,1,2))].">
      <j1 rule="para" parents="22 5041"/>
    </justification>
  </clause>

  <clause id="5047">
    <literal><![CDATA[
      (x * y) \ (T(x,y) * R(T(x,y) \ (x * y),z,u)) = ((y * x) \ x) * R(((x * y) \ T(x,y)) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(5041(a,1),1538(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5041 1538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5048">
    <literal><![CDATA[
      T(x * y,(y * x) \ x) = T(x * y,y \ 1)
    ]]></literal>
    <justification jstring="[para(5046(a,1),3591(a,1,2))].">
      <j1 rule="para" parents="5046 3591"/>
    </justification>
  </clause>

  <clause id="5049">
    <literal><![CDATA[
      K(x \ y,x) * ((y / x) * z) = (x \ y) * z
    ]]></literal>
    <justification jstring="[hyper(4577,a,4875,a)].">
      <j1 rule="hyper" parents="4577 4875"/>
    </justification>
  </clause>

  <clause id="5051">
    <literal><![CDATA[
      (x * K(y,x)) \ L(x,y,x) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(121,a,4522,a(flip),b,4888,a)].">
      <j1 rule="hyper" parents="121 4522 4888"/>
    </justification>
  </clause>

  <clause id="5052">
    <literal><![CDATA[
      (x \ (x / (y \ 1))) * x = (x / (y \ 1)) * K(y,x)
    ]]></literal>
    <justification jstring="[para(76(a,1),4901(a,2,2,1))].">
      <j1 rule="para" parents="76 4901"/>
    </justification>
  </clause>

  <clause id="5053">
    <literal><![CDATA[
      K(x,(y / z) \ 1) * z = z * K(x,(z \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(113(a,1),4934(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="113 4934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5054">
    <literal><![CDATA[
      (x * K(y,x)) / L((y * x) / y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x * K(y,x),z,u) \ (x * K(y,x)) = w
    ]]></literal>
    <justification jstring="[para(4942(a,2),2560(a,1,2))].">
      <j1 rule="para" parents="4942 2560"/>
    </justification>
  </clause>

  <clause id="5055">
    <literal><![CDATA[
      K(x,(y / z) \ 1) = K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(63,a,4630,a(flip),b,4966,a),flip(a)].">
      <j1 rule="hyper" parents="63 4630 4966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5057">
    <literal><![CDATA[
      R(K(x,y / z),y / z,u) = K(x,(z / y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(333,a,4889,a,b,5055,a)].">
      <j1 rule="hyper" parents="333 4889 5055"/>
    </justification>
  </clause>

  <clause id="5058">
    <literal><![CDATA[
      K(x,1 / (y / z)) = K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(63,a,4615,a,b,5055,a)].">
      <j1 rule="hyper" parents="63 4615 5055"/>
    </justification>
  </clause>

  <clause id="5059">
    <literal><![CDATA[
      K(x,y / (z * y)) = K(x,z \ 1)
    ]]></literal>
    <justification jstring="[para(11(a,1),5055(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11 5055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5060">
    <literal><![CDATA[
      K(x,(y / (z * y)) \ 1) = K(x,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),5055(a,2,2))].">
      <j1 rule="para" parents="11 5055"/>
    </justification>
  </clause>

  <clause id="5061">
    <literal><![CDATA[
      K(x,(y \ z) / z) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(76(a,1),5055(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="76 5055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5062">
    <literal><![CDATA[
      K(x,R(y / z,z,u) \ 1) = K(x,(z * u) / (y * u))
    ]]></literal>
    <justification jstring="[para(108(a,2),5055(a,1,2,1))].">
      <j1 rule="para" parents="108 5055"/>
    </justification>
  </clause>

  <clause id="5064">
    <literal><![CDATA[
      K(x,y / (z * y)) = K(x,1 / z)
    ]]></literal>
    <justification jstring="[para(11(a,1),5058(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11 5058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5065">
    <literal><![CDATA[
      K(x,(y \ z) / z) = K(x,1 / y)
    ]]></literal>
    <justification jstring="[para(76(a,1),5058(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="76 5058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5066">
    <literal><![CDATA[
      K(x,y / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(z / y) \ 1) = u
    ]]></literal>
    <justification jstring="[para(5058(a,1),4618(a,1))].">
      <j1 rule="para" parents="5058 4618"/>
    </justification>
  </clause>

  <clause id="5067">
    <literal><![CDATA[
      R(K(x,y / (z * y)),y / (z * y),u) = K(x,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(4896,a,5059,a)].">
      <j1 rule="hyper" parents="4896 5059"/>
    </justification>
  </clause>

  <clause id="5068">
    <literal><![CDATA[
      K(x * y,x \ 1) * ((x * y) \ y) = y / (x * y)
    ]]></literal>
    <justification jstring="[para(5059(a,1),4312(a,1,1))].">
      <j1 rule="para" parents="5059 4312"/>
    </justification>
  </clause>

  <clause id="5069">
    <literal><![CDATA[
      K(x,x \ (y \ x)) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(4478,a,5061,a)].">
      <j1 rule="hyper" parents="4478 5061"/>
    </justification>
  </clause>

  <clause id="5070">
    <literal><![CDATA[
      K(x,y \ 1) * (((y \ z) / z) * x) = x * ((y \ z) / z)
    ]]></literal>
    <justification jstring="[hyper(125,a,5061,a(flip),b,4200,a(flip))].">
      <j1 rule="hyper" parents="125 5061 4200"/>
    </justification>
  </clause>

  <clause id="5071">
    <literal><![CDATA[
      K(x,y / (z * y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(5064(a,2),4618(a,1))].">
      <j1 rule="para" parents="5064 4618"/>
    </justification>
  </clause>

  <clause id="5072">
    <literal><![CDATA[
      K(x,(y \ z) / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ 1) = u
    ]]></literal>
    <justification jstring="[para(5065(a,2),4618(a,1))].">
      <j1 rule="para" parents="5065 4618"/>
    </justification>
  </clause>

  <clause id="5073">
    <literal><![CDATA[
      R(K(x,y / z),y / z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z / y) \ 1) = w
    ]]></literal>
    <justification jstring="[para(4889(a,2),5066(a,1))].">
      <j1 rule="para" parents="4889 5066"/>
    </justification>
  </clause>

  <clause id="5074">
    <literal><![CDATA[
      (x / (x / y)) \ ((x / y) \ z) = y \ ((y \ x) \ z)
    ]]></literal>
    <justification jstring="[hyper(121,a,4981,a(flip),b,4752,a),flip(a)].">
      <j1 rule="hyper" parents="121 4981 4752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5075">
    <literal><![CDATA[
      K(x \ y,x) * ((x \ y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      (y / x) \ z = u
    ]]></literal>
    <justification jstring="[para(4981(a,1),4590(a,1,2))].">
      <j1 rule="para" parents="4981 4590"/>
    </justification>
  </clause>

  <clause id="5077">
    <literal><![CDATA[
      K(x,((((y \ 1) \ 1) * z) \ u) \ w) = K(x,((y * z) \ u) \ w)
    ]]></literal>
    <justification jstring="[para(2854(a,1),5015(a,1,2,1))].">
      <j1 rule="para" parents="2854 5015"/>
    </justification>
  </clause>

  <clause id="5078">
    <literal><![CDATA[
      K(x,y * (((1 / (1 / z)) \ u) * w)) = K(x,y * ((z \ u) * w))
    ]]></literal>
    <justification jstring="[para(2838(a,1),5017(a,1,2,2))].">
      <j1 rule="para" parents="2838 5017"/>
    </justification>
  </clause>

  <clause id="5079">
    <literal><![CDATA[
      (x * (y / x)) \ (y / x) = y \ (x \ y)
    ]]></literal>
    <justification jstring="[para(113(a,1),5039(a,2,2))].">
      <j1 rule="para" parents="113 5039"/>
    </justification>
  </clause>

  <clause id="5081">
    <literal><![CDATA[
      (x \ y) * T(z,y / x) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,x) * (z * (y / x)) = u
    ]]></literal>
    <justification jstring="[para(5049(a,1),595(a,1))].">
      <j1 rule="para" parents="5049 595"/>
    </justification>
  </clause>

  <clause id="5082">
    <literal><![CDATA[
      K(x,x \ y) * ((x \ y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      (y / x) * z = u
    ]]></literal>
    <justification jstring="[para(5049(a,1),4590(a,1,2))].">
      <j1 rule="para" parents="5049 4590"/>
    </justification>
  </clause>

  <clause id="5084">
    <literal><![CDATA[
      K(R(x,y,z),x \ R(x,u,w)) = R(x,y,z) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(3021(a,1),4284(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3021 4284"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5085">
    <literal><![CDATA[
      (R(T(x,y),z,u) * (z * u)) / ((x * z) * u) = R(K(R(x,z,u),y),R(x,z,u),z * u)
    ]]></literal>
    <justification jstring="[para(4334(a,1),562(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4334 562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5086">
    <literal><![CDATA[
      L(T(x,y) \ 1,x,y) = (y * x) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(4222(a,2),4363(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4222 4363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5087">
    <literal><![CDATA[
      L(T(x,y) \ 1,x,y) = (x * y) \ y
    ]]></literal>
    <justification jstring="[hyper(333,a,5041,a(flip),b,5086,a),flip(a)].">
      <j1 rule="hyper" parents="333 5041 5086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5088">
    <literal><![CDATA[
      L(T(x,y) \ 1,x,y) != z
    ]]></literal>
    <literal><![CDATA[
      (x * y) \ y = z
    ]]></literal>
    <justification jstring="[para(5086(a,2),5044(a,1))].">
      <j1 rule="para" parents="5086 5044"/>
    </justification>
  </clause>

  <clause id="5089">
    <literal><![CDATA[
      K(R(x \ (y / z),x,y / (y / z)),x) = K(((z \ y) * z) / (x * (y / (y / z))),x)
    ]]></literal>
    <justification jstring="[para(3843(a,1),4379(a,2,1,1))].">
      <j1 rule="para" parents="3843 4379"/>
    </justification>
  </clause>

  <clause id="5090">
    <literal><![CDATA[
      K((x / y) \ 1,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(4484(a,1),4474(a,1))].">
      <j1 rule="para" parents="4484 4474"/>
    </justification>
  </clause>

  <clause id="5091">
    <literal><![CDATA[
      K(1 / (x / y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(4601(a,1),4474(a,1))].">
      <j1 rule="para" parents="4601 4474"/>
    </justification>
  </clause>

  <clause id="5093">
    <literal><![CDATA[
      K(T(x,T(y,z)),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(4475,a,4700,a(flip))].">
      <j1 rule="hyper" parents="4475 4700"/>
    </justification>
  </clause>

  <clause id="5094">
    <literal><![CDATA[
      K(x / T(y,z),y) = K(T(y,z) \ x,y)
    ]]></literal>
    <justification jstring="[para(113(a,1),5093(a,1,1)),flip(a)].">
      <j1 rule="para" parents="113 5093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5095">
    <literal><![CDATA[
      L(x,y * K(z,y \ 1),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,T(y \ 1,z),u) = w
    ]]></literal>
    <justification jstring="[para(2955(a,1),4563(a,1))].">
      <j1 rule="para" parents="2955 4563"/>
    </justification>
  </clause>

  <clause id="5096">
    <literal><![CDATA[
      x / y != K(z,u) * (u \ w)
    ]]></literal>
    <literal><![CDATA[
      (T(u,z) \ w) * y = x
    ]]></literal>
    <justification jstring="[para(4518(a,1),4596(a,2,2))].">
      <j1 rule="para" parents="4518 4596"/>
    </justification>
  </clause>

  <clause id="5097">
    <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(25(a,2),4610(a,1,2))].">
      <j1 rule="para" parents="25 4610"/>
    </justification>
  </clause>

  <clause id="5098">
    <literal><![CDATA[
      T(T(x * K(x * y,x),z),y) = R(T(x,z),y,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,27,a,b,4742,a),flip(a)].">
      <j1 rule="hyper" parents="333 27 4742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5099">
    <literal><![CDATA[
      L(x,T(y,z),T(z,y)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(3654,a,4846,a)].">
      <j1 rule="hyper" parents="3654 4846"/>
    </justification>
  </clause>

  <clause id="5100">
    <literal><![CDATA[
      (x * y) \ (x * (y * z)) = L(z,T(y,x),T(x,y))
    ]]></literal>
    <justification jstring="[hyper(333,a,18,a(flip),b,5099,a)].">
      <j1 rule="hyper" parents="333 18 5099"/>
    </justification>
  </clause>

  <clause id="5101">
    <literal><![CDATA[
      L(x,y \ z,T(y,z / y)) = L(x,z / y,y)
    ]]></literal>
    <justification jstring="[para(113(a,1),5099(a,1,2))].">
      <j1 rule="para" parents="113 5099"/>
    </justification>
  </clause>

  <clause id="5102">
    <literal><![CDATA[
      L(x,y \ z,T(y,y \ z)) = L(x,z / y,y)
    ]]></literal>
    <justification jstring="[para(3633(a,1),5101(a,1,3))].">
      <j1 rule="para" parents="3633 5101"/>
    </justification>
  </clause>

  <clause id="5103">
    <literal><![CDATA[
      K(x,(y / z) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(5057(a,1),547(a,1))].">
      <j1 rule="para" parents="5057 547"/>
    </justification>
  </clause>

  <clause id="5104">
    <literal><![CDATA[
      K(x,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,1 / y) = z
    ]]></literal>
    <justification jstring="[para(74(a,1),5103(a,1,2,1))].">
      <j1 rule="para" parents="74 5103"/>
    </justification>
  </clause>

  <clause id="5105">
    <literal><![CDATA[
      K(x,y / (z * y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,1 / z) = u
    ]]></literal>
    <justification jstring="[para(5059(a,2),5104(a,1))].">
      <j1 rule="para" parents="5059 5104"/>
    </justification>
  </clause>

  <clause id="5106">
    <literal><![CDATA[
      L(x,T(y,z),T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(5100(a,1),504(a,1))].">
      <j1 rule="para" parents="5100 504"/>
    </justification>
  </clause>

  <clause id="5107">
    <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(3593(a,1),5106(a,1,2))].">
      <j1 rule="para" parents="3593 5106"/>
    </justification>
  </clause>

  <clause id="5108">
    <literal><![CDATA[
      x * ((x \ y) * K(z,x \ y)) = y * K(z,(y \ x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(333,a,4413,a(flip),b,4270,a)].">
      <j1 rule="hyper" parents="333 4413 4270"/>
    </justification>
  </clause>

  <clause id="5109">
    <literal><![CDATA[
      ((x \ y) * x) * K(z,(x \ y) * x) = (x \ (y * K(z,y))) * x
    ]]></literal>
    <justification jstring="[hyper(35,a,4291,a,b,4331,a)].">
      <j1 rule="hyper" parents="35 4291 4331"/>
    </justification>
  </clause>

  <clause id="5110">
    <literal><![CDATA[
      a(1 / R(x,y,z),x,x \ 1) = K(R(x,y,z) \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,4043,a,b,4482,a)].">
      <j1 rule="hyper" parents="63 4043 4482"/>
    </justification>
  </clause>

  <clause id="5111">
    <literal><![CDATA[
      R(K(x \ 1,y),z,u) = K(R(x,z,u) \ 1,y)
    ]]></literal>
    <justification jstring="[para(4216(a,1),4482(a,1,1))].">
      <j1 rule="para" parents="4216 4482"/>
    </justification>
  </clause>

  <clause id="5112">
    <literal><![CDATA[
      K(R(x,y,z) \ 1,y) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,4889,a(flip),b,5111,a),flip(a)].">
      <j1 rule="hyper" parents="63 4889 5111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5113">
    <literal><![CDATA[
      K(R(1 / x,y,z) \ 1,u) = R(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(79(a,1),5111(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="79 5111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5114">
    <literal><![CDATA[
      K(R(x \ 1,y,z) \ 1,u) = R(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(3334(a,1),5111(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3334 5111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5115">
    <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(804(a,1),5112(a,1,1,1))].">
      <j1 rule="para" parents="804 5112"/>
    </justification>
  </clause>

  <clause id="5116">
    <literal><![CDATA[
      K(x,R(1 / y,z,u) \ 1) = R(K(y,x),z,u) \ 1
    ]]></literal>
    <justification jstring="[para(5113(a,1),4367(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5113 4367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5117">
    <literal><![CDATA[
      K(R(R(1 / x,y,z),u,w) \ 1,v5) = R(R(K(x,v5),y,z),u,w)
    ]]></literal>
    <justification jstring="[para(5113(a,1),5111(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5113 5111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5118">
    <literal><![CDATA[
      K(x,R(y \ 1,z,u) \ 1) * w = R(K(y,x),z,u) \ w
    ]]></literal>
    <justification jstring="[para(5114(a,1),4567(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5114 4567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5119">
    <literal><![CDATA[
      x * ((y \ (x \ 1)) * y) = K((x * y) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(595,a,4493,a)].">
      <j1 rule="hyper" parents="595 4493"/>
    </justification>
  </clause>

  <clause id="5120">
    <literal><![CDATA[
      (x * T(x \ y,z)) * (y \ 1) = K((x * (y \ 1)) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,1360,a(flip),b,4493,a)].">
      <j1 rule="hyper" parents="63 1360 4493"/>
    </justification>
  </clause>

  <clause id="5121">
    <literal><![CDATA[
      x * (y \ T(y * (x \ 1),z)) = K((x * (y \ 1)) \ 1,z)
    ]]></literal>
    <justification jstring="[para(953(a,1),4493(a,1,2))].">
      <j1 rule="para" parents="953 4493"/>
    </justification>
  </clause>

  <clause id="5122">
    <literal><![CDATA[
      x * (y \ K((y * (x \ 1)) \ 1,z)) = T(x * (y \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(126,a,4495,a,b,953,a(flip))].">
      <j1 rule="hyper" parents="126 4495 953"/>
    </justification>
  </clause>

  <clause id="5123">
    <literal><![CDATA[
      K(x \ 1,x) * (x \ y) = y * T(y \ (x \ y),T(x,z))
    ]]></literal>
    <justification jstring="[para(3442(a,1),4497(a,1,1))].">
      <j1 rule="para" parents="3442 4497"/>
    </justification>
  </clause>

  <clause id="5124">
    <literal><![CDATA[
      (x * y) \ (K(x \ 1,z) * y) = T((x * y) \ y,z)
    ]]></literal>
    <justification jstring="[hyper(121,a,4498,a(flip),b,940,a)].">
      <j1 rule="hyper" parents="121 4498 940"/>
    </justification>
  </clause>

  <clause id="5125">
    <literal><![CDATA[
      x * (y \ T(y * (x \ (y \ 1)),z)) = K(x \ 1,z) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(953(a,1),4498(a,1,2))].">
      <j1 rule="para" parents="953 4498"/>
    </justification>
  </clause>

  <clause id="5126">
    <literal><![CDATA[
      x * (K(x \ 1,y) * (x \ z)) = K(x \ 1,y) * z
    ]]></literal>
    <justification jstring="[para(4497(a,2),4498(a,1,2))].">
      <j1 rule="para" parents="4497 4498"/>
    </justification>
  </clause>

  <clause id="5127">
    <literal><![CDATA[
      T(x,y) * z != R(x,u,w) * K(x,y)
    ]]></literal>
    <literal><![CDATA[
      x \ R(x,u,w) = z
    ]]></literal>
    <justification jstring="[para(4529(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="4529 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5129">
    <literal><![CDATA[
      K(((x \ 1) / (y / x)) \ 1,z) = (T(y,z) / x) / (y / x)
    ]]></literal>
    <justification jstring="[hyper(63,a,4965,a,b,4707,a)].">
      <j1 rule="hyper" parents="63 4965 4707"/>
    </justification>
  </clause>

  <clause id="5130">
    <literal><![CDATA[
      K(((x \ 1) * (x * y)) \ z,u) = K(L(y,x,x \ 1) \ z,u)
    ]]></literal>
    <justification jstring="[para(2652(a,1),4769(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="2652 4769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5131">
    <literal><![CDATA[
      (x * ((y * (x \ z)) / y)) / z = K(y,z / x)
    ]]></literal>
    <justification jstring="[hyper(333,a,5055,a(flip),b,4772,a),flip(a)].">
      <j1 rule="hyper" parents="333 5055 4772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5132">
    <literal><![CDATA[
      (x * (y * ((z * (y \ (x \ u))) / z))) / u = K(z,((x * y) / u) \ 1)
    ]]></literal>
    <justification jstring="[para(1171(a,1),4772(a,1,1))].">
      <j1 rule="para" parents="1171 4772"/>
    </justification>
  </clause>

  <clause id="5133">
    <literal><![CDATA[
      T(x * ((y * (x \ z)) / y),z) / z = K(y,(T(x,z) / z) \ 1)
    ]]></literal>
    <justification jstring="[para(2024(a,1),4772(a,1,1))].">
      <j1 rule="para" parents="2024 4772"/>
    </justification>
  </clause>

  <clause id="5134">
    <literal><![CDATA[
      K(x,y \ 1) * (y \ z) = z * ((x * (z \ (y \ z))) / x)
    ]]></literal>
    <justification jstring="[hyper(125,a,5061,a(flip),b,5131,a)].">
      <j1 rule="hyper" parents="125 5061 5131"/>
    </justification>
  </clause>

  <clause id="5135">
    <literal><![CDATA[
      K(x,y * (((1 / z) * (u * z)) \ (u * (u * z)))) = K(x,y * ((z \ 1) \ u))
    ]]></literal>
    <justification jstring="[para(1962(a,2),4805(a,1,2,2))].">
      <j1 rule="para" parents="1962 4805"/>
    </justification>
  </clause>

  <clause id="5136">
    <literal><![CDATA[
      x / (y * ((z \ (y \ x)) * z)) = K(z,x / (z / (y \ 1)))
    ]]></literal>
    <justification jstring="[para(4145(a,1),4849(a,1,2))].">
      <j1 rule="para" parents="4145 4849"/>
    </justification>
  </clause>

  <clause id="5137">
    <literal><![CDATA[
      x / (y * ((z \ (y \ x)) * z)) = K(z,x / (z * y))
    ]]></literal>
    <justification jstring="[para(4132(a,1),4850(a,1,2))].">
      <j1 rule="para" parents="4132 4850"/>
    </justification>
  </clause>

  <clause id="5138">
    <literal><![CDATA[
      (x * K(y,x \ 1)) * z = K(y,x \ 1) * (x * z)
    ]]></literal>
    <justification jstring="[para(2042(a,1),4897(a,1,1))].">
      <j1 rule="para" parents="2042 4897"/>
    </justification>
  </clause>

  <clause id="5139">
    <literal><![CDATA[
      K(x \ (y * (((y \ z) \ 1) \ 1)),u) = K(x \ z,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),5002(a,2,1,2))].">
      <j1 rule="para" parents="10 5002"/>
    </justification>
  </clause>

  <clause id="5140">
    <literal><![CDATA[
      T(x,y \ (z * (1 / u))) = T(x,y \ (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[hyper(124,a,5012,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 5012 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5141">
    <literal><![CDATA[
      T(x,y \ ((1 / z) * u)) = T(x,y \ ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[hyper(124,a,5013,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 5013 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5142">
    <literal><![CDATA[
      K(x,y \ ((z \ 1) * (z * u))) = K(x,y \ L(u,z,z \ 1))
    ]]></literal>
    <justification jstring="[para(2652(a,1),5013(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2652 5013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5143">
    <literal><![CDATA[
      K(x,y \ (T(1 / z,u) * w)) = K(x,y \ (T(z \ 1,u) * w))
    ]]></literal>
    <justification jstring="[para(2383(a,1),5014(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="2383 5014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5144">
    <literal><![CDATA[
      K(x,T((y \ 1) * ((z \ y) * z),u)) = K(x,T(K(z \ y,z),u))
    ]]></literal>
    <justification jstring="[para(4177(a,1),5023(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4177 5023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5145">
    <literal><![CDATA[
      ((x \ y) \ y) \ ((x \ y) \ z) = x \ ((y / x) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,326,a(flip),b,5033,a)].">
      <j1 rule="hyper" parents="63 326 5033"/>
    </justification>
  </clause>

  <clause id="5146">
    <literal><![CDATA[
      ((x \ y) \ y) * ((x \ y) * z) = x * ((y / x) * z)
    ]]></literal>
    <justification jstring="[hyper(736,a,5036,a)].">
      <j1 rule="hyper" parents="736 5036"/>
    </justification>
  </clause>

  <clause id="5147">
    <literal><![CDATA[
      ((x * y) \ y) * T(y * x,x \ 1) = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(126,a,5048,a(flip),b,5043,a(flip))].">
      <j1 rule="hyper" parents="126 5048 5043"/>
    </justification>
  </clause>

  <clause id="5148">
    <literal><![CDATA[
      K(x,y \ K(y,z)) * z = z * K(x,(z \ (z * y)) \ 1)
    ]]></literal>
    <justification jstring="[para(4355(a,1),5053(a,1,1,2))].">
      <j1 rule="para" parents="4355 5053"/>
    </justification>
  </clause>

  <clause id="5149">
    <literal><![CDATA[
      x * K(y,(x \ z) \ 1) = K(y,x / z) * x
    ]]></literal>
    <justification jstring="[para(5055(a,1),5053(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5055 5053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5150">
    <literal><![CDATA[
      T(K(x,y / z),y) = K(x,(y \ z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(254,a,5149,a)].">
      <j1 rule="hyper" parents="254 5149"/>
    </justification>
  </clause>

  <clause id="5153">
    <literal><![CDATA[
      T((x * y) \ y,T(x,z)) = (x * y) \ (K(x \ 1,x) * y)
    ]]></literal>
    <justification jstring="[para(3442(a,1),5124(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3442 5124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5154">
    <literal><![CDATA[
      (1 / x) * (K(x,y) * ((1 / x) \ z)) = K((1 / x) \ 1,y) * z
    ]]></literal>
    <justification jstring="[para(79(a,1),5126(a,1,2,1,1))].">
      <j1 rule="para" parents="79 5126"/>
    </justification>
  </clause>

  <clause id="5155">
    <literal><![CDATA[
      (x \ 1) * (K(x,y) * ((x \ 1) \ z)) = K((x \ 1) \ 1,y) * z
    ]]></literal>
    <justification jstring="[para(3334(a,1),5126(a,1,2,1))].">
      <j1 rule="para" parents="3334 5126"/>
    </justification>
  </clause>

  <clause id="5156">
    <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(4581(a,1),50(a,1)),flip(a)].">
      <j1 rule="para" parents="4581 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5157">
    <literal><![CDATA[
      L(T(x,x \ (K(y,z) * u)),x \ (K(y,z) * u),K(z,y)) = (K(z,y) * (x \ (K(y,z) * u))) \ u
    ]]></literal>
    <justification jstring="[para(112(a,2),4581(a,1,1))].">
      <j1 rule="para" parents="112 4581"/>
    </justification>
  </clause>

  <clause id="5158">
    <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(4567(a,1),4581(a,1,1))].">
      <j1 rule="para" parents="4567 4581"/>
    </justification>
  </clause>

  <clause id="5159">
    <literal><![CDATA[
      (K(x,y) \ (z * u)) / L(u,z,K(y,x)) = K(x,y) \ z
    ]]></literal>
    <justification jstring="[hyper(123,a,4567,a,b,4588,a)].">
      <j1 rule="hyper" parents="123 4567 4588"/>
    </justification>
  </clause>

  <clause id="5160">
    <literal><![CDATA[
      (K(x,y) \ z) \ (K(x,y) \ (z * u)) = L(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(121,a,4567,a,b,4588,a)].">
      <j1 rule="hyper" parents="121 4567 4588"/>
    </justification>
  </clause>

  <clause id="5161">
    <literal><![CDATA[
      (x * K(y,x)) \ z != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * (x \ z) = u
    ]]></literal>
    <justification jstring="[para(4591(a,1),3549(a,1))].">
      <j1 rule="para" parents="4591 3549"/>
    </justification>
  </clause>

  <clause id="5162">
    <literal><![CDATA[
      a(T(x,y),T(y,x),z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(752,a,4847,a),flip(a)].">
      <j1 rule="hyper" parents="752 4847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5163">
    <literal><![CDATA[
      a(T(x,y),T(y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(4847(a,1),752(a,1))].">
      <j1 rule="para" parents="4847 752"/>
    </justification>
  </clause>

  <clause id="5164">
    <literal><![CDATA[
      a(T(x,T(y,x)),T(T(y,x),x),R(T(x,y),z,u)) = a(R(x,z,u),y,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,3917,a(flip),b,5162,a),flip(a)].">
      <j1 rule="hyper" parents="333 3917 5162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5165">
    <literal><![CDATA[
      a(T(x * (y / x),x),T(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x * (y / x),x,z) = u
    ]]></literal>
    <justification jstring="[para(3677(a,1),5163(a,1,2))].">
      <j1 rule="para" parents="3677 5163"/>
    </justification>
  </clause>

  <clause id="5166">
    <literal><![CDATA[
      x \ (((y \ (x / z)) * y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K((x \ (y * z)) \ 1,y) = u
    ]]></literal>
    <justification jstring="[para(1112(a,1),4909(a,1,2))].">
      <j1 rule="para" parents="1112 4909"/>
    </justification>
  </clause>

  <clause id="5167">
    <literal><![CDATA[
      T(x,y) \ T(z * T(z \ x,u),y) != w
    ]]></literal>
    <literal><![CDATA[
      K((T(x,y) \ T(z,y)) \ 1,u) = w
    ]]></literal>
    <justification jstring="[para(1780(a,1),4909(a,1,2))].">
      <j1 rule="para" parents="1780 4909"/>
    </justification>
  </clause>

  <clause id="5169">
    <literal><![CDATA[
      K(x \ 1,L(x,y,z)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(34,a,2529,a(flip),b,4941,a),flip(a)].">
      <j1 rule="hyper" parents="34 2529 4941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5171">
    <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(4941(a,1),2719(a,1,1))].">
      <j1 rule="para" parents="4941 2719"/>
    </justification>
  </clause>

  <clause id="5172">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,x) = K(x \ 1,L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(333,a,2471,a,b,5169,a)].">
      <j1 rule="hyper" parents="333 2471 5169"/>
    </justification>
  </clause>

  <clause id="5173">
    <literal><![CDATA[
      L(K(x \ 1,L(x,y,z)),u,w) = K(L(x,u,w) \ 1,x)
    ]]></literal>
    <justification jstring="[para(5169(a,2),2421(a,1,1))].">
      <j1 rule="para" parents="5169 2421"/>
    </justification>
  </clause>

  <clause id="5175">
    <literal><![CDATA[
      L(x / (x / y),z,u) \ L(y,z,u) = K(L(y,z,u),y \ x)
    ]]></literal>
    <justification jstring="[para(4176(a,2),4948(a,1,1,1))].">
      <j1 rule="para" parents="4176 4948"/>
    </justification>
  </clause>

  <clause id="5176">
    <literal><![CDATA[
      R(K(x,y / (z * y)),R(1 / z,z,y),u) = K(x,z \ 1)
    ]]></literal>
    <justification jstring="[para(230(a,2),5067(a,1,2))].">
      <j1 rule="para" parents="230 5067"/>
    </justification>
  </clause>

  <clause id="5177">
    <literal><![CDATA[
      K(x \ y,x) * T(z,x \ y) != u
    ]]></literal>
    <literal><![CDATA[
      (y / x) \ (z * (x \ y)) = u
    ]]></literal>
    <justification jstring="[para(22(a,2),5075(a,1,2))].">
      <j1 rule="para" parents="22 5075"/>
    </justification>
  </clause>

  <clause id="5178">
    <literal><![CDATA[
      ((x \ 1) \ y) * K(x \ 1,x) != z
    ]]></literal>
    <literal><![CDATA[
      (1 / x) \ y = z
    ]]></literal>
    <justification jstring="[para(2412(a,1),5075(a,1))].">
      <j1 rule="para" parents="2412 5075"/>
    </justification>
  </clause>

  <clause id="5179">
    <literal><![CDATA[
      (x \ 1) * (y / (x \ 1)) != z
    ]]></literal>
    <literal><![CDATA[
      (1 / x) * (y / (1 / x)) = z
    ]]></literal>
    <justification jstring="[para(2507(a,1),5082(a,1))].">
      <j1 rule="para" parents="2507 5082"/>
    </justification>
  </clause>

  <clause id="5180">
    <literal><![CDATA[
      (x \ y) * (K(x,x \ y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      (y / x) * z = u
    ]]></literal>
    <justification jstring="[para(4712(a,1),5082(a,1))].">
      <j1 rule="para" parents="4712 5082"/>
    </justification>
  </clause>

  <clause id="5181">
    <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(126,a,5110,a(flip),b,226,a)].">
      <j1 rule="hyper" parents="126 5110 226"/>
    </justification>
  </clause>

  <clause id="5182">
    <literal><![CDATA[
      L(x \ y,x,K(z,u)) = (K(u,z) \ x) \ (K(u,z) \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),5160(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 5160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5183">
    <literal><![CDATA[
      (x \ y) * (((x \ y) \ y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      (y / x) * (x * z) = u
    ]]></literal>
    <justification jstring="[para(4605(a,1),5180(a,1,2))].">
      <j1 rule="para" parents="4605 5180"/>
    </justification>
  </clause>

  <clause id="5184">
    <literal><![CDATA[
      L(x \ (y * z),x,K(z,y)) = (K(y,z) \ x) \ (z * y)
    ]]></literal>
    <justification jstring="[para(4199(a,1),5182(a,2,2))].">
      <j1 rule="para" parents="4199 5182"/>
    </justification>
  </clause>

  <clause id="5185">
    <literal><![CDATA[
      L(x \ T(y,z),x,K(y,z)) = (K(z,y) \ x) \ T(T(y,z),z)
    ]]></literal>
    <justification jstring="[para(4400(a,1),5182(a,2,2))].">
      <j1 rule="para" parents="4400 5182"/>
    </justification>
  </clause>

  <clause id="5186">
    <literal><![CDATA[
      K(x,y) * ((x \ 1) \ y) = (y \ ((x \ 1) \ y)) * y
    ]]></literal>
    <justification jstring="[hyper(333,a,111,a(flip),b,4288,a),flip(a)].">
      <j1 rule="hyper" parents="333 111 4288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5187">
    <literal><![CDATA[
      K(x,x \ 1) / ((y * x) \ y) = ((y * x) \ y) \ 1
    ]]></literal>
    <justification jstring="[hyper(333,a,2292,a(flip),b,4359,a),flip(a)].">
      <j1 rule="hyper" parents="333 2292 4359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5188">
    <literal><![CDATA[
      (1 / ((x * y) \ x)) * K(y,y \ 1) = ((x * y) \ x) \ 1
    ]]></literal>
    <justification jstring="[hyper(2803,a,5187,a)].">
      <j1 rule="hyper" parents="2803 5187"/>
    </justification>
  </clause>

  <clause id="5189">
    <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(27(a,2),4489(a,2,2))].">
      <j1 rule="para" parents="27 4489"/>
    </justification>
  </clause>

  <clause id="5190">
    <literal><![CDATA[
      K(x,x * y) * (R(y,z,u) * x) = R(y,z,u) * T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(3735,a,4609,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="3735 4609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5191">
    <literal><![CDATA[
      R(x,y,z * K(u \ z,u)) = R(x,y,u * (z / u))
    ]]></literal>
    <justification jstring="[para(4367(a,1),4673(a,1,3,2))].">
      <j1 rule="para" parents="4367 4673"/>
    </justification>
  </clause>

  <clause id="5192">
    <literal><![CDATA[
      R(x,y,(z \ u) * z) = R(x,y,z * (u / z))
    ]]></literal>
    <justification jstring="[para(317(a,1),5191(a,1,3))].">
      <j1 rule="para" parents="317 5191"/>
    </justification>
  </clause>

  <clause id="5193">
    <literal><![CDATA[
      K(1 / x,y) / (x \ 1) = 1 / (x \ K(y,1 / x))
    ]]></literal>
    <justification jstring="[para(4826(a,1),4728(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4826 4728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5194">
    <literal><![CDATA[
      K((x * ((1 / y) / z)) \ u,w) = K((x * ((y \ 1) / z)) \ u,w)
    ]]></literal>
    <justification jstring="[para(2864(a,1),4770(a,1,1,1,2))].">
      <j1 rule="para" parents="2864 4770"/>
    </justification>
  </clause>

  <clause id="5195">
    <literal><![CDATA[
      x * (y * ((x \ 1) / y)) = K(y,(x * y) \ 1)
    ]]></literal>
    <justification jstring="[para(10(a,1),4771(a,1,2,2,1))].">
      <j1 rule="para" parents="10 4771"/>
    </justification>
  </clause>

  <clause id="5196">
    <literal><![CDATA[
      ((x * y) * ((z * ((x * y) \ x)) / z)) * y = (x * y) * K(z,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,1979,a(flip),b,4776,a)].">
      <j1 rule="hyper" parents="63 1979 4776"/>
    </justification>
  </clause>

  <clause id="5197">
    <literal><![CDATA[
      (x * y) * (x / (x * y)) = x * K(x * y,y \ 1)
    ]]></literal>
    <justification jstring="[para(10(a,1),4776(a,1,2,1))].">
      <j1 rule="para" parents="10 4776"/>
    </justification>
  </clause>

  <clause id="5198">
    <literal><![CDATA[
      (x * (1 / y)) * (x / (x * (1 / y))) = x * K(x * (1 / y),y)
    ]]></literal>
    <justification jstring="[para(79(a,1),5197(a,2,2,2))].">
      <j1 rule="para" parents="79 5197"/>
    </justification>
  </clause>

  <clause id="5199">
    <literal><![CDATA[
      x * (y * ((z * (y \ (x \ y))) / z)) = K(z,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(1172,a,4777,a)].">
      <j1 rule="hyper" parents="1172 4777"/>
    </justification>
  </clause>

  <clause id="5200">
    <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(4818(a,2),4803(a,1,2,2))].">
      <j1 rule="para" parents="4818 4803"/>
    </justification>
  </clause>

  <clause id="5201">
    <literal><![CDATA[
      ((x \ 1) \ y) * K(x \ 1,(x \ 1) \ y) = (x \ K((x \ 1) \ y,x \ 1)) \ y
    ]]></literal>
    <justification jstring="[hyper(2726,a,4834,a)].">
      <j1 rule="hyper" parents="2726 4834"/>
    </justification>
  </clause>

  <clause id="5202">
    <literal><![CDATA[
      K((x \ (y / (z \ 1))) \ 1,y) = x \ (((y \ (x / z)) * y) * z)
    ]]></literal>
    <justification jstring="[para(3044(a,1),4956(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3044 4956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5203">
    <literal><![CDATA[
      x * K((x \ (y * z)) \ 1,y) = z * ((y \ (z \ x)) * y)
    ]]></literal>
    <justification jstring="[hyper(4148,a,4960,a),flip(a)].">
      <j1 rule="hyper" parents="4148 4960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5204">
    <literal><![CDATA[
      K(x,(y / (1 / (1 / z))) * u) = K(x,(y / z) * u)
    ]]></literal>
    <justification jstring="[para(4979(a,1),4796(a,1,2))].">
      <j1 rule="para" parents="4979 4796"/>
    </justification>
  </clause>

  <clause id="5205">
    <literal><![CDATA[
      K(x,y) * (K(x,y) * z) = y * (T(T(y,x),x) \ z)
    ]]></literal>
    <justification jstring="[para(4556(a,1),4992(a,1,2))].">
      <j1 rule="para" parents="4556 4992"/>
    </justification>
  </clause>

  <clause id="5206">
    <literal><![CDATA[
      (T(K(x,y),z) * (z * K(x,y))) * u = (y * (T(T(y,x),x) \ z)) * u
    ]]></literal>
    <justification jstring="[para(5205(a,1),3712(a,2,1))].">
      <j1 rule="para" parents="5205 3712"/>
    </justification>
  </clause>

  <clause id="5207">
    <literal><![CDATA[
      K(x * y,T(y,z)) = K(y * x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(4984,a,5028,a),flip(a)].">
      <j1 rule="hyper" parents="4984 5028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5208">
    <literal><![CDATA[
      (x \ 1) \ ((x \ y) / y) = x * ((x \ y) / y)
    ]]></literal>
    <justification jstring="[hyper(63,a,2672,a(flip),b,5070,a)].">
      <j1 rule="hyper" parents="63 2672 5070"/>
    </justification>
  </clause>

  <clause id="5209">
    <literal><![CDATA[
      K(R(x,y,z),x \ R(x,u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(333,a,66,a(flip),b,5084,a),flip(a)].">
      <j1 rule="hyper" parents="333 66 5084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5211">
    <literal><![CDATA[
      K((x * (y \ 1)) \ 1,y) = K(x \ y,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,4600,a(flip),b,5120,a),flip(a)].">
      <j1 rule="hyper" parents="63 4600 5120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5212">
    <literal><![CDATA[
      (x * K((x \ y) \ 1,z)) * (x \ 1) = K((y * (x \ 1)) \ 1,z)
    ]]></literal>
    <justification jstring="[para(4486(a,1),5120(a,1,1))].">
      <j1 rule="para" parents="4486 5120"/>
    </justification>
  </clause>

  <clause id="5213">
    <literal><![CDATA[
      K(x \ y,y) / (y \ T(y * (x \ 1),y)) = x
    ]]></literal>
    <justification jstring="[hyper(123,a,5211,a(flip),b,5121,a)].">
      <j1 rule="hyper" parents="123 5211 5121"/>
    </justification>
  </clause>

  <clause id="5214">
    <literal><![CDATA[
      K(((1 / x) * (y \ 1)) \ 1,z) = (1 / x) * (y \ T(y * x,z))
    ]]></literal>
    <justification jstring="[para(79(a,1),5121(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="79 5121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5215">
    <literal><![CDATA[
      x * (y \ K(y \ x,x)) = T(x * (y \ 1),x)
    ]]></literal>
    <justification jstring="[para(5211(a,1),5122(a,1,2,2))].">
      <j1 rule="para" parents="5211 5122"/>
    </justification>
  </clause>

  <clause id="5216">
    <literal><![CDATA[
      ((x * (K(y \ x,x) * (y \ 1))) / x) / (y \ 1) = y * (T(x * (y \ 1),x) / x)
    ]]></literal>
    <justification jstring="[para(5215(a,1),1677(a,2,2,1))].">
      <j1 rule="para" parents="5215 1677"/>
    </justification>
  </clause>

  <clause id="5217">
    <literal><![CDATA[
      x * T(x \ (y \ x),T(y,z)) = ((y \ 1) \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,4703,a,b,5123,a),flip(a)].">
      <j1 rule="hyper" parents="63 4703 5123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5218">
    <literal><![CDATA[
      K(x,((y \ 1) / (z / y)) \ 1) \ (z / y) = T(z,x) / y
    ]]></literal>
    <justification jstring="[hyper(4584,a,5129,a)].">
      <j1 rule="hyper" parents="4584 5129"/>
    </justification>
  </clause>

  <clause id="5219">
    <literal><![CDATA[
      K(((1 / x) / (y / x)) \ 1,z) = (T(y,z) / x) / (y / x)
    ]]></literal>
    <justification jstring="[hyper(63,a,5010,a,b,5129,a)].">
      <j1 rule="hyper" parents="63 5010 5129"/>
    </justification>
  </clause>

  <clause id="5220">
    <literal><![CDATA[
      K(((1 / x) / (y / x)) \ 1,z) * (y / x) = T(y,z) / x
    ]]></literal>
    <justification jstring="[hyper(125,a,5010,a,b,5129,a(flip))].">
      <j1 rule="hyper" parents="125 5010 5129"/>
    </justification>
  </clause>

  <clause id="5221">
    <literal><![CDATA[
      K(x,y / (x / (z \ 1))) = K(x,y / (x * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,5137,a(flip),b,5136,a),flip(a)].">
      <j1 rule="hyper" parents="63 5137 5136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5222">
    <literal><![CDATA[
      K(x,y \ K(y,z)) * z = z * K(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(9(a,1),5148(a,2,2,2,1))].">
      <j1 rule="para" parents="9 5148"/>
    </justification>
  </clause>

  <clause id="5223">
    <literal><![CDATA[
      T((x * y) \ y,T(x,z)) = T((x * y) \ y,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,5124,a(flip),b,5153,a),flip(a)].">
      <j1 rule="hyper" parents="333 5124 5153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5224">
    <literal><![CDATA[
      (((x * y) \ x) \ 1) / ((y \ 1) \ 1) = (1 / ((x * y) \ x)) / y
    ]]></literal>
    <justification jstring="[hyper(123,a,5188,a(flip),b,2146,a)].">
      <j1 rule="hyper" parents="123 5188 2146"/>
    </justification>
  </clause>

  <clause id="5225">
    <literal><![CDATA[
      x * (K(y,x \ 1) * (x \ z)) = K(y,x \ 1) * z
    ]]></literal>
    <justification jstring="[para(5134(a,2),5199(a,1,2))].">
      <j1 rule="para" parents="5134 5199"/>
    </justification>
  </clause>

  <clause id="5226">
    <literal><![CDATA[
      K(x,y \ 1) * (y * z) = y * (K(x,y \ 1) * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),5225(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 5225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5228">
    <literal><![CDATA[
      1 \ (x * (K(y,x \ 1) * z)) = K(y,x \ 1) * (x * z)
    ]]></literal>
    <justification jstring="[hyper(333,a,65,a,b,5226,a)].">
      <j1 rule="hyper" parents="333 65 5226"/>
    </justification>
  </clause>

  <clause id="5229">
    <literal><![CDATA[
      (x * K(y,x \ 1)) * z = x * (K(y,x \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5138,a,b,5226,a)].">
      <j1 rule="hyper" parents="63 5138 5226"/>
    </justification>
  </clause>

  <clause id="5230">
    <literal><![CDATA[
      L(x,K(y,z \ 1),z) = x
    ]]></literal>
    <justification jstring="[hyper(501,a,5229,a)].">
      <j1 rule="hyper" parents="501 5229"/>
    </justification>
  </clause>

  <clause id="5231">
    <literal><![CDATA[
      L(x,K(y \ 1,z),y) = x
    ]]></literal>
    <justification jstring="[hyper(4391,a,5230,a)].">
      <j1 rule="hyper" parents="4391 5230"/>
    </justification>
  </clause>

  <clause id="5232">
    <literal><![CDATA[
      L(x,K(y,z),z \ 1) = x
    ]]></literal>
    <justification jstring="[para(4621(a,1),5230(a,1,2))].">
      <j1 rule="para" parents="4621 5230"/>
    </justification>
  </clause>

  <clause id="5233">
    <literal><![CDATA[
      L(x,K(y,z),u / (z * u)) = x
    ]]></literal>
    <justification jstring="[para(5060(a,1),5230(a,1,2))].">
      <j1 rule="para" parents="5060 5230"/>
    </justification>
  </clause>

  <clause id="5234">
    <literal><![CDATA[
      L(x,K(y,z),1 / y) = x
    ]]></literal>
    <justification jstring="[para(79(a,1),5231(a,1,2,1))].">
      <j1 rule="para" parents="79 5231"/>
    </justification>
  </clause>

  <clause id="5235">
    <literal><![CDATA[
      ((x \ 1) * K(y,x)) \ z = K(y,x) \ ((x \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(578,a,5232,a),flip(a)].">
      <j1 rule="hyper" parents="578 5232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5236">
    <literal><![CDATA[
      (1 / x) * (K(x,y) * z) = (K(x,y) / x) * z
    ]]></literal>
    <justification jstring="[para(5234(a,1),3562(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5234 3562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5237">
    <literal><![CDATA[
      ((x / (y * x)) * K(z,y)) \ u = K(y,z) * ((x / (y * x)) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,4591,a(flip),b,5233,a)].">
      <j1 rule="hyper" parents="63 4591 5233"/>
    </justification>
  </clause>

  <clause id="5238">
    <literal><![CDATA[
      (K(x,y) / x) * (x * z) = (1 / x) * (T(x,y) * z)
    ]]></literal>
    <justification jstring="[para(4273(a,1),5236(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4273 5236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5239">
    <literal><![CDATA[
      K(x,y) \ ((y \ 1) \ z) = (y \ K(x,y)) \ z
    ]]></literal>
    <justification jstring="[para(3976(a,1),5235(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3976 5235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5240">
    <literal><![CDATA[
      K(x,y) * ((x \ 1) \ z) = (x \ K(y,x)) \ z
    ]]></literal>
    <justification jstring="[hyper(4580,a,5239,a)].">
      <j1 rule="hyper" parents="4580 5239"/>
    </justification>
  </clause>

  <clause id="5241">
    <literal><![CDATA[
      (x \ K(y,x)) \ L((x \ 1) * z,u,w) = K(x,y) * (x * L(x \ z,u,w))
    ]]></literal>
    <justification jstring="[para(2548(a,1),5240(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2548 5240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5242">
    <literal><![CDATA[
      K(x,y) * ((x \ 1) \ z) = (T(x,y) \ 1) \ z
    ]]></literal>
    <justification jstring="[para(4226(a,2),5240(a,2,1))].">
      <j1 rule="para" parents="4226 5240"/>
    </justification>
  </clause>

  <clause id="5243">
    <literal><![CDATA[
      (x \ ((y \ 1) \ x)) * x = (T(y,x) \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,5186,a(flip),b,5242,a)].">
      <j1 rule="hyper" parents="63 5186 5242"/>
    </justification>
  </clause>

  <clause id="5244">
    <literal><![CDATA[
      T(x,y) / ((y \ 1) \ x) = T(y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(39,a,3869,a,b,5243,a(flip))].">
      <j1 rule="hyper" parents="39 3869 5243"/>
    </justification>
  </clause>

  <clause id="5245">
    <literal><![CDATA[
      (T(1 / x,y) \ 1) \ y = (y \ (x \ y)) * y
    ]]></literal>
    <justification jstring="[para(79(a,1),5243(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="79 5243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5246">
    <literal><![CDATA[
      x / ((x \ (y \ x)) * x) = T(1 / y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(198,a,5245,a)].">
      <j1 rule="hyper" parents="198 5245"/>
    </justification>
  </clause>

  <clause id="5247">
    <literal><![CDATA[
      T(1 / (x / y),x) \ 1 = x / ((x \ y) * x)
    ]]></literal>
    <justification jstring="[para(79(a,1),5246(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="79 5246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5248">
    <literal><![CDATA[
      (K(x,y) / x) * (x * (T(y,x) * z)) = (1 / x) * (x * (y * z))
    ]]></literal>
    <justification jstring="[para(4613(a,1),5238(a,2,2))].">
      <j1 rule="para" parents="4613 5238"/>
    </justification>
  </clause>

  <clause id="5249">
    <literal><![CDATA[
      x * ((y \ (x \ y)) * y) = y * K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(9(a,1),5203(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="9 5203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5250">
    <literal><![CDATA[
      (x * K(y \ 1,x)) / ((x \ (y \ x)) * x) = y
    ]]></literal>
    <justification jstring="[hyper(138,a,5249,a)].">
      <j1 rule="hyper" parents="138 5249"/>
    </justification>
  </clause>

  <clause id="5251">
    <literal><![CDATA[
      ((x \ y) \ ((x \ 1) \ (x \ y))) * (x \ y) = (x \ 1) \ (y / x)
    ]]></literal>
    <justification jstring="[hyper(121,a,4626,a(flip),b,5249,a),flip(a)].">
      <j1 rule="hyper" parents="121 4626 5249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5252">
    <literal><![CDATA[
      (x * K((x / y) \ 1,x)) / ((x \ y) * x) = x / y
    ]]></literal>
    <justification jstring="[para(79(a,1),5250(a,1,2,1,2))].">
      <j1 rule="para" parents="79 5250"/>
    </justification>
  </clause>

  <clause id="5253">
    <literal><![CDATA[
      (x * K(x \ y,x)) / ((x \ y) * x) = x / y
    ]]></literal>
    <justification jstring="[para(4969(a,1),5252(a,1,1,2))].">
      <j1 rule="para" parents="4969 5252"/>
    </justification>
  </clause>

  <clause id="5254">
    <literal><![CDATA[
      (x / (x / y)) / ((y \ x) * y) = y / x
    ]]></literal>
    <justification jstring="[para(4176(a,2),5253(a,1,1))].">
      <j1 rule="para" parents="4176 5253"/>
    </justification>
  </clause>

  <clause id="5255">
    <literal><![CDATA[
      (x / y) \ (y / (y / x)) = (x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(192,a,5254,a)].">
      <j1 rule="hyper" parents="192 5254"/>
    </justification>
  </clause>

  <clause id="5256">
    <literal><![CDATA[
      x * (((x * y) \ y) * (x * y)) = y / (y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(125,a,11,a(flip),b,5254,a)].">
      <j1 rule="hyper" parents="125 11 5254"/>
    </justification>
  </clause>

  <clause id="5257">
    <literal><![CDATA[
      T(x \ y,z) \ T((x \ y) * (y \ x),z) = y \ (x * K(z,x \ y))
    ]]></literal>
    <justification jstring="[hyper(63,a,1972,a,b,4364,a)].">
      <j1 rule="hyper" parents="63 1972 4364"/>
    </justification>
  </clause>

  <clause id="5258">
    <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(863(a,1),4440(a,2,1,1))].">
      <j1 rule="para" parents="863 4440"/>
    </justification>
  </clause>

  <clause id="5259">
    <literal><![CDATA[
      (x * y) \ (y * (T(x,y) * z)) = L(z,x,y * K(x,y))
    ]]></literal>
    <justification jstring="[para(4273(a,1),4453(a,1,2,2))].">
      <j1 rule="para" parents="4273 4453"/>
    </justification>
  </clause>

  <clause id="5260">
    <literal><![CDATA[
      L(x,y,z * K(y,z)) = L(x,T(y,z),z)
    ]]></literal>
    <justification jstring="[hyper(876,a,5259,a),flip(a)].">
      <j1 rule="hyper" parents="876 5259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5262">
    <literal><![CDATA[
      (T(x * y,z) * L(u,y,x)) \ (K(x * y,z) * ((x * y) * u)) = L(a(x,y,u),x * (y * u),K(x * y,z))
    ]]></literal>
    <justification jstring="[para(4536(a,1),519(a,1,1))].">
      <j1 rule="para" parents="4536 519"/>
    </justification>
  </clause>

  <clause id="5264">
    <literal><![CDATA[
      (x \ y) \ T(y,y \ x) = y * (T(x,x \ y) / y)
    ]]></literal>
    <justification jstring="[hyper(4853,a,4088,a(flip))].">
      <j1 rule="hyper" parents="4853 4088"/>
    </justification>
  </clause>

  <clause id="5265">
    <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(4856(a,1),3662(a,1,1))].">
      <j1 rule="para" parents="4856 3662"/>
    </justification>
  </clause>

  <clause id="5266">
    <literal><![CDATA[
      T(K(x * (y \ 1),y \ 1) / y,x) = R(1 / y,x,1 / y)
    ]]></literal>
    <justification jstring="[para(4757(a,1),4871(a,1,1,1))].">
      <j1 rule="para" parents="4757 4871"/>
    </justification>
  </clause>

  <clause id="5268">
    <literal><![CDATA[
      a((x * y) / x,x,z) = a(y,T(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(333,a,243,a(flip),b,5032,a),flip(a)].">
      <j1 rule="hyper" parents="333 243 5032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5269">
    <literal><![CDATA[
      a(x * K(y,x),y,z) = a(x,T(y,x),z)
    ]]></literal>
    <justification jstring="[para(4238(a,1),5268(a,1,1))].">
      <j1 rule="para" parents="4238 5268"/>
    </justification>
  </clause>

  <clause id="5270">
    <literal><![CDATA[
      a((x \ y) * K(y / (y / x),x \ y),y / (y / x),z) = a(x \ y,x,z)
    ]]></literal>
    <justification jstring="[para(3701(a,1),5269(a,2,2))].">
      <j1 rule="para" parents="3701 5269"/>
    </justification>
  </clause>

  <clause id="5271">
    <literal><![CDATA[
      K(L(x,y,z),u / x) = K(L(x,y,z),x \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,4356,a(flip),b,5175,a)].">
      <j1 rule="hyper" parents="63 4356 5175"/>
    </justification>
  </clause>

  <clause id="5272">
    <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(3411(a,1),5185(a,1,1,2))].">
      <j1 rule="para" parents="3411 5185"/>
    </justification>
  </clause>

  <clause id="5273">
    <literal><![CDATA[
      T(K(x * (y \ 1),y \ 1) / y,x) = R(1 / y,x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(333,a,1863,a(flip),b,5266,a),flip(a)].">
      <j1 rule="hyper" parents="333 1863 5266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5274">
    <literal><![CDATA[
      (x * y) * K(R(y,x,y),x * y) = ((y * x) / R(y,x,y)) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,1576,a(flip),b,4418,a),flip(a)].">
      <j1 rule="hyper" parents="63 1576 4418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5275">
    <literal><![CDATA[
      T(x,y) / (T(x,y) * y) = x / ((y * K(x,y)) * x)
    ]]></literal>
    <justification jstring="[para(4328(a,1),4645(a,1,1))].">
      <j1 rule="para" parents="4328 4645"/>
    </justification>
  </clause>

  <clause id="5276">
    <literal><![CDATA[
      T(x,y) / (T(x,y) * y) = x / (x * y)
    ]]></literal>
    <justification jstring="[para(4291(a,1),5275(a,2,2))].">
      <j1 rule="para" parents="4291 5275"/>
    </justification>
  </clause>

  <clause id="5277">
    <literal><![CDATA[
      (x / (x * y)) \ T(x,y) = T(x,y) * y
    ]]></literal>
    <justification jstring="[hyper(192,a,5276,a)].">
      <j1 rule="hyper" parents="192 5276"/>
    </justification>
  </clause>

  <clause id="5278">
    <literal><![CDATA[
      x * (K(y,x) * L(x \ z,u,w)) = T(x,y) \ L(x * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(4887,a,4694,a)].">
      <j1 rule="hyper" parents="4887 4694"/>
    </justification>
  </clause>

  <clause id="5279">
    <literal><![CDATA[
      (x * (y \ T(y * z,u))) / (x * z) = K((x * z) / (x * (y \ 1)),u)
    ]]></literal>
    <justification jstring="[para(953(a,1),4753(a,1,1,2))].">
      <j1 rule="para" parents="953 4753"/>
    </justification>
  </clause>

  <clause id="5280">
    <literal><![CDATA[
      K((x * y) / (x * (z \ y)),u) = (x * (K(z,u) * y)) / (x * y)
    ]]></literal>
    <justification jstring="[para(4533(a,1),4753(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4533 4753"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5281">
    <literal><![CDATA[
      ((x \ T(x * (y / z),u)) * z) / y = K((((x \ 1) * z) / y) \ 1,u)
    ]]></literal>
    <justification jstring="[para(1362(a,1),4957(a,1,1))].">
      <j1 rule="para" parents="1362 4957"/>
    </justification>
  </clause>

  <clause id="5282">
    <literal><![CDATA[
      x * K((x \ (y * z)) \ 1,z) = y * ((z \ (y \ x)) * z)
    ]]></literal>
    <justification jstring="[hyper(333,a,235,a(flip),b,4958,a),flip(a)].">
      <j1 rule="hyper" parents="333 235 4958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5283">
    <literal><![CDATA[
      x * (y * T(y \ (x \ y),z)) = y * K(T(x,y) \ 1,z)
    ]]></literal>
    <justification jstring="[para(22(a,2),4958(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="22 4958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5284">
    <literal><![CDATA[
      K(T(x,y) \ 1,z) = T(K(x \ 1,z),y)
    ]]></literal>
    <justification jstring="[hyper(253,a,4498,a(flip),b,5283,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="253 4498 5283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5285">
    <literal><![CDATA[
      K(T(1 / x,y) \ 1,z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[para(79(a,1),5284(a,2,1,1))].">
      <j1 rule="para" parents="79 5284"/>
    </justification>
  </clause>

  <clause id="5286">
    <literal><![CDATA[
      K(T(x \ 1,y) \ 1,z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[para(3334(a,1),5284(a,2,1))].">
      <j1 rule="para" parents="3334 5284"/>
    </justification>
  </clause>

  <clause id="5287">
    <literal><![CDATA[
      K(1 / T(x,y),z) = T(K(1 / x,z),y)
    ]]></literal>
    <justification jstring="[para(2381(a,1),5285(a,1,1))].">
      <j1 rule="para" parents="2381 5285"/>
    </justification>
  </clause>

  <clause id="5288">
    <literal><![CDATA[
      K(x,T(y \ 1,z) \ 1) = 1 / T(K(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(197,a,5286,a(flip),b,4367,a),flip(a)].">
      <j1 rule="hyper" parents="197 5286 4367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5290">
    <literal><![CDATA[
      T(x,y) != K(1 / T(z,y),u)
    ]]></literal>
    <literal><![CDATA[
      K(1 / z,u) = x
    ]]></literal>
    <justification jstring="[para(5287(a,2),49(a,1)),flip(a)].">
      <j1 rule="para" parents="5287 49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5291">
    <literal><![CDATA[
      1 / T(K(x,y),z) = T(K(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,4937,a(flip),b,5288,a),flip(a)].">
      <j1 rule="hyper" parents="63 4937 5288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5292">
    <literal><![CDATA[
      T(K(x,y),z) \ 1 = T(K(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(192,a,5291,a)].">
      <j1 rule="hyper" parents="192 5291"/>
    </justification>
  </clause>

  <clause id="5294">
    <literal><![CDATA[
      K(x,y) * T(K(y,x),z) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(126,a,5292,a(flip),b,4226,a(flip))].">
      <j1 rule="hyper" parents="126 5292 4226"/>
    </justification>
  </clause>

  <clause id="5295">
    <literal><![CDATA[
      K(x,y) * K(z,K(y,x)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(4577,a,5294,a)].">
      <j1 rule="hyper" parents="4577 5294"/>
    </justification>
  </clause>

  <clause id="5296">
    <literal><![CDATA[
      K(K(x,y),z) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(34,a,4222,a(flip),b,5295,a)].">
      <j1 rule="hyper" parents="34 4222 5295"/>
    </justification>
  </clause>

  <clause id="5297">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(z,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(120,a,5295,a(flip),b,4250,a),flip(a)].">
      <j1 rule="hyper" parents="120 5295 4250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5298">
    <literal><![CDATA[
      x * K(K(y,z),x) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(126,a,5296,a,b,4215,a(flip))].">
      <j1 rule="hyper" parents="126 5296 4215"/>
    </justification>
  </clause>

  <clause id="5299">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(z,y) * u) = T(K(z,y),x) * u
    ]]></literal>
    <justification jstring="[hyper(125,a,5296,a(flip),b,4259,a)].">
      <j1 rule="hyper" parents="125 5296 4259"/>
    </justification>
  </clause>

  <clause id="5300">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z,y) = T(K(z,y),x)
    ]]></literal>
    <justification jstring="[hyper(125,a,5296,a(flip),b,4261,a(flip))].">
      <j1 rule="hyper" parents="125 5296 4261"/>
    </justification>
  </clause>

  <clause id="5301">
    <literal><![CDATA[
      K(x,K(y,z)) * u != 1
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(5296(a,1),4381(a,1,1))].">
      <j1 rule="para" parents="5296 4381"/>
    </justification>
  </clause>

  <clause id="5302">
    <literal><![CDATA[
      T(K(x,y) \ z,K(y,x)) = z / K(x,y)
    ]]></literal>
    <justification jstring="[hyper(4420,a,5298,a),flip(a)].">
      <j1 rule="hyper" parents="4420 5298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5303">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(4417,a,5298,a),flip(a)].">
      <j1 rule="hyper" parents="4417 5298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5304">
    <literal><![CDATA[
      T(x,K(y,z)) * K(z,y) = K(z,y) * x
    ]]></literal>
    <justification jstring="[hyper(125,a,5298,a(flip),b,4238,a)].">
      <j1 rule="hyper" parents="125 5298 4238"/>
    </justification>
  </clause>

  <clause id="5305">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      u = x
    ]]></literal>
    <justification jstring="[para(5298(a,1),4416(a,1))].">
      <j1 rule="para" parents="5298 4416"/>
    </justification>
  </clause>

  <clause id="5306">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(5298(a,1),4417(a,1))].">
      <j1 rule="para" parents="5298 4417"/>
    </justification>
  </clause>

  <clause id="5307">
    <literal><![CDATA[
      T(K(x,y) * z,T(z,K(y,x))) = T(K(x,y) * z,z)
    ]]></literal>
    <justification jstring="[para(5298(a,1),4433(a,1,2))].">
      <j1 rule="para" parents="5298 4433"/>
    </justification>
  </clause>

  <clause id="5308">
    <literal><![CDATA[
      T(K(x,y),K(x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(40,a,2004,a,b,5303,a),flip(a)].">
      <j1 rule="hyper" parents="40 2004 5303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5309">
    <literal><![CDATA[
      T(K(x,y),K(z,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(40,a,2003,a,b,5303,a),flip(a)].">
      <j1 rule="hyper" parents="40 2003 5303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5310">
    <literal><![CDATA[
      T(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(u,K(z,y)) = x
    ]]></literal>
    <justification jstring="[para(5303(a,1),49(a,1)),flip(a)].">
      <j1 rule="para" parents="5303 49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5313">
    <literal><![CDATA[
      K(x,y) * K(x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(5308(a,1),300(a,1,2))].">
      <j1 rule="para" parents="5308 300"/>
    </justification>
  </clause>

  <clause id="5314">
    <literal><![CDATA[
      K(x,y) \ K(z,x) = K(z,x) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(126,a,5309,a(flip),b,4566,a),flip(a)].">
      <j1 rule="hyper" parents="126 5309 4566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5316">
    <literal><![CDATA[
      T(K(x,y),K(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(2004(a,1),5305(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2004 5305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5318">
    <literal><![CDATA[
      T(K(x,y) * z,K(x,y)) = z / K(y,x)
    ]]></literal>
    <justification jstring="[para(4567(a,1),5302(a,1,1))].">
      <j1 rule="para" parents="4567 5302"/>
    </justification>
  </clause>

  <clause id="5319">
    <literal><![CDATA[
      (x * T(x \ y,z)) / K((x / y) \ 1,z) = T(y,K(z,(x / y) \ 1))
    ]]></literal>
    <justification jstring="[hyper(123,a,4487,a(flip),b,5304,a)].">
      <j1 rule="hyper" parents="123 4487 5304"/>
    </justification>
  </clause>

  <clause id="5320">
    <literal><![CDATA[
      x \ K(y,z) != K(y,z) * K(u,z)
    ]]></literal>
    <literal><![CDATA[
      K(z,u) = x
    ]]></literal>
    <justification jstring="[para(5314(a,1),48(a,1)),flip(a)].">
      <j1 rule="para" parents="5314 48"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5321">
    <literal><![CDATA[
      x * K((T(x,y) \ y) \ 1,z) = T(y * T(y \ x,z),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1704,a(flip),b,4961,a),flip(a)].">
      <j1 rule="hyper" parents="63 1704 4961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5322">
    <literal><![CDATA[
      T(x * T(x \ y,z),y) != y * u
    ]]></literal>
    <literal><![CDATA[
      K((T(y,x) \ x) \ 1,z) = u
    ]]></literal>
    <justification jstring="[para(5321(a,1),43(a,1))].">
      <j1 rule="para" parents="5321 43"/>
    </justification>
  </clause>

  <clause id="5323">
    <literal><![CDATA[
      K(x,y) * (z * K((z \ K(y,x)) \ 1,u)) = T(K(x,y) * z,u)
    ]]></literal>
    <justification jstring="[hyper(4577,a,4962,a)].">
      <j1 rule="hyper" parents="4577 4962"/>
    </justification>
  </clause>

  <clause id="5324">
    <literal><![CDATA[
      T(x,1 / y) / ((x / y) \ x) = (x / y) * K(x,1 / y)
    ]]></literal>
    <justification jstring="[para(4881(a,1),4995(a,1,1))].">
      <j1 rule="para" parents="4881 4995"/>
    </justification>
  </clause>

  <clause id="5325">
    <literal><![CDATA[
      (x / y) * K(x,1 / y) = T(x,1 / y) / y
    ]]></literal>
    <justification jstring="[para(79(a,1),5324(a,1,2)),flip(a)].">
      <j1 rule="para" parents="79 5324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5326">
    <literal><![CDATA[
      K(x,y / (K((z \ 1) \ u,z \ 1) \ u)) = K(x,y / ((z \ 1) * (u / (1 / z))))
    ]]></literal>
    <justification jstring="[para(4192(a,2),5026(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4192 5026"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5327">
    <literal><![CDATA[
      K(x,y * ((z \ L(u,1 / z,z)) * w)) = K(x,y * (((1 / z) * u) * w))
    ]]></literal>
    <justification jstring="[para(2663(a,1),5078(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="2663 5078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5328">
    <literal><![CDATA[
      R(R(K(x,y),x,x \ z),z,u) = K((((x \ z) * u) / (z * u)) \ 1,y)
    ]]></literal>
    <justification jstring="[para(618(a,1),5117(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="618 5117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5329">
    <literal><![CDATA[
      T(((x * y) / x) * (y \ z),z) / z = K(x,(T(y \ z,z) / z) \ 1)
    ]]></literal>
    <justification jstring="[para(1002(a,1),5133(a,1,1,1))].">
      <j1 rule="para" parents="1002 5133"/>
    </justification>
  </clause>

  <clause id="5330">
    <literal><![CDATA[
      (1 / x) * (K(x,y) * ((1 / x) \ z)) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(79(a,1),5154(a,2,1,1))].">
      <j1 rule="para" parents="79 5154"/>
    </justification>
  </clause>

  <clause id="5331">
    <literal><![CDATA[
      K(x,y) * ((1 / x) * z) = (1 / x) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),5330(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 5330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5334">
    <literal><![CDATA[
      K(x,y) * ((1 / x) * z) = (K(x,y) / x) * z
    ]]></literal>
    <justification jstring="[hyper(333,a,5236,a(flip),b,5331,a),flip(a)].">
      <j1 rule="hyper" parents="333 5236 5331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5336">
    <literal><![CDATA[
      (x \ 1) * (K(x,y) * ((x \ 1) \ z)) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(3334(a,1),5155(a,2,1))].">
      <j1 rule="para" parents="3334 5155"/>
    </justification>
  </clause>

  <clause id="5338">
    <literal><![CDATA[
      K(x,y) * ((x \ 1) * z) = (x \ 1) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),5336(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 5336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5340">
    <literal><![CDATA[
      K(x,y) * ((x \ 1) * T(z,K(x,y))) = (x \ 1) * (z * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(333,a,235,a(flip),b,5338,a),flip(a)].">
      <j1 rule="hyper" parents="333 235 5338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5341">
    <literal><![CDATA[
      x * (K(x,y) * ((x \ 1) * z)) = L(K(x,y) * z,x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(126,a,5338,a,b,439,a)].">
      <j1 rule="hyper" parents="126 5338 439"/>
    </justification>
  </clause>

  <clause id="5342">
    <literal><![CDATA[
      ((x \ 1) * y) / ((x \ 1) * (K(x,z) * y)) = K(z,x)
    ]]></literal>
    <justification jstring="[hyper(197,a,5338,a(flip),b,4567,a)].">
      <j1 rule="hyper" parents="197 5338 4567"/>
    </justification>
  </clause>

  <clause id="5343">
    <literal><![CDATA[
      ((x \ 1) * (K(y,x) * z)) / ((x \ 1) * z) = K(y,x)
    ]]></literal>
    <justification jstring="[para(4558(a,1),5342(a,1,2,2))].">
      <j1 rule="para" parents="4558 5342"/>
    </justification>
  </clause>

  <clause id="5344">
    <literal><![CDATA[
      L(K(x,y) * z,x \ 1,x) = T(x,y) * ((x \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(4684,a,5341,a),flip(a)].">
      <j1 rule="hyper" parents="4684 5341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5345">
    <literal><![CDATA[
      T(x,y) * ((x \ 1) * (K(y,x) * z)) = L(z,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(4558(a,1),5344(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4558 5344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5346">
    <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(3744(a,1),5190(a,1,2))].">
      <j1 rule="para" parents="3744 5190"/>
    </justification>
  </clause>

  <clause id="5347">
    <literal><![CDATA[
      K((x * ((1 / y) \ 1)) \ 1,z) / y = (1 / y) * K(((1 / y) \ x) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(466,a,5212,a)].">
      <j1 rule="hyper" parents="466 5212"/>
    </justification>
  </clause>

  <clause id="5348">
    <literal><![CDATA[
      ((1 / x) * T((1 / x) \ y,z)) * (y \ 1) = (1 / x) * (y \ T(y * x,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,5120,a,b,5214,a)].">
      <j1 rule="hyper" parents="63 5120 5214"/>
    </justification>
  </clause>

  <clause id="5349">
    <literal><![CDATA[
      K(((x \ 1) * (y \ 1)) \ 1,z) = (1 / x) * (y \ T(y * x,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,4769,a(flip),b,5214,a)].">
      <j1 rule="hyper" parents="63 4769 5214"/>
    </justification>
  </clause>

  <clause id="5350">
    <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(5248(a,2),2664(a,1))].">
      <j1 rule="para" parents="5248 2664"/>
    </justification>
  </clause>

  <clause id="5351">
    <literal><![CDATA[
      T(x \ y,x) / ((x \ 1) \ (x \ y)) = (x \ y) / ((x \ 1) \ (y / x))
    ]]></literal>
    <justification jstring="[hyper(197,a,5251,a(flip),b,3869,a),flip(a)].">
      <j1 rule="hyper" parents="197 5251 3869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5353">
    <literal><![CDATA[
      ((x * y) / R(x,y,x)) * x = (y * x) * K(T(x,y),y * x)
    ]]></literal>
    <justification jstring="[para(4380(a,1),5274(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4380 5274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5354">
    <literal><![CDATA[
      K(x,(y * z) / (y * (u \ z))) * (y * (K(u,x) * z)) = y * z
    ]]></literal>
    <justification jstring="[hyper(36,a,4569,a,b,5280,a(flip))].">
      <j1 rule="hyper" parents="36 4569 5280"/>
    </justification>
  </clause>

  <clause id="5355">
    <literal><![CDATA[
      K(x,y) * (K(y,x) * T(K(y,x) \ z,u)) = T(K(x,y) * z,u)
    ]]></literal>
    <justification jstring="[para(4486(a,2),5323(a,1,2))].">
      <j1 rule="para" parents="4486 5323"/>
    </justification>
  </clause>

  <clause id="5356">
    <literal><![CDATA[
      T(K(x,y) * (z * K(y,x)),u) = K(x,y) * (T(z,u) * K(y,x))
    ]]></literal>
    <justification jstring="[para(4959(a,1),5323(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4959 5323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5357">
    <literal><![CDATA[
      1 / ((1 / x) * (y \ T(y * x,z))) = K(z,((x \ 1) * (y \ 1)) \ 1)
    ]]></literal>
    <justification jstring="[hyper(197,a,5349,a(flip),b,4367,a)].">
      <j1 rule="hyper" parents="197 5349 4367"/>
    </justification>
  </clause>

  <clause id="5358">
    <literal><![CDATA[
      K((((x \ y) \ 1) * (x \ 1)) \ 1,z) = (1 / (x \ y)) * (x \ T(y,z))
    ]]></literal>
    <justification jstring="[para(10(a,1),5349(a,2,2,2,1))].">
      <j1 rule="para" parents="10 5349"/>
    </justification>
  </clause>

  <clause id="5359">
    <literal><![CDATA[
      (x * y) / (x * (K(z,u) * y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(u,(x * y) / (x * (z \ y))) = w
    ]]></literal>
    <justification jstring="[para(5354(a,1),268(a,1,1)),flip(b)].">
      <j1 rule="para" parents="5354 268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5360">
    <literal><![CDATA[
      K(x,y) * (R(y,z,u) * (K(y,x) * w)) = R(y,z,u) * w
    ]]></literal>
    <justification jstring="[para(1512(a,1),5354(a,1,1,2))].">
      <j1 rule="para" parents="1512 5354"/>
    </justification>
  </clause>

  <clause id="5361">
    <literal><![CDATA[
      L(a(x,K(y,z),u),x * (K(y,z) * u),K(z,(x * u) / (x * (y \ u)))) = (x * u) \ (K(z,(x * u) / (x * (y \ u))) * ((x * K(y,z)) * u))
    ]]></literal>
    <justification jstring="[para(5354(a,1),519(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5354 519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5365">
    <literal><![CDATA[
      K(x,y) \ T(K(x,y) * z,u) = K(y,x) * T(K(y,x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(129,a,5355,a)].">
      <j1 rule="hyper" parents="129 5355"/>
    </justification>
  </clause>

  <clause id="5366">
    <literal><![CDATA[
      (K(x,y) * T(K(x,y) \ z,u)) * K(y,x) = T(z * K(y,x),u)
    ]]></literal>
    <justification jstring="[hyper(125,a,5365,a(flip),b,4085,a)].">
      <j1 rule="hyper" parents="125 5365 4085"/>
    </justification>
  </clause>

  <clause id="5367">
    <literal><![CDATA[
      T((K(x,y) * z) * K(y,x),u) = (K(x,y) * T(z,u)) * K(y,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),5366(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 5366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5368">
    <literal><![CDATA[
      (x * y) * K(L(z,y,x) \ 1,u) = x * (y * K(z \ 1,u))
    ]]></literal>
    <justification jstring="[para(4216(a,1),4491(a,2,2,2))].">
      <j1 rule="para" parents="4216 4491"/>
    </justification>
  </clause>

  <clause id="5369">
    <literal><![CDATA[
      L(K(x \ 1,y),z,u) = K(L(x,z,u) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(501,a,5368,a)].">
      <j1 rule="hyper" parents="501 5368"/>
    </justification>
  </clause>

  <clause id="5370">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,L(x,u,w)) = K(L(x,y,z) \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,5173,a(flip),b,5369,a),flip(a)].">
      <j1 rule="hyper" parents="63 5173 5369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5371">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,(x \ 1) * L((x \ 1) \ 1,u,w)) = L(1,y,z)
    ]]></literal>
    <justification jstring="[para(1607(a,1),5369(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1607 5369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5372">
    <literal><![CDATA[
      K(L(x \ 1,y,z) \ 1,u) = L(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(3334(a,1),5369(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3334 5369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5373">
    <literal><![CDATA[
      K(L(K(x,y),z,u) \ 1,w) = L(K(K(y,x),w),z,u)
    ]]></literal>
    <justification jstring="[para(4367(a,1),5369(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4367 5369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5374">
    <literal><![CDATA[
      K(L(T(x \ 1,y),z,u) \ 1,w) = L(T(K(x,w),y),z,u)
    ]]></literal>
    <justification jstring="[para(5286(a,1),5369(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5286 5369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5375">
    <literal><![CDATA[
      L(K(x,y),x,z / x) = K((z \ (z / x)) \ 1,y)
    ]]></literal>
    <justification jstring="[para(393(a,1),5372(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="393 5372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5376">
    <literal><![CDATA[
      K(x,L(y \ 1,z,u) \ 1) * w = L(K(y,x),z,u) \ w
    ]]></literal>
    <justification jstring="[para(5372(a,1),4567(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5372 4567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5377">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,L(x,u,w)) = K(x \ 1,L(x,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(333,a,5172,a(flip),b,5370,a),flip(a)].">
      <j1 rule="hyper" parents="333 5172 5370"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5379">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,L(x,u,w)) * K(L(x,v5,v6),x \ 1) = 1
    ]]></literal>
    <justification jstring="[hyper(125,a,5377,a,b,4371,a)].">
      <j1 rule="hyper" parents="125 5377 4371"/>
    </justification>
  </clause>

  <clause id="5380">
    <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(5374(a,1),4567(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5374 4567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5381">
    <literal><![CDATA[
      K(L(x,y,z),L(x,u,w) \ 1) = K(L(x,v5,v6),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(4381,a,5379,a)].">
      <j1 rule="hyper" parents="4381 5379"/>
    </justification>
  </clause>

  <clause id="5382">
    <literal><![CDATA[
      K(L(x,y,z),L(x,u,w) \ 1) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(371(a,1),5381(a,2,1))].">
      <j1 rule="para" parents="371 5381"/>
    </justification>
  </clause>

  <clause id="5383">
    <literal><![CDATA[
      L(x,y,z) \ K(x,x \ 1) = 1 / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(121,a,5382,a(flip),b,2098,a(flip))].">
      <j1 rule="hyper" parents="121 5382 2098"/>
    </justification>
  </clause>

  <clause id="5384">
    <literal><![CDATA[
      K(x,L(x,y,z) \ 1) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(371(a,1),5382(a,1,1))].">
      <j1 rule="para" parents="371 5382"/>
    </justification>
  </clause>

  <clause id="5385">
    <literal><![CDATA[
      T(x,L(x,y,z) \ 1) = K(x,x \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(125,a,5384,a(flip),b,4261,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="125 5384 4261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5386">
    <literal><![CDATA[
      K(x,T(y,L(y,z,u) \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(5385(a,2),4787(a,1,2))].">
      <j1 rule="para" parents="5385 4787"/>
    </justification>
  </clause>

  <clause id="5387">
    <literal><![CDATA[
      L(x,y,z) \ (1 / x) = x \ (1 / L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(121,a,5383,a(flip),b,2124,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="121 5383 2124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5388">
    <literal><![CDATA[
      (x * y) * L((z \ (y \ z)) * z,y,x) = (x * K(y \ 1,z)) * z
    ]]></literal>
    <justification jstring="[para(2549(a,2),4504(a,1,2))].">
      <j1 rule="para" parents="2549 4504"/>
    </justification>
  </clause>

  <clause id="5389">
    <literal><![CDATA[
      (x * y) * K(1 / L(z,y,x),u) = x * (y * K(1 / z,u))
    ]]></literal>
    <justification jstring="[para(4268(a,1),4603(a,2,2,2))].">
      <j1 rule="para" parents="4268 4603"/>
    </justification>
  </clause>

  <clause id="5390">
    <literal><![CDATA[
      L(K(1 / x,y),z,u) = K(1 / L(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(501,a,5389,a)].">
      <j1 rule="hyper" parents="501 5389"/>
    </justification>
  </clause>

  <clause id="5395">
    <literal><![CDATA[
      L(K(x \ y,x) * z,K(x,x \ y),y) = (x * (y / x)) \ (y * z)
    ]]></literal>
    <justification jstring="[para(4558(a,1),4671(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4558 4671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5396">
    <literal><![CDATA[
      K(x,x * y) * (L(y,z,u) * x) = L(y,z,u) * T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(5097,a,3734,a)].">
      <j1 rule="hyper" parents="5097 3734"/>
    </justification>
  </clause>

  <clause id="5397">
    <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(3744(a,1),5396(a,1,2))].">
      <j1 rule="para" parents="3744 5396"/>
    </justification>
  </clause>

  <clause id="5398">
    <literal><![CDATA[
      K((x \ (y / (z \ 1))) \ 1,y) != u
    ]]></literal>
    <literal><![CDATA[
      K((x \ (y * z)) \ 1,y) = u
    ]]></literal>
    <justification jstring="[para(5202(a,2),5166(a,1))].">
      <j1 rule="para" parents="5202 5166"/>
    </justification>
  </clause>

  <clause id="5399">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,(x \ 1) * L((x \ 1) \ 1,u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(333,a,378,a(flip),b,5371,a),flip(a)].">
      <j1 rule="hyper" parents="333 378 5371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5401">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,x \ L(x,u,w)) = 1
    ]]></literal>
    <justification jstring="[para(1264(a,1),5399(a,1,2))].">
      <j1 rule="para" parents="1264 5399"/>
    </justification>
  </clause>

  <clause id="5402">
    <literal><![CDATA[
      T(L(x,y,z) \ 1,x \ L(x,u,w)) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(56,a,5401,a)].">
      <j1 rule="hyper" parents="56 5401"/>
    </justification>
  </clause>

  <clause id="5403">
    <literal><![CDATA[
      T(x \ L(x,y,z),L(x,u,w) \ 1) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(54,a,5402,a)].">
      <j1 rule="hyper" parents="54 5402"/>
    </justification>
  </clause>

  <clause id="5404">
    <literal><![CDATA[
      T(L(x,y,z) * (x \ 1),L(x,u,w) \ 1) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(1255(a,2),5403(a,1,1))].">
      <j1 rule="para" parents="1255 5403"/>
    </justification>
  </clause>

  <clause id="5405">
    <literal><![CDATA[
      (L(x,y,z) * (x \ 1)) \ (x \ 1) = (x \ 1) / (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(197,a,5404,a(flip),b,3762,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="197 5404 3762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5406">
    <literal><![CDATA[
      (L(x,y,z) * (x \ 1)) \ (x \ 1) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(333,a,4025,a(flip),b,5405,a),flip(a)].">
      <j1 rule="hyper" parents="333 4025 5405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5407">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ (x \ 1) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(1255(a,1),5406(a,1,1))].">
      <j1 rule="para" parents="1255 5406"/>
    </justification>
  </clause>

  <clause id="5408">
    <literal><![CDATA[
      (x \ 1) * (L(x,y,z) \ x) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,3261,a(flip),b,5407,a)].">
      <j1 rule="hyper" parents="63 3261 5407"/>
    </justification>
  </clause>

  <clause id="5409">
    <literal><![CDATA[
      (x \ 1) \ (L(x,y,z) \ 1) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(121,a,5407,a(flip),b,3261,a(flip))].">
      <j1 rule="hyper" parents="121 5407 3261"/>
    </justification>
  </clause>

  <clause id="5410">
    <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(5407(a,1),4486(a,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5407 4486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5411">
    <literal><![CDATA[
      R(x,y,(z \ 1) * ((L(z,u,w) \ z) \ 1)) = R(x,y,L(z,u,w) \ 1)
    ]]></literal>
    <justification jstring="[para(5408(a,1),1873(a,2,3))].">
      <j1 rule="para" parents="5408 1873"/>
    </justification>
  </clause>

  <clause id="5412">
    <literal><![CDATA[
      (x \ (L(x \ 1,y,z) \ 1)) * K(x \ 1,x) = L(x \ 1,y,z) \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(2694,a,5409,a)].">
      <j1 rule="hyper" parents="2694 5409"/>
    </justification>
  </clause>

  <clause id="5413">
    <literal><![CDATA[
      x * (y * ((z \ (y \ z)) * z)) = (x * K(y \ 1,z)) * z
    ]]></literal>
    <justification jstring="[hyper(306,a,5388,a)].">
      <j1 rule="hyper" parents="306 5388"/>
    </justification>
  </clause>

  <clause id="5414">
    <literal><![CDATA[
      (x * K(y \ 1,z)) * z = x * (z * K(y \ 1,z))
    ]]></literal>
    <justification jstring="[para(5249(a,1),5413(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5249 5413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5415">
    <literal><![CDATA[
      R(x,K(y \ 1,z),z) = x
    ]]></literal>
    <justification jstring="[hyper(2744,a,5414,a)].">
      <j1 rule="hyper" parents="2744 5414"/>
    </justification>
  </clause>

  <clause id="5416">
    <literal><![CDATA[
      R(x,K(y,z),z) = x
    ]]></literal>
    <justification jstring="[para(79(a,1),5415(a,1,2,1))].">
      <j1 rule="para" parents="79 5415"/>
    </justification>
  </clause>

  <clause id="5417">
    <literal><![CDATA[
      (x * K(y,z)) * z = x * (z * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(125,a,5416,a(flip),b,2743,a),flip(a)].">
      <j1 rule="hyper" parents="125 5416 2743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5418">
    <literal><![CDATA[
      R(x,K(y,z),z) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(5416(a,1),51(a,2))].">
      <j1 rule="para" parents="5416 51"/>
    </justification>
  </clause>

  <clause id="5419">
    <literal><![CDATA[
      (x * K(y,z)) \ (x * (z * K(y,z))) = z
    ]]></literal>
    <justification jstring="[hyper(129,a,5417,a)].">
      <j1 rule="hyper" parents="129 5417"/>
    </justification>
  </clause>

  <clause id="5421">
    <literal><![CDATA[
      L(T(x,K(y,x)),K(y,x),z) = x
    ]]></literal>
    <justification jstring="[hyper(787,a,5419,a)].">
      <j1 rule="hyper" parents="787 5419"/>
    </justification>
  </clause>

  <clause id="5422">
    <literal><![CDATA[
      L(x,K(y,x),z) = x
    ]]></literal>
    <justification jstring="[para(2716(a,1),5421(a,1,1))].">
      <j1 rule="para" parents="2716 5421"/>
    </justification>
  </clause>

  <clause id="5423">
    <literal><![CDATA[
      L(x,K(x,y),z) = x
    ]]></literal>
    <justification jstring="[hyper(4391,a,5422,a)].">
      <j1 rule="hyper" parents="4391 5422"/>
    </justification>
  </clause>

  <clause id="5424">
    <literal><![CDATA[
      L(x,K(y,T(x,z)),u) = x
    ]]></literal>
    <justification jstring="[hyper(148,a,5422,a(flip))].">
      <j1 rule="hyper" parents="148 5422"/>
    </justification>
  </clause>

  <clause id="5426">
    <literal><![CDATA[
      L((x \ y) \ y,K(z,x),u) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(5422(a,1),331(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5422 331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5427">
    <literal><![CDATA[
      (x * K(y,z)) * T(z,u) = x * (K(y,z) * T(z,u))
    ]]></literal>
    <justification jstring="[para(5422(a,1),465(a,1,2,1))].">
      <j1 rule="para" parents="5422 465"/>
    </justification>
  </clause>

  <clause id="5428">
    <literal><![CDATA[
      (x * K(y,z)) * L(z,u,w) = x * (K(y,z) * L(z,u,w))
    ]]></literal>
    <justification jstring="[para(5422(a,1),461(a,1,2,1))].">
      <j1 rule="para" parents="5422 461"/>
    </justification>
  </clause>

  <clause id="5431">
    <literal><![CDATA[
      L(T(x,y),K(x,z),u) = T(x,y)
    ]]></literal>
    <justification jstring="[para(5423(a,1),25(a,2,1))].">
      <j1 rule="para" parents="5423 25"/>
    </justification>
  </clause>

  <clause id="5432">
    <literal><![CDATA[
      (x * K(y,z)) * L(y,u,w) = x * (K(y,z) * L(y,u,w))
    ]]></literal>
    <justification jstring="[para(5423(a,1),461(a,1,2,1))].">
      <j1 rule="para" parents="5423 461"/>
    </justification>
  </clause>

  <clause id="5434">
    <literal><![CDATA[
      L(x * y,K(y * x,z),u) = (y \ (y * x)) * y
    ]]></literal>
    <justification jstring="[para(5423(a,1),2547(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5423 2547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5435">
    <literal><![CDATA[
      L(x,x \ T(x,y),z) = x
    ]]></literal>
    <justification jstring="[para(4215(a,1),5423(a,1,2))].">
      <j1 rule="para" parents="4215 5423"/>
    </justification>
  </clause>

  <clause id="5437">
    <literal><![CDATA[
      L(L(T(x,y),z,u),K(x,w),v5) = L(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(5431(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5431 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5439">
    <literal><![CDATA[
      L(x * y,K(y * x,z),u) = x * y
    ]]></literal>
    <justification jstring="[para(9(a,1),5434(a,2,1))].">
      <j1 rule="para" parents="9 5434"/>
    </justification>
  </clause>

  <clause id="5440">
    <literal><![CDATA[
      (x * K(y * z,u)) * (z * y) = x * (K(y * z,u) * (z * y))
    ]]></literal>
    <justification jstring="[hyper(126,a,5439,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="126 5439 18"/>
    </justification>
  </clause>

  <clause id="5441">
    <literal><![CDATA[
      (x * K(y,z)) * L(T(y,u),w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      x * (K(y,z) * L(T(y,u),w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(5437(a,1),306(a,1,2))].">
      <j1 rule="para" parents="5437 306"/>
    </justification>
  </clause>

  <clause id="5442">
    <literal><![CDATA[
      R(x,K(y,z),T(z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(543,a,5427,a)].">
      <j1 rule="hyper" parents="543 5427"/>
    </justification>
  </clause>

  <clause id="5443">
    <literal><![CDATA[
      (x * K(y,z)) * T(z,y) = x * z
    ]]></literal>
    <justification jstring="[para(4224(a,1),5427(a,2,2))].">
      <j1 rule="para" parents="4224 5427"/>
    </justification>
  </clause>

  <clause id="5444">
    <literal><![CDATA[
      (x / T(y,z)) * y = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(1436,a,5443,a)].">
      <j1 rule="hyper" parents="1436 5443"/>
    </justification>
  </clause>

  <clause id="5445">
    <literal><![CDATA[
      (x / T(y,z)) / K(z,y) = x / y
    ]]></literal>
    <justification jstring="[hyper(620,a,5443,a),flip(a)].">
      <j1 rule="hyper" parents="620 5443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5446">
    <literal><![CDATA[
      (x * y) / T(y,z) = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(138,a,5443,a)].">
      <j1 rule="hyper" parents="138 5443"/>
    </justification>
  </clause>

  <clause id="5447">
    <literal><![CDATA[
      (x * K(y,z)) \ (x * z) = T(z,y)
    ]]></literal>
    <justification jstring="[hyper(129,a,5443,a)].">
      <j1 rule="hyper" parents="129 5443"/>
    </justification>
  </clause>

  <clause id="5448">
    <literal><![CDATA[
      T(x,y) / T(x,z) = K(x,y) * K(z,x)
    ]]></literal>
    <justification jstring="[hyper(123,a,4274,a,b,5443,a)].">
      <j1 rule="hyper" parents="123 4274 5443"/>
    </justification>
  </clause>

  <clause id="5449">
    <literal><![CDATA[
      (x / T(y,x)) * K(z,y) = T(x,y) / T(y,z)
    ]]></literal>
    <justification jstring="[hyper(123,a,3619,a(flip),b,5443,a),flip(a)].">
      <j1 rule="hyper" parents="123 3619 5443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5450">
    <literal><![CDATA[
      (x / y) * K(z,y) = x / T(y,z)
    ]]></literal>
    <justification jstring="[hyper(123,a,12,a(flip),b,5443,a),flip(a)].">
      <j1 rule="hyper" parents="123 12 5443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5451">
    <literal><![CDATA[
      x / T(y \ x,z) = y * K(z,y \ x)
    ]]></literal>
    <justification jstring="[hyper(123,a,10,a(flip),b,5443,a)].">
      <j1 rule="hyper" parents="123 10 5443"/>
    </justification>
  </clause>

  <clause id="5452">
    <literal><![CDATA[
      (x * K(y,x \ z)) \ z = T(x \ z,y)
    ]]></literal>
    <justification jstring="[hyper(121,a,10,a(flip),b,5443,a)].">
      <j1 rule="hyper" parents="121 10 5443"/>
    </justification>
  </clause>

  <clause id="5454">
    <literal><![CDATA[
      (x \ y) * K(y,x) = x \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,3834,a,b,5443,a),flip(a)].">
      <j1 rule="hyper" parents="35 3834 5443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5455">
    <literal><![CDATA[
      (x * T(y,z)) * K(z,y) = x * y
    ]]></literal>
    <justification jstring="[hyper(35,a,1415,a(flip),b,5443,a),flip(a)].">
      <j1 rule="hyper" parents="35 1415 5443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5456">
    <literal><![CDATA[
      x * T(y,z) != u * y
    ]]></literal>
    <literal><![CDATA[
      u * K(z,y) = x
    ]]></literal>
    <justification jstring="[para(5443(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="5443 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5457">
    <literal><![CDATA[
      (x * y) / T(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x * K(z,y) = u
    ]]></literal>
    <justification jstring="[para(5443(a,1),268(a,1,1)),flip(b)].">
      <j1 rule="para" parents="5443 268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5458">
    <literal><![CDATA[
      (x * K(y,z)) \ (x * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(z,y) = u
    ]]></literal>
    <justification jstring="[para(5443(a,1),342(a,1,2))].">
      <j1 rule="para" parents="5443 342"/>
    </justification>
  </clause>

  <clause id="5459">
    <literal><![CDATA[
      T(x / T(y,z),y) = y \ (x * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(444,a,xx,b,5444,a)].">
      <j1 rule="hyper" parents="444 5444"/>
    </justification>
  </clause>

  <clause id="5460">
    <literal><![CDATA[
      (x * K(y,z)) / z = x / T(z,y)
    ]]></literal>
    <justification jstring="[hyper(138,a,5444,a)].">
      <j1 rule="hyper" parents="138 5444"/>
    </justification>
  </clause>

  <clause id="5461">
    <literal><![CDATA[
      (x / T(y,z)) \ (x * K(z,y)) = y
    ]]></literal>
    <justification jstring="[hyper(129,a,5444,a)].">
      <j1 rule="hyper" parents="129 5444"/>
    </justification>
  </clause>

  <clause id="5462">
    <literal><![CDATA[
      R(x / T(y,z),y,y \ 1) = (x * K(z,y)) * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(125,a,5444,a(flip),b,537,a),flip(a)].">
      <j1 rule="hyper" parents="125 5444 537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5464">
    <literal><![CDATA[
      x \ (y * K(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      T(y / T(x,z),x) = u
    ]]></literal>
    <justification jstring="[para(5444(a,1),347(a,1,2))].">
      <j1 rule="para" parents="5444 347"/>
    </justification>
  </clause>

  <clause id="5465">
    <literal><![CDATA[
      (x / y) \ (x / T(y,z)) = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(192,a,5445,a)].">
      <j1 rule="hyper" parents="192 5445"/>
    </justification>
  </clause>

  <clause id="5466">
    <literal><![CDATA[
      (x / y) * K(z,y) != u
    ]]></literal>
    <literal><![CDATA[
      x / T(y,z) = u
    ]]></literal>
    <justification jstring="[para(5445(a,1),264(a,1,1)),flip(b)].">
      <j1 rule="para" parents="5445 264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5467">
    <literal><![CDATA[
      x \ y != (z / u) * K(w,u)
    ]]></literal>
    <literal><![CDATA[
      x * (z / T(u,w)) = y
    ]]></literal>
    <justification jstring="[para(5445(a,1),591(a,2,1))].">
      <j1 rule="para" parents="5445 591"/>
    </justification>
  </clause>

  <clause id="5469">
    <literal><![CDATA[
      (x * (y / z)) / T(y / z,z) = x * K(z,z \ y)
    ]]></literal>
    <justification jstring="[para(4368(a,1),5446(a,2,2))].">
      <j1 rule="para" parents="4368 5446"/>
    </justification>
  </clause>

  <clause id="5471">
    <literal><![CDATA[
      x * (K(y,x) * K(z,y)) = (y * x) / T(y,z)
    ]]></literal>
    <justification jstring="[hyper(4435,a,5450,a)].">
      <j1 rule="hyper" parents="4435 5450"/>
    </justification>
  </clause>

  <clause id="5473">
    <literal><![CDATA[
      (x / y) * K(x,y) = T(x,y) / y
    ]]></literal>
    <justification jstring="[hyper(333,a,3625,a,b,5450,a),flip(a)].">
      <j1 rule="hyper" parents="333 3625 5450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5474">
    <literal><![CDATA[
      T(x / y,K(x,y)) = x / y
    ]]></literal>
    <justification jstring="[hyper(253,a,5450,a,b,4813,a)].">
      <j1 rule="hyper" parents="253 5450 4813"/>
    </justification>
  </clause>

  <clause id="5475">
    <literal><![CDATA[
      K(x \ y,x) * K(z,y / x) = x \ (y / T(y / x,z))
    ]]></literal>
    <justification jstring="[hyper(121,a,5450,a(flip),b,4187,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="121 5450 4187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5477">
    <literal><![CDATA[
      T(x / y,K(y,x)) = x / y
    ]]></literal>
    <justification jstring="[hyper(5310,a,5474,a)].">
      <j1 rule="hyper" parents="5310 5474"/>
    </justification>
  </clause>

  <clause id="5478">
    <literal><![CDATA[
      K(x,y) * (y / x) = (y / x) * K(x,y)
    ]]></literal>
    <justification jstring="[para(5474(a,1),5304(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5474 5304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5479">
    <literal><![CDATA[
      x \ T(x * y,x) = y * K(x * y,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),5454(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 5454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5480">
    <literal><![CDATA[
      (x \ T(y,x)) \ ((x \ y) * (K(y,x) * z)) = L(z,K(y,x),x \ y)
    ]]></literal>
    <justification jstring="[para(5454(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5454 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5481">
    <literal><![CDATA[
      (x * y) / K(z,y) = x * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(138,a,5455,a)].">
      <j1 rule="hyper" parents="138 5455"/>
    </justification>
  </clause>

  <clause id="5482">
    <literal><![CDATA[
      (x * T(y,z)) \ (x * y) = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(129,a,5455,a)].">
      <j1 rule="hyper" parents="129 5455"/>
    </justification>
  </clause>

  <clause id="5483">
    <literal><![CDATA[
      ((x * y) * T(L(z,y,x),u)) \ (x * (y * z)) = K(u,L(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(121,a,97,a(flip),b,5455,a)].">
      <j1 rule="hyper" parents="121 97 5455"/>
    </justification>
  </clause>

  <clause id="5484">
    <literal><![CDATA[
      ((x / y) * T(y,z)) \ x = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(121,a,12,a(flip),b,5455,a)].">
      <j1 rule="hyper" parents="121 12 5455"/>
    </justification>
  </clause>

  <clause id="5485">
    <literal><![CDATA[
      (x * T(x \ y,z)) \ y = K(z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(121,a,10,a(flip),b,5455,a)].">
      <j1 rule="hyper" parents="121 10 5455"/>
    </justification>
  </clause>

  <clause id="5486">
    <literal><![CDATA[
      (x \ (x / (y \ 1))) * T(x,y) = x / (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(35,a,5052,a(flip),b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="35 5052 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5487">
    <literal><![CDATA[
      (x * ((y \ z) \ z)) * K(y \ z,y) = x * y
    ]]></literal>
    <justification jstring="[para(112(a,1),5455(a,1,1,2))].">
      <j1 rule="para" parents="112 5455"/>
    </justification>
  </clause>

  <clause id="5488">
    <literal><![CDATA[
      (x * T(y,z)) \ (x * y) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) = u
    ]]></literal>
    <justification jstring="[para(5455(a,1),342(a,1,2))].">
      <j1 rule="para" parents="5455 342"/>
    </justification>
  </clause>

  <clause id="5489">
    <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(5455(a,1),541(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5455 541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5490">
    <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(5460(a,1),3778(a,1,1,2))].">
      <j1 rule="para" parents="5460 3778"/>
    </justification>
  </clause>

  <clause id="5491">
    <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(5460(a,1),3780(a,1,1,1,2))].">
      <j1 rule="para" parents="5460 3780"/>
    </justification>
  </clause>

  <clause id="5494">
    <literal><![CDATA[
      x * (K(y,x) * K(y * x,y)) = T(y * x,y) / y
    ]]></literal>
    <justification jstring="[hyper(4435,a,5473,a)].">
      <j1 rule="hyper" parents="4435 5473"/>
    </justification>
  </clause>

  <clause id="5495">
    <literal><![CDATA[
      R(x / (y \ 1),y \ 1,y) = x * T(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(885,a,5481,a)].">
      <j1 rule="hyper" parents="885 5481"/>
    </justification>
  </clause>

  <clause id="5498">
    <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(5479(a,2),4363(a,1,1))].">
      <j1 rule="para" parents="5479 4363"/>
    </justification>
  </clause>

  <clause id="5500">
    <literal><![CDATA[
      (x \ T(x * y,z)) \ y = K(z,(x \ 1) \ y)
    ]]></literal>
    <justification jstring="[para(953(a,1),5485(a,1,1))].">
      <j1 rule="para" parents="953 5485"/>
    </justification>
  </clause>

  <clause id="5501">
    <literal><![CDATA[
      (x * (y * T(y \ (x \ z),u))) \ z = K(u,(x * y) \ z)
    ]]></literal>
    <justification jstring="[para(940(a,1),5485(a,1,1))].">
      <j1 rule="para" parents="940 5485"/>
    </justification>
  </clause>

  <clause id="5502">
    <literal><![CDATA[
      ((x * T(x \ y,z)) * u) \ (y * u) = K(z,(x * u) \ (y * u))
    ]]></literal>
    <justification jstring="[para(1392(a,1),5485(a,1,1))].">
      <j1 rule="para" parents="1392 5485"/>
    </justification>
  </clause>

  <clause id="5503">
    <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(5485(a,1),4039(a,2,1,2,1))].">
      <j1 rule="para" parents="5485 4039"/>
    </justification>
  </clause>

  <clause id="5504">
    <literal><![CDATA[
      x * K(y,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      (z * x) / T(T(z,x),y) = u
    ]]></literal>
    <justification jstring="[para(191(a,1),5466(a,1,1))].">
      <j1 rule="para" parents="191 5466"/>
    </justification>
  </clause>

  <clause id="5505">
    <literal><![CDATA[
      K(x,y) * K(z,x) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) / T(x,z) = u
    ]]></literal>
    <justification jstring="[para(4261(a,2),5466(a,1,1))].">
      <j1 rule="para" parents="4261 5466"/>
    </justification>
  </clause>

  <clause id="5506">
    <literal><![CDATA[
      x * (K(R(y,z,u),x) * K(w,R(y,z,u))) = (R(y,z,u) * x) / R(T(y,w),z,u)
    ]]></literal>
    <justification jstring="[para(27(a,2),5471(a,2,2))].">
      <j1 rule="para" parents="27 5471"/>
    </justification>
  </clause>

  <clause id="5507">
    <literal><![CDATA[
      (T(x,y) \ y) * ((x \ y) \ y) = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,3831,a,b,5487,a),flip(a)].">
      <j1 rule="hyper" parents="35 3831 5487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5517">
    <literal><![CDATA[
      R(x / (y \ 1),y,y) = x * T(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(1941,a,5495,a)].">
      <j1 rule="hyper" parents="1941 5495"/>
    </justification>
  </clause>

  <clause id="5518">
    <literal><![CDATA[
      L((x \ y) * T(x,x \ 1),x,x) = (x * x) \ ((x * y) * x)
    ]]></literal>
    <justification jstring="[para(5517(a,1),1599(a,1,1))].">
      <j1 rule="para" parents="5517 1599"/>
    </justification>
  </clause>

  <clause id="5519">
    <literal><![CDATA[
      (x * (y / z)) / (z \ y) = x * K(z,z \ y)
    ]]></literal>
    <justification jstring="[para(113(a,1),5469(a,1,2))].">
      <j1 rule="para" parents="113 5469"/>
    </justification>
  </clause>

  <clause id="5520">
    <literal><![CDATA[
      (x / (y / z)) * K(z,z \ y) = x / (z \ y)
    ]]></literal>
    <justification jstring="[hyper(422,a,5519,a),flip(a)].">
      <j1 rule="hyper" parents="422 5519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5521">
    <literal><![CDATA[
      (x / (y \ z)) * (z / y) = x * K(y,y \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,1447,a(flip),b,5519,a)].">
      <j1 rule="hyper" parents="63 1447 5519"/>
    </justification>
  </clause>

  <clause id="5522">
    <literal><![CDATA[
      K(x,x \ y) / (y / x) = 1 / (x \ y)
    ]]></literal>
    <justification jstring="[hyper(123,a,7,a(flip),b,5521,a)].">
      <j1 rule="hyper" parents="123 7 5521"/>
    </justification>
  </clause>

  <clause id="5523">
    <literal><![CDATA[
      (x * (y \ z)) * K(y,y \ z) = x * (z / y)
    ]]></literal>
    <justification jstring="[para(11(a,1),5521(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 5521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5524">
    <literal><![CDATA[
      x * (y \ R(y,x,y)) = T(y * x,y) / y
    ]]></literal>
    <justification jstring="[para(4746(a,1),5494(a,1,2))].">
      <j1 rule="para" parents="4746 5494"/>
    </justification>
  </clause>

  <clause id="5525">
    <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="[hyper(197,a,5524,a(flip),b,430,a),flip(a)].">
      <j1 rule="hyper" parents="197 5524 430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5527">
    <literal><![CDATA[
      R(x,K(y,z),L(z,u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(543,a,5428,a)].">
      <j1 rule="hyper" parents="543 5428"/>
    </justification>
  </clause>

  <clause id="5529">
    <literal><![CDATA[
      (x * (y * (z * T(z \ (y \ (x \ u)),w)))) \ u = K(w,(x * (y * z)) \ u)
    ]]></literal>
    <justification jstring="[para(940(a,1),5501(a,1,1,2))].">
      <j1 rule="para" parents="940 5501"/>
    </justification>
  </clause>

  <clause id="5530">
    <literal><![CDATA[
      (x * (y \ ((z \ (y * (x \ u))) * z))) \ u = K(z,(x * (y \ z)) \ u)
    ]]></literal>
    <justification jstring="[para(1276(a,1),5501(a,1,1,2))].">
      <j1 rule="para" parents="1276 5501"/>
    </justification>
  </clause>

  <clause id="5531">
    <literal><![CDATA[
      (x * (((y \ ((x \ z) * u)) * y) / u)) \ z = K(y,(x * (y / u)) \ z)
    ]]></literal>
    <justification jstring="[para(1733(a,1),5501(a,1,1,2))].">
      <j1 rule="para" parents="1733 5501"/>
    </justification>
  </clause>

  <clause id="5532">
    <literal><![CDATA[
      L(x \ y,x,x \ 1) * x = (x * x) \ ((x * y) * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,2916,a(flip),b,5518,a)].">
      <j1 rule="hyper" parents="63 2916 5518"/>
    </justification>
  </clause>

  <clause id="5533">
    <literal><![CDATA[
      (x * x) \ ((x * y) * x) = ((1 / x) * y) * x
    ]]></literal>
    <justification jstring="[para(2655(a,1),5532(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2655 5532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5534">
    <literal><![CDATA[
      x * ((x \ 1) * ((x \ (y * (x \ 1))) / (x \ 1))) = ((1 / x) * (y / x)) * x
    ]]></literal>
    <justification jstring="[hyper(63,a,3271,a,b,5533,a)].">
      <j1 rule="hyper" parents="63 3271 5533"/>
    </justification>
  </clause>

  <clause id="5535">
    <literal><![CDATA[
      (x * (y * T(z,u))) \ (x * (y * z)) = K(u,L(z,y,x))
    ]]></literal>
    <justification jstring="[para(465(a,1),5483(a,1,1))].">
      <j1 rule="para" parents="465 5483"/>
    </justification>
  </clause>

  <clause id="5536">
    <literal><![CDATA[
      (((x / y) * T(y,z)) * u) \ (x * u) = K(z,((x / y) * u) \ (x * u))
    ]]></literal>
    <justification jstring="[para(79(a,1),5502(a,1,1,1,2,1))].">
      <j1 rule="para" parents="79 5502"/>
    </justification>
  </clause>

  <clause id="5537">
    <literal><![CDATA[
      L(x,y \ 1,y) / (L(x,y \ 1,y) / y) = y * K(y \ x,y)
    ]]></literal>
    <justification jstring="[para(4779(a,1),4188(a,2,2))].">
      <j1 rule="para" parents="4779 4188"/>
    </justification>
  </clause>

  <clause id="5538">
    <literal><![CDATA[
      (x * (1 / T(y,z))) * T(y,z) = R(x,1 / T(y,z),y)
    ]]></literal>
    <justification jstring="[hyper(4361,a,5481,a),flip(a)].">
      <j1 rule="hyper" parents="4361 5481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5539">
    <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(5538(a,1),1950(a,1))].">
      <j1 rule="para" parents="5538 1950"/>
    </justification>
  </clause>

  <clause id="5540">
    <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(1937(a,1),5539(a,1))].">
      <j1 rule="para" parents="1937 5539"/>
    </justification>
  </clause>

  <clause id="5541">
    <literal><![CDATA[
      T(x,y) * K(x * y,(y * x) \ x) = (x * y) * (x / (y * x))
    ]]></literal>
    <justification jstring="[para(5041(a,1),4674(a,1,2,2))].">
      <j1 rule="para" parents="5041 4674"/>
    </justification>
  </clause>

  <clause id="5542">
    <literal><![CDATA[
      T(x,y) \ (x * L(K(x,y),z,u)) = K(y,x) \ L(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(4367(a,1),4699(a,1,2,2,1))].">
      <j1 rule="para" parents="4367 4699"/>
    </justification>
  </clause>

  <clause id="5543">
    <literal><![CDATA[
      (x * (y * ((x \ z) / y))) / z = K(y,((x * y) / z) \ 1)
    ]]></literal>
    <justification jstring="[para(10(a,1),5132(a,1,1,2,2,1))].">
      <j1 rule="para" parents="10 5132"/>
    </justification>
  </clause>

  <clause id="5544">
    <literal><![CDATA[
      (x * (y * ((x \ z) / y))) / z = K(y,z / (x * y))
    ]]></literal>
    <justification jstring="[hyper(333,a,5055,a(flip),b,5543,a),flip(a)].">
      <j1 rule="hyper" parents="333 5055 5543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5545">
    <literal><![CDATA[
      (x * (y * ((x \ z) / y))) / z != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z / (x * y)) = u
    ]]></literal>
    <justification jstring="[para(5543(a,2),5103(a,1))].">
      <j1 rule="para" parents="5543 5103"/>
    </justification>
  </clause>

  <clause id="5546">
    <literal><![CDATA[
      R(K(x,(y / z) / (u * x)),y / z,z) = ((u * (x * ((u \ (y / z)) / x))) * z) / y
    ]]></literal>
    <justification jstring="[para(5544(a,1),556(a,1,1))].">
      <j1 rule="para" parents="5544 556"/>
    </justification>
  </clause>

  <clause id="5549">
    <literal><![CDATA[
      a(T(x,y),T(T(y,x),x),R(T(x,y),z,u)) = a(R(x,z,u),y,x)
    ]]></literal>
    <justification jstring="[para(3613(a,1),5164(a,1,1))].">
      <j1 rule="para" parents="3613 5164"/>
    </justification>
  </clause>

  <clause id="5550">
    <literal><![CDATA[
      (x * K(y,z \ 1)) * z = (x * z) * K(y,z \ 1)
    ]]></literal>
    <justification jstring="[para(4776(a,1),5196(a,1,1))].">
      <j1 rule="para" parents="4776 5196"/>
    </justification>
  </clause>

  <clause id="5554">
    <literal><![CDATA[
      (x * (y \ 1)) * K(z,(y \ 1) \ 1) = (x * K(z,y)) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(4621(a,1),5550(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4621 5550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5555">
    <literal><![CDATA[
      (x * K(y,z)) * (z \ 1) = (x * (z \ 1)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(4621(a,1),5554(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4621 5554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5556">
    <literal><![CDATA[
      K((((x \ y) * z) / (y * z)) \ 1,u) = R(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(3556(a,1),5328(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3556 5328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5557">
    <literal><![CDATA[
      K((x * y) / ((z \ x) * y),u) = R(K(z,u),x,y)
    ]]></literal>
    <justification jstring="[hyper(5090,a,5556,a)].">
      <j1 rule="hyper" parents="5090 5556"/>
    </justification>
  </clause>

  <clause id="5559">
    <literal><![CDATA[
      R(K(x / y,z),x,u) = K((x * u) / (y * u),z)
    ]]></literal>
    <justification jstring="[para(79(a,1),5557(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="79 5557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5560">
    <literal><![CDATA[
      K(R(x,x \ y,z),u) = R(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(104(a,2),5557(a,1,1))].">
      <j1 rule="para" parents="104 5557"/>
    </justification>
  </clause>

  <clause id="5561">
    <literal><![CDATA[
      K(R(x,x \ 1,y),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,549,a(flip),b,5560,a),flip(a)].">
      <j1 rule="hyper" parents="333 549 5560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5562">
    <literal><![CDATA[
      R(K(x,y),x * z,u) = K(R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(9(a,1),5560(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 5560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5563">
    <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(4532(a,1),5562(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4532 5562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5564">
    <literal><![CDATA[
      R(K(x / (y / z),u),x,z) = K((x * z) / y,u)
    ]]></literal>
    <justification jstring="[para(12(a,1),5559(a,2,1,2))].">
      <j1 rule="para" parents="12 5559"/>
    </justification>
  </clause>

  <clause id="5565">
    <literal><![CDATA[
      K((x * y) / z,x) = K(x / (z / y),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,4889,a(flip),b,5564,a),flip(a)].">
      <j1 rule="hyper" parents="63 4889 5564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5566">
    <literal><![CDATA[
      K(x,(T(y \ z,z) / z) \ 1) = T(K(x,y) * z,z) / z
    ]]></literal>
    <justification jstring="[para(4824(a,1),5329(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4824 5329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5567">
    <literal><![CDATA[
      K(x,(T(y \ z,z) / z) \ 1) = z \ T(z * K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(333,a,4085,a(flip),b,5566,a),flip(a)].">
      <j1 rule="hyper" parents="333 4085 5566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5568">
    <literal><![CDATA[
      K(x,y / T(z \ y,y)) = y \ T(y * K(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(5103,a,5567,a)].">
      <j1 rule="hyper" parents="5103 5567"/>
    </justification>
  </clause>

  <clause id="5569">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) = y \ T(y * K(x,z),y)
    ]]></literal>
    <justification jstring="[para(3879(a,1),5568(a,1,2))].">
      <j1 rule="para" parents="3879 5568"/>
    </justification>
  </clause>

  <clause id="5570">
    <literal><![CDATA[
      R(x,y,(z \ 1) * (z \ L(z,u,w))) = R(x,y,L(z,u,w) \ 1)
    ]]></literal>
    <justification jstring="[para(3253(a,1),5411(a,1,3,2))].">
      <j1 rule="para" parents="3253 5411"/>
    </justification>
  </clause>

  <clause id="5571">
    <literal><![CDATA[
      R(x,y,L(z \ 1,u,w)) = R(x,y,L(z,u,w) \ 1)
    ]]></literal>
    <justification jstring="[para(2588(a,1),5570(a,1,3))].">
      <j1 rule="para" parents="2588 5570"/>
    </justification>
  </clause>

  <clause id="5572">
    <literal><![CDATA[
      R(x,y,L(z \ 1,u,w)) = R(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(333,a,1858,a(flip),b,5571,a),flip(a)].">
      <j1 rule="hyper" parents="333 1858 5571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5573">
    <literal><![CDATA[
      (x * (y \ ((z \ (y * (x \ u))) * z))) \ u = K(z,(x * (z / y)) \ u)
    ]]></literal>
    <justification jstring="[para(4162(a,1),5531(a,1,1,2))].">
      <j1 rule="para" parents="4162 5531"/>
    </justification>
  </clause>

  <clause id="5574">
    <literal><![CDATA[
      K(x,(y * (x / z)) \ u) = K(x,(y * (z \ x)) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,5530,a(flip),b,5573,a),flip(a)].">
      <j1 rule="hyper" parents="63 5530 5573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5575">
    <literal><![CDATA[
      K(x,(y * (x / y)) \ z) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[para(10(a,1),5574(a,2,2,1))].">
      <j1 rule="para" parents="10 5574"/>
    </justification>
  </clause>

  <clause id="5576">
    <literal><![CDATA[
      K(x,(y * ((z \ x) \ x)) \ u) = K(x,(y * z) \ u)
    ]]></literal>
    <justification jstring="[para(76(a,1),5574(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="76 5574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5577">
    <literal><![CDATA[
      K(x,((y / T(z,z \ x)) * z) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(464(a,1),5576(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="464 5576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5578">
    <literal><![CDATA[
      K(x,(y * K(z \ x,z)) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(5444(a,1),5577(a,1,2,1))].">
      <j1 rule="para" parents="5444 5577"/>
    </justification>
  </clause>

  <clause id="5579">
    <literal><![CDATA[
      K(x,((y \ x) \ x) \ z) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(4223(a,1),5578(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4223 5578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5580">
    <literal><![CDATA[
      ((1 / x) \ L(T(y,z),x,x \ 1)) * (1 / x) = T((x * y) * (1 / x),z)
    ]]></literal>
    <justification jstring="[para(25(a,2),4122(a,1,1,2))].">
      <j1 rule="para" parents="25 4122"/>
    </justification>
  </clause>

  <clause id="5581">
    <literal><![CDATA[
      L(T(x,y),T(z,x),K(x,z)) * z = K(x,z) * (T(x,y) * T(z,x))
    ]]></literal>
    <justification jstring="[para(4212(a,2),4257(a,1,1,3))].">
      <j1 rule="para" parents="4212 4257"/>
    </justification>
  </clause>

  <clause id="5582">
    <literal><![CDATA[
      T(x * K(y * R(x,z,u),x),y) = R(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[para(4431(a,1),830(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4431 830"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5583">
    <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(4431(a,1),1005(a,1,1,1))].">
      <j1 rule="para" parents="4431 1005"/>
    </justification>
  </clause>

  <clause id="5584">
    <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(4985,a,5582,a)].">
      <j1 rule="hyper" parents="4985 5582"/>
    </justification>
  </clause>

  <clause id="5585">
    <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(230(a,1),5582(a,2,3))].">
      <j1 rule="para" parents="230 5582"/>
    </justification>
  </clause>

  <clause id="5586">
    <literal><![CDATA[
      T(x * K(y * L(x,z,u),x),y) = R(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(4432(a,1),830(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4432 830"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5587">
    <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(4985,a,5586,a)].">
      <j1 rule="hyper" parents="4985 5586"/>
    </justification>
  </clause>

  <clause id="5588">
    <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(953(a,1),4503(a,1,2))].">
      <j1 rule="para" parents="953 4503"/>
    </justification>
  </clause>

  <clause id="5589">
    <literal><![CDATA[
      L(x,y / z,y / (y / z)) = y \ (z * ((z \ y) * x))
    ]]></literal>
    <justification jstring="[para(5049(a,1),4931(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5049 4931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5590">
    <literal><![CDATA[
      L(x,y / z,y / (y / z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,z \ y,z) = u
    ]]></literal>
    <justification jstring="[para(5589(a,2),784(a,1))].">
      <j1 rule="para" parents="5589 784"/>
    </justification>
  </clause>

  <clause id="5591">
    <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(4941(a,1),4943(a,1,1,1))].">
      <j1 rule="para" parents="4941 4943"/>
    </justification>
  </clause>

  <clause id="5592">
    <literal><![CDATA[
      K(x,y * (((1 / z) * u) * w)) = K(x,y * (((z \ 1) * u) * w))
    ]]></literal>
    <justification jstring="[para(2608(a,1),5327(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="2608 5327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5593">
    <literal><![CDATA[
      T(x,y * (((1 / z) * u) * w)) = T(x,y * (((z \ 1) * u) * w))
    ]]></literal>
    <justification jstring="[hyper(124,a,5592,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 5592 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5594">
    <literal><![CDATA[
      K(x,y * ((((K(z,u) / z) \ 1) * u) * w)) = K(x,y * ((u * (1 / (1 / z))) * w))
    ]]></literal>
    <justification jstring="[para(4945(a,1),5592(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4945 5592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5595">
    <literal><![CDATA[
      T((x * y) * (1 / x),z) = (x * T(y,z)) * (1 / x)
    ]]></literal>
    <justification jstring="[para(2656(a,1),5580(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2656 5580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5596">
    <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(276(a,2),4142(a,2,1,2,1,2))].">
      <j1 rule="para" parents="276 4142"/>
    </justification>
  </clause>

  <clause id="5597">
    <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(121,a,4317,a(flip),b,4556,a),flip(a)].">
      <j1 rule="hyper" parents="121 4317 4556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5598">
    <literal><![CDATA[
      T(x,y * ((z \ 1) * (K(z \ 1,u) * w))) = T(x,y * (T(1 / z,u) * w))
    ]]></literal>
    <justification jstring="[para(3333(a,1),4527(a,1,2,2,2,1))].">
      <j1 rule="para" parents="3333 4527"/>
    </justification>
  </clause>

  <clause id="5599">
    <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(4273(a,1),4612(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4273 4612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5600">
    <literal><![CDATA[
      L(L(x,y,z),z * y,K(z,u)) = L(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(333,a,18,a,b,5599,a),flip(a)].">
      <j1 rule="hyper" parents="333 18 5599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5601">
    <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(5599(a,2),504(a,1))].">
      <j1 rule="para" parents="5599 504"/>
    </justification>
  </clause>

  <clause id="5602">
    <literal><![CDATA[
      L(L(x,y * z,K(y,u)),z,y) = L(x,z,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,30,a,b,5600,a)].">
      <j1 rule="hyper" parents="63 30 5600"/>
    </justification>
  </clause>

  <clause id="5603">
    <literal><![CDATA[
      L(T(x \ 1,y) \ z,x \ 1,x) = K(y,x \ 1) * (x * z)
    ]]></literal>
    <justification jstring="[hyper(4709,a,5228,a)].">
      <j1 rule="hyper" parents="4709 5228"/>
    </justification>
  </clause>

  <clause id="5604">
    <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(5205(a,1),5135(a,1,2,2,2))].">
      <j1 rule="para" parents="5205 5135"/>
    </justification>
  </clause>

  <clause id="5605">
    <literal><![CDATA[
      (x \ K(y,x)) \ L((x \ 1) * z,u,w) = T(x,y) * L(x \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(333,a,4273,a(flip),b,5241,a),flip(a)].">
      <j1 rule="hyper" parents="333 4273 5241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5606">
    <literal><![CDATA[
      (1 / x) * K(((1 / x) \ y) \ 1,z) = K((y * x) \ 1,z) / x
    ]]></literal>
    <justification jstring="[para(79(a,1),5347(a,1,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="79 5347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5607">
    <literal><![CDATA[
      (T(x * y,z) / y) * (x \ 1) = (1 / y) * (x \ T(x * y,z))
    ]]></literal>
    <justification jstring="[para(1648(a,1),5348(a,1,1))].">
      <j1 rule="para" parents="1648 5348"/>
    </justification>
  </clause>

  <clause id="5608">
    <literal><![CDATA[
      (1 / x) * ((x \ y) \ T((x \ y) * x,x)) = (x \ T(y,x)) * ((x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(1398(a,1),5607(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1398 5607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5610">
    <literal><![CDATA[
      (L(x \ 1,y,z) \ (x \ 1)) \ ((L(x \ 1,y,z) \ 1) * K(x \ 1,x)) = T(x,x \ (L(x \ 1,y,z) \ 1))
    ]]></literal>
    <justification jstring="[para(5412(a,1),2839(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5412 2839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5611">
    <literal><![CDATA[
      (x * (y * ((z \ (y \ (x \ u))) * z))) \ u = K(z,(x * (y * z)) \ u)
    ]]></literal>
    <justification jstring="[para(111(a,1),5529(a,1,1,2,2))].">
      <j1 rule="para" parents="111 5529"/>
    </justification>
  </clause>

  <clause id="5612">
    <literal><![CDATA[
      ((x * y) * ((z \ ((x * y) \ u)) * z)) \ u = K(z,(x * (y * z)) \ u)
    ]]></literal>
    <justification jstring="[para(2572(a,2),5611(a,1,1))].">
      <j1 rule="para" parents="2572 5611"/>
    </justification>
  </clause>

  <clause id="5613">
    <literal><![CDATA[
      T(x,y * (T(1 / z,u) * w)) = T(x,y * (T(z \ 1,u) * w))
    ]]></literal>
    <justification jstring="[para(4241(a,1),5598(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4241 5598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5614">
    <literal><![CDATA[
      (x \ T(y,x)) * ((x \ y) \ 1) = (1 / x) * ((y * x) / y)
    ]]></literal>
    <justification jstring="[para(4136(a,1),5608(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4136 5608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5615">
    <literal><![CDATA[
      K(x,y) = (y \ T(x,y)) * ((y \ x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(333,a,4439,a,b,5614,a)].">
      <j1 rule="hyper" parents="333 4439 5614"/>
    </justification>
  </clause>

  <clause id="5616">
    <literal><![CDATA[
      (x \ T(x * y,x)) * (y \ 1) = K(x * y,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),5615(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="9 5615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5617">
    <literal><![CDATA[
      (x \ T(x * K(y,z),x)) * (K(z,y) * 1) = K(x * K(y,z),x)
    ]]></literal>
    <justification jstring="[para(4567(a,1),5616(a,1,2))].">
      <j1 rule="para" parents="4567 5616"/>
    </justification>
  </clause>

  <clause id="5618">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) * (K(z,x) * 1) = K(y * K(x,z),y)
    ]]></literal>
    <justification jstring="[para(5569(a,2),5617(a,1,1))].">
      <j1 rule="para" parents="5569 5617"/>
    </justification>
  </clause>

  <clause id="5619">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) * K(z,x) = K(y * K(x,z),y)
    ]]></literal>
    <justification jstring="[para(8(a,1),5618(a,1,2))].">
      <j1 rule="para" parents="8 5618"/>
    </justification>
  </clause>

  <clause id="5620">
    <literal><![CDATA[
      T((x \ L(y,y \ z,y)) * x,T(z,y) / y) = (x \ T(y,z)) * x
    ]]></literal>
    <justification jstring="[para(3655(a,1),4135(a,2,1,2))].">
      <j1 rule="para" parents="3655 4135"/>
    </justification>
  </clause>

  <clause id="5621">
    <literal><![CDATA[
      T((x \ L(y,y \ z,y)) * x,T(z,y) / y) != u
    ]]></literal>
    <literal><![CDATA[
      T((x \ y) * x,z) = u
    ]]></literal>
    <justification jstring="[para(5620(a,2),4116(a,1))].">
      <j1 rule="para" parents="5620 4116"/>
    </justification>
  </clause>

  <clause id="5622">
    <literal><![CDATA[
      (x * y) * (z * (L(y \ 1,y,x) / z)) = (x * y) * (z * (((x * y) \ x) / z))
    ]]></literal>
    <justification jstring="[hyper(63,a,4127,a(flip),b,4144,a),flip(a)].">
      <j1 rule="hyper" parents="63 4127 4144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5623">
    <literal><![CDATA[
      R((x \ (1 / y)) * x,y,z) * (y * z) = (y * z) * ((x \ ((y * z) \ z)) * x)
    ]]></literal>
    <justification jstring="[para(3013(a,2),4146(a,1,1))].">
      <j1 rule="para" parents="3013 4146"/>
    </justification>
  </clause>

  <clause id="5624">
    <literal><![CDATA[
      L(T(x,K(y,x) * z),K(x,y) \ z,K(x,y)) = z \ (T(x,y) * (K(x,y) \ z))
    ]]></literal>
    <justification jstring="[para(4567(a,1),4611(a,1,1,2))].">
      <j1 rule="para" parents="4567 4611"/>
    </justification>
  </clause>

  <clause id="5625">
    <literal><![CDATA[
      (x * x) \ T(x * x,x \ y) = K(x * x,(x \ 1) \ y)
    ]]></literal>
    <justification jstring="[para(534(a,1),4749(a,1,1))].">
      <j1 rule="para" parents="534 4749"/>
    </justification>
  </clause>

  <clause id="5627">
    <literal><![CDATA[
      K(x * x,(x \ 1) \ y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x * x,x \ y) = z
    ]]></literal>
    <justification jstring="[para(5625(a,1),4306(a,1))].">
      <j1 rule="para" parents="5625 4306"/>
    </justification>
  </clause>

  <clause id="5628">
    <literal><![CDATA[
      K(x,R(y,z,u) \ 1) * (z * u) = (K(x,y \ 1) * z) * u
    ]]></literal>
    <justification jstring="[para(4777(a,1),4778(a,2,1))].">
      <j1 rule="para" parents="4777 4778"/>
    </justification>
  </clause>

  <clause id="5629">
    <literal><![CDATA[
      R(K(x,y \ 1),z,u) = K(x,R(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(35,a,107,a,b,5628,a)].">
      <j1 rule="hyper" parents="35 107 5628"/>
    </justification>
  </clause>

  <clause id="5630">
    <literal><![CDATA[
      K(x,R(y,x,z) \ 1) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(35,a,3559,a(flip),b,5628,a),flip(a)].">
      <j1 rule="hyper" parents="35 3559 5628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5631">
    <literal><![CDATA[
      K(x,R(R(y,x,z),u,w) \ 1) = K(x,R(y,u,w) \ 1)
    ]]></literal>
    <justification jstring="[para(31(a,1),5630(a,1,2,1))].">
      <j1 rule="para" parents="31 5630"/>
    </justification>
  </clause>

  <clause id="5632">
    <literal><![CDATA[
      K(x,R(y \ 1,z,u) \ 1) = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(4621(a,1),5629(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4621 5629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5633">
    <literal><![CDATA[
      K(x,R(y / z,u,w) \ 1) = R(K(x,z / y),u,w)
    ]]></literal>
    <justification jstring="[para(5055(a,1),5629(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5055 5629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5634">
    <literal><![CDATA[
      R(K(x,y),z,u) \ w = R(K(y,x),z,u) * w
    ]]></literal>
    <justification jstring="[para(5632(a,1),5118(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5632 5118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5635">
    <literal><![CDATA[
      R(K(x,y),z,u) \ 1 = R(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(4729,a,5634,a)].">
      <j1 rule="hyper" parents="4729 5634"/>
    </justification>
  </clause>

  <clause id="5636">
    <literal><![CDATA[
      (x * y) / ((K(z,u) * x) * y) = R(K(u,z),x,y)
    ]]></literal>
    <justification jstring="[hyper(601,a,5634,a)].">
      <j1 rule="hyper" parents="601 5634"/>
    </justification>
  </clause>

  <clause id="5637">
    <literal><![CDATA[
      x / (R(K(y,z),u,w) * x) = R(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(565,a,5634,a)].">
      <j1 rule="hyper" parents="565 5634"/>
    </justification>
  </clause>

  <clause id="5638">
    <literal><![CDATA[
      R(K(x,y),z,u) \ (z * u) = (K(y,x) * z) * u
    ]]></literal>
    <justification jstring="[hyper(333,a,107,a(flip),b,5634,a),flip(a)].">
      <j1 rule="hyper" parents="333 107 5634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5639">
    <literal><![CDATA[
      R(K(x,y),y / x,z) * ((y / T(x,y)) * z) = (y / x) * z
    ]]></literal>
    <justification jstring="[hyper(63,a,4823,a(flip),b,5634,a),flip(a)].">
      <j1 rule="hyper" parents="63 4823 5634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5640">
    <literal><![CDATA[
      R(K(x,y),z,u) \ 1 != w
    ]]></literal>
    <literal><![CDATA[
      R(K(y,x),z,u) = w
    ]]></literal>
    <justification jstring="[para(5634(a,2),134(a,1)),flip(b)].">
      <j1 rule="para" parents="5634 134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5641">
    <literal><![CDATA[
      R(K(x,y),z,(K(y,x) * z) \ 1) = z * ((K(y,x) * z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,364,a(flip),b,5635,a),flip(a)].">
      <j1 rule="hyper" parents="63 364 5635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5642">
    <literal><![CDATA[
      K(x,R(1 / y,z,u) \ 1) != w
    ]]></literal>
    <literal><![CDATA[
      R(K(x,y),z,u) = w
    ]]></literal>
    <justification jstring="[para(5116(a,2),5640(a,1))].">
      <j1 rule="para" parents="5116 5640"/>
    </justification>
  </clause>

  <clause id="5643">
    <literal><![CDATA[
      R(K(x,y / z),y,u) = K(x,(y * u) / (z * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,5062,a(flip),b,5633,a),flip(a)].">
      <j1 rule="hyper" parents="63 5062 5633"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5644">
    <literal><![CDATA[
      R(K(x,y / z),y,y \ 1) = K(x,(z * (y \ 1)) \ 1)
    ]]></literal>
    <justification jstring="[para(554(a,1),5633(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="554 5633"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5645">
    <literal><![CDATA[
      R(K(x,y / z),y,z \ 1) = K(x,y * (z \ 1))
    ]]></literal>
    <justification jstring="[para(527(a,1),5633(a,1,2)),flip(a)].">
      <j1 rule="para" parents="527 5633"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5646">
    <literal><![CDATA[
      R(K(x,(y / z) / u),y / z,z) = K(x,y / (u * z))
    ]]></literal>
    <justification jstring="[para(12(a,1),5643(a,2,2,1))].">
      <j1 rule="para" parents="12 5643"/>
    </justification>
  </clause>

  <clause id="5647">
    <literal><![CDATA[
      R(K(x,y / (z / u)),y,u) = K(x,(y * u) / z)
    ]]></literal>
    <justification jstring="[para(12(a,1),5643(a,2,2,2))].">
      <j1 rule="para" parents="12 5643"/>
    </justification>
  </clause>

  <clause id="5648">
    <literal><![CDATA[
      K(x,(y * z) / ((u \ y) * z)) = R(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(76(a,1),5643(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="76 5643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5649">
    <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(3019(a,1),5643(a,1,1,2))].">
      <j1 rule="para" parents="3019 5643"/>
    </justification>
  </clause>

  <clause id="5650">
    <literal><![CDATA[
      R(K(x,(y / z) \ x),x,z) = K(x,(x * z) / y)
    ]]></literal>
    <justification jstring="[para(4644(a,1),5647(a,1,1))].">
      <j1 rule="para" parents="4644 5647"/>
    </justification>
  </clause>

  <clause id="5651">
    <literal><![CDATA[
      K(x,R(y,y \ z,u)) = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(104(a,2),5648(a,1,2))].">
      <j1 rule="para" parents="104 5648"/>
    </justification>
  </clause>

  <clause id="5652">
    <literal><![CDATA[
      R(K(x,y),T(y,z),u) = K(x,y)
    ]]></literal>
    <justification jstring="[para(3295(a,1),5648(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3295 5648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5653">
    <literal><![CDATA[
      (K(x,y) * T(y,z)) * u = K(x,y) * (T(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(125,a,5652,a(flip),b,20,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="125 5652 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5654">
    <literal><![CDATA[
      R(K(x,y),y * z,u) = K(x,R(y,z,u))
    ]]></literal>
    <justification jstring="[para(9(a,1),5651(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 5651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5655">
    <literal><![CDATA[
      R(K(x,y),z * y,u) = K(x,R(y,T(z,y),u))
    ]]></literal>
    <justification jstring="[para(22(a,2),5651(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="22 5651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5656">
    <literal><![CDATA[
      R(K(x,R(y,z,u)),(y * z) * u,w) = K(x,R(R(y,z,u),z * u,w))
    ]]></literal>
    <justification jstring="[para(187(a,1),5651(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="187 5651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5657">
    <literal><![CDATA[
      K(x * y,R(x,y,z)) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(3568,a,5654,a),flip(a)].">
      <j1 rule="hyper" parents="3568 5654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5658">
    <literal><![CDATA[
      K(R(x,y * z,u) \ 1,y) = K(x \ 1,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,5111,a(flip),b,5654,a)].">
      <j1 rule="hyper" parents="63 5111 5654"/>
    </justification>
  </clause>

  <clause id="5659">
    <literal><![CDATA[
      R(T(K(x,y),z),y * u,w) = T(K(x,R(y,u,w)),z)
    ]]></literal>
    <justification jstring="[para(5654(a,1),27(a,2,1))].">
      <j1 rule="para" parents="5654 27"/>
    </justification>
  </clause>

  <clause id="5660">
    <literal><![CDATA[
      K(x,R(y,z,u)) * ((y * z) * u) = (y * (K(x,y) * z)) * u
    ]]></literal>
    <justification jstring="[para(5654(a,1),4859(a,1,1))].">
      <j1 rule="para" parents="5654 4859"/>
    </justification>
  </clause>

  <clause id="5661">
    <literal><![CDATA[
      K(x,(x * y) / z) = K(x,(z / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(3568,a,5650,a),flip(a)].">
      <j1 rule="hyper" parents="3568 5650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5662">
    <literal><![CDATA[
      R(K(x,(y / z) \ x),x,z) = K(x,(y / (x * z)) \ 1)
    ]]></literal>
    <justification jstring="[hyper(333,a,5055,a,b,5650,a),flip(a)].">
      <j1 rule="hyper" parents="333 5055 5650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5663">
    <literal><![CDATA[
      K(x,(x * y) / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(z / y) \ x) = u
    ]]></literal>
    <justification jstring="[para(5650(a,1),3568(a,1))].">
      <j1 rule="para" parents="5650 3568"/>
    </justification>
  </clause>

  <clause id="5665">
    <literal><![CDATA[
      K(x,(L(y,z,u) / y) \ x) = K(x,(x / L(y,z,u)) * y)
    ]]></literal>
    <justification jstring="[para(1820(a,1),5661(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1820 5661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5666">
    <literal><![CDATA[
      L(x,T(y,z),K(u,y)) = x
    ]]></literal>
    <justification jstring="[hyper(501,a,5653,a)].">
      <j1 rule="hyper" parents="501 5653"/>
    </justification>
  </clause>

  <clause id="5667">
    <literal><![CDATA[
      L(T(x,y) \ z,T(u,w),K(v5,u)) = x \ (K(y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(333,a,4576,a,b,5666,a),flip(a)].">
      <j1 rule="hyper" parents="333 4576 5666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5668">
    <literal><![CDATA[
      K(x,y) * (T(x,z) * T(y,x)) = T(x,z) * y
    ]]></literal>
    <justification jstring="[para(5666(a,1),5581(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5666 5581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5669">
    <literal><![CDATA[
      K(x,y) * (K(x,z) * (y * x)) = T(x,z) * y
    ]]></literal>
    <justification jstring="[para(4520(a,2),5668(a,1,2))].">
      <j1 rule="para" parents="4520 5668"/>
    </justification>
  </clause>

  <clause id="5671">
    <literal><![CDATA[
      K(x,R(y / x,x * z,u) \ 1) = K(x,(((y * z) * u) / ((x * z) * u)) \ 1)
    ]]></literal>
    <justification jstring="[para(563(a,1),5631(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="563 5631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5672">
    <literal><![CDATA[
      K(x,R(y,z,u) \ 1) != w
    ]]></literal>
    <literal><![CDATA[
      R(K(x,y \ 1),z,u) = w
    ]]></literal>
    <justification jstring="[para(76(a,1),5642(a,1,2,1,1))].">
      <j1 rule="para" parents="76 5642"/>
    </justification>
  </clause>

  <clause id="5673">
    <literal><![CDATA[
      K(x,((y \ z) * (z \ 1)) \ 1) = R(K(x,y),z,z \ 1)
    ]]></literal>
    <justification jstring="[para(76(a,1),5644(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="76 5644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5674">
    <literal><![CDATA[
      R(T(K(x,(y / z) \ x),u),x,z) = T(K(x,(y / (x * z)) \ 1),u)
    ]]></literal>
    <justification jstring="[para(5662(a,1),27(a,2,1))].">
      <j1 rule="para" parents="5662 27"/>
    </justification>
  </clause>

  <clause id="5675">
    <literal><![CDATA[
      K(x,(y \ L(y,z,u)) \ x) = K(x,(x / L(y,z,u)) * y)
    ]]></literal>
    <justification jstring="[para(2516(a,1),5665(a,1,2,1))].">
      <j1 rule="para" parents="2516 5665"/>
    </justification>
  </clause>

  <clause id="5676">
    <literal><![CDATA[
      x / (R(K(y,z),u,(K(y,z) * u) \ 1) * x) = u * ((K(y,z) * u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,5637,a,b,5641,a)].">
      <j1 rule="hyper" parents="63 5637 5641"/>
    </justification>
  </clause>

  <clause id="5677">
    <literal><![CDATA[
      K((x \ y) \ 1,T(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K((T(x,z) \ T(y,z)) \ 1,x) = u
    ]]></literal>
    <justification jstring="[para(5029(a,1),5167(a,1))].">
      <j1 rule="para" parents="5029 5167"/>
    </justification>
  </clause>

  <clause id="5678">
    <literal><![CDATA[
      ((1 / R(x,y,z)) * x) * (x \ 1) = T(1 / R(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,4282,a(flip),b,5181,a),flip(a)].">
      <j1 rule="hyper" parents="63 4282 5181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5679">
    <literal><![CDATA[
      (x / R(x,y,z)) * (x \ 1) = T(1 / R(x,y,z),x)
    ]]></literal>
    <justification jstring="[para(1578(a,1),5678(a,1,1))].">
      <j1 rule="para" parents="1578 5678"/>
    </justification>
  </clause>

  <clause id="5680">
    <literal><![CDATA[
      (x / R(x,y,z)) * (x \ 1) = R(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(333,a,3038,a(flip),b,5679,a),flip(a)].">
      <j1 rule="hyper" parents="333 3038 5679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5681">
    <literal><![CDATA[
      T(R(x,y,z) \ x,x \ 1) = (x \ 1) \ (R(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(3040,a,5680,a)].">
      <j1 rule="hyper" parents="3040 5680"/>
    </justification>
  </clause>

  <clause id="5682">
    <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(5459(a,2),5490(a,2,2))].">
      <j1 rule="para" parents="5459 5490"/>
    </justification>
  </clause>

  <clause id="5683">
    <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(9(a,1),5583(a,2,1,1))].">
      <j1 rule="para" parents="9 5583"/>
    </justification>
  </clause>

  <clause id="5684">
    <literal><![CDATA[
      (x * y) * L(z * ((y \ 1) / z),y,x) = (x * y) * (z * (((x * y) \ x) / z))
    ]]></literal>
    <justification jstring="[para(2545(a,2),5622(a,1,2))].">
      <j1 rule="para" parents="2545 5622"/>
    </justification>
  </clause>

  <clause id="5685">
    <literal><![CDATA[
      (x * y) * ((z \ ((x * y) \ y)) * z) = (((z \ (1 / x)) * z) * x) * y
    ]]></literal>
    <justification jstring="[hyper(299,a,5623,a),flip(a)].">
      <j1 rule="hyper" parents="299 5623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5686">
    <literal><![CDATA[
      K(x,R(y / x,x * z,u) \ 1) = K(x,((x * z) * u) / ((y * z) * u))
    ]]></literal>
    <justification jstring="[hyper(333,a,5055,a(flip),b,5671,a),flip(a)].">
      <j1 rule="hyper" parents="333 5055 5671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5687">
    <literal><![CDATA[
      R(K(x,x / y),x * z,u) = K(x,((x * z) * u) / ((y * z) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,5633,a(flip),b,5686,a)].">
      <j1 rule="hyper" parents="63 5633 5686"/>
    </justification>
  </clause>

  <clause id="5688">
    <literal><![CDATA[
      R(K(x,y \ x),x * z,u) = K(x,((x * z) * u) / ((y * z) * u))
    ]]></literal>
    <justification jstring="[para(4644(a,1),5687(a,1,1))].">
      <j1 rule="para" parents="4644 5687"/>
    </justification>
  </clause>

  <clause id="5689">
    <literal><![CDATA[
      K(x,((x * y) * z) / ((u * y) * z)) = K(R(x,y,z),u \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,5562,a(flip),b,5688,a),flip(a)].">
      <j1 rule="hyper" parents="63 5562 5688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5690">
    <literal><![CDATA[
      K(R(x,x \ y,z),u \ x) = K(x,(y * z) / ((u * (x \ y)) * z))
    ]]></literal>
    <justification jstring="[para(10(a,1),5689(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="10 5689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5691">
    <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(4815(a,1),5689(a,1,2,1))].">
      <j1 rule="para" parents="4815 5689"/>
    </justification>
  </clause>

  <clause id="5692">
    <literal><![CDATA[
      K(x,(y * z) / ((u * (x \ y)) * z)) = R(K(x,u \ x),y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5560,a(flip),b,5690,a),flip(a)].">
      <j1 rule="hyper" parents="63 5560 5690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5693">
    <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(333,a,3823,a(flip),b,5682,a),flip(a)].">
      <j1 rule="hyper" parents="333 3823 5682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5694">
    <literal><![CDATA[
      (x * y) * (z * (((x * y) \ x) / z)) = x * (y * (z * ((y \ 1) / z)))
    ]]></literal>
    <justification jstring="[hyper(306,a,5684,a),flip(a)].">
      <j1 rule="hyper" parents="306 5684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5695">
    <literal><![CDATA[
      (x \ (y * (T(z,x) \ z))) * x = ((x \ y) * x) * (T(z,x) \ z)
    ]]></literal>
    <justification jstring="[para(239(a,1),4126(a,1,1)),flip(a)].">
      <j1 rule="para" parents="239 4126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5697">
    <literal><![CDATA[
      ((x \ y) * x) * (T(z,x) \ z) = (x \ (y * K(x,z))) * x
    ]]></literal>
    <justification jstring="[para(4205(a,2),5695(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4205 5695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5698">
    <literal><![CDATA[
      (x \ (y * K(x,z))) * x = ((x \ y) * x) * K(x,z)
    ]]></literal>
    <justification jstring="[para(4205(a,2),5697(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4205 5697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5699">
    <literal><![CDATA[
      ((x * (y / x)) \ T(y,z)) * (x * (y / x)) = T(y,z)
    ]]></literal>
    <justification jstring="[para(4466(a,1),4194(a,1,1,2,1))].">
      <j1 rule="para" parents="4466 4194"/>
    </justification>
  </clause>

  <clause id="5700">
    <literal><![CDATA[
      T(x,y) / (z * (x / z)) = (z * (x / z)) \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(138,a,5699,a)].">
      <j1 rule="hyper" parents="138 5699"/>
    </justification>
  </clause>

  <clause id="5701">
    <literal><![CDATA[
      T(x,y) / (T(x,y) / (z * (x / z))) = z * (x / z)
    ]]></literal>
    <justification jstring="[hyper(197,a,5700,a,b,xx)].">
      <j1 rule="hyper" parents="197 5700"/>
    </justification>
  </clause>

  <clause id="5702">
    <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(5292(a,1),4389(a,1,2,1))].">
      <j1 rule="para" parents="5292 4389"/>
    </justification>
  </clause>

  <clause id="5703">
    <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(252(a,1),4717(a,1,2)),flip(a)].">
      <j1 rule="para" parents="252 4717"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5704">
    <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(4367(a,1),5703(a,1,1,2,1))].">
      <j1 rule="para" parents="4367 5703"/>
    </justification>
  </clause>

  <clause id="5705">
    <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(251(a,1),4718(a,1,2)),flip(a)].">
      <j1 rule="para" parents="251 4718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5706">
    <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(4367(a,1),5705(a,1,1,2,1))].">
      <j1 rule="para" parents="4367 5705"/>
    </justification>
  </clause>

  <clause id="5707">
    <literal><![CDATA[
      (x * (K(y,x) * z)) \ (x * (K(y,x) * (z * u))) = L(L(u,z,x),x * z,K(y,x))
    ]]></literal>
    <justification jstring="[para(4712(a,1),4862(a,1,2))].">
      <j1 rule="para" parents="4712 4862"/>
    </justification>
  </clause>

  <clause id="5708">
    <literal><![CDATA[
      T(x * x,y) * (y / T(x * x,y)) = T(y,y / (x * x))
    ]]></literal>
    <justification jstring="[para(12(a,1),4878(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12 4878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5709">
    <literal><![CDATA[
      T(x * x,y) * (y / T(x * x,y)) = T(y,(x * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(333,a,3363,a(flip),b,5708,a),flip(a)].">
      <j1 rule="hyper" parents="333 3363 5708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5711">
    <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(4869(a,1),5585(a,1,1))].">
      <j1 rule="para" parents="4869 5585"/>
    </justification>
  </clause>

  <clause id="5712">
    <literal><![CDATA[
      K(x,y * (((z * K(u,z)) * u) * w)) = K(x,y * ((u * (1 / (1 / z))) * w))
    ]]></literal>
    <justification jstring="[para(4727(a,1),5594(a,1,2,2,1,1))].">
      <j1 rule="para" parents="4727 5594"/>
    </justification>
  </clause>

  <clause id="5713">
    <literal><![CDATA[
      K(x,y * ((z * (1 / (1 / u))) * w)) = K(x,y * ((z * u) * w))
    ]]></literal>
    <justification jstring="[para(4291(a,1),5712(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4291 5712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5714">
    <literal><![CDATA[
      ((x \ y) \ y) \ R((x \ y) \ y,z,u) = x \ (y \ ((R(x,z,u) * (x \ y)) * x))
    ]]></literal>
    <justification jstring="[hyper(63,a,1048,a(flip),b,5597,a)].">
      <j1 rule="hyper" parents="63 1048 5597"/>
    </justification>
  </clause>

  <clause id="5715">
    <literal><![CDATA[
      L(L(x,y,z),z * y,K(u,z)) = L(x,y,z * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,3553,a(flip),b,5707,a),flip(a)].">
      <j1 rule="hyper" parents="63 3553 5707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5716">
    <literal><![CDATA[
      L(L(x,y,z),z * y,K(y,z)) = L(x,T(y,z),z)
    ]]></literal>
    <justification jstring="[hyper(333,a,5260,a(flip),b,5715,a),flip(a)].">
      <j1 rule="hyper" parents="333 5260 5715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5717">
    <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(4046(a,1),5189(a,1,2,1,1))].">
      <j1 rule="para" parents="4046 5189"/>
    </justification>
  </clause>

  <clause id="5718">
    <literal><![CDATA[
      (x \ R(x,y,z)) * K(R(x,y,z),u) = x \ R(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(3334(a,1),5717(a,1,2))].">
      <j1 rule="para" parents="3334 5717"/>
    </justification>
  </clause>

  <clause id="5719">
    <literal><![CDATA[
      ((x * T(x \ (y / z),y / z)) * z) / y = K(x \ (y / z),(z / y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(5073,a,5258,a),flip(a)].">
      <j1 rule="hyper" parents="5073 5258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5721">
    <literal><![CDATA[
      (x * (y * T(y \ (x \ z),z / y))) / z = K(x \ (z / y),(y / z) \ 1)
    ]]></literal>
    <justification jstring="[para(1357(a,1),5719(a,1,1))].">
      <j1 rule="para" parents="1357 5719"/>
    </justification>
  </clause>

  <clause id="5722">
    <literal><![CDATA[
      K(((x * y) / z) \ 1,z / y) = K(x \ (z / y),(y / z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,4957,a(flip),b,5721,a)].">
      <j1 rule="hyper" parents="63 4957 5721"/>
    </justification>
  </clause>

  <clause id="5723">
    <literal><![CDATA[
      ((x * (y * ((x \ (z / u)) / y))) * u) / z = K(y,z / ((x * y) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,5646,a(flip),b,5546,a),flip(a)].">
      <j1 rule="hyper" parents="63 5646 5546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5724">
    <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(1635(a,2),5588(a,1,2))].">
      <j1 rule="para" parents="1635 5588"/>
    </justification>
  </clause>

  <clause id="5725">
    <literal><![CDATA[
      x * (y * (z \ T(z * (y \ (z \ 1)),z))) = (x * K(y \ 1,z)) * (z \ 1)
    ]]></literal>
    <justification jstring="[hyper(306,a,5724,a)].">
      <j1 rule="hyper" parents="306 5724"/>
    </justification>
  </clause>

  <clause id="5726">
    <literal><![CDATA[
      (x * K(y \ 1,z)) * (z \ 1) = x * (K(y \ 1,z) * (z \ 1))
    ]]></literal>
    <justification jstring="[para(5125(a,1),5725(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5125 5725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5727">
    <literal><![CDATA[
      (x * K(y \ 1,z)) * (z \ 1) = x * (T(z,y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(4555(a,1),5726(a,2,2))].">
      <j1 rule="para" parents="4555 5726"/>
    </justification>
  </clause>

  <clause id="5728">
    <literal><![CDATA[
      (x * K(y,z)) * (z \ 1) = x * (T(z,(1 / y) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(79(a,1),5727(a,1,1,2,1))].">
      <j1 rule="para" parents="79 5727"/>
    </justification>
  </clause>

  <clause id="5729">
    <literal><![CDATA[
      (x * K(y,z)) * (z \ 1) = x * (T(z,y) \ 1)
    ]]></literal>
    <justification jstring="[para(79(a,1),5728(a,2,2,1,2))].">
      <j1 rule="para" parents="79 5728"/>
    </justification>
  </clause>

  <clause id="5730">
    <literal><![CDATA[
      x \ T(x * (y \ 1),y) = T(y,y \ x) \ 1
    ]]></literal>
    <justification jstring="[hyper(1004,a,5729,a)].">
      <j1 rule="hyper" parents="1004 5729"/>
    </justification>
  </clause>

  <clause id="5731">
    <literal><![CDATA[
      R(x / T(y,z),y,y \ 1) = x * (T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,5462,a,b,5729,a)].">
      <j1 rule="hyper" parents="63 5462 5729"/>
    </justification>
  </clause>

  <clause id="5733">
    <literal><![CDATA[
      (x * K(y,z)) * (z \ 1) = x * (z \ K(y,z))
    ]]></literal>
    <justification jstring="[para(4226(a,1),5729(a,2,2))].">
      <j1 rule="para" parents="4226 5729"/>
    </justification>
  </clause>

  <clause id="5735">
    <literal><![CDATA[
      x \ T(x * (y \ 1),y) = ((y \ x) \ x) \ 1
    ]]></literal>
    <justification jstring="[hyper(333,a,326,a(flip),b,5730,a),flip(a)].">
      <j1 rule="hyper" parents="333 326 5730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5736">
    <literal><![CDATA[
      (x * (y \ 1)) * K(z,y) = x * (y \ K(z,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,5555,a(flip),b,5733,a)].">
      <j1 rule="hyper" parents="63 5555 5733"/>
    </justification>
  </clause>

  <clause id="5737">
    <literal><![CDATA[
      T((x \ 1) * y,x) = (((x \ y) \ y) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(125,a,5735,a(flip),b,4085,a),flip(a)].">
      <j1 rule="hyper" parents="125 5735 4085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5738">
    <literal><![CDATA[
      (x * (y \ K(z,y))) / (y \ K(z,y)) = R(x,y \ 1,K(z,y))
    ]]></literal>
    <justification jstring="[para(5736(a,1),3977(a,1,1))].">
      <j1 rule="para" parents="5736 3977"/>
    </justification>
  </clause>

  <clause id="5739">
    <literal><![CDATA[
      (((x \ 1) * y) \ y) \ y = (((x \ y) \ y) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,3791,a(flip),b,5737,a)].">
      <j1 rule="hyper" parents="63 3791 5737"/>
    </justification>
  </clause>

  <clause id="5740">
    <literal><![CDATA[
      (x * T(y,z)) * (T(y,z) \ 1) = R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(11(a,1),5731(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 5731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5741">
    <literal><![CDATA[
      (x * T(y,z)) * (y \ K(z,y)) = R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(4226(a,1),5740(a,1,2))].">
      <j1 rule="para" parents="4226 5740"/>
    </justification>
  </clause>

  <clause id="5742">
    <literal><![CDATA[
      (x * y) * (x \ K(y,x)) = R(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(583,a,5741,a)].">
      <j1 rule="hyper" parents="583 5741"/>
    </justification>
  </clause>

  <clause id="5743">
    <literal><![CDATA[
      ((((x / y) \ 1) * x) \ x) \ x = ((y \ x) \ 1) * x
    ]]></literal>
    <justification jstring="[para(79(a,1),5739(a,2,1,1,1))].">
      <j1 rule="para" parents="79 5739"/>
    </justification>
  </clause>

  <clause id="5744">
    <literal><![CDATA[
      ((x / y) \ 1) * (y * (x / y)) = ((y \ x) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(63,a,3816,a(flip),b,5743,a)].">
      <j1 rule="hyper" parents="63 3816 5743"/>
    </justification>
  </clause>

  <clause id="5745">
    <literal><![CDATA[
      R(x,y \ 1,K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(269,a,5738,a),flip(a)].">
      <j1 rule="hyper" parents="269 5738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5746">
    <literal><![CDATA[
      R(x,y,K(z,y \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(1951,a,5745,a)].">
      <j1 rule="hyper" parents="1951 5745"/>
    </justification>
  </clause>

  <clause id="5747">
    <literal><![CDATA[
      R(x,y,K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(1941,a,5745,a)].">
      <j1 rule="hyper" parents="1941 5745"/>
    </justification>
  </clause>

  <clause id="5749">
    <literal><![CDATA[
      ((x \ 1) \ 1) * K(y,x) = (x \ 1) \ K(y,x)
    ]]></literal>
    <justification jstring="[para(5745(a,1),1934(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5745 1934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5750">
    <literal><![CDATA[
      (x * y) * K(z,y) = x * (y * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(125,a,5747,a(flip),b,20,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="125 5747 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5751">
    <literal><![CDATA[
      (x * y) * K(z,y \ 1) = x * (y * K(z,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(125,a,5746,a(flip),b,20,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="125 5746 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5752">
    <literal><![CDATA[
      L(K(x,y),y,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(501,a,5750,a)].">
      <j1 rule="hyper" parents="501 5750"/>
    </justification>
  </clause>

  <clause id="5753">
    <literal><![CDATA[
      (x * y) * K(z,y) = x * ((z * y) / z)
    ]]></literal>
    <justification jstring="[hyper(333,a,4413,a,b,5750,a),flip(a)].">
      <j1 rule="hyper" parents="333 4413 5750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5754">
    <literal><![CDATA[
      a(x,y,K(z,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(120,a,5750,a(flip),b,84,a),flip(a)].">
      <j1 rule="hyper" parents="120 5750 84"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5756">
    <literal><![CDATA[
      L(K(x,y),y,z) = L(K(x,y),y,u)
    ]]></literal>
    <justification jstring="[hyper(333,a,5752,a,b,5752,a)].">
      <j1 rule="hyper" parents="333 5752 5752"/>
    </justification>
  </clause>

  <clause id="5757">
    <literal><![CDATA[
      L(L(K(x,y),z,u),y,w) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(5752(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5752 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5759">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      L(K(x,y),y \ 1,u) = z
    ]]></literal>
    <justification jstring="[para(5752(a,1),2626(a,1))].">
      <j1 rule="para" parents="5752 2626"/>
    </justification>
  </clause>

  <clause id="5761">
    <literal><![CDATA[
      L(K(x,y),y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(5756(a,1),372(a,1)),flip(b)].">
      <j1 rule="para" parents="5756 372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5762">
    <literal><![CDATA[
      L(K(x,y),y \ 1,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(2596(a,2),5761(a,1))].">
      <j1 rule="para" parents="2596 5761"/>
    </justification>
  </clause>

  <clause id="5763">
    <literal><![CDATA[
      x * K(y,z \ x) = z * ((y * (z \ x)) / y)
    ]]></literal>
    <justification jstring="[hyper(582,a,5753,a)].">
      <j1 rule="hyper" parents="582 5753"/>
    </justification>
  </clause>

  <clause id="5764">
    <literal><![CDATA[
      L(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(L(K(x,y),z,u),y,v5) = w
    ]]></literal>
    <justification jstring="[para(5757(a,1),3141(a,1))].">
      <j1 rule="para" parents="5757 3141"/>
    </justification>
  </clause>

  <clause id="5765">
    <literal><![CDATA[
      (x * ((y / z) / x)) * z = y * K(x,(x * z) \ y)
    ]]></literal>
    <justification jstring="[hyper(333,a,1980,a(flip),b,5763,a)].">
      <j1 rule="hyper" parents="333 1980 5763"/>
    </justification>
  </clause>

  <clause id="5766">
    <literal><![CDATA[
      K(x,(y \ z) \ 1) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(34,a,4270,a,b,5763,a)].">
      <j1 rule="hyper" parents="34 4270 5763"/>
    </justification>
  </clause>

  <clause id="5767">
    <literal><![CDATA[
      K(x,(y * z) \ y) = K(x,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(34,a,4776,a(flip),b,5763,a),flip(a)].">
      <j1 rule="hyper" parents="34 4776 5763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5768">
    <literal><![CDATA[
      K(x,1 / (y \ z)) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(5104,a,5766,a)].">
      <j1 rule="hyper" parents="5104 5766"/>
    </justification>
  </clause>

  <clause id="5769">
    <literal><![CDATA[
      L(K(x,y \ z),y \ z,u) = K(x,(z \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(333,a,5752,a,b,5766,a)].">
      <j1 rule="hyper" parents="333 5752 5766"/>
    </justification>
  </clause>

  <clause id="5770">
    <literal><![CDATA[
      (x * T(x \ y,z)) \ y = K(z,(y \ x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(333,a,5485,a,b,5766,a)].">
      <j1 rule="hyper" parents="333 5485 5766"/>
    </justification>
  </clause>

  <clause id="5771">
    <literal><![CDATA[
      K(x,(y \ z) \ 1) = K(z \ y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(333,a,4367,a,b,5766,a),flip(a)].">
      <j1 rule="hyper" parents="333 4367 5766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5772">
    <literal><![CDATA[
      T(x,(y \ z) \ 1) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(124,a,5766,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 5766 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5773">
    <literal><![CDATA[
      T(K(x,y / z),y) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,5150,a,b,5766,a)].">
      <j1 rule="hyper" parents="63 5150 5766"/>
    </justification>
  </clause>

  <clause id="5774">
    <literal><![CDATA[
      K(x,((y * z) \ y) \ 1) = K(x,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),5766(a,2,2))].">
      <j1 rule="para" parents="9 5766"/>
    </justification>
  </clause>

  <clause id="5775">
    <literal><![CDATA[
      K(x,((y * z) * u) \ (y * (z * u))) = K(x,a(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(14(a,2),5766(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14 5766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5776">
    <literal><![CDATA[
      K(x,y \ (y / z)) = K(x,z \ 1)
    ]]></literal>
    <justification jstring="[para(79(a,1),5766(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="79 5766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5778">
    <literal><![CDATA[
      K(x,R(y,z,z \ 1) \ y) = K(x,a(y,z,z \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(767(a,1),5766(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="767 5766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5779">
    <literal><![CDATA[
      K(x,(T(y,z) * (y \ u)) \ 1) = K(x,(T(y,z) * u) \ y)
    ]]></literal>
    <justification jstring="[para(1053(a,1),5766(a,1,2,1))].">
      <j1 rule="para" parents="1053 5766"/>
    </justification>
  </clause>

  <clause id="5782">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ 1) = K(x,u \ K(z,y))
    ]]></literal>
    <justification jstring="[para(4567(a,1),5766(a,1,2,1))].">
      <j1 rule="para" parents="4567 5766"/>
    </justification>
  </clause>

  <clause id="5783">
    <literal><![CDATA[
      K(x,(y \ K(z,u)) \ 1) = K(x,K(u,z) * y)
    ]]></literal>
    <justification jstring="[para(4567(a,1),5766(a,2,2))].">
      <j1 rule="para" parents="4567 5766"/>
    </justification>
  </clause>

  <clause id="5784">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ 1) = K(x,(z * u) \ T(z,y))
    ]]></literal>
    <justification jstring="[para(4550(a,1),5766(a,1,2,1))].">
      <j1 rule="para" parents="4550 5766"/>
    </justification>
  </clause>

  <clause id="5785">
    <literal><![CDATA[
      T((x \ y) \ K(z,y \ x),z) = (x \ y) \ 1
    ]]></literal>
    <justification jstring="[para(5766(a,1),4780(a,1,1,2))].">
      <j1 rule="para" parents="5766 4780"/>
    </justification>
  </clause>

  <clause id="5786">
    <literal><![CDATA[
      L(x,y \ z,K(u,z \ y)) = x
    ]]></literal>
    <justification jstring="[para(5766(a,1),4892(a,1,3))].">
      <j1 rule="para" parents="5766 4892"/>
    </justification>
  </clause>

  <clause id="5787">
    <literal><![CDATA[
      T(x \ y,z) * T(x,x \ y) = K(z,(y \ x) \ 1) \ y
    ]]></literal>
    <justification jstring="[para(5766(a,2),4714(a,2,1))].">
      <j1 rule="para" parents="5766 4714"/>
    </justification>
  </clause>

  <clause id="5790">
    <literal><![CDATA[
      L(x,K(y,z \ u),u \ z) = x
    ]]></literal>
    <justification jstring="[para(5766(a,1),5230(a,1,2))].">
      <j1 rule="para" parents="5766 5230"/>
    </justification>
  </clause>

  <clause id="5791">
    <literal><![CDATA[
      K(x,R(y \ z,u,w) \ 1) = R(K(x,z \ y),u,w)
    ]]></literal>
    <justification jstring="[para(5766(a,1),5629(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5766 5629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5792">
    <literal><![CDATA[
      R(x,y \ z,K(u,z \ y)) = x
    ]]></literal>
    <justification jstring="[para(5766(a,1),5746(a,1,3))].">
      <j1 rule="para" parents="5766 5746"/>
    </justification>
  </clause>

  <clause id="5793">
    <literal><![CDATA[
      (K(x,y \ z) * (z \ y)) * u = K(x,y \ z) * ((z \ y) * u)
    ]]></literal>
    <justification jstring="[hyper(1170,a,5786,a),flip(a)].">
      <j1 rule="hyper" parents="1170 5786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5794">
    <literal><![CDATA[
      L(x,y \ (y / z),K(u,z)) = x
    ]]></literal>
    <justification jstring="[para(79(a,1),5786(a,1,3,2))].">
      <j1 rule="para" parents="79 5786"/>
    </justification>
  </clause>

  <clause id="5795">
    <literal><![CDATA[
      L(x,K(y,z),u \ (u / z)) = x
    ]]></literal>
    <justification jstring="[para(79(a,1),5790(a,1,2,2))].">
      <j1 rule="para" parents="79 5790"/>
    </justification>
  </clause>

  <clause id="5796">
    <literal><![CDATA[
      ((x \ y) * K(z,y \ x)) * u != w
    ]]></literal>
    <literal><![CDATA[
      (x \ y) * (K(z,y \ x) * u) = w
    ]]></literal>
    <justification jstring="[para(5790(a,1),306(a,1,2))].">
      <j1 rule="para" parents="5790 306"/>
    </justification>
  </clause>

  <clause id="5797">
    <literal><![CDATA[
      x \ (y * K(z,y \ x)) = (x \ y) * K(z,y \ x)
    ]]></literal>
    <justification jstring="[para(5792(a,1),529(a,1,1))].">
      <j1 rule="para" parents="5792 529"/>
    </justification>
  </clause>

  <clause id="5798">
    <literal><![CDATA[
      (K(x,y) \ (z \ (z / x))) * u = K(y,x) * ((z \ (z / x)) * u)
    ]]></literal>
    <justification jstring="[para(5794(a,1),4588(a,1,2))].">
      <j1 rule="para" parents="5794 4588"/>
    </justification>
  </clause>

  <clause id="5799">
    <literal><![CDATA[
      L(x,K(y,z),u \ (u / z)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(5795(a,1),50(a,2))].">
      <j1 rule="para" parents="5795 50"/>
    </justification>
  </clause>

  <clause id="5801">
    <literal><![CDATA[
      T(x,(y * z) \ y) = T(x,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(124,a,5767,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 5767 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5804">
    <literal><![CDATA[
      K(x,(y * (z / u)) \ y) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u / z) = w
    ]]></literal>
    <justification jstring="[para(5767(a,2),5103(a,1))].">
      <j1 rule="para" parents="5767 5103"/>
    </justification>
  </clause>

  <clause id="5805">
    <literal><![CDATA[
      K(x,(y * (z * u)) \ (y * z)) = K(x,1 / L(u,z,y))
    ]]></literal>
    <justification jstring="[para(18(a,2),5768(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="18 5768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5806">
    <literal><![CDATA[
      K(x,y \ (y / z)) = K(x,1 / z)
    ]]></literal>
    <justification jstring="[para(79(a,1),5768(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="79 5768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5810">
    <literal><![CDATA[
      T(x,((y * z) \ y) \ 1) = T(x,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),5772(a,2,2))].">
      <j1 rule="para" parents="9 5772"/>
    </justification>
  </clause>

  <clause id="5812">
    <literal><![CDATA[
      T(x,T(y,z) \ 1) = T(x,(y * z) \ z)
    ]]></literal>
    <justification jstring="[para(22(a,2),5772(a,1,2,1))].">
      <j1 rule="para" parents="22 5772"/>
    </justification>
  </clause>

  <clause id="5813">
    <literal><![CDATA[
      T(x,y \ (y / z)) = T(x,z \ 1)
    ]]></literal>
    <justification jstring="[para(79(a,1),5772(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="79 5772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5814">
    <literal><![CDATA[
      T(x \ y,y \ x) != z
    ]]></literal>
    <literal><![CDATA[
      ((x \ y) \ 1) \ 1 = z
    ]]></literal>
    <justification jstring="[para(5772(a,1),432(a,1))].">
      <j1 rule="para" parents="5772 432"/>
    </justification>
  </clause>

  <clause id="5815">
    <literal><![CDATA[
      K(x,T(x,y) / z) = K(x,z \ T(x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,3407,a(flip),b,5773,a)].">
      <j1 rule="hyper" parents="63 3407 5773"/>
    </justification>
  </clause>

  <clause id="5816">
    <literal><![CDATA[
      K(x \ 1,x / y) = K(x \ 1,y \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1380,a(flip),b,5773,a)].">
      <j1 rule="hyper" parents="63 1380 5773"/>
    </justification>
  </clause>

  <clause id="5817">
    <literal><![CDATA[
      T(x,y) != K(z,u \ y)
    ]]></literal>
    <literal><![CDATA[
      K(z,y / u) = x
    ]]></literal>
    <justification jstring="[para(5773(a,1),49(a,1)),flip(a)].">
      <j1 rule="para" parents="5773 49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5818">
    <literal><![CDATA[
      K(x,(y \ z) \ z) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(76(a,1),5773(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="76 5773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5819">
    <literal><![CDATA[
      T(x,K(y,x / z)) = T(x,K(y,z \ x))
    ]]></literal>
    <justification jstring="[para(5773(a,1),3613(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5773 3613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5820">
    <literal><![CDATA[
      K(x,K(y,z \ x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,x / z)) = u
    ]]></literal>
    <justification jstring="[para(5773(a,1),4393(a,1,2))].">
      <j1 rule="para" parents="5773 4393"/>
    </justification>
  </clause>

  <clause id="5822">
    <literal><![CDATA[
      K(x,y \ (y / z)) = K(x,(z \ u) / u)
    ]]></literal>
    <justification jstring="[hyper(333,a,5061,a,b,5776,a),flip(a)].">
      <j1 rule="hyper" parents="333 5061 5776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5824">
    <literal><![CDATA[
      T(x * y,y \ 1) = ((x * y) \ x) \ x
    ]]></literal>
    <justification jstring="[hyper(432,a,5801,a),flip(a)].">
      <j1 rule="hyper" parents="432 5801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5825">
    <literal><![CDATA[
      T(x / ((y * z) \ y),z \ 1) = ((y * z) \ y) \ x
    ]]></literal>
    <justification jstring="[hyper(423,a,5801,a),flip(a)].">
      <j1 rule="hyper" parents="423 5801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5826">
    <literal><![CDATA[
      ((x * y) \ x) * T(z,y \ 1) = z * ((x * y) \ x)
    ]]></literal>
    <justification jstring="[hyper(126,a,5801,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="126 5801 22"/>
    </justification>
  </clause>

  <clause id="5828">
    <literal><![CDATA[
      T(x,y \ (y / z)) = T(x,1 / z)
    ]]></literal>
    <justification jstring="[hyper(124,a,5806,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 5806 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5829">
    <literal><![CDATA[
      K(x,L(1 / y,y,z)) = K(x,1 / y)
    ]]></literal>
    <justification jstring="[para(2883(a,2),5806(a,1,2))].">
      <j1 rule="para" parents="2883 5806"/>
    </justification>
  </clause>

  <clause id="5830">
    <literal><![CDATA[
      K(x,y \ (y / z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(5806(a,2),4618(a,1))].">
      <j1 rule="para" parents="5806 4618"/>
    </justification>
  </clause>

  <clause id="5831">
    <literal><![CDATA[
      ((x * y) \ x) \ T(((x * y) \ x) * z,y) = ((((x * y) \ x) \ 1) \ z) * (((x * y) \ x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(121,a,5810,a(flip),b,962,a)].">
      <j1 rule="hyper" parents="121 5810 962"/>
    </justification>
  </clause>

  <clause id="5835">
    <literal><![CDATA[
      (1 / ((x * y) \ x)) * T(z,y) = z * (1 / ((x * y) \ x))
    ]]></literal>
    <justification jstring="[para(5810(a,1),2993(a,1,2))].">
      <j1 rule="para" parents="5810 2993"/>
    </justification>
  </clause>

  <clause id="5836">
    <literal><![CDATA[
      T(T(x \ (x / y),z),y \ 1) = T(x \ (x / y),z)
    ]]></literal>
    <justification jstring="[hyper(836,a,5813,a),flip(a)].">
      <j1 rule="hyper" parents="836 5813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5838">
    <literal><![CDATA[
      (x \ (x / y)) * T(x,y \ 1) = x / y
    ]]></literal>
    <justification jstring="[hyper(126,a,5813,a(flip),b,112,a(flip))].">
      <j1 rule="hyper" parents="126 5813 112"/>
    </justification>
  </clause>

  <clause id="5841">
    <literal><![CDATA[
      K(x,(y \ 1) \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(5818(a,2),203(a,1)),flip(b)].">
      <j1 rule="para" parents="5818 203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5842">
    <literal><![CDATA[
      K(x,T(y,y \ z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(112(a,2),5818(a,1,2))].">
      <j1 rule="para" parents="112 5818"/>
    </justification>
  </clause>

  <clause id="5843">
    <literal><![CDATA[
      K(x,T(y,z / y)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(3665(a,2),5818(a,1,2))].">
      <j1 rule="para" parents="3665 5818"/>
    </justification>
  </clause>

  <clause id="5844">
    <literal><![CDATA[
      T(K(x,y),z * y) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(3649(a,2),5818(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3649 5818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5845">
    <literal><![CDATA[
      T(K(x,y),y * z) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(9(a,1),5842(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 5842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5846">
    <literal><![CDATA[
      T(K(x,y),z * y) = T(K(x,y),y * z)
    ]]></literal>
    <justification jstring="[hyper(333,a,5844,a,b,5845,a)].">
      <j1 rule="hyper" parents="333 5844 5845"/>
    </justification>
  </clause>

  <clause id="5847">
    <literal><![CDATA[
      (x * y) * K(z,T(x,y)) = K(z,x) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(126,a,5845,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="126 5845 22"/>
    </justification>
  </clause>

  <clause id="5848">
    <literal><![CDATA[
      K(x,y) * K(y,T(x,z)) = K(x * z,K(x,y))
    ]]></literal>
    <justification jstring="[para(5845(a,1),5294(a,1,2))].">
      <j1 rule="para" parents="5845 5294"/>
    </justification>
  </clause>

  <clause id="5849">
    <literal><![CDATA[
      K(x,T(y / z,z / y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / z) = u
    ]]></literal>
    <justification jstring="[para(2231(a,2),5841(a,1,2))].">
      <j1 rule="para" parents="2231 5841"/>
    </justification>
  </clause>

  <clause id="5850">
    <literal><![CDATA[
      K(x,T(y \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(1 / y,z)) = u
    ]]></literal>
    <justification jstring="[para(2383(a,1),5841(a,1,2))].">
      <j1 rule="para" parents="2383 5841"/>
    </justification>
  </clause>

  <clause id="5851">
    <literal><![CDATA[
      K(x,T(y / z,y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / z) = u
    ]]></literal>
    <justification jstring="[para(2496(a,2),5841(a,1,2))].">
      <j1 rule="para" parents="2496 5841"/>
    </justification>
  </clause>

  <clause id="5852">
    <literal><![CDATA[
      K((x \ y) \ 1,z) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(39,a,4367,a,b,5771,a(flip))].">
      <j1 rule="hyper" parents="39 4367 5771"/>
    </justification>
  </clause>

  <clause id="5853">
    <literal><![CDATA[
      K(x,(y \ z) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(5771(a,2),4382(a,1))].">
      <j1 rule="para" parents="5771 4382"/>
    </justification>
  </clause>

  <clause id="5854">
    <literal><![CDATA[
      K((T(x,y) \ T(z,y)) \ 1,x) = K(z \ x,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(5677,a,5852,a)].">
      <j1 rule="hyper" parents="5677 5852"/>
    </justification>
  </clause>

  <clause id="5855">
    <literal><![CDATA[
      K((x \ (y * z)) \ 1,y) = K((y / (z \ 1)) \ x,y)
    ]]></literal>
    <justification jstring="[hyper(5398,a,5852,a)].">
      <j1 rule="hyper" parents="5398 5852"/>
    </justification>
  </clause>

  <clause id="5856">
    <literal><![CDATA[
      K(1 / (x \ y),z) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(3400,a,5852,a)].">
      <j1 rule="hyper" parents="3400 5852"/>
    </justification>
  </clause>

  <clause id="5857">
    <literal><![CDATA[
      K(((x * y) \ x) \ 1,z) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,705,a(flip),b,5852,a),flip(a)].">
      <j1 rule="hyper" parents="333 705 5852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5858">
    <literal><![CDATA[
      x \ (((y \ (x * z)) * y) / z) = K((y / z) \ x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,4956,a,b,5852,a)].">
      <j1 rule="hyper" parents="63 4956 5852"/>
    </justification>
  </clause>

  <clause id="5859">
    <literal><![CDATA[
      x \ (y * T(y \ x,z)) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,4483,a,b,5852,a)].">
      <j1 rule="hyper" parents="63 4483 5852"/>
    </justification>
  </clause>

  <clause id="5860">
    <literal><![CDATA[
      x * T(x \ y,z) = y * K(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(126,a,5852,a(flip),b,4483,a),flip(a)].">
      <j1 rule="hyper" parents="126 5852 4483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5861">
    <literal><![CDATA[
      K((x * y) \ x,z) = K(y \ 1,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),5852(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 5852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5862">
    <literal><![CDATA[
      K(T(x,y) \ 1,z) = K((x * y) \ y,z)
    ]]></literal>
    <justification jstring="[para(22(a,2),5852(a,1,1,1))].">
      <j1 rule="para" parents="22 5852"/>
    </justification>
  </clause>

  <clause id="5863">
    <literal><![CDATA[
      K(x \ (x / y),z) = K(y \ 1,z)
    ]]></literal>
    <justification jstring="[para(79(a,1),5852(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="79 5852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5864">
    <literal><![CDATA[
      K(L(x \ y,x,z) \ 1,u) = K((z * y) \ (z * x),u)
    ]]></literal>
    <justification jstring="[para(99(a,2),5852(a,1,1,1))].">
      <j1 rule="para" parents="99 5852"/>
    </justification>
  </clause>

  <clause id="5867">
    <literal><![CDATA[
      K((K(x,y) * z) \ 1,u) = K(z \ K(y,x),u)
    ]]></literal>
    <justification jstring="[para(4567(a,1),5852(a,1,1,1))].">
      <j1 rule="para" parents="4567 5852"/>
    </justification>
  </clause>

  <clause id="5868">
    <literal><![CDATA[
      K(((x * y) \ x) \ 1,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) = u
    ]]></literal>
    <justification jstring="[para(5852(a,2),4614(a,1))].">
      <j1 rule="para" parents="5852 4614"/>
    </justification>
  </clause>

  <clause id="5870">
    <literal><![CDATA[
      (((x \ y) * z) \ z) * ((x \ y) * z) = z * K(y \ x,(x \ y) * z)
    ]]></literal>
    <justification jstring="[para(5852(a,1),4977(a,2,2))].">
      <j1 rule="para" parents="5852 4977"/>
    </justification>
  </clause>

  <clause id="5871">
    <literal><![CDATA[
      (x \ y) * K((x \ 1) \ (x \ y),z) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[para(5852(a,1),4489(a,1,2))].">
      <j1 rule="para" parents="5852 4489"/>
    </justification>
  </clause>

  <clause id="5872">
    <literal><![CDATA[
      x * K((y * z) \ x,y) = z * ((y \ (z \ x)) * y)
    ]]></literal>
    <justification jstring="[para(5852(a,1),5203(a,1,2))].">
      <j1 rule="para" parents="5852 5203"/>
    </justification>
  </clause>

  <clause id="5873">
    <literal><![CDATA[
      x * K((y * z) \ x,z) = y * ((z \ (y \ x)) * z)
    ]]></literal>
    <justification jstring="[para(5852(a,1),5282(a,1,2))].">
      <j1 rule="para" parents="5852 5282"/>
    </justification>
  </clause>

  <clause id="5874">
    <literal><![CDATA[
      K(L(x \ y,z,u) \ 1,w) = L(K(y \ x,w),z,u)
    ]]></literal>
    <justification jstring="[para(5852(a,1),5369(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5852 5369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5875">
    <literal><![CDATA[
      (1 / x) * K(y \ (1 / x),z) = K((y * x) \ 1,z) / x
    ]]></literal>
    <justification jstring="[para(5852(a,1),5606(a,1,2))].">
      <j1 rule="para" parents="5852 5606"/>
    </justification>
  </clause>

  <clause id="5877">
    <literal><![CDATA[
      K(1 / L(x \ y,z,u),w) = L(K(y \ x,w),z,u)
    ]]></literal>
    <justification jstring="[para(5856(a,1),5390(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5856 5390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5879">
    <literal><![CDATA[
      T(((x * y) \ x) \ 1,z) = ((x * y) \ x) \ K(y,z)
    ]]></literal>
    <justification jstring="[hyper(121,a,5857,a(flip),b,4216,a),flip(a)].">
      <j1 rule="hyper" parents="121 5857 4216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5881">
    <literal><![CDATA[
      (1 / ((x * y) \ x)) * K(y,z) = T(1 / ((x * y) \ x),z)
    ]]></literal>
    <justification jstring="[para(5857(a,1),4282(a,1,2))].">
      <j1 rule="para" parents="5857 4282"/>
    </justification>
  </clause>

  <clause id="5888">
    <literal><![CDATA[
      K(x \ (x / y),z) = y * T(y \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,4216,a,b,5863,a),flip(a)].">
      <j1 rule="hyper" parents="333 4216 5863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5896">
    <literal><![CDATA[
      T(x,T(x,y) / z) = T(x,z \ T(x,y))
    ]]></literal>
    <justification jstring="[hyper(124,a,5815,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 5815 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5897">
    <literal><![CDATA[
      T(x,K(y,(z / x) \ 1)) = T(x,K(y,z \ x))
    ]]></literal>
    <justification jstring="[para(5055(a,2),5819(a,1,2))].">
      <j1 rule="para" parents="5055 5819"/>
    </justification>
  </clause>

  <clause id="5898">
    <literal><![CDATA[
      x / T(x * y,y \ 1) = L(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(197,a,5824,a,b,389,a)].">
      <j1 rule="hyper" parents="197 5824 389"/>
    </justification>
  </clause>

  <clause id="5899">
    <literal><![CDATA[
      (x \ 1) * (((y * x) \ y) \ y) = R(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(126,a,5824,a(flip),b,609,a)].">
      <j1 rule="hyper" parents="126 5824 609"/>
    </justification>
  </clause>

  <clause id="5900">
    <literal><![CDATA[
      T(x * (1 / y),y) = ((x * (1 / y)) \ x) \ x
    ]]></literal>
    <justification jstring="[para(79(a,1),5824(a,1,2))].">
      <j1 rule="para" parents="79 5824"/>
    </justification>
  </clause>

  <clause id="5901">
    <literal><![CDATA[
      T(K(x,y),z * y) * K(y,x) = K(K(x,y),y * z)
    ]]></literal>
    <justification jstring="[para(5846(a,2),4449(a,1,1))].">
      <j1 rule="para" parents="5846 4449"/>
    </justification>
  </clause>

  <clause id="5902">
    <literal><![CDATA[
      x \ (y * K(x \ y,z)) = T(x \ y,z)
    ]]></literal>
    <justification jstring="[para(5859(a,1),70(a,1,2,2))].">
      <j1 rule="para" parents="5859 70"/>
    </justification>
  </clause>

  <clause id="5903">
    <literal><![CDATA[
      L(K(x \ (y \ z),u),y \ z,y) = z \ (y * (x * T(x \ (y \ z),u)))
    ]]></literal>
    <justification jstring="[para(5859(a,1),515(a,1,1))].">
      <j1 rule="para" parents="5859 515"/>
    </justification>
  </clause>

  <clause id="5904">
    <literal><![CDATA[
      x \ (y \ T(y * x,z)) = K((y \ 1) \ x,z)
    ]]></literal>
    <justification jstring="[para(953(a,1),5859(a,1,2))].">
      <j1 rule="para" parents="953 5859"/>
    </justification>
  </clause>

  <clause id="5905">
    <literal><![CDATA[
      x \ (y \ ((z \ (y * x)) * z)) = K((y \ z) \ x,z)
    ]]></literal>
    <justification jstring="[para(1276(a,1),5859(a,1,2))].">
      <j1 rule="para" parents="1276 5859"/>
    </justification>
  </clause>

  <clause id="5907">
    <literal><![CDATA[
      K((x \ y) \ y,z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(4978,a,5860,a),flip(a)].">
      <j1 rule="hyper" parents="4978 5860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5908">
    <literal><![CDATA[
      K(x / y,z) * x = x * K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(4851,a,5860,a)].">
      <j1 rule="hyper" parents="4851 5860"/>
    </justification>
  </clause>

  <clause id="5909">
    <literal><![CDATA[
      x \ T(x * y,z) = y * K((x \ 1) \ y,z)
    ]]></literal>
    <justification jstring="[hyper(1017,a,5860,a)].">
      <j1 rule="hyper" parents="1017 5860"/>
    </justification>
  </clause>

  <clause id="5910">
    <literal><![CDATA[
      T(K(x / y,z),x) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(253,a,4243,a,b,5860,a(flip))].">
      <j1 rule="hyper" parents="253 4243 5860"/>
    </justification>
  </clause>

  <clause id="5913">
    <literal><![CDATA[
      (x * K((y \ 1) \ x,z)) * y = T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(125,a,5860,a(flip),b,4107,a(flip))].">
      <j1 rule="hyper" parents="125 5860 4107"/>
    </justification>
  </clause>

  <clause id="5914">
    <literal><![CDATA[
      (x * K(y \ x,z)) / y = T(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(123,a,5860,a(flip),b,471,a)].">
      <j1 rule="hyper" parents="123 5860 471"/>
    </justification>
  </clause>

  <clause id="5915">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ y,z) = T(y * K(x \ y,z),y)
    ]]></literal>
    <justification jstring="[para(5860(a,1),1704(a,2,1))].">
      <j1 rule="para" parents="5860 1704"/>
    </justification>
  </clause>

  <clause id="5917">
    <literal><![CDATA[
      K((x \ y) \ y,y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,2714,a(flip),b,5907,a),flip(a)].">
      <j1 rule="hyper" parents="333 2714 5907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5918">
    <literal><![CDATA[
      K(T(x,x \ y),z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[para(112(a,2),5907(a,1,1))].">
      <j1 rule="para" parents="112 5907"/>
    </justification>
  </clause>

  <clause id="5919">
    <literal><![CDATA[
      K((x \ y) \ y,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(5907(a,2),2742(a,1))].">
      <j1 rule="para" parents="5907 2742"/>
    </justification>
  </clause>

  <clause id="5920">
    <literal><![CDATA[
      T(K(x,y),z * x) = K(T(x,z),y)
    ]]></literal>
    <justification jstring="[para(3649(a,2),5907(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3649 5907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5921">
    <literal><![CDATA[
      K(x / y,x) = K(y \ x,x)
    ]]></literal>
    <justification jstring="[para(79(a,1),5917(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="79 5917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5922">
    <literal><![CDATA[
      K((x * y) / z,x) = K((z / y) \ x,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,5565,a,b,5921,a)].">
      <j1 rule="hyper" parents="63 5565 5921"/>
    </justification>
  </clause>

  <clause id="5923">
    <literal><![CDATA[
      K(x,K(y,x / z)) * K(x / z,y) = K(z \ x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,5300,a,b,5910,a)].">
      <j1 rule="hyper" parents="63 5300 5910"/>
    </justification>
  </clause>

  <clause id="5924">
    <literal><![CDATA[
      K(x / y,z \ x) = K(y \ x,x / z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5773,a(flip),b,5910,a)].">
      <j1 rule="hyper" parents="63 5773 5910"/>
    </justification>
  </clause>

  <clause id="5925">
    <literal><![CDATA[
      T(K(x,y),x * z) = K(T(x,z),y)
    ]]></literal>
    <justification jstring="[para(9(a,1),5918(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 5918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5927">
    <literal><![CDATA[
      K(((x \ 1) * y) \ y,z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,5286,a(flip),b,5862,a),flip(a)].">
      <j1 rule="hyper" parents="63 5286 5862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5933">
    <literal><![CDATA[
      K(x \ (x / y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ 1,z) = u
    ]]></literal>
    <justification jstring="[para(5888(a,2),4471(a,1))].">
      <j1 rule="para" parents="5888 4471"/>
    </justification>
  </clause>

  <clause id="5934">
    <literal><![CDATA[
      K(L(x,y,z) / u,x) = K(u \ L(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(35,a,2728,a(flip),b,5908,a),flip(a)].">
      <j1 rule="hyper" parents="35 2728 5908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5935">
    <literal><![CDATA[
      (x * K(y,z)) / (x / y) = T(x / (x / y),z)
    ]]></literal>
    <justification jstring="[para(79(a,1),5914(a,1,1,2,1))].">
      <j1 rule="para" parents="79 5914"/>
    </justification>
  </clause>

  <clause id="5936">
    <literal><![CDATA[
      T(x,((y * K((1 / z) \ y,u)) / (z \ 1)) * w) = T(x,T(y / (1 / z),u) * w)
    ]]></literal>
    <justification jstring="[para(5914(a,1),3183(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5914 3183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5937">
    <literal><![CDATA[
      K((1 / x) \ y,y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[para(74(a,1),5922(a,1,1)),flip(a)].">
      <j1 rule="para" parents="74 5922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5938">
    <literal><![CDATA[
      K((x \ 1) \ y,y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,4763,a(flip),b,5937,a)].">
      <j1 rule="hyper" parents="63 4763 5937"/>
    </justification>
  </clause>

  <clause id="5939">
    <literal><![CDATA[
      K(x * (y \ 1),x) = K(y \ x,x)
    ]]></literal>
    <justification jstring="[para(76(a,1),5937(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="76 5937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5940">
    <literal><![CDATA[
      K((x \ 1) \ y,y) = K(x * y,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,4543,a,b,5938,a),flip(a)].">
      <j1 rule="hyper" parents="333 4543 5938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5941">
    <literal><![CDATA[
      K((x \ 1) * y,y) = K(x \ y,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,4543,a,b,5939,a)].">
      <j1 rule="hyper" parents="63 4543 5939"/>
    </justification>
  </clause>

  <clause id="5942">
    <literal><![CDATA[
      T(x * K(y \ x,x),y \ 1) = R(x,y \ 1,x)
    ]]></literal>
    <justification jstring="[para(5939(a,1),4650(a,1,1,2))].">
      <j1 rule="para" parents="5939 4650"/>
    </justification>
  </clause>

  <clause id="5943">
    <literal><![CDATA[
      x * (K(y \ x,x) * (y \ 1)) = T(x * (y \ 1),x)
    ]]></literal>
    <justification jstring="[para(5939(a,1),4701(a,1,2,1))].">
      <j1 rule="para" parents="5939 4701"/>
    </justification>
  </clause>

  <clause id="5944">
    <literal><![CDATA[
      K((1 / x) * y,y) = K(x \ y,y)
    ]]></literal>
    <justification jstring="[para(79(a,1),5940(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="79 5940"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5945">
    <literal><![CDATA[
      a((x \ y) * K((y / x) \ y,y / x),y / (y / x),z) = a(x \ y,x,z)
    ]]></literal>
    <justification jstring="[para(5924(a,1),5270(a,1,1,2))].">
      <j1 rule="para" parents="5924 5270"/>
    </justification>
  </clause>

  <clause id="5949">
    <literal><![CDATA[
      K(x,(y * z) \ y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(11(a,1),5830(a,1,2,2))].">
      <j1 rule="para" parents="11 5830"/>
    </justification>
  </clause>

  <clause id="5950">
    <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(446(a,1),5830(a,1,2,2))].">
      <j1 rule="para" parents="446 5830"/>
    </justification>
  </clause>

  <clause id="5951">
    <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(99(a,2),5853(a,1,2,1))].">
      <j1 rule="para" parents="99 5853"/>
    </justification>
  </clause>

  <clause id="5952">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ 1) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u \ K(z,y)) = w
    ]]></literal>
    <justification jstring="[para(4567(a,1),5853(a,1,2,1))].">
      <j1 rule="para" parents="4567 5853"/>
    </justification>
  </clause>

  <clause id="5953">
    <literal><![CDATA[
      K(x,1 / (y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(4615(a,2),5853(a,1))].">
      <j1 rule="para" parents="4615 5853"/>
    </justification>
  </clause>

  <clause id="5954">
    <literal><![CDATA[
      T(K(x,y / z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(5150(a,2),5853(a,1))].">
      <j1 rule="para" parents="5150 5853"/>
    </justification>
  </clause>

  <clause id="5955">
    <literal><![CDATA[
      K((x \ y) \ 1,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(10(a,1),5868(a,1,1,1,1))].">
      <j1 rule="para" parents="10 5868"/>
    </justification>
  </clause>

  <clause id="5958">
    <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(3380(a,1),5954(a,1))].">
      <j1 rule="para" parents="3380 5954"/>
    </justification>
  </clause>

  <clause id="5960">
    <literal><![CDATA[
      K(1 / (x \ y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(3333(a,2),5955(a,1))].">
      <j1 rule="para" parents="3333 5955"/>
    </justification>
  </clause>

  <clause id="5962">
    <literal><![CDATA[
      x \ (y * (z * T(z \ (y \ x),u))) != w
    ]]></literal>
    <literal><![CDATA[
      K((y * z) \ x,u) = w
    ]]></literal>
    <justification jstring="[para(4955(a,2),5955(a,1))].">
      <j1 rule="para" parents="4955 5955"/>
    </justification>
  </clause>

  <clause id="5963">
    <literal><![CDATA[
      T(x,K(y,(x \ z) \ 1)) / (z * T(z \ x,y)) = (x * (x / (z * T(z \ x,y)))) / x
    ]]></literal>
    <justification jstring="[para(5770(a,1),3366(a,1,1,2))].">
      <j1 rule="para" parents="5770 3366"/>
    </justification>
  </clause>

  <clause id="5964">
    <literal><![CDATA[
      K(x,(T(y,z) * (y \ u)) \ 1) = K(x,u \ K(z,y))
    ]]></literal>
    <justification jstring="[para(4242(a,2),5782(a,1,2,1))].">
      <j1 rule="para" parents="4242 5782"/>
    </justification>
  </clause>

  <clause id="5965">
    <literal><![CDATA[
      T((x \ L(x,y,z)) \ 1,L(x,u,w)) = (x \ L(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(2567(a,1),5785(a,1,1,2))].">
      <j1 rule="para" parents="2567 5785"/>
    </justification>
  </clause>

  <clause id="5966">
    <literal><![CDATA[
      ((x \ y) * z) * K(x,T(x \ y,z)) = (y / x) * z
    ]]></literal>
    <justification jstring="[hyper(333,a,4875,a(flip),b,5847,a),flip(a)].">
      <j1 rule="hyper" parents="333 4875 5847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5967">
    <literal><![CDATA[
      K(T(K(x,y) * z,u) \ 1,w) = T(K(z \ K(y,x),w),u)
    ]]></literal>
    <justification jstring="[para(5867(a,1),5284(a,2,1))].">
      <j1 rule="para" parents="5867 5284"/>
    </justification>
  </clause>

  <clause id="5968">
    <literal><![CDATA[
      (x * T(x \ y,z)) / K((x / y) \ 1,z) = T(y,K(z,x \ y))
    ]]></literal>
    <justification jstring="[hyper(63,a,5319,a,b,5897,a)].">
      <j1 rule="hyper" parents="63 5319 5897"/>
    </justification>
  </clause>

  <clause id="5969">
    <literal><![CDATA[
      x / T(x * (1 / y),y) = (x * (1 / y)) \ x
    ]]></literal>
    <justification jstring="[hyper(197,a,5900,a,b,xx)].">
      <j1 rule="hyper" parents="197 5900"/>
    </justification>
  </clause>

  <clause id="5970">
    <literal><![CDATA[
      T(x,y) / (z \ x) = z * K(((z \ x) \ 1) \ z,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,4086,a(flip),b,5909,a)].">
      <j1 rule="hyper" parents="63 4086 5909"/>
    </justification>
  </clause>

  <clause id="5971">
    <literal><![CDATA[
      K((x \ 1) \ y,x) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(34,a,5479,a(flip),b,5909,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="34 5479 5909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5972">
    <literal><![CDATA[
      T(x * K((y \ 1) \ x,z),y) = y \ T(x * y,z)
    ]]></literal>
    <justification jstring="[para(5909(a,1),4112(a,1,1))].">
      <j1 rule="para" parents="5909 4112"/>
    </justification>
  </clause>

  <clause id="5973">
    <literal><![CDATA[
      K((x \ 1) * y,x \ 1) = K(x \ y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,4764,a(flip),b,5971,a),flip(a)].">
      <j1 rule="hyper" parents="63 4764 5971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5974">
    <literal><![CDATA[
      (x / y) * T(y,z) = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(37,a,477,a,b,5935,a)].">
      <j1 rule="hyper" parents="37 477 5935"/>
    </justification>
  </clause>

  <clause id="5975">
    <literal><![CDATA[
      (x / T(y,z)) * K(y,z) = x / y
    ]]></literal>
    <justification jstring="[hyper(1434,a,5974,a),flip(a)].">
      <j1 rule="hyper" parents="1434 5974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5976">
    <literal><![CDATA[
      x \ ((x / y) * T(y,z)) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(564,a,5974,a)].">
      <j1 rule="hyper" parents="564 5974"/>
    </justification>
  </clause>

  <clause id="5977">
    <literal><![CDATA[
      (x * K(y,z)) / T(y,z) = x / y
    ]]></literal>
    <justification jstring="[hyper(138,a,5974,a)].">
      <j1 rule="hyper" parents="138 5974"/>
    </justification>
  </clause>

  <clause id="5978">
    <literal><![CDATA[
      (x / y) \ (x * K(y,z)) = T(y,z)
    ]]></literal>
    <justification jstring="[hyper(129,a,5974,a)].">
      <j1 rule="hyper" parents="129 5974"/>
    </justification>
  </clause>

  <clause id="5979">
    <literal><![CDATA[
      (x * T(y,z)) / y = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,1419,a,b,5974,a)].">
      <j1 rule="hyper" parents="63 1419 5974"/>
    </justification>
  </clause>

  <clause id="5980">
    <literal><![CDATA[
      (x * y) * R(1 / x,x,y) = y * K(x * y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,3842,a(flip),b,5974,a)].">
      <j1 rule="hyper" parents="63 3842 5974"/>
    </justification>
  </clause>

  <clause id="5981">
    <literal><![CDATA[
      (x / y) * ((y \ z) \ z) = x * K(y,y \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,328,a(flip),b,5974,a)].">
      <j1 rule="hyper" parents="63 328 5974"/>
    </justification>
  </clause>

  <clause id="5982">
    <literal><![CDATA[
      (x * K(y,z)) * y = x * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(125,a,5974,a(flip),b,1419,a)].">
      <j1 rule="hyper" parents="125 5974 1419"/>
    </justification>
  </clause>

  <clause id="5983">
    <literal><![CDATA[
      (x / T(y,z)) \ (x / y) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(121,a,1420,a(flip),b,5974,a(flip))].">
      <j1 rule="hyper" parents="121 1420 5974"/>
    </justification>
  </clause>

  <clause id="5984">
    <literal><![CDATA[
      (x * y) * K(y,z) = x * T(y,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),5974(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 5974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5985">
    <literal><![CDATA[
      (x / y) \ (x * K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) = u
    ]]></literal>
    <justification jstring="[para(5974(a,1),342(a,1,2))].">
      <j1 rule="para" parents="5974 342"/>
    </justification>
  </clause>

  <clause id="5986">
    <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(5974(a,1),963(a,1,2,1))].">
      <j1 rule="para" parents="5974 963"/>
    </justification>
  </clause>

  <clause id="5987">
    <literal><![CDATA[
      (x / T(y,z)) * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x / y = u
    ]]></literal>
    <justification jstring="[para(5974(a,1),1434(a,1))].">
      <j1 rule="para" parents="5974 1434"/>
    </justification>
  </clause>

  <clause id="5988">
    <literal><![CDATA[
      K(x,y) * T(y * x,z) = (x * y) * K(y * x,z)
    ]]></literal>
    <justification jstring="[para(4200(a,2),5974(a,1,1))].">
      <j1 rule="para" parents="4200 5974"/>
    </justification>
  </clause>

  <clause id="5989">
    <literal><![CDATA[
      (x / T(y,z)) * T(y,u) = (x * K(z,y)) * K(y,u)
    ]]></literal>
    <justification jstring="[para(5460(a,1),5974(a,1,1))].">
      <j1 rule="para" parents="5460 5974"/>
    </justification>
  </clause>

  <clause id="5990">
    <literal><![CDATA[
      (x * K(y,z)) \ x = K(z,y)
    ]]></literal>
    <justification jstring="[para(5974(a,1),5484(a,1,1))].">
      <j1 rule="para" parents="5974 5484"/>
    </justification>
  </clause>

  <clause id="5991">
    <literal><![CDATA[
      K(x,((y / z) * u) \ (y * u)) = ((y * K(z,x)) * u) \ (y * u)
    ]]></literal>
    <justification jstring="[para(5974(a,1),5536(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5974 5536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5992">
    <literal><![CDATA[
      (((x \ y) \ y) * K(z,u)) \ T(x,x \ y) = K(u,z)
    ]]></literal>
    <justification jstring="[hyper(693,a,5990,a)].">
      <j1 rule="hyper" parents="693 5990"/>
    </justification>
  </clause>

  <clause id="5994">
    <literal><![CDATA[
      x / K(y,z) = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(198,a,5990,a)].">
      <j1 rule="hyper" parents="198 5990"/>
    </justification>
  </clause>

  <clause id="5995">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,y) = x
    ]]></literal>
    <justification jstring="[hyper(144,a,5990,a),flip(a)].">
      <j1 rule="hyper" parents="144 5990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5996">
    <literal><![CDATA[
      (x * (y * z)) * K(L(z,y,x),u) = x * (y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(39,a,5535,a,b,5990,a),flip(a)].">
      <j1 rule="hyper" parents="39 5535 5990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5997">
    <literal><![CDATA[
      x * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      u * K(z,y) = x
    ]]></literal>
    <justification jstring="[para(5990(a,1),137(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5990 137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5998">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,y) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(5990(a,1),274(a,1,2))].">
      <j1 rule="para" parents="5990 274"/>
    </justification>
  </clause>

  <clause id="5999">
    <literal><![CDATA[
      x / K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x * K(z,y) = u
    ]]></literal>
    <justification jstring="[para(5990(a,1),301(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5990 301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6000">
    <literal><![CDATA[
      x \ y != (z * K(u,w)) * K(w,u)
    ]]></literal>
    <literal><![CDATA[
      y / z = x
    ]]></literal>
    <justification jstring="[para(5990(a,1),354(a,2,2))].">
      <j1 rule="para" parents="5990 354"/>
    </justification>
  </clause>

  <clause id="6001">
    <literal><![CDATA[
      ((x * K(y,z)) \ x) \ u = K(y,z) * u
    ]]></literal>
    <justification jstring="[para(5990(a,2),4567(a,1,1))].">
      <j1 rule="para" parents="5990 4567"/>
    </justification>
  </clause>

  <clause id="6002">
    <literal><![CDATA[
      (x \ R(x,y,x)) \ K(x * y,x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(4920(a,1),5990(a,1,1))].">
      <j1 rule="para" parents="4920 5990"/>
    </justification>
  </clause>

  <clause id="6003">
    <literal><![CDATA[
      K(x,L(y \ 1,z,u) \ 1) = (w * L(K(y,x),z,u)) \ w
    ]]></literal>
    <justification jstring="[para(5372(a,1),5990(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5372 5990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6004">
    <literal><![CDATA[
      K(x,y) = (x \ T(y,x)) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(5454(a,1),5990(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5454 5990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6005">
    <literal><![CDATA[
      (x * y) \ (x * T(y,z)) = K(y,z)
    ]]></literal>
    <justification jstring="[para(5455(a,1),5990(a,1,1))].">
      <j1 rule="para" parents="5455 5990"/>
    </justification>
  </clause>

  <clause id="6006">
    <literal><![CDATA[
      K(x,R(y,y \ z,u)) = (w * R(K(y,x),z,u)) \ w
    ]]></literal>
    <justification jstring="[para(5560(a,1),5990(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5560 5990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6007">
    <literal><![CDATA[
      ((x \ 1) \ K(y,x)) \ ((x \ 1) \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[para(5749(a,1),5990(a,1,1))].">
      <j1 rule="para" parents="5749 5990"/>
    </justification>
  </clause>

  <clause id="6009">
    <literal><![CDATA[
      (x * (y \ z)) / K(y \ z,y) = x * (z / y)
    ]]></literal>
    <justification jstring="[hyper(333,a,5523,a(flip),b,5994,a),flip(a)].">
      <j1 rule="hyper" parents="333 5523 5994"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6011">
    <literal><![CDATA[
      (x * (y / z)) * K(z \ y,z) = x * (z \ y)
    ]]></literal>
    <justification jstring="[hyper(125,a,5523,a(flip),b,5994,a)].">
      <j1 rule="hyper" parents="125 5523 5994"/>
    </justification>
  </clause>

  <clause id="6012">
    <literal><![CDATA[
      (x / (y \ z)) * K(y \ z,y) = x / (z / y)
    ]]></literal>
    <justification jstring="[hyper(125,a,5520,a(flip),b,5994,a)].">
      <j1 rule="hyper" parents="125 5520 5994"/>
    </justification>
  </clause>

  <clause id="6014">
    <literal><![CDATA[
      (T(x,y) / y) * K(y,x) = x / y
    ]]></literal>
    <justification jstring="[hyper(125,a,5473,a(flip),b,5994,a)].">
      <j1 rule="hyper" parents="125 5473 5994"/>
    </justification>
  </clause>

  <clause id="6015">
    <literal><![CDATA[
      (K(x,y) * z) * K(y,x) = T(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(125,a,5304,a(flip),b,5994,a)].">
      <j1 rule="hyper" parents="125 5304 5994"/>
    </justification>
  </clause>

  <clause id="6016">
    <literal><![CDATA[
      (x \ K(x,y)) * K(y,x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(125,a,4686,a(flip),b,5994,a)].">
      <j1 rule="hyper" parents="125 4686 5994"/>
    </justification>
  </clause>

  <clause id="6018">
    <literal><![CDATA[
      (K(x,y) * K(y,z)) * K(y,x) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(125,a,2005,a(flip),b,5994,a)].">
      <j1 rule="hyper" parents="125 2005 5994"/>
    </justification>
  </clause>

  <clause id="6019">
    <literal><![CDATA[
      T(K(x,y) * z,K(x,y)) = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,5318,a,b,5994,a)].">
      <j1 rule="hyper" parents="63 5318 5994"/>
    </justification>
  </clause>

  <clause id="6020">
    <literal><![CDATA[
      T(K(x,y) \ z,K(y,x)) = z * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,5302,a,b,5994,a)].">
      <j1 rule="hyper" parents="63 5302 5994"/>
    </justification>
  </clause>

  <clause id="6021">
    <literal><![CDATA[
      K(x,y) \ (z * T(x,y)) = T(z * x,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(444,a,5481,a(flip),b,5994,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="444 5481 5994"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6023">
    <literal><![CDATA[
      T((K(x,y) * z) * K(y,x),K(x,y)) = z
    ]]></literal>
    <justification jstring="[hyper(253,a,5994,a(flip),b,11,a(flip))].">
      <j1 rule="hyper" parents="253 5994 11"/>
    </justification>
  </clause>

  <clause id="6024">
    <literal><![CDATA[
      (x * K(y,z)) \ x != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) = u
    ]]></literal>
    <justification jstring="[para(5994(a,1),345(a,1,1))].">
      <j1 rule="para" parents="5994 345"/>
    </justification>
  </clause>

  <clause id="6025">
    <literal><![CDATA[
      x / K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(z,y)) = K(z,y) \ u
    ]]></literal>
    <justification jstring="[para(5994(a,2),296(a,1))].">
      <j1 rule="para" parents="5994 296"/>
    </justification>
  </clause>

  <clause id="6027">
    <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(5994(a,1),632(a,1,1,1))].">
      <j1 rule="para" parents="5994 632"/>
    </justification>
  </clause>

  <clause id="6028">
    <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(5994(a,1),632(a,1,1))].">
      <j1 rule="para" parents="5994 632"/>
    </justification>
  </clause>

  <clause id="6029">
    <literal><![CDATA[
      ((K(x,y) / z) * (z * K(y,x))) \ (K(x,y) / z) = 1 / (z / K(x,y))
    ]]></literal>
    <justification jstring="[para(5994(a,1),2210(a,1,1,2))].">
      <j1 rule="para" parents="5994 2210"/>
    </justification>
  </clause>

  <clause id="6032">
    <literal><![CDATA[
      K(x,1 / (K(y,z) / u)) = K(x,u * K(z,y))
    ]]></literal>
    <justification jstring="[para(5994(a,1),5058(a,2,2))].">
      <j1 rule="para" parents="5994 5058"/>
    </justification>
  </clause>

  <clause id="6033">
    <literal><![CDATA[
      R(x * K(y,z),K(z,y),y) = (x * y) / ((z * y) / z)
    ]]></literal>
    <justification jstring="[para(5994(a,1),4450(a,1,1))].">
      <j1 rule="para" parents="5994 4450"/>
    </justification>
  </clause>

  <clause id="6035">
    <literal><![CDATA[
      T(x * K(y,z),K(z,y)) = K(y,z) * x
    ]]></literal>
    <justification jstring="[hyper(253,a,5995,a,b,4558,a)].">
      <j1 rule="hyper" parents="253 5995 4558"/>
    </justification>
  </clause>

  <clause id="6036">
    <literal><![CDATA[
      x * L(y,K(z,u),x * K(u,z)) = (x * K(u,z)) * (K(z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(125,a,5995,a(flip),b,190,a)].">
      <j1 rule="hyper" parents="125 5995 190"/>
    </justification>
  </clause>

  <clause id="6037">
    <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(5995(a,1),504(a,1,1))].">
      <j1 rule="para" parents="5995 504"/>
    </justification>
  </clause>

  <clause id="6038">
    <literal><![CDATA[
      (x * y) \ ((x * (y * K(z,u))) * K(u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y * K(z,u),K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(5995(a,1),752(a,1,1,2))].">
      <j1 rule="para" parents="5995 752"/>
    </justification>
  </clause>

  <clause id="6039">
    <literal><![CDATA[
      (x * K(y,z)) * (T(y,z) \ 1) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[para(5995(a,1),5729(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5995 5729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6040">
    <literal><![CDATA[
      ((x * (y * z)) / T(L(z,y,x),u)) \ (x * y) = K(L(z,y,x),u)
    ]]></literal>
    <justification jstring="[hyper(121,a,190,a(flip),b,5975,a)].">
      <j1 rule="hyper" parents="121 190 5975"/>
    </justification>
  </clause>

  <clause id="6042">
    <literal><![CDATA[
      (x / ((y * y) \ y)) * K(y \ 1,y) = x / (y \ 1)
    ]]></literal>
    <justification jstring="[para(716(a,1),5975(a,1,1,2))].">
      <j1 rule="para" parents="716 5975"/>
    </justification>
  </clause>

  <clause id="6043">
    <literal><![CDATA[
      ((x \ 1) \ y) * K(x \ 1,x * y) = y / (x \ 1)
    ]]></literal>
    <justification jstring="[para(3934(a,1),5975(a,1,1))].">
      <j1 rule="para" parents="3934 5975"/>
    </justification>
  </clause>

  <clause id="6045">
    <literal><![CDATA[
      (x * (y / x)) \ (K(x,x \ y) * T(y,z)) = K(y,z)
    ]]></literal>
    <justification jstring="[para(4535(a,1),5976(a,1,2,1))].">
      <j1 rule="para" parents="4535 5976"/>
    </justification>
  </clause>

  <clause id="6046">
    <literal><![CDATA[
      (x * K(y,z)) / y = (x / y) * K(y,z)
    ]]></literal>
    <justification jstring="[para(5977(a,1),5975(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5977 5975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6047">
    <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(5978(a,1),4990(a,1,2))].">
      <j1 rule="para" parents="5978 4990"/>
    </justification>
  </clause>

  <clause id="6048">
    <literal><![CDATA[
      T(x,y) / ((z / x) \ T(z * K(x,y),(z / x) \ 1)) = K((z / x) \ 1,z * K(x,y))
    ]]></literal>
    <justification jstring="[para(5978(a,1),4991(a,1,1))].">
      <j1 rule="para" parents="5978 4991"/>
    </justification>
  </clause>

  <clause id="6049">
    <literal><![CDATA[
      (T(x,y) \ 1) * y = (x \ 1) * T(y,x)
    ]]></literal>
    <justification jstring="[hyper(4506,a,5979,a)].">
      <j1 rule="hyper" parents="4506 5979"/>
    </justification>
  </clause>

  <clause id="6050">
    <literal><![CDATA[
      (x * ((y * z) / y)) * y = (x * z) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(125,a,5753,a(flip),b,5979,a)].">
      <j1 rule="hyper" parents="125 5753 5979"/>
    </justification>
  </clause>

  <clause id="6051">
    <literal><![CDATA[
      (x * (y * K(z,y))) * z = (x * y) * T(z,y)
    ]]></literal>
    <justification jstring="[hyper(125,a,5750,a(flip),b,5979,a)].">
      <j1 rule="hyper" parents="125 5750 5979"/>
    </justification>
  </clause>

  <clause id="6052">
    <literal><![CDATA[
      (x * (y \ z)) * T(y,y \ z) = (x * (z / y)) * y
    ]]></literal>
    <justification jstring="[hyper(125,a,5523,a(flip),b,5979,a),flip(a)].">
      <j1 rule="hyper" parents="125 5523 5979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6053">
    <literal><![CDATA[
      (x * T(y,z)) * T(z,y) = (x * y) * z
    ]]></literal>
    <justification jstring="[hyper(125,a,5455,a(flip),b,5979,a),flip(a)].">
      <j1 rule="hyper" parents="125 5455 5979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6054">
    <literal><![CDATA[
      T(x * K(y,z),y) = y \ (x * T(y,z))
    ]]></literal>
    <justification jstring="[para(5979(a,1),113(a,1,1))].">
      <j1 rule="para" parents="5979 113"/>
    </justification>
  </clause>

  <clause id="6055">
    <literal><![CDATA[
      (x * K(y,z)) * y != u
    ]]></literal>
    <literal><![CDATA[
      x * T(y,z) = u
    ]]></literal>
    <justification jstring="[para(5979(a,1),264(a,1,1)),flip(b)].">
      <j1 rule="para" parents="5979 264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6056">
    <literal><![CDATA[
      (x * ((y \ z) \ z)) / y = x * K(y,y \ z)
    ]]></literal>
    <justification jstring="[para(112(a,1),5979(a,1,1,2))].">
      <j1 rule="para" parents="112 5979"/>
    </justification>
  </clause>

  <clause id="6057">
    <literal><![CDATA[
      T(x * K(y,z),y) != u
    ]]></literal>
    <literal><![CDATA[
      y \ (x * T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(5979(a,1),423(a,1,1))].">
      <j1 rule="para" parents="5979 423"/>
    </justification>
  </clause>

  <clause id="6058">
    <literal><![CDATA[
      R(x,1 / T(y,z),y) / y = (x * (1 / T(y,z))) * K(y,z)
    ]]></literal>
    <justification jstring="[para(5538(a,1),5979(a,1,1))].">
      <j1 rule="para" parents="5538 5979"/>
    </justification>
  </clause>

  <clause id="6059">
    <literal><![CDATA[
      R(x,K(y,z),y) = x
    ]]></literal>
    <justification jstring="[hyper(4348,a,5982,a)].">
      <j1 rule="hyper" parents="4348 5982"/>
    </justification>
  </clause>

  <clause id="6062">
    <literal><![CDATA[
      ((x / y) * K(y,z)) \ (x * K(y,z)) = y
    ]]></literal>
    <justification jstring="[hyper(121,a,5974,a(flip),b,5982,a)].">
      <j1 rule="hyper" parents="121 5974 5982"/>
    </justification>
  </clause>

  <clause id="6063">
    <literal><![CDATA[
      ((x * y) * K(L(z,y,x),u)) \ (x * (y * T(z,u))) = L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(121,a,465,a(flip),b,5982,a)].">
      <j1 rule="hyper" parents="121 465 5982"/>
    </justification>
  </clause>

  <clause id="6065">
    <literal><![CDATA[
      (x * (y * T(z,u))) \ ((x * (y * K(z,u))) * z) = a(x,y * K(z,u),z)
    ]]></literal>
    <justification jstring="[para(5982(a,1),14(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="5982 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6066">
    <literal><![CDATA[
      x * T(y,z) != y * u
    ]]></literal>
    <literal><![CDATA[
      T(x * K(y,z),y) = u
    ]]></literal>
    <justification jstring="[para(5982(a,1),254(a,2)),flip(a)].">
      <j1 rule="para" parents="5982 254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6068">
    <literal><![CDATA[
      (x * T(y,z)) \ (x * K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(y \ 1,y,x * K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(5982(a,1),426(a,1,1))].">
      <j1 rule="para" parents="5982 426"/>
    </justification>
  </clause>

  <clause id="6069">
    <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(5982(a,1),504(a,1,2,2))].">
      <j1 rule="para" parents="5982 504"/>
    </justification>
  </clause>

  <clause id="6070">
    <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(5982(a,1),4923(a,1,2,1))].">
      <j1 rule="para" parents="5982 4923"/>
    </justification>
  </clause>

  <clause id="6071">
    <literal><![CDATA[
      R(x,K(y \ 1,z),y) = x
    ]]></literal>
    <justification jstring="[hyper(1872,a,6059,a)].">
      <j1 rule="hyper" parents="1872 6059"/>
    </justification>
  </clause>

  <clause id="6072">
    <literal><![CDATA[
      R(x * K(y,z),K(u,w),u) = (x * z) / T(z,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,5446,a,b,6059,a),flip(a)].">
      <j1 rule="hyper" parents="333 5446 6059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6073">
    <literal><![CDATA[
      (x * K(y,z)) * y = (x * y) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,5982,a,b,5984,a)].">
      <j1 rule="hyper" parents="333 5982 5984"/>
    </justification>
  </clause>

  <clause id="6074">
    <literal><![CDATA[
      (T(x,y) * T(y,x)) * K(T(y,x),z) = T(y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,3635,a(flip),b,5984,a),flip(a)].">
      <j1 rule="hyper" parents="333 3635 5984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6075">
    <literal><![CDATA[
      K(x,y) * (z * T(y,x)) = T(z * y,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(253,a,5984,a,b,4558,a),flip(a)].">
      <j1 rule="hyper" parents="253 5984 4558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6078">
    <literal><![CDATA[
      ((x * (y * z)) * K(z,u)) / (y * T(z,u)) = R(x,y * z,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(197,a,5984,a(flip),b,187,a)].">
      <j1 rule="hyper" parents="197 5984 187"/>
    </justification>
  </clause>

  <clause id="6081">
    <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(5984(a,1),566(a,1,2))].">
      <j1 rule="para" parents="5984 566"/>
    </justification>
  </clause>

  <clause id="6082">
    <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(5984(a,1),541(a,1,1))].">
      <j1 rule="para" parents="5984 541"/>
    </justification>
  </clause>

  <clause id="6084">
    <literal><![CDATA[
      (x * y) * K(y,z) = x * (y * K(y,z))
    ]]></literal>
    <justification jstring="[para(4222(a,1),5984(a,2,2))].">
      <j1 rule="para" parents="4222 5984"/>
    </justification>
  </clause>

  <clause id="6085">
    <literal><![CDATA[
      (x * y) * (z * K(y,z)) = (x * T(y,z)) * z
    ]]></literal>
    <justification jstring="[para(5984(a,1),5417(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5984 5417"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6086">
    <literal><![CDATA[
      (x * T(y,z)) \ ((x * y) * z) = T(z,y)
    ]]></literal>
    <justification jstring="[para(5984(a,1),5447(a,1,1))].">
      <j1 rule="para" parents="5984 5447"/>
    </justification>
  </clause>

  <clause id="6089">
    <literal><![CDATA[
      (x * y) * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x * T(y,z) = u
    ]]></literal>
    <justification jstring="[para(6005(a,1),273(a,1,2)),flip(b)].">
      <j1 rule="para" parents="6005 273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6090">
    <literal><![CDATA[
      x \ y != (z * u) * K(u,w)
    ]]></literal>
    <literal><![CDATA[
      y / (z * T(u,w)) = x
    ]]></literal>
    <justification jstring="[para(6005(a,1),354(a,2,2))].">
      <j1 rule="para" parents="6005 354"/>
    </justification>
  </clause>

  <clause id="6093">
    <literal><![CDATA[
      R(x / (y \ K(y,z)),y \ K(y,z),K(z,y)) = (x * K(z,y)) / (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(197,a,6016,a(flip),b,530,a),flip(a)].">
      <j1 rule="hyper" parents="197 6016 530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6095">
    <literal><![CDATA[
      T(K(x,y),z) * K(y,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,K(y,x)) = u
    ]]></literal>
    <justification jstring="[para(5300(a,1),5998(a,1,1))].">
      <j1 rule="para" parents="5300 5998"/>
    </justification>
  </clause>

  <clause id="6096">
    <literal><![CDATA[
      T(K(x,y) \ z,K(y,x)) != u
    ]]></literal>
    <literal><![CDATA[
      z * K(y,x) = u
    ]]></literal>
    <justification jstring="[para(5302(a,2),5999(a,1))].">
      <j1 rule="para" parents="5302 5999"/>
    </justification>
  </clause>

  <clause id="6097">
    <literal><![CDATA[
      T(K(x,y) * z,K(x,y)) != u
    ]]></literal>
    <literal><![CDATA[
      z * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(5318(a,2),5999(a,1))].">
      <j1 rule="para" parents="5318 5999"/>
    </justification>
  </clause>

  <clause id="6098">
    <literal><![CDATA[
      L(x * K(y,x),z,u) \ L(x,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(L(x,z,u),y) = w
    ]]></literal>
    <justification jstring="[para(4941(a,1),6024(a,1,1))].">
      <j1 rule="para" parents="4941 6024"/>
    </justification>
  </clause>

  <clause id="6099">
    <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(4949(a,1),6024(a,1,1))].">
      <j1 rule="para" parents="4949 6024"/>
    </justification>
  </clause>

  <clause id="6100">
    <literal><![CDATA[
      (K(x,y) * z) * K(y,x) = K(x,y) * (z * K(y,x))
    ]]></literal>
    <justification jstring="[hyper(333,a,4565,a,b,6015,a),flip(a)].">
      <j1 rule="hyper" parents="333 4565 6015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6101">
    <literal><![CDATA[
      (K(x,y) \ z) * K(x,y) = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(4567(a,2),6015(a,1,1))].">
      <j1 rule="para" parents="4567 6015"/>
    </justification>
  </clause>

  <clause id="6102">
    <literal><![CDATA[
      T(T(x,y) * z,K(x,y)) = (x * z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(4557(a,1),6015(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4557 6015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6103">
    <literal><![CDATA[
      R(K(x,y),z,K(x,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(3750,a,6019,a)].">
      <j1 rule="hyper" parents="3750 6019"/>
    </justification>
  </clause>

  <clause id="6104">
    <literal><![CDATA[
      T(T(K(x,y) * z,u),K(x,y)) = T(z * K(x,y),u)
    ]]></literal>
    <justification jstring="[para(6019(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6019 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6105">
    <literal><![CDATA[
      T((x \ K(y,x)) \ z,K(x,y)) = ((x \ 1) \ z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(5240(a,1),6019(a,1,1))].">
      <j1 rule="para" parents="5240 6019"/>
    </justification>
  </clause>

  <clause id="6106">
    <literal><![CDATA[
      T(x * K(y,z),K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) * x = u
    ]]></literal>
    <justification jstring="[para(6019(a,1),5305(a,1,1)),flip(b)].">
      <j1 rule="para" parents="6019 5305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6107">
    <literal><![CDATA[
      L(K(x,y),z,K(x,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(3743,a,6103,a)].">
      <j1 rule="hyper" parents="3743 6103"/>
    </justification>
  </clause>

  <clause id="6108">
    <literal><![CDATA[
      T(L(K(x,y),z,u),K(x,y) * w) = T(L(K(x,y),z,u),w)
    ]]></literal>
    <justification jstring="[para(6107(a,1),961(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6107 961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6109">
    <literal><![CDATA[
      x / T(K(y,z),x) = K(y,z) \ x
    ]]></literal>
    <justification jstring="[para(6107(a,1),3880(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6107 3880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6110">
    <literal><![CDATA[
      (K(x,y) \ z) \ z = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(192,a,6109,a)].">
      <j1 rule="hyper" parents="192 6109"/>
    </justification>
  </clause>

  <clause id="6112">
    <literal><![CDATA[
      (K(x,y) * z) \ z = T(K(y,x),z)
    ]]></literal>
    <justification jstring="[para(4567(a,1),6110(a,1,1))].">
      <j1 rule="para" parents="4567 6110"/>
    </justification>
  </clause>

  <clause id="6113">
    <literal><![CDATA[
      T(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      (K(z,y) * x) * K(y,z) = u
    ]]></literal>
    <justification jstring="[para(6023(a,1),5305(a,1,1)),flip(b)].">
      <j1 rule="para" parents="6023 5305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6114">
    <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(6035(a,1),251(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6035 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6116">
    <literal><![CDATA[
      (x * T(y,L(z,y,x))) \ (x * (y * z)) = T(L(z,y,x),y)
    ]]></literal>
    <justification jstring="[hyper(121,a,97,a(flip),b,6053,a)].">
      <j1 rule="hyper" parents="121 97 6053"/>
    </justification>
  </clause>

  <clause id="6117">
    <literal><![CDATA[
      ((x * y) * z) / (y * z) = R(x,T(y,z),T(z,y))
    ]]></literal>
    <justification jstring="[hyper(123,a,6053,a(flip),b,3651,a)].">
      <j1 rule="hyper" parents="123 6053 3651"/>
    </justification>
  </clause>

  <clause id="6119">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * z) = a(x,T(y,z),T(z,y))
    ]]></literal>
    <justification jstring="[para(6053(a,1),3652(a,1,2))].">
      <j1 rule="para" parents="6053 3652"/>
    </justification>
  </clause>

  <clause id="6120">
    <literal><![CDATA[
      (x * K(y,z)) / y != u
    ]]></literal>
    <literal><![CDATA[
      (x / y) * K(y,z) = u
    ]]></literal>
    <justification jstring="[para(6062(a,1),301(a,1,2)),flip(b)].">
      <j1 rule="para" parents="6062 301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6121">
    <literal><![CDATA[
      x \ (y * K(x,z)) = (x \ y) * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(35,a,5698,a,b,6073,a)].">
      <j1 rule="hyper" parents="35 5698 6073"/>
    </justification>
  </clause>

  <clause id="6122">
    <literal><![CDATA[
      R(x,y,K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(543,a,6084,a)].">
      <j1 rule="hyper" parents="543 6084"/>
    </justification>
  </clause>

  <clause id="6123">
    <literal><![CDATA[
      L(K(x,y),x,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(501,a,6084,a)].">
      <j1 rule="hyper" parents="501 6084"/>
    </justification>
  </clause>

  <clause id="6124">
    <literal><![CDATA[
      R(x,y,K(y \ 1,z)) = x
    ]]></literal>
    <justification jstring="[hyper(1941,a,6122,a)].">
      <j1 rule="hyper" parents="1941 6122"/>
    </justification>
  </clause>

  <clause id="6125">
    <literal><![CDATA[
      (x * R(R(x,y,K(y,z)) \ (x * y),u,w)) * K(y,z) = R(x,y,K(y,z)) * (R(y,u,w) * K(y,z))
    ]]></literal>
    <justification jstring="[para(6122(a,1),2347(a,1,1,1))].">
      <j1 rule="para" parents="6122 2347"/>
    </justification>
  </clause>

  <clause id="6126">
    <literal><![CDATA[
      L(K(x,y),1 / x,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(2632,a,6123,a)].">
      <j1 rule="hyper" parents="2632 6123"/>
    </justification>
  </clause>

  <clause id="6127">
    <literal><![CDATA[
      L(K(x,y),x \ 1,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(2626,a,6123,a)].">
      <j1 rule="hyper" parents="2626 6123"/>
    </justification>
  </clause>

  <clause id="6130">
    <literal><![CDATA[
      R(K(x,y),x,z) = L(K(x,y),x,u)
    ]]></literal>
    <justification jstring="[hyper(333,a,3556,a,b,6123,a)].">
      <j1 rule="hyper" parents="333 3556 6123"/>
    </justification>
  </clause>

  <clause id="6131">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      L(K(x,y),x,u) = z
    ]]></literal>
    <justification jstring="[para(6123(a,1),3141(a,1))].">
      <j1 rule="para" parents="6123 3141"/>
    </justification>
  </clause>

  <clause id="6132">
    <literal><![CDATA[
      R(x,K(y \ 1,z),y) = R(x,u,K(u \ 1,w))
    ]]></literal>
    <justification jstring="[hyper(333,a,6071,a,b,6124,a)].">
      <j1 rule="hyper" parents="333 6071 6124"/>
    </justification>
  </clause>

  <clause id="6133">
    <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(2899(a,1),6126(a,1,2))].">
      <j1 rule="para" parents="2899 6126"/>
    </justification>
  </clause>

  <clause id="6134">
    <literal><![CDATA[
      a(x,y \ 1,K(y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(53,a,6127,a)].">
      <j1 rule="hyper" parents="53 6127"/>
    </justification>
  </clause>

  <clause id="6135">
    <literal><![CDATA[
      a(x,y,K(y \ 1,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(63,a,3214,a(flip),b,6134,a)].">
      <j1 rule="hyper" parents="63 3214 6134"/>
    </justification>
  </clause>

  <clause id="6136">
    <literal><![CDATA[
      L(K(x,y),x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(6130(a,1),547(a,1))].">
      <j1 rule="para" parents="6130 547"/>
    </justification>
  </clause>

  <clause id="6137">
    <literal><![CDATA[
      L(K(x,y),x,z) != u
    ]]></literal>
    <literal><![CDATA[
      L(K(x,y),x,w) = u
    ]]></literal>
    <justification jstring="[para(6123(a,2),6131(a,1))].">
      <j1 rule="para" parents="6123 6131"/>
    </justification>
  </clause>

  <clause id="6138">
    <literal><![CDATA[
      x * ((x \ y) * K(x,z)) = y * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(142,a,6121,a)].">
      <j1 rule="hyper" parents="142 6121"/>
    </justification>
  </clause>

  <clause id="6139">
    <literal><![CDATA[
      (x \ (y / z)) * K(x,z) = x \ (y / T(z,x))
    ]]></literal>
    <justification jstring="[para(5450(a,1),6121(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5450 6121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6140">
    <literal><![CDATA[
      (x * y) * K(x,z) = x * (y * K(x,z))
    ]]></literal>
    <justification jstring="[para(9(a,1),6138(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 6138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6141">
    <literal><![CDATA[
      L(K(x,y),z,x) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(2942,a,6140,a)].">
      <j1 rule="hyper" parents="2942 6140"/>
    </justification>
  </clause>

  <clause id="6142">
    <literal><![CDATA[
      R(x,y,K(x,z)) = x
    ]]></literal>
    <justification jstring="[hyper(543,a,6140,a)].">
      <j1 rule="hyper" parents="543 6140"/>
    </justification>
  </clause>

  <clause id="6143">
    <literal><![CDATA[
      T(x,y) * T(z,K(x,y)) = (x * z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,4512,a,b,6140,a)].">
      <j1 rule="hyper" parents="333 4512 6140"/>
    </justification>
  </clause>

  <clause id="6144">
    <literal><![CDATA[
      (x * (y * K(x,z))) * x = (x * y) * T(x,z)
    ]]></literal>
    <justification jstring="[hyper(125,a,6140,a(flip),b,5979,a)].">
      <j1 rule="hyper" parents="125 6140 5979"/>
    </justification>
  </clause>

  <clause id="6145">
    <literal><![CDATA[
      (x * (y * K(x,z))) / T(x,z) = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(123,a,6140,a(flip),b,5974,a)].">
      <j1 rule="hyper" parents="123 6140 5974"/>
    </justification>
  </clause>

  <clause id="6146">
    <literal><![CDATA[
      R(R(x / y,y,z),y * z,K(y,u)) = ((x * z) * K(y,u)) / (y * (z * K(y,u)))
    ]]></literal>
    <justification jstring="[para(6140(a,1),563(a,2,2))].">
      <j1 rule="para" parents="6140 563"/>
    </justification>
  </clause>

  <clause id="6147">
    <literal><![CDATA[
      (x * (y * K(x,z))) / x = ((x * y) / x) * K(x,z)
    ]]></literal>
    <justification jstring="[para(6140(a,1),6046(a,1,1))].">
      <j1 rule="para" parents="6140 6046"/>
    </justification>
  </clause>

  <clause id="6148">
    <literal><![CDATA[
      R(T(x,y),z,K(x,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(6142(a,1),27(a,2,1))].">
      <j1 rule="para" parents="6142 27"/>
    </justification>
  </clause>

  <clause id="6149">
    <literal><![CDATA[
      (T(x,y) * z) * K(x,u) = T(x,y) * (z * K(x,u))
    ]]></literal>
    <justification jstring="[para(6142(a,1),458(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6142 458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6150">
    <literal><![CDATA[
      (R(x,y,z) * u) * K(x,w) = R(x,y,z) * (u * K(x,w))
    ]]></literal>
    <justification jstring="[para(6142(a,1),453(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6142 453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6151">
    <literal><![CDATA[
      (L(x,y,z) * u) * K(x,w) = L(x,y,z) * (u * K(x,w))
    ]]></literal>
    <justification jstring="[para(6142(a,1),457(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6142 457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6153">
    <literal><![CDATA[
      (x * y) * K(x,z) != u
    ]]></literal>
    <literal><![CDATA[
      x * (y * K(x,z)) = u
    ]]></literal>
    <justification jstring="[para(6141(a,1),306(a,1,2))].">
      <j1 rule="para" parents="6141 306"/>
    </justification>
  </clause>

  <clause id="6155">
    <literal><![CDATA[
      ((x \ 1) \ y) * K(x \ 1,x * y) != z
    ]]></literal>
    <literal><![CDATA[
      y / (x \ 1) = z
    ]]></literal>
    <justification jstring="[para(3934(a,1),5987(a,1,1))].">
      <j1 rule="para" parents="3934 5987"/>
    </justification>
  </clause>

  <clause id="6156">
    <literal><![CDATA[
      (x * y) * z != u
    ]]></literal>
    <literal><![CDATA[
      (x * T(y,z)) * T(z,y) = u
    ]]></literal>
    <justification jstring="[para(5455(a,1),6055(a,1,1))].">
      <j1 rule="para" parents="5455 6055"/>
    </justification>
  </clause>

  <clause id="6157">
    <literal><![CDATA[
      (x * ((y * z) / y)) * y != u
    ]]></literal>
    <literal><![CDATA[
      (x * z) * T(y,z) = u
    ]]></literal>
    <justification jstring="[para(5753(a,1),6055(a,1,1))].">
      <j1 rule="para" parents="5753 6055"/>
    </justification>
  </clause>

  <clause id="6158">
    <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(668(a,1),6089(a,1,1))].">
      <j1 rule="para" parents="668 6089"/>
    </justification>
  </clause>

  <clause id="6160">
    <literal><![CDATA[
      L(K(x,y),x,z) = K((u \ (u / x)) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(6137,a,5375,a)].">
      <j1 rule="hyper" parents="6137 5375"/>
    </justification>
  </clause>

  <clause id="6161">
    <literal><![CDATA[
      L(K(x,y),x,z) \ (u \ (u / x)) = T(1 / (u \ (u / x)),y) \ 1
    ]]></literal>
    <justification jstring="[para(6160(a,2),4501(a,2,1)),flip(a)].">
      <j1 rule="para" parents="6160 4501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6162">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,y \ x) = K((x \ y) \ z,(x \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(5853,a,5973,a)].">
      <j1 rule="hyper" parents="5853 5973"/>
    </justification>
  </clause>

  <clause id="6163">
    <literal><![CDATA[
      K(x * (y \ 1),y \ 1) = K(y \ x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,4543,a,b,5973,a)].">
      <j1 rule="hyper" parents="63 4543 5973"/>
    </justification>
  </clause>

  <clause id="6165">
    <literal><![CDATA[
      (x / (y / z)) * (z \ y) = x * K(z \ y,z)
    ]]></literal>
    <justification jstring="[hyper(338,a,6009,a),flip(a)].">
      <j1 rule="hyper" parents="338 6009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6167">
    <literal><![CDATA[
      T(x * y,K(y,z)) = y * T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,4606,a(flip),b,6021,a),flip(a)].">
      <j1 rule="hyper" parents="63 4606 6021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6168">
    <literal><![CDATA[
      x * T(y / x,T(x,z)) = T(y,K(x,z))
    ]]></literal>
    <justification jstring="[para(12(a,1),6167(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12 6167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6169">
    <literal><![CDATA[
      T(x / y,T(y,z)) = y \ T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(129,a,6168,a),flip(a)].">
      <j1 rule="hyper" parents="129 6168"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6170">
    <literal><![CDATA[
      (x / (y \ 1)) * K(y,z) = x / (T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(123,a,12,a(flip),b,6039,a),flip(a)].">
      <j1 rule="hyper" parents="123 12 6039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6172">
    <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(333,a,3438,a,b,6050,a),flip(a)].">
      <j1 rule="hyper" parents="333 3438 6050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6173">
    <literal><![CDATA[
      ((x * T(y,z)) * z) / (T(y,z) * z) = R(x,y,z * K(y,z))
    ]]></literal>
    <justification jstring="[para(6085(a,1),4646(a,1,1))].">
      <j1 rule="para" parents="6085 4646"/>
    </justification>
  </clause>

  <clause id="6174">
    <literal><![CDATA[
      T(T(x,y) * z,K(x,y)) = x * (z * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(333,a,6140,a(flip),b,6102,a),flip(a)].">
      <j1 rule="hyper" parents="333 6140 6102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6175">
    <literal><![CDATA[
      R(x,K(y \ 1,z),y) = ((x * u) * K(u \ 1,w)) / (u * K(u \ 1,w))
    ]]></literal>
    <justification jstring="[hyper(333,a,20,a(flip),b,6132,a),flip(a)].">
      <j1 rule="hyper" parents="333 20 6132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6176">
    <literal><![CDATA[
      T(x \ (y / z),K(x,z)) = T(x,z) \ (y / T(z,x))
    ]]></literal>
    <justification jstring="[hyper(253,a,6139,a,b,4518,a)].">
      <j1 rule="hyper" parents="253 6139 4518"/>
    </justification>
  </clause>

  <clause id="6177">
    <literal><![CDATA[
      (x \ 1) \ ((x \ y) / T(y,x \ 1)) = (x * ((x \ y) / y)) * K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(5208(a,1),6139(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5208 6139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6179">
    <literal><![CDATA[
      T(x * y,K(x,z)) = x * T(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(253,a,6143,a(flip),b,4273,a)].">
      <j1 rule="hyper" parents="253 6143 4273"/>
    </justification>
  </clause>

  <clause id="6180">
    <literal><![CDATA[
      T(x * y,K(y,z)) / y = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(4119,a,6179,a)].">
      <j1 rule="hyper" parents="4119 6179"/>
    </justification>
  </clause>

  <clause id="6181">
    <literal><![CDATA[
      T(x \ y,K(x,z)) = x \ T(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(121,a,679,a(flip),b,6179,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="121 679 6179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6182">
    <literal><![CDATA[
      T(x,K(y,y * x)) = x
    ]]></literal>
    <justification jstring="[hyper(34,a,2716,a(flip),b,6179,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="34 2716 6179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6184">
    <literal><![CDATA[
      T(x \ y,K(x,y)) = x \ y
    ]]></literal>
    <justification jstring="[para(10(a,1),6182(a,1,2,2))].">
      <j1 rule="para" parents="10 6182"/>
    </justification>
  </clause>

  <clause id="6185">
    <literal><![CDATA[
      K(x,y) * (x \ y) = (x \ y) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(126,a,6184,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="126 6184 22"/>
    </justification>
  </clause>

  <clause id="6186">
    <literal><![CDATA[
      T(x * y,K(y,z)) = T(x,K(y,z)) * y
    ]]></literal>
    <justification jstring="[hyper(140,a,6180,a),flip(a)].">
      <j1 rule="hyper" parents="140 6180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6187">
    <literal><![CDATA[
      T(x,K(y,z)) * y != u
    ]]></literal>
    <literal><![CDATA[
      T(x * y,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(6180(a,1),264(a,1,1)),flip(b)].">
      <j1 rule="para" parents="6180 264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6188">
    <literal><![CDATA[
      T(x / y,T(y,z)) = T(y \ x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(333,a,6169,a,b,6181,a)].">
      <j1 rule="hyper" parents="333 6169 6181"/>
    </justification>
  </clause>

  <clause id="6189">
    <literal><![CDATA[
      x \ T(L(y,x \ 1,x),K(x,z)) = T((x \ 1) * y,K(x,z))
    ]]></literal>
    <justification jstring="[para(439(a,1),6181(a,1,1)),flip(a)].">
      <j1 rule="para" parents="439 6181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6190">
    <literal><![CDATA[
      T(T(x,K(y,z)),y) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(253,a,6186,a(flip),b,6167,a(flip))].">
      <j1 rule="hyper" parents="253 6186 6167"/>
    </justification>
  </clause>

  <clause id="6191">
    <literal><![CDATA[
      T(T(x,y),K(y,z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(437,a,6190,a)].">
      <j1 rule="hyper" parents="437 6190"/>
    </justification>
  </clause>

  <clause id="6192">
    <literal><![CDATA[
      T(x,T(y,z)) != T(u,K(y,z))
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = u
    ]]></literal>
    <justification jstring="[para(6190(a,1),147(a,1))].">
      <j1 rule="para" parents="6190 147"/>
    </justification>
  </clause>

  <clause id="6193">
    <literal><![CDATA[
      T(x,T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(T(x,y),K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(6190(a,1),437(a,1))].">
      <j1 rule="para" parents="6190 437"/>
    </justification>
  </clause>

  <clause id="6194">
    <literal><![CDATA[
      T(T(T(x,y),z),K(y,u)) = T(T(x,T(y,u)),z)
    ]]></literal>
    <justification jstring="[para(6190(a,1),116(a,2,1))].">
      <j1 rule="para" parents="6190 116"/>
    </justification>
  </clause>

  <clause id="6195">
    <literal><![CDATA[
      T(x / y,T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(y \ x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(6190(a,1),740(a,1))].">
      <j1 rule="para" parents="6190 740"/>
    </justification>
  </clause>

  <clause id="6196">
    <literal><![CDATA[
      T(K(x,y),T(z,x)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(2004(a,1),6190(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2004 6190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6197">
    <literal><![CDATA[
      T(x \ 1,T(y,x)) = T(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(2044(a,1),6190(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2044 6190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6198">
    <literal><![CDATA[
      L(x,T(y,K(x,z)),x) = L(x,T(y,T(x,z)),x)
    ]]></literal>
    <justification jstring="[para(6190(a,1),3823(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6190 3823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6199">
    <literal><![CDATA[
      T(K(x,y),T(z,y)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(5309(a,1),6190(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5309 6190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6200">
    <literal><![CDATA[
      T(K(x,y) * z,T(x,y)) = T(z * K(x,y),x)
    ]]></literal>
    <justification jstring="[para(6019(a,1),6190(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6019 6190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6201">
    <literal><![CDATA[
      T(x * K(y,z),T(z,y)) = T(K(y,z) * x,z)
    ]]></literal>
    <justification jstring="[para(6035(a,1),6190(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6035 6190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6202">
    <literal><![CDATA[
      T(x * T(y,T(x,z)),x) = T(y * x,T(x,z))
    ]]></literal>
    <justification jstring="[para(6167(a,1),6190(a,1,1))].">
      <j1 rule="para" parents="6167 6190"/>
    </justification>
  </clause>

  <clause id="6203">
    <literal><![CDATA[
      T(x * T(y,K(x,z)),x) = T(x * y,T(x,z))
    ]]></literal>
    <justification jstring="[para(6179(a,1),6190(a,1,1))].">
      <j1 rule="para" parents="6179 6190"/>
    </justification>
  </clause>

  <clause id="6204">
    <literal><![CDATA[
      T(T(x,((1 / y) * z) \ u),K(((y \ 1) * z) \ u,w)) = T(x,T(((1 / y) * z) \ u,w))
    ]]></literal>
    <justification jstring="[para(4769(a,1),6191(a,1,2))].">
      <j1 rule="para" parents="4769 6191"/>
    </justification>
  </clause>

  <clause id="6205">
    <literal><![CDATA[
      (L(x,y,z) * (u * K(L(x,y,z),w))) / L(T(x,w),y,z) = (L(x,y,z) * u) / L(x,y,z)
    ]]></literal>
    <justification jstring="[para(25(a,2),6145(a,1,2))].">
      <j1 rule="para" parents="25 6145"/>
    </justification>
  </clause>

  <clause id="6206">
    <literal><![CDATA[
      (R(x,y,z) * (u * K(R(x,y,z),w))) / R(T(x,w),y,z) = (R(x,y,z) * u) / R(x,y,z)
    ]]></literal>
    <justification jstring="[para(27(a,2),6145(a,1,2))].">
      <j1 rule="para" parents="27 6145"/>
    </justification>
  </clause>

  <clause id="6207">
    <literal><![CDATA[
      (x * (y * K(z,x))) / x = (x * y) / T(x,z)
    ]]></literal>
    <justification jstring="[para(5995(a,1),6145(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5995 6145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6208">
    <literal><![CDATA[
      T(K(x \ y,x \ 1) / x,y) = R(1 / x,y,x \ 1)
    ]]></literal>
    <justification jstring="[para(6163(a,1),5273(a,1,1,1))].">
      <j1 rule="para" parents="6163 5273"/>
    </justification>
  </clause>

  <clause id="6209">
    <literal><![CDATA[
      (x \ (x / (y \ 1))) * x = x / (T(y,x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,5052,a,b,6170,a)].">
      <j1 rule="hyper" parents="63 5052 6170"/>
    </justification>
  </clause>

  <clause id="6210">
    <literal><![CDATA[
      T(T(x * K(y,z),u),T(z,y)) = T(T(K(y,z) * x,z),u)
    ]]></literal>
    <justification jstring="[para(6201(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6201 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6211">
    <literal><![CDATA[
      K(T(x * y,T(x,z)) \ ((x * T(y,K(x,z))) * u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(K(x * T(y,K(x,z)),x) \ u,w) = v5
    ]]></literal>
    <justification jstring="[para(6203(a,1),4740(a,1,1,1))].">
      <j1 rule="para" parents="6203 4740"/>
    </justification>
  </clause>

  <clause id="6212">
    <literal><![CDATA[
      (x * y) * K(z,x) = x * (y * K(z,x))
    ]]></literal>
    <justification jstring="[hyper(37,a,5460,a,b,6207,a)].">
      <j1 rule="hyper" parents="37 5460 6207"/>
    </justification>
  </clause>

  <clause id="6213">
    <literal><![CDATA[
      L(K(x,y),z,y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(2942,a,6212,a)].">
      <j1 rule="hyper" parents="2942 6212"/>
    </justification>
  </clause>

  <clause id="6214">
    <literal><![CDATA[
      x \ (y * K(z,x)) = (x \ y) * K(z,x)
    ]]></literal>
    <justification jstring="[hyper(648,a,6212,a)].">
      <j1 rule="hyper" parents="648 6212"/>
    </justification>
  </clause>

  <clause id="6215">
    <literal><![CDATA[
      R(x,y,K(z,x)) = x
    ]]></literal>
    <justification jstring="[hyper(543,a,6212,a)].">
      <j1 rule="hyper" parents="543 6212"/>
    </justification>
  </clause>

  <clause id="6216">
    <literal><![CDATA[
      (x / y) * (y * K(z,x / y)) = x * K(z,x / y)
    ]]></literal>
    <justification jstring="[hyper(339,a,6212,a),flip(a)].">
      <j1 rule="hyper" parents="339 6212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6217">
    <literal><![CDATA[
      (x * (y * K(z,x))) * z = (x * y) * T(z,x)
    ]]></literal>
    <justification jstring="[hyper(125,a,6212,a(flip),b,5979,a)].">
      <j1 rule="hyper" parents="125 6212 5979"/>
    </justification>
  </clause>

  <clause id="6218">
    <literal><![CDATA[
      a(x,y,K(z,x)) = 1
    ]]></literal>
    <justification jstring="[hyper(120,a,6212,a(flip),b,84,a),flip(a)].">
      <j1 rule="hyper" parents="120 6212 84"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6219">
    <literal><![CDATA[
      R(x,y,K(z,T(x,u))) = x
    ]]></literal>
    <justification jstring="[hyper(149,a,6215,a(flip))].">
      <j1 rule="hyper" parents="149 6215"/>
    </justification>
  </clause>

  <clause id="6220">
    <literal><![CDATA[
      R(T(x,y),z,K(u,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(6215(a,1),27(a,2,1))].">
      <j1 rule="para" parents="6215 27"/>
    </justification>
  </clause>

  <clause id="6221">
    <literal><![CDATA[
      (T(x,y) * z) * K(u,x) = T(x,y) * (z * K(u,x))
    ]]></literal>
    <justification jstring="[para(6215(a,1),458(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6215 458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6222">
    <literal><![CDATA[
      R(x,y,T(K(z,x),u)) = x
    ]]></literal>
    <justification jstring="[para(2078(a,1),6215(a,1,3))].">
      <j1 rule="para" parents="2078 6215"/>
    </justification>
  </clause>

  <clause id="6224">
    <literal><![CDATA[
      ((x * y) / x) * z = (y * (K(x,y) * z)) * a(u,w,K(v5,u))
    ]]></literal>
    <justification jstring="[para(6218(a,2),4814(a,2,2))].">
      <j1 rule="para" parents="6218 4814"/>
    </justification>
  </clause>

  <clause id="6226">
    <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(6219(a,1),457(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6219 457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6227">
    <literal><![CDATA[
      x \ (y * T(K(z,x),u)) = (x \ y) * T(K(z,x),u)
    ]]></literal>
    <justification jstring="[para(6222(a,1),529(a,1,1))].">
      <j1 rule="para" parents="6222 529"/>
    </justification>
  </clause>

  <clause id="6228">
    <literal><![CDATA[
      T(x,y) \ (z * K(u,x)) = (T(x,y) \ z) * K(u,x)
    ]]></literal>
    <justification jstring="[para(6220(a,1),529(a,1,1))].">
      <j1 rule="para" parents="6220 529"/>
    </justification>
  </clause>

  <clause id="6229">
    <literal><![CDATA[
      T(x / T(y,z),y) = (y \ x) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(5464,a,6214,a)].">
      <j1 rule="hyper" parents="5464 6214"/>
    </justification>
  </clause>

  <clause id="6230">
    <literal><![CDATA[
      T(x / T(y,z),y) * y = (y \ x) * (y * K(z,y))
    ]]></literal>
    <justification jstring="[para(6229(a,2),5417(a,1,1))].">
      <j1 rule="para" parents="6229 5417"/>
    </justification>
  </clause>

  <clause id="6231">
    <literal><![CDATA[
      L(T(K(x,y \ z),u),y \ z,w) = T(K(x,(z \ y) \ 1),u)
    ]]></literal>
    <justification jstring="[para(5769(a,1),25(a,2,1))].">
      <j1 rule="para" parents="5769 25"/>
    </justification>
  </clause>

  <clause id="6232">
    <literal><![CDATA[
      R(x,x \ (y \ x),x) = R(x,y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,4811,a(flip),b,5942,a)].">
      <j1 rule="hyper" parents="63 4811 5942"/>
    </justification>
  </clause>

  <clause id="6234">
    <literal><![CDATA[
      K(K(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,K(y,x)) = u
    ]]></literal>
    <justification jstring="[para(4449(a,1),6095(a,1))].">
      <j1 rule="para" parents="4449 6095"/>
    </justification>
  </clause>

  <clause id="6236">
    <literal><![CDATA[
      T(T(x,y) * z,K(x,y)) != u
    ]]></literal>
    <literal><![CDATA[
      x * (z * K(x,y)) = u
    ]]></literal>
    <justification jstring="[para(6102(a,2),6153(a,1))].">
      <j1 rule="para" parents="6102 6153"/>
    </justification>
  </clause>

  <clause id="6237">
    <literal><![CDATA[
      K(x,(y * z) \ T(y,u)) = K(x,z \ K(y,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,5782,a(flip),b,5784,a),flip(a)].">
      <j1 rule="hyper" parents="63 5782 5784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6238">
    <literal><![CDATA[
      K((x * y) \ T(x,z),u) = (u \ 1) / (u \ K(u,y \ K(x,z)))
    ]]></literal>
    <justification jstring="[para(6237(a,1),4688(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6237 4688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6239">
    <literal><![CDATA[
      T(x \ y,z) * ((y \ x) * K(z,x \ y)) = T((x \ y) * (y \ x),z)
    ]]></literal>
    <justification jstring="[hyper(126,a,5797,a(flip),b,5257,a)].">
      <j1 rule="hyper" parents="126 5797 5257"/>
    </justification>
  </clause>

  <clause id="6240">
    <literal><![CDATA[
      K(T(x,y) \ T(z,y),z) = K(x \ z,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(5955,a,5854,a)].">
      <j1 rule="hyper" parents="5955 5854"/>
    </justification>
  </clause>

  <clause id="6241">
    <literal><![CDATA[
      T(x,T(y,z) \ T(x,z)) = x / K(y \ x,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(197,a,6240,a(flip),b,4205,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="197 6240 4205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6242">
    <literal><![CDATA[
      K((x / (y \ 1)) \ z,x) = K((x * y) \ z,x)
    ]]></literal>
    <justification jstring="[hyper(5955,a,5855,a),flip(a)].">
      <j1 rule="hyper" parents="5955 5855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6243">
    <literal><![CDATA[
      x \ (y \ ((z \ (y * x)) * z)) = K((z / y) \ x,z)
    ]]></literal>
    <justification jstring="[para(4162(a,1),5858(a,1,2))].">
      <j1 rule="para" parents="4162 5858"/>
    </justification>
  </clause>

  <clause id="6244">
    <literal><![CDATA[
      (x \ T(y,z)) * K(z,(x \ 1) \ (x \ y)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(5997,a,5871,a)].">
      <j1 rule="hyper" parents="5997 5871"/>
    </justification>
  </clause>

  <clause id="6245">
    <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(5871(a,1),3415(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5871 3415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6246">
    <literal><![CDATA[
      K((x * y) \ z,y) = K((y * x) \ z,y)
    ]]></literal>
    <justification jstring="[hyper(34,a,5872,a,b,5873,a),flip(a)].">
      <j1 rule="hyper" parents="34 5872 5873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6247">
    <literal><![CDATA[
      (x * ((y \ (x \ z)) * y)) \ z != u
    ]]></literal>
    <literal><![CDATA[
      K(y,(x * y) \ z) = u
    ]]></literal>
    <justification jstring="[para(5873(a,1),6024(a,1,1))].">
      <j1 rule="para" parents="5873 6024"/>
    </justification>
  </clause>

  <clause id="6248">
    <literal><![CDATA[
      T(L(x \ 1,x,y) \ 1,z) = ((y * x) \ y) \ K(x,z)
    ]]></literal>
    <justification jstring="[para(227(a,2),5879(a,1,1,1))].">
      <j1 rule="para" parents="227 5879"/>
    </justification>
  </clause>

  <clause id="6251">
    <literal><![CDATA[
      K(K(x,y),y * z) = K(z * y,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(6095,a,5901,a),flip(a)].">
      <j1 rule="hyper" parents="6095 5901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6252">
    <literal><![CDATA[
      K(x * y,K(y,z)) = K(y * x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(6234,a,6251,a),flip(a)].">
      <j1 rule="hyper" parents="6234 6251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6253">
    <literal><![CDATA[
      (T(x * (y \ 1),x) / x) / (y \ 1) = y * (T(x * (y \ 1),x) / x)
    ]]></literal>
    <justification jstring="[para(5943(a,1),5216(a,1,1,1))].">
      <j1 rule="para" parents="5943 5216"/>
    </justification>
  </clause>

  <clause id="6254">
    <literal><![CDATA[
      T(x,y) / ((1 / z) \ x) = (1 / z) * K((((1 / z) \ x) \ 1) \ (z \ 1),y)
    ]]></literal>
    <justification jstring="[para(4766(a,1),5970(a,2,2))].">
      <j1 rule="para" parents="4766 5970"/>
    </justification>
  </clause>

  <clause id="6255">
    <literal><![CDATA[
      (x * R(K(y,z),u,w)) * R(K(z,y),u,w) = x
    ]]></literal>
    <justification jstring="[hyper(126,a,5651,a(flip),b,6006,a(flip))].">
      <j1 rule="hyper" parents="126 5651 6006"/>
    </justification>
  </clause>

  <clause id="6257">
    <literal><![CDATA[
      ((x / y) * (y * y)) * K(y \ 1,y) = x / (y \ 1)
    ]]></literal>
    <justification jstring="[para(794(a,1),6042(a,1,1))].">
      <j1 rule="para" parents="794 6042"/>
    </justification>
  </clause>

  <clause id="6258">
    <literal><![CDATA[
      K(x \ 1,(x \ 1) \ y) = K(x \ 1,x * y)
    ]]></literal>
    <justification jstring="[hyper(4625,a,6043,a)].">
      <j1 rule="hyper" parents="4625 6043"/>
    </justification>
  </clause>

  <clause id="6259">
    <literal><![CDATA[
      (x \ K((x \ 1) \ y,x \ 1)) \ y = ((x \ 1) \ y) * K(x \ 1,x * y)
    ]]></literal>
    <justification jstring="[para(6258(a,1),5201(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6258 5201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6260">
    <literal><![CDATA[
      (x * (y \ z)) * T(y,y \ z) = R(x,z / y,y) * z
    ]]></literal>
    <justification jstring="[hyper(333,a,540,a,b,6052,a),flip(a)].">
      <j1 rule="hyper" parents="333 540 6052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6261">
    <literal><![CDATA[
      L(K(x,y),z,K(y,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(2942,a,6100,a)].">
      <j1 rule="hyper" parents="2942 6100"/>
    </justification>
  </clause>

  <clause id="6262">
    <literal><![CDATA[
      L(L(K(x,y),z,u),w,K(y,x)) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(6261(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6261 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6263">
    <literal><![CDATA[
      K(x,y) * (z * T(L(K(y,x),u,w),K(x,y) * z)) = L(K(y,x),u,w) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(6262(a,1),664(a,2,1))].">
      <j1 rule="para" parents="6262 664"/>
    </justification>
  </clause>

  <clause id="6264">
    <literal><![CDATA[
      L(K(x,y),z,T(x,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(2942,a,6149,a)].">
      <j1 rule="hyper" parents="2942 6149"/>
    </justification>
  </clause>

  <clause id="6265">
    <literal><![CDATA[
      (x / T(y,z)) * (K(y,z) * T(y,x / T(y,z))) = x * K(y,x / T(y,z))
    ]]></literal>
    <justification jstring="[para(4541(a,2),6216(a,1,2))].">
      <j1 rule="para" parents="4541 6216"/>
    </justification>
  </clause>

  <clause id="6266">
    <literal><![CDATA[
      L(K(x,y),z,T(y,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(2942,a,6221,a)].">
      <j1 rule="hyper" parents="2942 6221"/>
    </justification>
  </clause>

  <clause id="6267">
    <literal><![CDATA[
      T(x / T(y,z),y) * y = (y \ x) * (K(y,z) \ y)
    ]]></literal>
    <justification jstring="[para(4458(a,2),6230(a,2,2))].">
      <j1 rule="para" parents="4458 6230"/>
    </justification>
  </clause>

  <clause id="6268">
    <literal><![CDATA[
      K((x / y) \ z,x) = K((y \ x) \ z,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,5905,a(flip),b,6243,a),flip(a)].">
      <j1 rule="hyper" parents="63 5905 6243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6269">
    <literal><![CDATA[
      K(x,((T(y,x) / z) \ 1) \ ((T(y,x) / z) \ y)) = z \ ((T(y,x) / z) \ y)
    ]]></literal>
    <justification jstring="[hyper(355,a,6244,a),flip(a)].">
      <j1 rule="hyper" parents="355 6244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6270">
    <literal><![CDATA[
      (x \ y) * K((x \ 1) \ (x \ y),z) != u
    ]]></literal>
    <literal><![CDATA[
      x \ T(y,z) = u
    ]]></literal>
    <justification jstring="[para(6244(a,1),5998(a,1,1))].">
      <j1 rule="para" parents="6244 5998"/>
    </justification>
  </clause>

  <clause id="6271">
    <literal><![CDATA[
      (x / y) * ((y * y) * K(y \ 1,y)) = x / (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(1897,a,6257,a)].">
      <j1 rule="hyper" parents="1897 6257"/>
    </justification>
  </clause>

  <clause id="6272">
    <literal><![CDATA[
      (x / y) * (y * (y * K(y \ 1,y))) = x / (y \ 1)
    ]]></literal>
    <justification jstring="[para(1879(a,1),6271(a,1,2))].">
      <j1 rule="para" parents="1879 6271"/>
    </justification>
  </clause>

  <clause id="6273">
    <literal><![CDATA[
      x * (x * K(x \ 1,x)) = (1 / x) \ x
    ]]></literal>
    <justification jstring="[hyper(121,a,76,a(flip),b,6272,a),flip(a)].">
      <j1 rule="hyper" parents="121 76 6272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6274">
    <literal><![CDATA[
      (x / y) * ((1 / y) \ y) = x / (y \ 1)
    ]]></literal>
    <justification jstring="[para(6273(a,1),6272(a,1,2))].">
      <j1 rule="para" parents="6273 6272"/>
    </justification>
  </clause>

  <clause id="6275">
    <literal><![CDATA[
      (x * y) / (y \ 1) = x * ((1 / y) \ y)
    ]]></literal>
    <justification jstring="[para(11(a,1),6274(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 6274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6276">
    <literal><![CDATA[
      x * ((1 / (1 / y)) \ (1 / y)) = (x * (1 / y)) / y
    ]]></literal>
    <justification jstring="[para(79(a,1),6275(a,1,2)),flip(a)].">
      <j1 rule="para" parents="79 6275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6277">
    <literal><![CDATA[
      (x * (1 / y)) / y = x * ((1 / y) / y)
    ]]></literal>
    <justification jstring="[para(1471(a,1),6276(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1471 6276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6279">
    <literal><![CDATA[
      K(x,L(L(y \ 1,y,z),z * y,u)) = K(x,1 / L(y,z,u))
    ]]></literal>
    <justification jstring="[para(428(a,2),5805(a,1,2))].">
      <j1 rule="para" parents="428 5805"/>
    </justification>
  </clause>

  <clause id="6280">
    <literal><![CDATA[
      L(K(x \ y,z),y,u) = K((u * x) \ (u * y),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5874,a(flip),b,5864,a)].">
      <j1 rule="hyper" parents="63 5874 5864"/>
    </justification>
  </clause>

  <clause id="6281">
    <literal><![CDATA[
      L(K(x \ y,z),y,y \ 1) = K(((y \ 1) * x) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,5008,a(flip),b,6280,a),flip(a)].">
      <j1 rule="hyper" parents="333 5008 6280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6282">
    <literal><![CDATA[
      L(K((x \ y) \ z,u),z,x) = K(y \ (x * z),u)
    ]]></literal>
    <justification jstring="[para(10(a,1),6280(a,2,1,1))].">
      <j1 rule="para" parents="10 6280"/>
    </justification>
  </clause>

  <clause id="6283">
    <literal><![CDATA[
      L(K(x \ (y \ z),u),y \ z,y) = K((y * x) \ z,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),6280(a,2,1,2))].">
      <j1 rule="para" parents="10 6280"/>
    </justification>
  </clause>

  <clause id="6284">
    <literal><![CDATA[
      K((x * (y / z)) \ (x * y),u) = L(K(z,u),y,x)
    ]]></literal>
    <justification jstring="[para(79(a,1),6280(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="79 6280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6285">
    <literal><![CDATA[
      L(K(x \ T(y,z),u),T(y,z),z) = K((z * x) \ (y * z),u)
    ]]></literal>
    <justification jstring="[para(111(a,1),6280(a,2,1,2))].">
      <j1 rule="para" parents="111 6280"/>
    </justification>
  </clause>

  <clause id="6286">
    <literal><![CDATA[
      L(K(x \ y,z),y,u) = K(L(x \ y,x,u),z)
    ]]></literal>
    <justification jstring="[para(99(a,2),6280(a,2,1))].">
      <j1 rule="para" parents="99 6280"/>
    </justification>
  </clause>

  <clause id="6287">
    <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(4558(a,1),6280(a,2,1,1))].">
      <j1 rule="para" parents="4558 6280"/>
    </justification>
  </clause>

  <clause id="6288">
    <literal><![CDATA[
      K(L(x \ y,x,K(y,z)),u) = K(x \ y,u)
    ]]></literal>
    <justification jstring="[hyper(3567,a,6286,a),flip(a)].">
      <j1 rule="hyper" parents="3567 6286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6289">
    <literal><![CDATA[
      L(K(L(x,y,z) \ x,u),x,z * y) = K(a(z,y,x),u)
    ]]></literal>
    <justification jstring="[para(1638(a,2),6286(a,2,1))].">
      <j1 rule="para" parents="1638 6286"/>
    </justification>
  </clause>

  <clause id="6290">
    <literal><![CDATA[
      L(K(x \ y,z),y,x \ 1) = K((1 / x) * y,z)
    ]]></literal>
    <justification jstring="[para(2655(a,1),6286(a,2,1))].">
      <j1 rule="para" parents="2655 6286"/>
    </justification>
  </clause>

  <clause id="6291">
    <literal><![CDATA[
      K(x \ y,K(y,z) * x) * (K(y,z) * (x * (x \ y))) = L(x \ y,x,K(y,z)) * (K(y,z) * x)
    ]]></literal>
    <justification jstring="[para(6288(a,1),4202(a,1,1))].">
      <j1 rule="para" parents="6288 4202"/>
    </justification>
  </clause>

  <clause id="6292">
    <literal><![CDATA[
      K((x \ y) \ z,z) = K(y \ (x * z),z)
    ]]></literal>
    <justification jstring="[hyper(5761,a,6282,a)].">
      <j1 rule="hyper" parents="5761 6282"/>
    </justification>
  </clause>

  <clause id="6293">
    <literal><![CDATA[
      K((x \ y) \ z,x) = K(y \ (x * z),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,6213,a(flip),b,6282,a)].">
      <j1 rule="hyper" parents="63 6213 6282"/>
    </justification>
  </clause>

  <clause id="6295">
    <literal><![CDATA[
      K(x \ (y * z),z) != u
    ]]></literal>
    <literal><![CDATA[
      K((y \ x) \ z,z) = u
    ]]></literal>
    <justification jstring="[para(6282(a,1),5761(a,1))].">
      <j1 rule="para" parents="6282 5761"/>
    </justification>
  </clause>

  <clause id="6296">
    <literal><![CDATA[
      K(x \ (y * z),z) / (z \ T(z * ((y \ x) \ 1),z)) = y \ x
    ]]></literal>
    <justification jstring="[para(6292(a,1),5213(a,1,1))].">
      <j1 rule="para" parents="6292 5213"/>
    </justification>
  </clause>

  <clause id="6297">
    <literal><![CDATA[
      K(L(x,y / x,z),u) = L(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(101(a,2),6284(a,1,1))].">
      <j1 rule="para" parents="101 6284"/>
    </justification>
  </clause>

  <clause id="6298">
    <literal><![CDATA[
      L(K(x,y),z * x,u) = K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(11(a,1),6297(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="11 6297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6299">
    <literal><![CDATA[
      K(x,L(y,z / y,u)) = L(K(y,x),z,u) \ 1
    ]]></literal>
    <justification jstring="[para(6297(a,1),4367(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6297 4367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6300">
    <literal><![CDATA[
      K(L(x,y,z),y * x) = K(x,y * x)
    ]]></literal>
    <justification jstring="[hyper(5761,a,6298,a),flip(a)].">
      <j1 rule="hyper" parents="5761 6298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6301">
    <literal><![CDATA[
      K(L(1 / x,x,y),z) = K(1 / x,z)
    ]]></literal>
    <justification jstring="[hyper(2639,a,6298,a)].">
      <j1 rule="hyper" parents="2639 6298"/>
    </justification>
  </clause>

  <clause id="6302">
    <literal><![CDATA[
      K(L(x,y,z),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,6213,a(flip),b,6298,a),flip(a)].">
      <j1 rule="hyper" parents="63 6213 6298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6303">
    <literal><![CDATA[
      K(L(x,y,x),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,6141,a(flip),b,6298,a),flip(a)].">
      <j1 rule="hyper" parents="63 6141 6298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6304">
    <literal><![CDATA[
      (x * (y * z)) / K(L(y,z,x),z) = x * (z * y)
    ]]></literal>
    <justification jstring="[hyper(197,a,6298,a(flip),b,319,a)].">
      <j1 rule="hyper" parents="197 6298 319"/>
    </justification>
  </clause>

  <clause id="6305">
    <literal><![CDATA[
      (x * (y * z)) * K(L(z,y,x),y) = x * (z * y)
    ]]></literal>
    <justification jstring="[hyper(126,a,6298,a(flip),b,319,a)].">
      <j1 rule="hyper" parents="126 6298 319"/>
    </justification>
  </clause>

  <clause id="6306">
    <literal><![CDATA[
      K(L(L(x,y,z),u,w),z) = K(L(x,u,w),z)
    ]]></literal>
    <justification jstring="[para(30(a,1),6302(a,1,1))].">
      <j1 rule="para" parents="30 6302"/>
    </justification>
  </clause>

  <clause id="6307">
    <literal><![CDATA[
      K((x * y) \ z,x) = K(y \ (x \ z),x)
    ]]></literal>
    <justification jstring="[para(311(a,1),6302(a,1,1))].">
      <j1 rule="para" parents="311 6302"/>
    </justification>
  </clause>

  <clause id="6308">
    <literal><![CDATA[
      T(x * K(y,x),L(y,z,x)) = x
    ]]></literal>
    <justification jstring="[para(6302(a,1),4239(a,1,1,2))].">
      <j1 rule="para" parents="6302 4239"/>
    </justification>
  </clause>

  <clause id="6309">
    <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(6302(a,1),4950(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="6302 4950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6310">
    <literal><![CDATA[
      K((x * (y / x)) \ (y * z),y) = K(K(x \ y,x) * z,y)
    ]]></literal>
    <justification jstring="[para(5395(a,1),6302(a,1,1))].">
      <j1 rule="para" parents="5395 6302"/>
    </justification>
  </clause>

  <clause id="6311">
    <literal><![CDATA[
      K(L(x,y,x),z) = u / (K(z,x) * u)
    ]]></literal>
    <justification jstring="[hyper(333,a,4569,a,b,6303,a),flip(a)].">
      <j1 rule="hyper" parents="333 4569 6303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6312">
    <literal><![CDATA[
      K(T(x,x * y),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,4378,a,b,6303,a)].">
      <j1 rule="hyper" parents="63 4378 6303"/>
    </justification>
  </clause>

  <clause id="6313">
    <literal><![CDATA[
      K(T(x / (x / y),x),z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(3778(a,2),6303(a,1,1))].">
      <j1 rule="para" parents="3778 6303"/>
    </justification>
  </clause>

  <clause id="6315">
    <literal><![CDATA[
      K(R(x,y,x),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(3905(a,1),6303(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3905 6303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6316">
    <literal><![CDATA[
      (x * K(y,x)) * L(y,z,y) = L(y,z,y) * x
    ]]></literal>
    <justification jstring="[para(6303(a,1),4291(a,1,1,2))].">
      <j1 rule="para" parents="6303 4291"/>
    </justification>
  </clause>

  <clause id="6317">
    <literal><![CDATA[
      K(x,y) * L(x,z,x) = L(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[para(6303(a,1),4341(a,1,1))].">
      <j1 rule="para" parents="6303 4341"/>
    </justification>
  </clause>

  <clause id="6318">
    <literal><![CDATA[
      R(K(x,y),z,x) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,5560,a(flip),b,6315,a)].">
      <j1 rule="hyper" parents="63 5560 6315"/>
    </justification>
  </clause>

  <clause id="6319">
    <literal><![CDATA[
      K(x,R(y,z,y)) = 1 / K(y,x)
    ]]></literal>
    <justification jstring="[hyper(197,a,6315,a(flip),b,4367,a),flip(a)].">
      <j1 rule="hyper" parents="197 6315 4367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6320">
    <literal><![CDATA[
      R(x,y,x) * K(x,z) = R(T(x,z),y,x)
    ]]></literal>
    <justification jstring="[hyper(126,a,6315,a(flip),b,4284,a)].">
      <j1 rule="hyper" parents="126 6315 4284"/>
    </justification>
  </clause>

  <clause id="6321">
    <literal><![CDATA[
      K(x,y) * R(x,z,x) = R(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[hyper(125,a,6315,a(flip),b,4334,a)].">
      <j1 rule="hyper" parents="125 6315 4334"/>
    </justification>
  </clause>

  <clause id="6322">
    <literal><![CDATA[
      K((x \ y) \ T(y,x),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(3746(a,1),6315(a,1,1))].">
      <j1 rule="para" parents="3746 6315"/>
    </justification>
  </clause>

  <clause id="6323">
    <literal><![CDATA[
      K(T(x,x \ y),z) = K(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(3849(a,1),6315(a,1,1))].">
      <j1 rule="para" parents="3849 6315"/>
    </justification>
  </clause>

  <clause id="6324">
    <literal><![CDATA[
      R(K(x,y),z,x \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(1870,a,6318,a)].">
      <j1 rule="hyper" parents="1870 6318"/>
    </justification>
  </clause>

  <clause id="6325">
    <literal><![CDATA[
      R(K(x,y),z,x) = L(K(x,y),u,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,6141,a,b,6318,a),flip(a)].">
      <j1 rule="hyper" parents="333 6141 6318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6326">
    <literal><![CDATA[
      K(x,R(y,z,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,5654,a(flip),b,6318,a)].">
      <j1 rule="hyper" parents="63 5654 6318"/>
    </justification>
  </clause>

  <clause id="6327">
    <literal><![CDATA[
      K(x,(y * x) / z) = K(x,y / (z / x))
    ]]></literal>
    <justification jstring="[hyper(63,a,5647,a(flip),b,6318,a)].">
      <j1 rule="hyper" parents="63 5647 6318"/>
    </justification>
  </clause>

  <clause id="6328">
    <literal><![CDATA[
      K(x,(y / x) / z) = K(x,y / (z * x))
    ]]></literal>
    <justification jstring="[hyper(63,a,5646,a(flip),b,6318,a),flip(a)].">
      <j1 rule="hyper" parents="63 5646 6318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6329">
    <literal><![CDATA[
      (K(x,y) * z) * x = K(x,y) * (z * x)
    ]]></literal>
    <justification jstring="[hyper(125,a,6318,a(flip),b,20,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="125 6318 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6330">
    <literal><![CDATA[
      R(x,y,z) != K(z,u)
    ]]></literal>
    <literal><![CDATA[
      K(z,u) = x
    ]]></literal>
    <justification jstring="[para(6318(a,1),51(a,1)),flip(a)].">
      <j1 rule="para" parents="6318 51"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6331">
    <literal><![CDATA[
      (x * (K(y,x) * z)) * y = K(y,x) * ((x * z) * y)
    ]]></literal>
    <justification jstring="[para(6318(a,1),4859(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6318 4859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6333">
    <literal><![CDATA[
      K(x,R(y,z,x \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(1858(a,2),6326(a,1,2))].">
      <j1 rule="para" parents="1858 6326"/>
    </justification>
  </clause>

  <clause id="6335">
    <literal><![CDATA[
      T(x,x * y) \ K(x,y) = L(x,y,x) \ 1
    ]]></literal>
    <justification jstring="[para(6312(a,1),4655(a,1,2))].">
      <j1 rule="para" parents="6312 4655"/>
    </justification>
  </clause>

  <clause id="6336">
    <literal><![CDATA[
      K(x,R(y,z,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,4371,a(flip),b,6319,a),flip(a)].">
      <j1 rule="hyper" parents="333 4371 6319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6337">
    <literal><![CDATA[
      K(x,R(y,z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(6319(a,2),4388(a,1))].">
      <j1 rule="para" parents="6319 4388"/>
    </justification>
  </clause>

  <clause id="6338">
    <literal><![CDATA[
      T(x,R(y,z,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(124,a,6336,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 6336 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6339">
    <literal><![CDATA[
      R(K(x,y),z,y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,5651,a(flip),b,6336,a)].">
      <j1 rule="hyper" parents="63 5651 6336"/>
    </justification>
  </clause>

  <clause id="6340">
    <literal><![CDATA[
      R(x * K(y,x),z,x) = R(x,z,x) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(126,a,6336,a(flip),b,4950,a),flip(a)].">
      <j1 rule="hyper" parents="126 6336 4950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6341">
    <literal><![CDATA[
      K(x,T(y,y \ z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(3849(a,1),6336(a,1,2))].">
      <j1 rule="para" parents="3849 6336"/>
    </justification>
  </clause>

  <clause id="6342">
    <literal><![CDATA[
      T(x / R(y,z,y),y) = R(y,z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(423,a,6338,a),flip(a)].">
      <j1 rule="hyper" parents="423 6338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6343">
    <literal><![CDATA[
      R(x,y,x) * T(z,x) = z * R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(126,a,6338,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="126 6338 22"/>
    </justification>
  </clause>

  <clause id="6344">
    <literal><![CDATA[
      T(x,(y \ z) \ T(z,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(3746(a,1),6338(a,1,2))].">
      <j1 rule="para" parents="3746 6338"/>
    </justification>
  </clause>

  <clause id="6345">
    <literal><![CDATA[
      T(x,T(y,y \ z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(3849(a,1),6338(a,1,2))].">
      <j1 rule="para" parents="3849 6338"/>
    </justification>
  </clause>

  <clause id="6346">
    <literal><![CDATA[
      (K(x,y) * z) * y = K(x,y) * (z * y)
    ]]></literal>
    <justification jstring="[hyper(125,a,6339,a(flip),b,20,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="125 6339 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6347">
    <literal><![CDATA[
      (K(x,y) * z) * (x \ 1) = K(x,y) * (z * (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(125,a,6324,a(flip),b,20,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="125 6324 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6348">
    <literal><![CDATA[
      T(x,R(y,z,x \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(124,a,6333,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 6333 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6349">
    <literal><![CDATA[
      R(x * K(y,x),z,y \ 1) = R(x,z,y \ 1) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(126,a,6333,a(flip),b,4950,a),flip(a)].">
      <j1 rule="hyper" parents="126 6333 4950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6350">
    <literal><![CDATA[
      T(x,y * (x \ 1)) = T(x,y / x)
    ]]></literal>
    <justification jstring="[para(554(a,1),6348(a,1,2))].">
      <j1 rule="para" parents="554 6348"/>
    </justification>
  </clause>

  <clause id="6351">
    <literal><![CDATA[
      K((x \ y) \ y,z) = K(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(193(a,1),6313(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="193 6313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6352">
    <literal><![CDATA[
      K(T(x,y),z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,5918,a(flip),b,6323,a),flip(a)].">
      <j1 rule="hyper" parents="63 5918 6323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6353">
    <literal><![CDATA[
      K(T(x,y),y / z) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(333,a,5773,a(flip),b,6352,a),flip(a)].">
      <j1 rule="hyper" parents="333 5773 6352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6354">
    <literal><![CDATA[
      K(T(x,K(y,z)),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,2003,a(flip),b,6352,a),flip(a)].">
      <j1 rule="hyper" parents="333 2003 6352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6355">
    <literal><![CDATA[
      (K(x,y) * z) * K(T(y,z),x) = z
    ]]></literal>
    <justification jstring="[hyper(126,a,6352,a,b,6112,a)].">
      <j1 rule="hyper" parents="126 6352 6112"/>
    </justification>
  </clause>

  <clause id="6356">
    <literal><![CDATA[
      x * K(T(y,x),z) = K(z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(126,a,6352,a,b,4566,a)].">
      <j1 rule="hyper" parents="126 6352 4566"/>
    </justification>
  </clause>

  <clause id="6357">
    <literal><![CDATA[
      x * K(T(y,x),z) = K(y,z) * x
    ]]></literal>
    <justification jstring="[hyper(126,a,6352,a,b,22,a(flip))].">
      <j1 rule="hyper" parents="126 6352 22"/>
    </justification>
  </clause>

  <clause id="6358">
    <literal><![CDATA[
      T(K(x,y),z) * T(x,z) = T(T(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(125,a,6352,a(flip),b,4261,a(flip))].">
      <j1 rule="hyper" parents="125 6352 4261"/>
    </justification>
  </clause>

  <clause id="6360">
    <literal><![CDATA[
      T(K(x,y),z * (x / z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(4099(a,1),6352(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4099 6352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6361">
    <literal><![CDATA[
      T(K(x,y),z) \ 1 = K(y,T(x,z))
    ]]></literal>
    <justification jstring="[para(6352(a,1),4367(a,1,1))].">
      <j1 rule="para" parents="6352 4367"/>
    </justification>
  </clause>

  <clause id="6362">
    <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(126,a,6354,a(flip),b,4735,a(flip))].">
      <j1 rule="hyper" parents="126 6354 4735"/>
    </justification>
  </clause>

  <clause id="6363">
    <literal><![CDATA[
      L(K(x,y),z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(6325(a,1),552(a,1)),flip(b)].">
      <j1 rule="para" parents="6325 552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6364">
    <literal><![CDATA[
      K(x,T(y,y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(3849(a,1),6337(a,1,2))].">
      <j1 rule="para" parents="3849 6337"/>
    </justification>
  </clause>

  <clause id="6365">
    <literal><![CDATA[
      K(x,T(y,z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5842,a(flip),b,6341,a),flip(a)].">
      <j1 rule="hyper" parents="63 5842 6341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6367">
    <literal><![CDATA[
      K(x,(y \ z) \ z) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(112(a,1),6341(a,1,2))].">
      <j1 rule="para" parents="112 6341"/>
    </justification>
  </clause>

  <clause id="6368">
    <literal><![CDATA[
      K(x,T(y / z,y)) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[para(332(a,1),6341(a,1,2)),flip(a)].">
      <j1 rule="para" parents="332 6341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6369">
    <literal><![CDATA[
      K(x,T(y,z \ 1)) = K(x,T(y,z \ y))
    ]]></literal>
    <justification jstring="[para(3591(a,1),6341(a,1,2))].">
      <j1 rule="para" parents="3591 6341"/>
    </justification>
  </clause>

  <clause id="6370">
    <literal><![CDATA[
      K(T(x,y),z) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(333,a,6352,a,b,6365,a)].">
      <j1 rule="hyper" parents="333 6352 6365"/>
    </justification>
  </clause>

  <clause id="6371">
    <literal><![CDATA[
      (K(x,y) * z) \ z = K(y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(333,a,6112,a,b,6365,a)].">
      <j1 rule="hyper" parents="333 6112 6365"/>
    </justification>
  </clause>

  <clause id="6372">
    <literal><![CDATA[
      (K(x,y) \ z) \ z = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(333,a,6110,a,b,6365,a)].">
      <j1 rule="hyper" parents="333 6110 6365"/>
    </justification>
  </clause>

  <clause id="6373">
    <literal><![CDATA[
      K((x \ y) \ y,z) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(333,a,5907,a,b,6365,a)].">
      <j1 rule="hyper" parents="333 5907 6365"/>
    </justification>
  </clause>

  <clause id="6374">
    <literal><![CDATA[
      R(T(K(x,(y / z) \ x),u),x,z) = K(x,T((y / (x * z)) \ 1,u))
    ]]></literal>
    <justification jstring="[hyper(333,a,5674,a,b,6365,a)].">
      <j1 rule="hyper" parents="333 5674 6365"/>
    </justification>
  </clause>

  <clause id="6375">
    <literal><![CDATA[
      R(T(K(x,y),z),y * u,w) = K(x,T(R(y,u,w),z))
    ]]></literal>
    <justification jstring="[hyper(333,a,5659,a,b,6365,a)].">
      <j1 rule="hyper" parents="333 5659 6365"/>
    </justification>
  </clause>

  <clause id="6376">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z,y) = K(z,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(333,a,5300,a,b,6365,a)].">
      <j1 rule="hyper" parents="333 5300 6365"/>
    </justification>
  </clause>

  <clause id="6377">
    <literal><![CDATA[
      K(x,y) * K(z,K(y,x)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(333,a,5295,a,b,6365,a)].">
      <j1 rule="hyper" parents="333 5295 6365"/>
    </justification>
  </clause>

  <clause id="6378">
    <literal><![CDATA[
      K(T(x,y) \ 1,z) = K(x \ 1,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(333,a,5284,a,b,6365,a)].">
      <j1 rule="hyper" parents="333 5284 6365"/>
    </justification>
  </clause>

  <clause id="6379">
    <literal><![CDATA[
      K(x,T(y \ 1,z)) = K(x,T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(333,a,4932,a,b,6365,a),flip(a)].">
      <j1 rule="hyper" parents="333 4932 6365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6380">
    <literal><![CDATA[
      x \ (K(y,z) \ x) = K(z,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(333,a,4566,a,b,6365,a)].">
      <j1 rule="hyper" parents="333 4566 6365"/>
    </justification>
  </clause>

  <clause id="6381">
    <literal><![CDATA[
      K(x,T(y,x * z)) = K(T(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(333,a,5925,a(flip),b,6365,a),flip(a)].">
      <j1 rule="hyper" parents="333 5925 6365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6382">
    <literal><![CDATA[
      K(x / y,T(z,x)) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,5910,a(flip),b,6365,a),flip(a)].">
      <j1 rule="hyper" parents="333 5910 6365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6383">
    <literal><![CDATA[
      K(x,T(y,z * y)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(333,a,5844,a(flip),b,6365,a),flip(a)].">
      <j1 rule="hyper" parents="333 5844 6365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6384">
    <literal><![CDATA[
      K(x,T(y,K(x,z))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,5308,a(flip),b,6365,a),flip(a)].">
      <j1 rule="hyper" parents="333 5308 6365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6385">
    <literal><![CDATA[
      K(x,T(y,T(T(x,z),u))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,3410,a(flip),b,6365,a),flip(a)].">
      <j1 rule="hyper" parents="333 3410 6365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6386">
    <literal><![CDATA[
      K(x,T(y,R(x,z,u))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,3380,a(flip),b,6365,a),flip(a)].">
      <j1 rule="hyper" parents="333 3380 6365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6387">
    <literal><![CDATA[
      K(x \ 1,T(y,x)) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,1380,a(flip),b,6365,a),flip(a)].">
      <j1 rule="hyper" parents="333 1380 6365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6388">
    <literal><![CDATA[
      x / K(y,T(z,x)) = K(z,y) * x
    ]]></literal>
    <justification jstring="[hyper(197,a,6365,a,b,6112,a)].">
      <j1 rule="hyper" parents="197 6365 6112"/>
    </justification>
  </clause>

  <clause id="6389">
    <literal><![CDATA[
      x * K(y,T(z,u)) = x * T(K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(126,a,6365,a,b,9,a)].">
      <j1 rule="hyper" parents="126 6365 9"/>
    </justification>
  </clause>

  <clause id="6390">
    <literal><![CDATA[
      x * K(y,T(z,x)) = K(y,z) * x
    ]]></literal>
    <justification jstring="[hyper(126,a,6365,a,b,22,a(flip))].">
      <j1 rule="hyper" parents="126 6365 22"/>
    </justification>
  </clause>

  <clause id="6391">
    <literal><![CDATA[
      T(K(x,y),z * y) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5844,a,b,6365,a)].">
      <j1 rule="hyper" parents="63 5844 6365"/>
    </justification>
  </clause>

  <clause id="6392">
    <literal><![CDATA[
      T(K(x,y),y \ z) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5842,a(flip),b,6365,a),flip(a)].">
      <j1 rule="hyper" parents="63 5842 6365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6393">
    <literal><![CDATA[
      x * T(K(x,y),z) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(126,a,6365,a(flip),b,4215,a(flip))].">
      <j1 rule="hyper" parents="126 6365 4215"/>
    </justification>
  </clause>

  <clause id="6394">
    <literal><![CDATA[
      K(x,T(T(y,z),u)) = T(K(x,T(y,u)),z)
    ]]></literal>
    <justification jstring="[para(23(a,1),6365(a,1,2))].">
      <j1 rule="para" parents="23 6365"/>
    </justification>
  </clause>

  <clause id="6395">
    <literal><![CDATA[
      L(K(x,T(y,z)),u,w) = T(L(K(x,y),u,w),z)
    ]]></literal>
    <justification jstring="[para(6365(a,2),25(a,1,1))].">
      <j1 rule="para" parents="6365 25"/>
    </justification>
  </clause>

  <clause id="6396">
    <literal><![CDATA[
      K(x,L(T(y,z),u,w)) = T(K(x,L(y,u,w)),z)
    ]]></literal>
    <justification jstring="[para(25(a,2),6365(a,1,2))].">
      <j1 rule="para" parents="25 6365"/>
    </justification>
  </clause>

  <clause id="6397">
    <literal><![CDATA[
      x * K(y,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) * x = u
    ]]></literal>
    <justification jstring="[para(6365(a,2),300(a,1,2))].">
      <j1 rule="para" parents="6365 300"/>
    </justification>
  </clause>

  <clause id="6398">
    <literal><![CDATA[
      x * (y * K(z,T(u,y))) = x * (K(z,u) * y)
    ]]></literal>
    <justification jstring="[para(6365(a,2),235(a,1,2,2))].">
      <j1 rule="para" parents="6365 235"/>
    </justification>
  </clause>

  <clause id="6399">
    <literal><![CDATA[
      x * L(K(y,T(z,x)),u,w) = L(K(y,z),u,w) * x
    ]]></literal>
    <justification jstring="[para(6365(a,2),251(a,1,2,1))].">
      <j1 rule="para" parents="6365 251"/>
    </justification>
  </clause>

  <clause id="6400">
    <literal><![CDATA[
      L(x \ K(y,T(z,u)),x,u) = (u * x) \ (K(y,z) * u)
    ]]></literal>
    <justification jstring="[para(6365(a,2),468(a,1,1,2))].">
      <j1 rule="para" parents="6365 468"/>
    </justification>
  </clause>

  <clause id="6401">
    <literal><![CDATA[
      x * (y * K(z,T(u,y))) != w
    ]]></literal>
    <literal><![CDATA[
      x * (K(z,u) * y) = w
    ]]></literal>
    <justification jstring="[para(6365(a,2),595(a,1,2,2))].">
      <j1 rule="para" parents="6365 595"/>
    </justification>
  </clause>

  <clause id="6403">
    <literal><![CDATA[
      T(x,K(y,T(z,x))) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(6365(a,2),3613(a,1,2))].">
      <j1 rule="para" parents="6365 3613"/>
    </justification>
  </clause>

  <clause id="6404">
    <literal><![CDATA[
      K(x,K(y,T(z,x))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(6365(a,2),4370(a,1,2))].">
      <j1 rule="para" parents="6365 4370"/>
    </justification>
  </clause>

  <clause id="6405">
    <literal><![CDATA[
      K(x,y) * (K(z,u) * x) = T(x,y) * K(z,T(u,x))
    ]]></literal>
    <justification jstring="[para(6365(a,2),4520(a,2,2))].">
      <j1 rule="para" parents="6365 4520"/>
    </justification>
  </clause>

  <clause id="6406">
    <literal><![CDATA[
      x * (K(x,T(y,z)) * (z * K(x,y))) = T(x,y) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(6365(a,2),4528(a,1,2,1))].">
      <j1 rule="para" parents="6365 4528"/>
    </justification>
  </clause>

  <clause id="6407">
    <literal><![CDATA[
      K(x,y) * K(y,T(x,z)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(6365(a,2),5294(a,1,2))].">
      <j1 rule="para" parents="6365 5294"/>
    </justification>
  </clause>

  <clause id="6408">
    <literal><![CDATA[
      K(x,T(y,K(x,z))) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(6365(a,2),5316(a,1))].">
      <j1 rule="para" parents="6365 5316"/>
    </justification>
  </clause>

  <clause id="6409">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(z,y) * u) = K(z,T(y,x)) * u
    ]]></literal>
    <justification jstring="[para(6365(a,2),5299(a,2,1))].">
      <j1 rule="para" parents="6365 5299"/>
    </justification>
  </clause>

  <clause id="6410">
    <literal><![CDATA[
      K(x,T((y \ 1) * ((z \ y) * z),u)) = K(x,K(z \ y,T(z,u)))
    ]]></literal>
    <justification jstring="[para(6365(a,2),5144(a,2,2))].">
      <j1 rule="para" parents="6365 5144"/>
    </justification>
  </clause>

  <clause id="6411">
    <literal><![CDATA[
      (K(x,T(y,z)) * (z * K(x,y))) * u = (y * (T(T(y,x),x) \ z)) * u
    ]]></literal>
    <justification jstring="[para(6365(a,2),5206(a,1,1,1))].">
      <j1 rule="para" parents="6365 5206"/>
    </justification>
  </clause>

  <clause id="6412">
    <literal><![CDATA[
      K(x,T(y,z)) * R(T(K(y,x),z),u,w) = T(K(x,y) * R(K(y,x),u,w),z)
    ]]></literal>
    <justification jstring="[para(6365(a,2),5702(a,1,1))].">
      <j1 rule="para" parents="6365 5702"/>
    </justification>
  </clause>

  <clause id="6413">
    <literal><![CDATA[
      K(x,T(y / z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(6365(a,2),5954(a,1))].">
      <j1 rule="para" parents="6365 5954"/>
    </justification>
  </clause>

  <clause id="6414">
    <literal><![CDATA[
      x \ (y * K(z,T(x,u))) = (x \ y) * T(K(z,x),u)
    ]]></literal>
    <justification jstring="[para(6365(a,2),6227(a,1,2,2))].">
      <j1 rule="para" parents="6365 6227"/>
    </justification>
  </clause>

  <clause id="6415">
    <literal><![CDATA[
      R(T(K(x,y),z),u,x) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(6365(a,1),6318(a,1,1))].">
      <j1 rule="para" parents="6365 6318"/>
    </justification>
  </clause>

  <clause id="6416">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) = T(K(x,K(y,z)),u)
    ]]></literal>
    <justification jstring="[para(6365(a,2),6365(a,1,2))].">
      <j1 rule="para" parents="6365 6365"/>
    </justification>
  </clause>

  <clause id="6417">
    <literal><![CDATA[
      K(T(T(x,y),z),u) = K(x,T(T(u,z),y))
    ]]></literal>
    <justification jstring="[hyper(333,a,6370,a(flip),b,6370,a),flip(a)].">
      <j1 rule="hyper" parents="333 6370 6370"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6419">
    <literal><![CDATA[
      x * K(T(x,y),z) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(126,a,6370,a,b,4215,a(flip))].">
      <j1 rule="hyper" parents="126 6370 4215"/>
    </justification>
  </clause>

  <clause id="6420">
    <literal><![CDATA[
      (x * K(y,T(z,u))) \ x = K(z,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,5990,a,b,6370,a)].">
      <j1 rule="hyper" parents="63 5990 6370"/>
    </justification>
  </clause>

  <clause id="6421">
    <literal><![CDATA[
      T(K(x,y),x * z) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,5925,a,b,6370,a)].">
      <j1 rule="hyper" parents="63 5925 6370"/>
    </justification>
  </clause>

  <clause id="6422">
    <literal><![CDATA[
      T(K(x,y),z * x) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,5920,a,b,6370,a)].">
      <j1 rule="hyper" parents="63 5920 6370"/>
    </justification>
  </clause>

  <clause id="6423">
    <literal><![CDATA[
      K(x,T(y,x \ z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5918,a(flip),b,6370,a),flip(a)].">
      <j1 rule="hyper" parents="63 5918 6370"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6424">
    <literal><![CDATA[
      x / K(y,T(z,u)) = x * K(z,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(197,a,6370,a(flip),b,5990,a)].">
      <j1 rule="hyper" parents="197 6370 5990"/>
    </justification>
  </clause>

  <clause id="6425">
    <literal><![CDATA[
      x / K(y,T(x,z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(197,a,6370,a(flip),b,4205,a(flip))].">
      <j1 rule="hyper" parents="197 6370 4205"/>
    </justification>
  </clause>

  <clause id="6426">
    <literal><![CDATA[
      (x / y) * K(z,T(y,u)) = x / T(y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(126,a,6370,a(flip),b,5465,a)].">
      <j1 rule="hyper" parents="126 6370 5465"/>
    </justification>
  </clause>

  <clause id="6427">
    <literal><![CDATA[
      K(x,T(y,z)) \ u = K(y,T(x,z)) * u
    ]]></literal>
    <justification jstring="[hyper(125,a,6370,a(flip),b,4564,a),flip(a)].">
      <j1 rule="hyper" parents="125 6370 4564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6428">
    <literal><![CDATA[
      T(x,T(y,z)) \ 1 = x \ K(y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(121,a,6370,a(flip),b,4214,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="121 6370 4214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6429">
    <literal><![CDATA[
      K(L(T(x,y),z,u),w) = K(L(x,z,u),T(w,y))
    ]]></literal>
    <justification jstring="[para(25(a,2),6370(a,1,1))].">
      <j1 rule="para" parents="25 6370"/>
    </justification>
  </clause>

  <clause id="6430">
    <literal><![CDATA[
      K(R(T(x,y),z,u),w) = K(R(x,z,u),T(w,y))
    ]]></literal>
    <justification jstring="[para(27(a,2),6370(a,1,1))].">
      <j1 rule="para" parents="27 6370"/>
    </justification>
  </clause>

  <clause id="6431">
    <literal><![CDATA[
      K(x / y,T(z,y)) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[para(113(a,1),6370(a,1,1)),flip(a)].">
      <j1 rule="para" parents="113 6370"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6432">
    <literal><![CDATA[
      K(T(x,y),z / y) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(113(a,1),6370(a,2,2))].">
      <j1 rule="para" parents="113 6370"/>
    </justification>
  </clause>

  <clause id="6433">
    <literal><![CDATA[
      K((x * y) / x,T(z,x)) = K(y,z)
    ]]></literal>
    <justification jstring="[para(238(a,1),6370(a,1,1)),flip(a)].">
      <j1 rule="para" parents="238 6370"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6434">
    <literal><![CDATA[
      K(x,T(y,R(T(x,z),u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(219(a,1),6370(a,1,1)),flip(a)].">
      <j1 rule="para" parents="219 6370"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6436">
    <literal><![CDATA[
      K(L(x,y,z),T(u,x)) = K(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(180(a,1),6370(a,1,1)),flip(a)].">
      <j1 rule="para" parents="180 6370"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6437">
    <literal><![CDATA[
      K(T(x,(1 / y) \ z),z * y) = K(x,z * y)
    ]]></literal>
    <justification jstring="[para(1228(a,1),6370(a,2,2))].">
      <j1 rule="para" parents="1228 6370"/>
    </justification>
  </clause>

  <clause id="6438">
    <literal><![CDATA[
      K(T(x,y),K(y,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(3335(a,1),6370(a,2,2))].">
      <j1 rule="para" parents="3335 6370"/>
    </justification>
  </clause>

  <clause id="6439">
    <literal><![CDATA[
      K(x \ y,T(z,y \ x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,z) = u
    ]]></literal>
    <justification jstring="[para(6370(a,1),3401(a,1))].">
      <j1 rule="para" parents="6370 3401"/>
    </justification>
  </clause>

  <clause id="6443">
    <literal><![CDATA[
      (x * y) / (K(z,T(x,u)) * y) = T(x,T(z,u))
    ]]></literal>
    <justification jstring="[para(6370(a,1),4549(a,1,2,1))].">
      <j1 rule="para" parents="6370 4549"/>
    </justification>
  </clause>

  <clause id="6444">
    <literal><![CDATA[
      K(x,T(y,z)) * (y \ u) = T(y,T(x,z)) \ u
    ]]></literal>
    <justification jstring="[para(6370(a,1),4555(a,1,1))].">
      <j1 rule="para" parents="6370 4555"/>
    </justification>
  </clause>

  <clause id="6445">
    <literal><![CDATA[
      K(x,T(y,z)) \ (y * u) = T(y,T(x,z)) * u
    ]]></literal>
    <justification jstring="[para(6370(a,1),4598(a,1,1))].">
      <j1 rule="para" parents="6370 4598"/>
    </justification>
  </clause>

  <clause id="6446">
    <literal><![CDATA[
      1 / (x \ K(y,T(x,z))) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(6370(a,1),4404(a,1,2,2))].">
      <j1 rule="para" parents="6370 4404"/>
    </justification>
  </clause>

  <clause id="6447">
    <literal><![CDATA[
      K(x,T(y,z)) \ u != w
    ]]></literal>
    <literal><![CDATA[
      K(y,T(x,z)) * u = w
    ]]></literal>
    <justification jstring="[para(6370(a,1),4580(a,1,1))].">
      <j1 rule="para" parents="6370 4580"/>
    </justification>
  </clause>

  <clause id="6448">
    <literal><![CDATA[
      K(x,T(y,z)) * u != w
    ]]></literal>
    <literal><![CDATA[
      K(y,T(x,z)) \ u = w
    ]]></literal>
    <justification jstring="[para(6370(a,1),4585(a,1,1))].">
      <j1 rule="para" parents="6370 4585"/>
    </justification>
  </clause>

  <clause id="6449">
    <literal><![CDATA[
      K(x,T(y,z)) \ (y * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(y,T(x,z)) * u = w
    ]]></literal>
    <justification jstring="[para(6370(a,1),4715(a,1,1))].">
      <j1 rule="para" parents="6370 4715"/>
    </justification>
  </clause>

  <clause id="6450">
    <literal><![CDATA[
      (x * K(y,T(z,u))) \ (x * z) != w
    ]]></literal>
    <literal><![CDATA[
      T(z,T(y,u)) = w
    ]]></literal>
    <justification jstring="[para(6370(a,1),5458(a,1,1,2))].">
      <j1 rule="para" parents="6370 5458"/>
    </justification>
  </clause>

  <clause id="6451">
    <literal><![CDATA[
      x \ (y * K(z,T(x,u))) != w
    ]]></literal>
    <literal><![CDATA[
      T(y / T(x,T(z,u)),x) = w
    ]]></literal>
    <justification jstring="[para(6370(a,1),5464(a,1,2,2))].">
      <j1 rule="para" parents="6370 5464"/>
    </justification>
  </clause>

  <clause id="6452">
    <literal><![CDATA[
      R(x,y \ 1,K(z,T(y,u))) = x
    ]]></literal>
    <justification jstring="[para(6370(a,1),5745(a,1,3))].">
      <j1 rule="para" parents="6370 5745"/>
    </justification>
  </clause>

  <clause id="6453">
    <literal><![CDATA[
      a(x,y,K(z,T(y,u))) = 1
    ]]></literal>
    <justification jstring="[para(6370(a,1),5754(a,1,3))].">
      <j1 rule="para" parents="6370 5754"/>
    </justification>
  </clause>

  <clause id="6454">
    <literal><![CDATA[
      x * K(y,T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      w * K(z,T(y,u)) = x
    ]]></literal>
    <justification jstring="[para(6370(a,1),5997(a,1,2))].">
      <j1 rule="para" parents="6370 5997"/>
    </justification>
  </clause>

  <clause id="6455">
    <literal><![CDATA[
      x / K(y,T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      x * K(z,T(y,u)) = w
    ]]></literal>
    <justification jstring="[para(6370(a,1),5999(a,1,2))].">
      <j1 rule="para" parents="6370 5999"/>
    </justification>
  </clause>

  <clause id="6456">
    <literal><![CDATA[
      (x * K(y,T(z,u))) \ x != w
    ]]></literal>
    <literal><![CDATA[
      K(z,T(y,u)) = w
    ]]></literal>
    <justification jstring="[para(6370(a,1),6024(a,1,1,2))].">
      <j1 rule="para" parents="6370 6024"/>
    </justification>
  </clause>

  <clause id="6457">
    <literal><![CDATA[
      L(K(x,T(y,z)),y,u) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(52,a,6453,a)].">
      <j1 rule="hyper" parents="52 6453"/>
    </justification>
  </clause>

  <clause id="6459">
    <literal><![CDATA[
      K(x,y / K(z,x)) = K(x,K(z,x) \ y)
    ]]></literal>
    <justification jstring="[para(5302(a,1),6384(a,1,2))].">
      <j1 rule="para" parents="5302 6384"/>
    </justification>
  </clause>

  <clause id="6460">
    <literal><![CDATA[
      R(x,(y * K(z,y)) \ 1,K(u,y)) = x
    ]]></literal>
    <justification jstring="[para(4239(a,1),6452(a,1,3,2))].">
      <j1 rule="para" parents="4239 6452"/>
    </justification>
  </clause>

  <clause id="6461">
    <literal><![CDATA[
      ((x \ y) \ y) \ (z * T(x,x \ y)) = T(z,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,697,a,b,6345,a)].">
      <j1 rule="hyper" parents="63 697 6345"/>
    </justification>
  </clause>

  <clause id="6462">
    <literal><![CDATA[
      T(K(x,y \ z),T(y,z)) = T(K(x,y \ z),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,6199,a(flip),b,6345,a),flip(a)].">
      <j1 rule="hyper" parents="63 6199 6345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6463">
    <literal><![CDATA[
      T((x \ y) \ 1,T(x,y)) = T((x \ y) \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,6197,a(flip),b,6345,a),flip(a)].">
      <j1 rule="hyper" parents="63 6197 6345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6464">
    <literal><![CDATA[
      T(x,T(y,y * z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(9(a,1),6345(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 6345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6465">
    <literal><![CDATA[
      T(x,(y \ z) \ z) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(112(a,1),6345(a,1,2))].">
      <j1 rule="para" parents="112 6345"/>
    </justification>
  </clause>

  <clause id="6466">
    <literal><![CDATA[
      T(x,T(y / z,y)) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[para(332(a,1),6345(a,1,2)),flip(a)].">
      <j1 rule="para" parents="332 6345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6467">
    <literal><![CDATA[
      T(x,T(y,z \ 1)) = T(x,T(y,z \ y))
    ]]></literal>
    <justification jstring="[para(3591(a,1),6345(a,1,2))].">
      <j1 rule="para" parents="3591 6345"/>
    </justification>
  </clause>

  <clause id="6468">
    <literal><![CDATA[
      T(x,y * (1 / x)) = T(x,y / x)
    ]]></literal>
    <justification jstring="[hyper(63,a,3165,a,b,6350,a)].">
      <j1 rule="hyper" parents="63 3165 6350"/>
    </justification>
  </clause>

  <clause id="6469">
    <literal><![CDATA[
      K(T(R(x,x \ y,y \ z),z),u) = K(((x \ y) * (y \ z)) \ z,u)
    ]]></literal>
    <justification jstring="[para(759(a,1),6351(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="759 6351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6470">
    <literal><![CDATA[
      K(T(x * K(y,z),x),u) = K(K(y,z) * x,u)
    ]]></literal>
    <justification jstring="[para(6001(a,1),6351(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6001 6351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6471">
    <literal><![CDATA[
      K((x * (y \ z)) \ (x * z),u) = L(K(T(y,z),u),z,x)
    ]]></literal>
    <justification jstring="[para(6351(a,1),6280(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6351 6280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6472">
    <literal><![CDATA[
      K(x,y \ z) * T(x,z) = T(T(x,z),z / y)
    ]]></literal>
    <justification jstring="[hyper(125,a,6353,a(flip),b,4261,a(flip))].">
      <j1 rule="hyper" parents="125 6353 4261"/>
    </justification>
  </clause>

  <clause id="6473">
    <literal><![CDATA[
      K(x,R(T(x,y),z,u) / w) = K(x,w \ R(T(x,y),z,u))
    ]]></literal>
    <justification jstring="[para(219(a,1),6353(a,1,1))].">
      <j1 rule="para" parents="219 6353"/>
    </justification>
  </clause>

  <clause id="6474">
    <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(221(a,1),6353(a,1,1))].">
      <j1 rule="para" parents="221 6353"/>
    </justification>
  </clause>

  <clause id="6476">
    <literal><![CDATA[
      K(x / y,z) * y = y * K(y \ x,z)
    ]]></literal>
    <justification jstring="[para(113(a,1),6357(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="113 6357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6477">
    <literal><![CDATA[
      T(K(x * y,z),y * x) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),6360(a,1,2,2))].">
      <j1 rule="para" parents="11 6360"/>
    </justification>
  </clause>

  <clause id="6478">
    <literal><![CDATA[
      K(L(x,y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(6298(a,1),6363(a,1))].">
      <j1 rule="para" parents="6298 6363"/>
    </justification>
  </clause>

  <clause id="6479">
    <literal><![CDATA[
      K(x,T(y * z,y \ 1)) = K(x,T(y * z,z))
    ]]></literal>
    <justification jstring="[para(3762(a,2),6367(a,1,2))].">
      <j1 rule="para" parents="3762 6367"/>
    </justification>
  </clause>

  <clause id="6480">
    <literal><![CDATA[
      ((x \ y) * K(z,T(x,y))) \ y = T((x \ y) \ y,z)
    ]]></literal>
    <justification jstring="[para(6367(a,1),5452(a,1,1,2))].">
      <j1 rule="para" parents="6367 5452"/>
    </justification>
  </clause>

  <clause id="6481">
    <literal><![CDATA[
      K(x,T(y * K(z,u),y)) = K(x,K(z,u) * y)
    ]]></literal>
    <justification jstring="[para(6001(a,1),6367(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6001 6367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6482">
    <literal><![CDATA[
      K(x,R(T(y / z,y * u),z,u)) = K(x,(z * u) \ (y * u))
    ]]></literal>
    <justification jstring="[para(557(a,1),6368(a,1,2))].">
      <j1 rule="para" parents="557 6368"/>
    </justification>
  </clause>

  <clause id="6483">
    <literal><![CDATA[
      K(x,y) * (z * K(y,T(x,z))) = z
    ]]></literal>
    <justification jstring="[para(6380(a,1),72(a,1,2,2))].">
      <j1 rule="para" parents="6380 72"/>
    </justification>
  </clause>

  <clause id="6484">
    <literal><![CDATA[
      K(x,T(y,x * z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(333,a,6370,a(flip),b,6381,a),flip(a)].">
      <j1 rule="hyper" parents="333 6370 6381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6485">
    <literal><![CDATA[
      (T(x,y) * (y / z)) * K(z \ y,x) = (y / z) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(126,a,6382,a(flip),b,16,a(flip))].">
      <j1 rule="hyper" parents="126 6382 16"/>
    </justification>
  </clause>

  <clause id="6486">
    <literal><![CDATA[
      K(R(x / y,z,u) / w,y \ x) = K(w \ R(x / y,z,u),y \ x)
    ]]></literal>
    <justification jstring="[para(4628(a,1),6382(a,1,2))].">
      <j1 rule="para" parents="4628 6382"/>
    </justification>
  </clause>

  <clause id="6487">
    <literal><![CDATA[
      K((x * y) / (z * y),T(u,x)) = R(K(z \ x,u),x,y)
    ]]></literal>
    <justification jstring="[para(6382(a,1),5559(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6382 5559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6488">
    <literal><![CDATA[
      (x * (y / z)) * K(z \ y,u) != w
    ]]></literal>
    <literal><![CDATA[
      x * T(y / z,T(u,y)) = w
    ]]></literal>
    <justification jstring="[para(6382(a,1),6089(a,1,2))].">
      <j1 rule="para" parents="6382 6089"/>
    </justification>
  </clause>

  <clause id="6489">
    <literal><![CDATA[
      T(x,T(y,T(T(x,z),u))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(124,a,6385,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 6385 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6490">
    <literal><![CDATA[
      (x * y) / T(T(x,y),z) = K(z,x) * y
    ]]></literal>
    <justification jstring="[hyper(5504,a,6390,a)].">
      <j1 rule="hyper" parents="5504 6390"/>
    </justification>
  </clause>

  <clause id="6491">
    <literal><![CDATA[
      x \ (y * K(z,T(x,y))) = T(x,z) \ y
    ]]></literal>
    <justification jstring="[hyper(121,a,6390,a,b,4556,a)].">
      <j1 rule="hyper" parents="121 6390 4556"/>
    </justification>
  </clause>

  <clause id="6492">
    <literal><![CDATA[
      K(x,T((y / z) \ 1,z)) = K(x,(z \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(34,a,5053,a(flip),b,6390,a),flip(a)].">
      <j1 rule="hyper" parents="34 5053 6390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6493">
    <literal><![CDATA[
      ((x * y) * K(z,T(u,y))) / (K(z,u) * y) = R(x,y,K(z,T(u,y)))
    ]]></literal>
    <justification jstring="[hyper(197,a,6390,a(flip),b,187,a)].">
      <j1 rule="hyper" parents="197 6390 187"/>
    </justification>
  </clause>

  <clause id="6494">
    <literal><![CDATA[
      x * K(y,T(T(z,x),u)) = K(y,T(z,u)) * x
    ]]></literal>
    <justification jstring="[para(23(a,1),6390(a,1,2,2))].">
      <j1 rule="para" parents="23 6390"/>
    </justification>
  </clause>

  <clause id="6495">
    <literal><![CDATA[
      x * K(y,L(T(z,x),u,w)) = K(y,L(z,u,w)) * x
    ]]></literal>
    <justification jstring="[para(25(a,2),6390(a,1,2,2))].">
      <j1 rule="para" parents="25 6390"/>
    </justification>
  </clause>

  <clause id="6496">
    <literal><![CDATA[
      K(x,y) * z != z * u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(6390(a,1),43(a,1))].">
      <j1 rule="para" parents="6390 43"/>
    </justification>
  </clause>

  <clause id="6497">
    <literal><![CDATA[
      K(x,y / z) * z = z * K(x,z \ y)
    ]]></literal>
    <justification jstring="[para(113(a,1),6390(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="113 6390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6498">
    <literal><![CDATA[
      K(x \ y,z) * K(u,y / x) = K(u,y / x) * K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(3346(a,1),6390(a,1,2,2))].">
      <j1 rule="para" parents="3346 6390"/>
    </justification>
  </clause>

  <clause id="6500">
    <literal><![CDATA[
      T(K(x,y),y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(6392(a,2),203(a,1)),flip(b)].">
      <j1 rule="para" parents="6392 203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6501">
    <literal><![CDATA[
      T(T(x,y),K(y,z)) = x * T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(333,a,6191,a,b,6393,a)].">
      <j1 rule="hyper" parents="333 6191 6393"/>
    </justification>
  </clause>

  <clause id="6502">
    <literal><![CDATA[
      T(x,K(y,z / x)) = T(x,K(y,x \ z))
    ]]></literal>
    <justification jstring="[para(113(a,1),6403(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="113 6403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6503">
    <literal><![CDATA[
      T(T(x,y),z) * K(y,x) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(4994,a,6419,a)].">
      <j1 rule="hyper" parents="4994 6419"/>
    </justification>
  </clause>

  <clause id="6504">
    <literal><![CDATA[
      (x * y) * K(x,T(z,y)) = K(x,z) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(126,a,6421,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="126 6421 22"/>
    </justification>
  </clause>

  <clause id="6506">
    <literal><![CDATA[
      K(x,T(y,z * x)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,6365,a,b,6422,a)].">
      <j1 rule="hyper" parents="63 6365 6422"/>
    </justification>
  </clause>

  <clause id="6508">
    <literal><![CDATA[
      K(x,T(y,x \ z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(333,a,6365,a,b,6423,a),flip(a)].">
      <j1 rule="hyper" parents="333 6365 6423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6509">
    <literal><![CDATA[
      T(x,T(y,z) \ T(x,z)) = T(x,T(y \ x,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,6241,a,b,6425,a)].">
      <j1 rule="hyper" parents="63 6241 6425"/>
    </justification>
  </clause>

  <clause id="6510">
    <literal><![CDATA[
      K(x \ (y \ x),z) = K(y \ 1,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,4972,a(flip),b,6431,a),flip(a)].">
      <j1 rule="hyper" parents="63 4972 6431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6511">
    <literal><![CDATA[
      K(x \ y,z) * (y / x) = T(y / x,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(125,a,6431,a(flip),b,4261,a(flip))].">
      <j1 rule="hyper" parents="125 6431 4261"/>
    </justification>
  </clause>

  <clause id="6512">
    <literal><![CDATA[
      K(x \ y,z) * (y / x) != u
    ]]></literal>
    <literal><![CDATA[
      T(y / x,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(6431(a,1),4335(a,1,1))].">
      <j1 rule="para" parents="6431 4335"/>
    </justification>
  </clause>

  <clause id="6513">
    <literal><![CDATA[
      (x / y) * (K(y \ x,z) * u) = T(x / y,T(z,y)) * u
    ]]></literal>
    <justification jstring="[para(6431(a,1),4241(a,1,2,1))].">
      <j1 rule="para" parents="6431 4241"/>
    </justification>
  </clause>

  <clause id="6515">
    <literal><![CDATA[
      K(x,y / R(T(x,z),u,w)) = K(x,R(T(x,z),u,w) \ y)
    ]]></literal>
    <justification jstring="[para(219(a,1),6432(a,1,1))].">
      <j1 rule="para" parents="219 6432"/>
    </justification>
  </clause>

  <clause id="6516">
    <literal><![CDATA[
      (x / (y / z)) * K(u,z \ y) != w
    ]]></literal>
    <literal><![CDATA[
      x / T(y / z,T(u,z)) = w
    ]]></literal>
    <justification jstring="[para(6432(a,1),5466(a,1,2))].">
      <j1 rule="para" parents="6432 5466"/>
    </justification>
  </clause>

  <clause id="6517">
    <literal><![CDATA[
      K(x / y,z) \ y = y * K(z,y \ x)
    ]]></literal>
    <justification jstring="[para(6432(a,1),6356(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6432 6356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6518">
    <literal><![CDATA[
      R(x,K(y,z),L(T(z,u),w,v5)) = x
    ]]></literal>
    <justification jstring="[para(6433(a,1),5527(a,1,2))].">
      <j1 rule="para" parents="6433 5527"/>
    </justification>
  </clause>

  <clause id="6519">
    <literal><![CDATA[
      L(x,T(T(y,z),u),K(w,y)) = x
    ]]></literal>
    <justification jstring="[para(6433(a,1),5666(a,1,3))].">
      <j1 rule="para" parents="6433 5666"/>
    </justification>
  </clause>

  <clause id="6520">
    <literal><![CDATA[
      a(x,T(y,z),K(u,y)) = 1
    ]]></literal>
    <justification jstring="[para(6433(a,1),5754(a,1,3))].">
      <j1 rule="para" parents="6433 5754"/>
    </justification>
  </clause>

  <clause id="6521">
    <literal><![CDATA[
      L(K(x,y),T(y,z),u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(52,a,6520,a)].">
      <j1 rule="hyper" parents="52 6520"/>
    </justification>
  </clause>

  <clause id="6522">
    <literal><![CDATA[
      (K(x,y) * T(T(y,z),u)) * w = K(x,y) * (T(T(y,z),u) * w)
    ]]></literal>
    <justification jstring="[hyper(1170,a,6519,a),flip(a)].">
      <j1 rule="hyper" parents="1170 6519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6523">
    <literal><![CDATA[
      (x * T(y,z)) \ (x * R(y,z,y)) = K(y * z,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,4747,a,b,6521,a)].">
      <j1 rule="hyper" parents="63 4747 6521"/>
    </justification>
  </clause>

  <clause id="6524">
    <literal><![CDATA[
      (x * T(y,z)) * K(u,y) = x * (T(y,z) * K(u,y))
    ]]></literal>
    <justification jstring="[hyper(126,a,6521,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="126 6521 18"/>
    </justification>
  </clause>

  <clause id="6525">
    <literal><![CDATA[
      (x * T(y,z)) * L(K(u,y),w,v5) = x * (T(y,z) * L(K(u,y),w,v5))
    ]]></literal>
    <justification jstring="[para(6521(a,1),461(a,1,2,1))].">
      <j1 rule="para" parents="6521 461"/>
    </justification>
  </clause>

  <clause id="6526">
    <literal><![CDATA[
      T(x,y) * K(x,K(y,z)) = T(T(x,y),K(y,z))
    ]]></literal>
    <justification jstring="[hyper(126,a,6438,a(flip),b,4215,a(flip))].">
      <j1 rule="hyper" parents="126 6438 4215"/>
    </justification>
  </clause>

  <clause id="6527">
    <literal><![CDATA[
      K(x,K(y,z)) * T(x,y) = T(T(x,y),K(y,z))
    ]]></literal>
    <justification jstring="[hyper(125,a,6438,a(flip),b,4261,a(flip))].">
      <j1 rule="hyper" parents="125 6438 4261"/>
    </justification>
  </clause>

  <clause id="6528">
    <literal><![CDATA[
      T(x,T(((y / z) \ 1) * y,y)) = T(x,((z \ y) \ 1) * y)
    ]]></literal>
    <justification jstring="[para(5743(a,1),6465(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5743 6465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6529">
    <literal><![CDATA[
      T(x,T((y \ 1) / z,y)) = T(x,(z * (y * y)) \ y)
    ]]></literal>
    <justification jstring="[para(909(a,1),6466(a,1,2,1))].">
      <j1 rule="para" parents="909 6466"/>
    </justification>
  </clause>

  <clause id="6530">
    <literal><![CDATA[
      T(x,(y / (1 / x)) / x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(12(a,1),6468(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12 6468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6531">
    <literal><![CDATA[
      K(T(x / y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(3781(a,1),6478(a,1,1))].">
      <j1 rule="para" parents="3781 6478"/>
    </justification>
  </clause>

  <clause id="6532">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(R(x,u,x),y) = z
    ]]></literal>
    <justification jstring="[para(3905(a,1),6478(a,1,1))].">
      <j1 rule="para" parents="3905 6478"/>
    </justification>
  </clause>

  <clause id="6533">
    <literal><![CDATA[
      K(x,T(y / (x * z),z)) = K(x,(x * z) \ y)
    ]]></literal>
    <justification jstring="[para(113(a,1),6484(a,1,2)),flip(a)].">
      <j1 rule="para" parents="113 6484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6534">
    <literal><![CDATA[
      T(x * K(y,x),T(z,T(x,u))) = T(x * K(y,x),z)
    ]]></literal>
    <justification jstring="[para(4239(a,1),6489(a,1,2,2,1))].">
      <j1 rule="para" parents="4239 6489"/>
    </justification>
  </clause>

  <clause id="6535">
    <literal><![CDATA[
      K(L(x,y,x),T(z,u)) = K(x,T(z,u * x))
    ]]></literal>
    <justification jstring="[hyper(333,a,6303,a,b,6506,a)].">
      <j1 rule="hyper" parents="333 6303 6506"/>
    </justification>
  </clause>

  <clause id="6536">
    <literal><![CDATA[
      K(x,T(y,z / x)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(12(a,1),6506(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 6506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6537">
    <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(84(a,1),6506(a,1,2,2))].">
      <j1 rule="para" parents="84 6506"/>
    </justification>
  </clause>

  <clause id="6538">
    <literal><![CDATA[
      T(x,T(y,x \ z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(124,a,6508,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 6508 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6539">
    <literal><![CDATA[
      R(K(x,T(y,z)),x * u,w) = K(R(x,u,w),T(y,x \ z))
    ]]></literal>
    <justification jstring="[para(6508(a,1),5562(a,1,1))].">
      <j1 rule="para" parents="6508 5562"/>
    </justification>
  </clause>

  <clause id="6540">
    <literal><![CDATA[
      K(x * y,T(z,y \ 1)) = K(x * y,T(z,x))
    ]]></literal>
    <justification jstring="[para(5801(a,1),6508(a,1,2))].">
      <j1 rule="para" parents="5801 6508"/>
    </justification>
  </clause>

  <clause id="6541">
    <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(6518(a,1),567(a,1,1))].">
      <j1 rule="para" parents="6518 567"/>
    </justification>
  </clause>

  <clause id="6542">
    <literal><![CDATA[
      T(x,T(y,z / x)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(124,a,6536,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 6536 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6543">
    <literal><![CDATA[
      K(x,T(y,z \ 1)) = K(x,T(y,z \ x))
    ]]></literal>
    <justification jstring="[para(3757(a,1),6536(a,1,2))].">
      <j1 rule="para" parents="3757 6536"/>
    </justification>
  </clause>

  <clause id="6544">
    <literal><![CDATA[
      K(x * y,T(z,x \ 1)) = K(x * y,T(z,y))
    ]]></literal>
    <justification jstring="[para(3759(a,1),6536(a,1,2))].">
      <j1 rule="para" parents="3759 6536"/>
    </justification>
  </clause>

  <clause id="6545">
    <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(6538(a,1),4283(a,1,2,1))].">
      <j1 rule="para" parents="6538 4283"/>
    </justification>
  </clause>

  <clause id="6546">
    <literal><![CDATA[
      T(x \ y,T(z,y)) = T(x \ y,T(z,x))
    ]]></literal>
    <justification jstring="[para(76(a,1),6542(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="76 6542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6547">
    <literal><![CDATA[
      K(L(x,y,z),y * x) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(333,a,4636,a(flip),b,6300,a),flip(a)].">
      <j1 rule="hyper" parents="333 4636 6300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6548">
    <literal><![CDATA[
      K(L(x,y,z),y * x) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,x * y) = u
    ]]></literal>
    <justification jstring="[para(6300(a,2),4637(a,1))].">
      <j1 rule="para" parents="6300 4637"/>
    </justification>
  </clause>

  <clause id="6549">
    <literal><![CDATA[
      K(L(x,x \ 1,y),z) = K(1 / (x \ 1),z)
    ]]></literal>
    <justification jstring="[para(76(a,1),6301(a,1,1,1))].">
      <j1 rule="para" parents="76 6301"/>
    </justification>
  </clause>

  <clause id="6550">
    <literal><![CDATA[
      K(x,y) * (L(y,z,y) \ u) = L(T(y,x),z,y) \ u
    ]]></literal>
    <justification jstring="[hyper(36,a,4725,a,b,6311,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="36 4725 6311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6552">
    <literal><![CDATA[
      K(x,T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(K(x,y),z) = u
    ]]></literal>
    <justification jstring="[para(6415(a,1),552(a,1)),flip(b)].">
      <j1 rule="para" parents="6415 552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6553">
    <literal><![CDATA[
      R(x,y \ K(y,z),K(u,y)) = x
    ]]></literal>
    <justification jstring="[para(4657(a,1),6460(a,1,2))].">
      <j1 rule="para" parents="4657 6460"/>
    </justification>
  </clause>

  <clause id="6554">
    <literal><![CDATA[
      T(K(x,y),(z * y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(5801(a,2),6500(a,1))].">
      <j1 rule="para" parents="5801 6500"/>
    </justification>
  </clause>

  <clause id="6555">
    <literal><![CDATA[
      K((x * y) \ z,y) = K(x \ (y \ z),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,6246,a,b,6307,a)].">
      <j1 rule="hyper" parents="63 6246 6307"/>
    </justification>
  </clause>

  <clause id="6556">
    <literal><![CDATA[
      K((x / (y \ 1)) \ z,x) = K(y \ (x \ z),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,6242,a,b,6307,a)].">
      <j1 rule="hyper" parents="63 6242 6307"/>
    </justification>
  </clause>

  <clause id="6557">
    <literal><![CDATA[
      ((x \ (1 / y)) * x) * y = K(y \ (x \ 1),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,4494,a,b,6307,a)].">
      <j1 rule="hyper" parents="63 4494 6307"/>
    </justification>
  </clause>

  <clause id="6558">
    <literal><![CDATA[
      K((x * ((y * x) \ y)) \ ((1 / ((y * x) \ y)) \ z),1 / ((y * x) \ y)) = K(x \ z,1 / ((y * x) \ y))
    ]]></literal>
    <justification jstring="[para(1484(a,1),6307(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="1484 6307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6559">
    <literal><![CDATA[
      x * K(y \ (z \ x),z) = y * ((z \ (y \ x)) * z)
    ]]></literal>
    <justification jstring="[para(6307(a,1),5872(a,1,2))].">
      <j1 rule="para" parents="6307 5872"/>
    </justification>
  </clause>

  <clause id="6560">
    <literal><![CDATA[
      T(x,y) \ L(T(x,y),z,x) = x \ L(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(121,a,6317,a(flip),b,4242,a)].">
      <j1 rule="hyper" parents="121 6317 4242"/>
    </justification>
  </clause>

  <clause id="6561">
    <literal><![CDATA[
      T(x,y) \ R(T(x,y),z,x) = x \ R(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(121,a,6320,a(flip),b,4529,a)].">
      <j1 rule="hyper" parents="121 6320 4529"/>
    </justification>
  </clause>

  <clause id="6562">
    <literal><![CDATA[
      K(x,y) \ R(y,z,y) = R(T(y,x),z,y)
    ]]></literal>
    <justification jstring="[hyper(4585,a,6321,a)].">
      <j1 rule="hyper" parents="4585 6321"/>
    </justification>
  </clause>

  <clause id="6563">
    <literal><![CDATA[
      K(x,y) * (x \ R(x,z,x)) = x \ R(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[hyper(121,a,6321,a(flip),b,4532,a),flip(a)].">
      <j1 rule="hyper" parents="121 6321 4532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6564">
    <literal><![CDATA[
      L(x,y,K(x,z)) = x
    ]]></literal>
    <justification jstring="[hyper(2942,a,6329,a)].">
      <j1 rule="hyper" parents="2942 6329"/>
    </justification>
  </clause>

  <clause id="6565">
    <literal><![CDATA[
      (K(x,y) * z) * x = T(x,y) * T(z,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,4520,a(flip),b,6329,a),flip(a)].">
      <j1 rule="hyper" parents="333 4520 6329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6567">
    <literal><![CDATA[
      (K(x,y) * (z * x)) \ (K(x,y) * z) = L(x \ 1,x,K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(6329(a,1),227(a,2,1)),flip(a)].">
      <j1 rule="para" parents="6329 227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6568">
    <literal><![CDATA[
      (K(x,y) * z) / x = K(x,y) * (z / x)
    ]]></literal>
    <justification jstring="[hyper(197,a,6564,a(flip),b,101,a(flip))].">
      <j1 rule="hyper" parents="197 6564 101"/>
    </justification>
  </clause>

  <clause id="6569">
    <literal><![CDATA[
      L(T(x,y),z,K(x,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(6564(a,1),25(a,2,1))].">
      <j1 rule="para" parents="6564 25"/>
    </justification>
  </clause>

  <clause id="6570">
    <literal><![CDATA[
      L(R(x,y,z),u,K(x,w)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(6564(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6564 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6572">
    <literal><![CDATA[
      (K(x,y) * z) * R(x,u,w) = K(x,y) * (z * R(x,u,w))
    ]]></literal>
    <justification jstring="[para(6564(a,1),462(a,1,2,1))].">
      <j1 rule="para" parents="6564 462"/>
    </justification>
  </clause>

  <clause id="6575">
    <literal><![CDATA[
      L(x,y,T(x,z)) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(6564(a,1),5602(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6564 5602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6576">
    <literal><![CDATA[
      L(K(x,y),z,K(x,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(6564(a,1),6297(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6564 6297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6577">
    <literal><![CDATA[
      L(x / y,z,K(y \ x,u)) = x / y
    ]]></literal>
    <justification jstring="[para(6382(a,1),6564(a,1,3))].">
      <j1 rule="para" parents="6382 6564"/>
    </justification>
  </clause>

  <clause id="6580">
    <literal><![CDATA[
      T(L(x / y,z,y \ x),y) = L(y \ x,z,T(y \ x,u))
    ]]></literal>
    <justification jstring="[hyper(333,a,260,a,b,6575,a)].">
      <j1 rule="hyper" parents="333 260 6575"/>
    </justification>
  </clause>

  <clause id="6581">
    <literal><![CDATA[
      L(T(x,y),z,T(x,u)) = T(L(x,z,x),y)
    ]]></literal>
    <justification jstring="[para(6575(a,1),25(a,2,1))].">
      <j1 rule="para" parents="6575 25"/>
    </justification>
  </clause>

  <clause id="6582">
    <literal><![CDATA[
      L(x / y,z,x / y) = L(x / y,z,y \ x)
    ]]></literal>
    <justification jstring="[para(113(a,1),6575(a,1,3)),flip(a)].">
      <j1 rule="para" parents="113 6575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6585">
    <literal><![CDATA[
      x \ (T(y,z) * (K(y,z) \ x)) = T(y,K(z,y) * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,5624,a(flip),b,6569,a)].">
      <j1 rule="hyper" parents="63 5624 6569"/>
    </justification>
  </clause>

  <clause id="6588">
    <literal><![CDATA[
      L(T(x,y),z,T(x,u)) = L(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[para(6569(a,1),5602(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6569 5602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6591">
    <literal><![CDATA[
      (K(x,y) * z) * K(x,u) = K(x,y) * (z * K(x,u))
    ]]></literal>
    <justification jstring="[hyper(126,a,6576,a(flip),b,3220,a(flip))].">
      <j1 rule="hyper" parents="126 6576 3220"/>
    </justification>
  </clause>

  <clause id="6592">
    <literal><![CDATA[
      K(x,y) * ((y * x) * R(x,z,u)) = (x * y) * R(x,z,u)
    ]]></literal>
    <justification jstring="[para(6570(a,1),4353(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6570 4353"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6593">
    <literal><![CDATA[
      (K(x \ y,z) * u) * (y / x) = K(x \ y,z) * (u * (y / x))
    ]]></literal>
    <justification jstring="[hyper(126,a,6577,a(flip),b,3220,a(flip))].">
      <j1 rule="hyper" parents="126 6577 3220"/>
    </justification>
  </clause>

  <clause id="6594">
    <literal><![CDATA[
      (x / R(y,z,y)) * y = y * (R(y,z,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(126,a,6342,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="126 6342 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6595">
    <literal><![CDATA[
      R(x,y,x) * (x \ z) = (z / x) * R(x,y,x)
    ]]></literal>
    <justification jstring="[para(113(a,1),6343(a,1,2))].">
      <j1 rule="para" parents="113 6343"/>
    </justification>
  </clause>

  <clause id="6597">
    <literal><![CDATA[
      L(x,y,K(z,x)) = x
    ]]></literal>
    <justification jstring="[hyper(2942,a,6346,a)].">
      <j1 rule="hyper" parents="2942 6346"/>
    </justification>
  </clause>

  <clause id="6599">
    <literal><![CDATA[
      T(K(x,y) * z,y) = T(y,x) \ (z * y)
    ]]></literal>
    <justification jstring="[hyper(253,a,6346,a,b,4556,a)].">
      <j1 rule="hyper" parents="253 6346 4556"/>
    </justification>
  </clause>

  <clause id="6600">
    <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(6346(a,1),4521(a,1,2,2))].">
      <j1 rule="para" parents="6346 4521"/>
    </justification>
  </clause>

  <clause id="6601">
    <literal><![CDATA[
      (K(x,y) * T(z * K(y,z),u)) * y = K(x,y) * (y * T(z,u))
    ]]></literal>
    <justification jstring="[para(4322(a,1),6346(a,2,2))].">
      <j1 rule="para" parents="4322 6346"/>
    </justification>
  </clause>

  <clause id="6602">
    <literal><![CDATA[
      L(x,K(y,T(x,z)),u) = L(x,w,K(v5,x))
    ]]></literal>
    <justification jstring="[hyper(333,a,5424,a,b,6597,a)].">
      <j1 rule="hyper" parents="333 5424 6597"/>
    </justification>
  </clause>

  <clause id="6604">
    <literal><![CDATA[
      (K(x,y) * z) * T(y,u) = K(x,y) * (z * T(y,u))
    ]]></literal>
    <justification jstring="[para(6597(a,1),465(a,1,2,1))].">
      <j1 rule="para" parents="6597 465"/>
    </justification>
  </clause>

  <clause id="6605">
    <literal><![CDATA[
      L(K(x,y),z,K(u,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(6597(a,1),6297(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6597 6297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6606">
    <literal><![CDATA[
      (K(x,y) * z) * K(y,u) = K(x,y) * (z * K(y,u))
    ]]></literal>
    <justification jstring="[hyper(126,a,6605,a(flip),b,3220,a(flip))].">
      <j1 rule="hyper" parents="126 6605 3220"/>
    </justification>
  </clause>

  <clause id="6608">
    <literal><![CDATA[
      K(x * y,K(x,z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,5848,a(flip),b,6407,a)].">
      <j1 rule="hyper" parents="63 5848 6407"/>
    </justification>
  </clause>

  <clause id="6609">
    <literal><![CDATA[
      K(x * y,K(y,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,6252,a,b,6608,a)].">
      <j1 rule="hyper" parents="63 6252 6608"/>
    </justification>
  </clause>

  <clause id="6610">
    <literal><![CDATA[
      K(x,T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(T(x,z),y) = u
    ]]></literal>
    <justification jstring="[para(6420(a,1),6024(a,1))].">
      <j1 rule="para" parents="6420 6024"/>
    </justification>
  </clause>

  <clause id="6611">
    <literal><![CDATA[
      T(K(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(T(x,z),y) = u
    ]]></literal>
    <justification jstring="[para(6365(a,1),6610(a,1))].">
      <j1 rule="para" parents="6365 6610"/>
    </justification>
  </clause>

  <clause id="6613">
    <literal><![CDATA[
      K(T(x,x \ y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(T(x,y),z) = u
    ]]></literal>
    <justification jstring="[para(5918(a,2),6611(a,1))].">
      <j1 rule="para" parents="5918 6611"/>
    </justification>
  </clause>

  <clause id="6614">
    <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(6428(a,1),1746(a,1,2))].">
      <j1 rule="para" parents="6428 1746"/>
    </justification>
  </clause>

  <clause id="6615">
    <literal><![CDATA[
      K(x / (y \ z),z \ y) = K((y \ z) \ x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(35,a,2049,a,b,6476,a),flip(a)].">
      <j1 rule="hyper" parents="35 2049 6476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6617">
    <literal><![CDATA[
      (x * y) * K(y * x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y * x,z) * (x * y) = u
    ]]></literal>
    <justification jstring="[para(6477(a,1),300(a,1,2))].">
      <j1 rule="para" parents="6477 300"/>
    </justification>
  </clause>

  <clause id="6618">
    <literal><![CDATA[
      K(x,(y / z) \ 1) * y = y * K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(5055(a,2),6497(a,1,1))].">
      <j1 rule="para" parents="5055 6497"/>
    </justification>
  </clause>

  <clause id="6619">
    <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(5969(a,1),6497(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5969 6497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6620">
    <literal><![CDATA[
      T(T(x,1 / y),K(1 / y,z)) = x * K(x,1 / T(y,z))
    ]]></literal>
    <justification jstring="[para(4939(a,2),6501(a,2,2))].">
      <j1 rule="para" parents="4939 6501"/>
    </justification>
  </clause>

  <clause id="6621">
    <literal><![CDATA[
      K(x,y) \ T(T(x,y),z) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(4738,a,6503,a)].">
      <j1 rule="hyper" parents="4738 6503"/>
    </justification>
  </clause>

  <clause id="6623">
    <literal><![CDATA[
      K(R(x,y,(x * y) \ z) \ 1,T(u,z)) = K(z \ (y * ((x * y) \ z)),u)
    ]]></literal>
    <justification jstring="[para(364(a,1),6510(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="364 6510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6624">
    <literal><![CDATA[
      T(x / y,z) \ x = y * K(z,y \ x)
    ]]></literal>
    <justification jstring="[hyper(4914,a,6517,a)].">
      <j1 rule="hyper" parents="4914 6517"/>
    </justification>
  </clause>

  <clause id="6627">
    <literal><![CDATA[
      T(K(x,y) * z,x) = K(x,y) * T(z,x)
    ]]></literal>
    <justification jstring="[hyper(253,a,6565,a,b,4241,a)].">
      <j1 rule="hyper" parents="253 6565 4241"/>
    </justification>
  </clause>

  <clause id="6628">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ z,x) = (x \ z) * x
    ]]></literal>
    <justification jstring="[para(4518(a,1),6565(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4518 6565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6629">
    <literal><![CDATA[
      K(x,y) * ((x * z) / x) = (T(x,y) * z) / x
    ]]></literal>
    <justification jstring="[para(4273(a,1),6568(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4273 6568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6632">
    <literal><![CDATA[
      T(K(x,y) * z,y) = K(x,y) * T(z,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,4554,a(flip),b,6599,a),flip(a)].">
      <j1 rule="hyper" parents="333 4554 6599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6634">
    <literal><![CDATA[
      T(K(x,y \ z) * y,y \ z) = T(y \ z,x) \ z
    ]]></literal>
    <justification jstring="[para(10(a,1),6599(a,2,2))].">
      <j1 rule="para" parents="10 6599"/>
    </justification>
  </clause>

  <clause id="6635">
    <literal><![CDATA[
      T(K(x,y) * (z / y),y) = T(y,x) \ z
    ]]></literal>
    <justification jstring="[para(12(a,1),6599(a,2,2))].">
      <j1 rule="para" parents="12 6599"/>
    </justification>
  </clause>

  <clause id="6636">
    <literal><![CDATA[
      T(K(x,y) * (z * (1 / y)),y) = T(y,x) \ R(z,y \ 1,y)
    ]]></literal>
    <justification jstring="[para(1943(a,1),6599(a,2,2))].">
      <j1 rule="para" parents="1943 6599"/>
    </justification>
  </clause>

  <clause id="6637">
    <literal><![CDATA[
      T(K(x,y) * (z / T(y,u)),y) = T(y,x) \ (z * K(u,y))
    ]]></literal>
    <justification jstring="[para(5444(a,1),6599(a,2,2))].">
      <j1 rule="para" parents="5444 6599"/>
    </justification>
  </clause>

  <clause id="6638">
    <literal><![CDATA[
      L(x,y,K(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(6602(a,1),2785(a,1))].">
      <j1 rule="para" parents="6602 2785"/>
    </justification>
  </clause>

  <clause id="6641">
    <literal><![CDATA[
      x / T(y \ x,z) = T(x / y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(333,a,5451,a,b,6624,a)].">
      <j1 rule="hyper" parents="333 5451 6624"/>
    </justification>
  </clause>

  <clause id="6642">
    <literal><![CDATA[
      x / (y * K(z,y \ x)) = T(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(198,a,6624,a)].">
      <j1 rule="hyper" parents="198 6624"/>
    </justification>
  </clause>

  <clause id="6643">
    <literal><![CDATA[
      x \ (T(y / x,z) \ y) = K(z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(121,a,6624,a,b,xx)].">
      <j1 rule="hyper" parents="121 6624"/>
    </justification>
  </clause>

  <clause id="6645">
    <literal><![CDATA[
      K(x,y) * T(K(x,y) \ z,x) = T(z,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,679,a(flip),b,6627,a),flip(a)].">
      <j1 rule="hyper" parents="63 679 6627"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6647">
    <literal><![CDATA[
      T(x * K(y,z),z) = T(x,z) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(34,a,5356,a(flip),b,6627,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="34 5356 6627"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6648">
    <literal><![CDATA[
      T(K(x,y) * L(z,u,w),x) = K(x,y) * L(T(z,x),u,w)
    ]]></literal>
    <justification jstring="[para(25(a,2),6627(a,2,2))].">
      <j1 rule="para" parents="25 6627"/>
    </justification>
  </clause>

  <clause id="6649">
    <literal><![CDATA[
      T(K(x \ y,x) * z,x \ y) != u
    ]]></literal>
    <literal><![CDATA[
      (y / x) \ (z * (x \ y)) = u
    ]]></literal>
    <justification jstring="[para(6627(a,2),5177(a,1))].">
      <j1 rule="para" parents="6627 5177"/>
    </justification>
  </clause>

  <clause id="6650">
    <literal><![CDATA[
      T(x * K(y,z),y) = T(x,y) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(34,a,5356,a(flip),b,6632,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="34 5356 6632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6651">
    <literal><![CDATA[
      T(x,y) != T(y,z) \ u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) * (u / y) = x
    ]]></literal>
    <justification jstring="[para(6635(a,1),49(a,1)),flip(a)].">
      <j1 rule="para" parents="6635 49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6653">
    <literal><![CDATA[
      x / T((y \ x) \ x,z) = T(y,z) \ x
    ]]></literal>
    <justification jstring="[para(76(a,1),6641(a,2,1,1))].">
      <j1 rule="para" parents="76 6641"/>
    </justification>
  </clause>

  <clause id="6654">
    <literal><![CDATA[
      T(x / (x / y),z) \ x = x / T(y,z)
    ]]></literal>
    <justification jstring="[para(79(a,1),6641(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="79 6641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6655">
    <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(6642(a,1),3775(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6642 3775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6656">
    <literal><![CDATA[
      x / ((x * y) * K(z,y \ 1)) = T(x / (x * y),z)
    ]]></literal>
    <justification jstring="[para(5767(a,1),6642(a,1,2,2))].">
      <j1 rule="para" parents="5767 6642"/>
    </justification>
  </clause>

  <clause id="6657">
    <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(5969(a,1),6642(a,2,1))].">
      <j1 rule="para" parents="5969 6642"/>
    </justification>
  </clause>

  <clause id="6658">
    <literal><![CDATA[
      (x * y) \ (T(R(z * K(x,z),x,y),u) \ ((x * z) * y)) = K(u,(x * y) \ ((x * z) * y))
    ]]></literal>
    <justification jstring="[para(4419(a,2),6643(a,1,2,1,1))].">
      <j1 rule="para" parents="4419 6643"/>
    </justification>
  </clause>

  <clause id="6660">
    <literal><![CDATA[
      (x \ K(y,z)) * T((x \ K(y,z)) \ u,y) = x \ T(x * u,y)
    ]]></literal>
    <justification jstring="[hyper(121,a,6645,a(flip),b,1037,a),flip(a)].">
      <j1 rule="hyper" parents="121 6645 1037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6662">
    <literal><![CDATA[
      T(L(x / y,z,u) * K(w,y),y) = L(y \ x,z,u) * K(w,y)
    ]]></literal>
    <justification jstring="[para(260(a,1),6647(a,2,1))].">
      <j1 rule="para" parents="260 6647"/>
    </justification>
  </clause>

  <clause id="6663">
    <literal><![CDATA[
      x \ (y * T(x,z)) = T(y,x) * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(6057,a,6650,a)].">
      <j1 rule="hyper" parents="6057 6650"/>
    </justification>
  </clause>

  <clause id="6664">
    <literal><![CDATA[
      (T(x,y) / y) * T(y,z) = T(x * K(y,z),y)
    ]]></literal>
    <justification jstring="[hyper(333,a,5974,a,b,6650,a)].">
      <j1 rule="hyper" parents="333 5974 6650"/>
    </justification>
  </clause>

  <clause id="6665">
    <literal><![CDATA[
      x \ T(x * K(y,z),y) = K(x,y) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(121,a,6650,a,b,4241,a)].">
      <j1 rule="hyper" parents="121 6650 4241"/>
    </justification>
  </clause>

  <clause id="6666">
    <literal><![CDATA[
      T((x / y) * K(y,z),y) = (y \ x) * K(y,z)
    ]]></literal>
    <justification jstring="[para(113(a,1),6650(a,2,1))].">
      <j1 rule="para" parents="113 6650"/>
    </justification>
  </clause>

  <clause id="6668">
    <literal><![CDATA[
      T((x \ y) \ y,z) = (T(x,z) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(192,a,6653,a),flip(a)].">
      <j1 rule="hyper" parents="192 6653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6669">
    <literal><![CDATA[
      x / T(T(y,y \ x),z) = T(y,z) \ x
    ]]></literal>
    <justification jstring="[para(112(a,2),6653(a,1,2,1))].">
      <j1 rule="para" parents="112 6653"/>
    </justification>
  </clause>

  <clause id="6670">
    <literal><![CDATA[
      T(x,y) / T(R(x,z,u),w) = T(R(x,z,u),w) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(4131(a,1),6653(a,1,2,1))].">
      <j1 rule="para" parents="4131 6653"/>
    </justification>
  </clause>

  <clause id="6672">
    <literal><![CDATA[
      T(x,y) / T(z * (x / z),u) = T(z * (x / z),u) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(5701(a,1),6654(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5701 6654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6673">
    <literal><![CDATA[
      (T(x,y) / y) * T(y,z) = y \ (x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(333,a,5974,a,b,6663,a)].">
      <j1 rule="hyper" parents="333 5974 6663"/>
    </justification>
  </clause>

  <clause id="6674">
    <literal><![CDATA[
      T(x \ (y * T(x,z)),x) = x \ (T(y,x) * T(x,z))
    ]]></literal>
    <justification jstring="[para(6663(a,2),6054(a,1,1))].">
      <j1 rule="para" parents="6663 6054"/>
    </justification>
  </clause>

  <clause id="6675">
    <literal><![CDATA[
      T(x,y) * L(K(y,z),y,u) = y \ (x * T(y,z))
    ]]></literal>
    <justification jstring="[para(6123(a,2),6663(a,2,2)),flip(a)].">
      <j1 rule="para" parents="6123 6663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6677">
    <literal><![CDATA[
      T(T(x,x \ y),z) = (T(x,z) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(63,a,694,a,b,6668,a)].">
      <j1 rule="hyper" parents="63 694 6668"/>
    </justification>
  </clause>

  <clause id="6678">
    <literal><![CDATA[
      T(T(x,y),x \ z) = (T(x,y) \ z) \ z
    ]]></literal>
    <justification jstring="[hyper(63,a,330,a,b,6668,a)].">
      <j1 rule="hyper" parents="63 330 6668"/>
    </justification>
  </clause>

  <clause id="6680">
    <literal><![CDATA[
      T(((x / y) \ z) \ z,y) = ((y \ x) \ z) \ z
    ]]></literal>
    <justification jstring="[para(113(a,1),6668(a,2,1,1))].">
      <j1 rule="para" parents="113 6668"/>
    </justification>
  </clause>

  <clause id="6682">
    <literal><![CDATA[
      K(x,T((y \ z) \ z,u)) = K(x,T(T(y,u),z))
    ]]></literal>
    <justification jstring="[para(6668(a,2),6367(a,1,2))].">
      <j1 rule="para" parents="6668 6367"/>
    </justification>
  </clause>

  <clause id="6683">
    <literal><![CDATA[
      ((x \ y) \ y) * (T(x,y) \ y) = x * (y / T(x,y))
    ]]></literal>
    <justification jstring="[para(6669(a,1),3907(a,1,2))].">
      <j1 rule="para" parents="6669 3907"/>
    </justification>
  </clause>

  <clause id="6685">
    <literal><![CDATA[
      T(T(x,y),x \ y) = (x \ T(y,x)) \ y
    ]]></literal>
    <justification jstring="[para(3628(a,1),6678(a,2,1))].">
      <j1 rule="para" parents="3628 6678"/>
    </justification>
  </clause>

  <clause id="6686">
    <literal><![CDATA[
      T(x,T(T(y,z),y \ u)) = T(x,T(T(y,z),u))
    ]]></literal>
    <justification jstring="[para(6678(a,2),6465(a,1,2))].">
      <j1 rule="para" parents="6678 6465"/>
    </justification>
  </clause>

  <clause id="6687">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) * (x \ y)) / T(x,y)) = ((x \ T(y,x)) \ y) * (x \ y)
    ]]></literal>
    <justification jstring="[para(6685(a,1),3311(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6685 3311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6688">
    <literal><![CDATA[
      x \ (x \ R(x,y,x)) = L(x,y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,4925,a(flip),b,6335,a)].">
      <j1 rule="hyper" parents="63 4925 6335"/>
    </justification>
  </clause>

  <clause id="6689">
    <literal><![CDATA[
      L(x,y,x) \ x = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(38,a,1268,a,b,6688,a)].">
      <j1 rule="hyper" parents="38 1268 6688"/>
    </justification>
  </clause>

  <clause id="6690">
    <literal><![CDATA[
      K(x,T(y,L(y,z,u) * (y \ w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,L(y,z,u) * w)) = v5
    ]]></literal>
    <justification jstring="[para(1254(a,1),6364(a,1,2,2))].">
      <j1 rule="para" parents="1254 6364"/>
    </justification>
  </clause>

  <clause id="6691">
    <literal><![CDATA[
      T(K(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(5842(a,1),6364(a,1))].">
      <j1 rule="para" parents="5842 6364"/>
    </justification>
  </clause>

  <clause id="6692">
    <literal><![CDATA[
      K(T(x,y) \ 1,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,T(z,y)) = u
    ]]></literal>
    <justification jstring="[para(5284(a,2),6691(a,1))].">
      <j1 rule="para" parents="5284 6691"/>
    </justification>
  </clause>

  <clause id="6693">
    <literal><![CDATA[
      K(1 / T(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(1 / x,T(z,y)) = u
    ]]></literal>
    <justification jstring="[para(5287(a,2),6691(a,1))].">
      <j1 rule="para" parents="5287 6691"/>
    </justification>
  </clause>

  <clause id="6694">
    <literal><![CDATA[
      K((x \ y) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y)) = u
    ]]></literal>
    <justification jstring="[para(5907(a,2),6691(a,1))].">
      <j1 rule="para" parents="5907 6691"/>
    </justification>
  </clause>

  <clause id="6695">
    <literal><![CDATA[
      K(T(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y)) = u
    ]]></literal>
    <justification jstring="[para(6352(a,2),6691(a,1))].">
      <j1 rule="para" parents="6352 6691"/>
    </justification>
  </clause>

  <clause id="6696">
    <literal><![CDATA[
      T(K(x,y),z * y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(6391(a,2),6691(a,1))].">
      <j1 rule="para" parents="6391 6691"/>
    </justification>
  </clause>

  <clause id="6697">
    <literal><![CDATA[
      K(x,T(y,x \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(6423(a,2),6691(a,1))].">
      <j1 rule="para" parents="6423 6691"/>
    </justification>
  </clause>

  <clause id="6698">
    <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(25(a,2),6695(a,1,1))].">
      <j1 rule="para" parents="25 6695"/>
    </justification>
  </clause>

  <clause id="6699">
    <literal><![CDATA[
      K(x,T(y,x * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(6381(a,2),6695(a,1))].">
      <j1 rule="para" parents="6381 6695"/>
    </justification>
  </clause>

  <clause id="6700">
    <literal><![CDATA[
      K(x / y,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(6370(a,1),6531(a,1))].">
      <j1 rule="para" parents="6370 6531"/>
    </justification>
  </clause>

  <clause id="6701">
    <literal><![CDATA[
      K(x,T(y,z * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(6535(a,1),6478(a,1))].">
      <j1 rule="para" parents="6535 6478"/>
    </justification>
  </clause>

  <clause id="6702">
    <literal><![CDATA[
      K(L(x,x \ 1,y),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(76(a,1),6549(a,2,1))].">
      <j1 rule="para" parents="76 6549"/>
    </justification>
  </clause>

  <clause id="6704">
    <literal><![CDATA[
      K(x,L(y,y \ 1,z)) = 1 / K(y,x)
    ]]></literal>
    <justification jstring="[hyper(197,a,6702,a(flip),b,4367,a),flip(a)].">
      <j1 rule="hyper" parents="197 6702 4367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6705">
    <literal><![CDATA[
      K(x,L(y,y \ 1,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,4371,a(flip),b,6704,a),flip(a)].">
      <j1 rule="hyper" parents="333 4371 6704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6706">
    <literal><![CDATA[
      T(x,L(y,y \ 1,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(124,a,6705,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 6705 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6707">
    <literal><![CDATA[
      K(x,L(y,y,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(2596(a,1),6705(a,1,2))].">
      <j1 rule="para" parents="2596 6705"/>
    </justification>
  </clause>

  <clause id="6708">
    <literal><![CDATA[
      K(x,L(y,1 / y,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(2604(a,2),6705(a,1,2))].">
      <j1 rule="para" parents="2604 6705"/>
    </justification>
  </clause>

  <clause id="6709">
    <literal><![CDATA[
      T(x,L(y,y,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(124,a,6707,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 6707 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6710">
    <literal><![CDATA[
      T(x / L(y,y,z),y) = L(y,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(423,a,6709,a),flip(a)].">
      <j1 rule="hyper" parents="423 6709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6711">
    <literal><![CDATA[
      T(x,y) = L(y,y,x) \ (x / (y \ 1))
    ]]></literal>
    <justification jstring="[para(2876(a,1),6710(a,1,1))].">
      <j1 rule="para" parents="2876 6710"/>
    </justification>
  </clause>

  <clause id="6712">
    <literal><![CDATA[
      (x / (y \ 1)) / T(x,y) = L(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(197,a,6711,a,b,xx)].">
      <j1 rule="hyper" parents="197 6711"/>
    </justification>
  </clause>

  <clause id="6713">
    <literal><![CDATA[
      (x * ((x \ y) / y)) / T((x \ y) / y,x) = L(x,x,(x \ y) / y)
    ]]></literal>
    <justification jstring="[para(2191(a,1),6712(a,1,1))].">
      <j1 rule="para" parents="2191 6712"/>
    </justification>
  </clause>

  <clause id="6714">
    <literal><![CDATA[
      K(x,T(y,z * y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(6365(a,2),6696(a,1))].">
      <j1 rule="para" parents="6365 6696"/>
    </justification>
  </clause>

  <clause id="6716">
    <literal><![CDATA[
      L(x,y,x) * (x \ z) = (z / x) * L(x,y,x)
    ]]></literal>
    <justification jstring="[para(4292(a,1),6316(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4292 6316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6717">
    <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(333,a,5521,a,b,6340,a)].">
      <j1 rule="hyper" parents="333 5521 6340"/>
    </justification>
  </clause>

  <clause id="6718">
    <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(6395(a,2),840(a,1))].">
      <j1 rule="para" parents="6395 840"/>
    </justification>
  </clause>

  <clause id="6719">
    <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(6396(a,2),623(a,1,2))].">
      <j1 rule="para" parents="6396 623"/>
    </justification>
  </clause>

  <clause id="6720">
    <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(180(a,1),6430(a,2,2))].">
      <j1 rule="para" parents="180 6430"/>
    </justification>
  </clause>

  <clause id="6721">
    <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(639(a,1),6430(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="639 6430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6722">
    <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(1585(a,1),6430(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1585 6430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6723">
    <literal><![CDATA[
      K(T(x,y \ x) / y,z \ x) * (x / y) = T(T(T(x,y \ x) / y,x),x / z)
    ]]></literal>
    <justification jstring="[para(3367(a,1),6472(a,1,2))].">
      <j1 rule="para" parents="3367 6472"/>
    </justification>
  </clause>

  <clause id="6724">
    <literal><![CDATA[
      (x * y) \ (T(x,z) * y) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(121,a,4273,a(flip),b,6504,a)].">
      <j1 rule="hyper" parents="121 4273 6504"/>
    </justification>
  </clause>

  <clause id="6726">
    <literal><![CDATA[
      L(K(x,T(y,z)),x,u) = (x * z) \ (T(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(333,a,6123,a,b,6724,a)].">
      <j1 rule="hyper" parents="333 6123 6724"/>
    </justification>
  </clause>

  <clause id="6727">
    <literal><![CDATA[
      T(x,y) * K(x,K(y,z)) = x * T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(333,a,6501,a(flip),b,6526,a),flip(a)].">
      <j1 rule="hyper" parents="333 6501 6526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6728">
    <literal><![CDATA[
      K(x,K(y,z)) * T(x,y) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(333,a,6191,a(flip),b,6527,a),flip(a)].">
      <j1 rule="hyper" parents="333 6191 6527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6729">
    <literal><![CDATA[
      K(x * L(y,z,u),T(y,x)) = K(x * L(y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,5386,a(flip),b,6540,a),flip(a)].">
      <j1 rule="hyper" parents="63 5386 6540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6730">
    <literal><![CDATA[
      K(L(x,y,z) * u,T(x,u)) = K(L(x,y,z) * u,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,5386,a(flip),b,6544,a),flip(a)].">
      <j1 rule="hyper" parents="63 5386 6544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6731">
    <literal><![CDATA[
      K(((x \ 1) \ y) \ z,y) = K(x \ (y \ z),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,6268,a(flip),b,6556,a)].">
      <j1 rule="hyper" parents="63 6268 6556"/>
    </justification>
  </clause>

  <clause id="6732">
    <literal><![CDATA[
      (x * y) * ((z \ ((x * y) \ y)) * z) = K(x \ (z \ 1),z) * y
    ]]></literal>
    <justification jstring="[para(6557(a,1),5685(a,2,1))].">
      <j1 rule="para" parents="6557 5685"/>
    </justification>
  </clause>

  <clause id="6733">
    <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(6560(a,1),4680(a,1,2))].">
      <j1 rule="para" parents="6560 4680"/>
    </justification>
  </clause>

  <clause id="6734">
    <literal><![CDATA[
      (x / R(y,z,y)) * y != y * u
    ]]></literal>
    <literal><![CDATA[
      R(y,z,y) \ x = u
    ]]></literal>
    <justification jstring="[para(6594(a,2),43(a,1))].">
      <j1 rule="para" parents="6594 43"/>
    </justification>
  </clause>

  <clause id="6735">
    <literal><![CDATA[
      K(x,T((y / z) \ 1,y)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(6496,a,6618,a)].">
      <j1 rule="hyper" parents="6496 6618"/>
    </justification>
  </clause>

  <clause id="6736">
    <literal><![CDATA[
      K(x,T(y \ 1,z)) = K(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[para(76(a,1),6735(a,1,2,1,1))].">
      <j1 rule="para" parents="76 6735"/>
    </justification>
  </clause>

  <clause id="6737">
    <literal><![CDATA[
      K(x,T(y,z) \ 1) = K(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(63,a,6379,a(flip),b,6736,a)].">
      <j1 rule="hyper" parents="63 6379 6736"/>
    </justification>
  </clause>

  <clause id="6738">
    <literal><![CDATA[
      T(x,T(y,z) \ 1) = T(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(124,a,6737,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 6737 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6739">
    <literal><![CDATA[
      K(x,y \ K(z,y)) = K(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[para(4226(a,1),6737(a,1,2))].">
      <j1 rule="para" parents="4226 6737"/>
    </justification>
  </clause>

  <clause id="6740">
    <literal><![CDATA[
      T(x,(y * z) \ z) = T(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(63,a,5812,a(flip),b,6738,a)].">
      <j1 rule="hyper" parents="63 5812 6738"/>
    </justification>
  </clause>

  <clause id="6741">
    <literal><![CDATA[
      x * K(x,y \ (z \ y)) = T(x,(z * y) \ y)
    ]]></literal>
    <justification jstring="[hyper(333,a,4222,a(flip),b,6740,a)].">
      <j1 rule="hyper" parents="333 4222 6740"/>
    </justification>
  </clause>

  <clause id="6742">
    <literal><![CDATA[
      T(T(x,y) \ T(x * z,u),x) = T(x,y) \ T(z * x,u)
    ]]></literal>
    <justification jstring="[hyper(121,a,4104,a(flip),b,6628,a),flip(a)].">
      <j1 rule="hyper" parents="121 4104 6628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6743">
    <literal><![CDATA[
      K(x,y) \ ((x \ z) * x) = (T(x,y) \ z) * x
    ]]></literal>
    <justification jstring="[hyper(121,a,6628,a(flip),b,4520,a)].">
      <j1 rule="hyper" parents="121 6628 4520"/>
    </justification>
  </clause>

  <clause id="6744">
    <literal><![CDATA[
      K(x,y) \ ((y * z) / y) = (T(y,x) * z) / y
    ]]></literal>
    <justification jstring="[hyper(4585,a,6629,a)].">
      <j1 rule="hyper" parents="4585 6629"/>
    </justification>
  </clause>

  <clause id="6745">
    <literal><![CDATA[
      K(x,y) * (z * K(x,z)) = (T(x,y) * z) / x
    ]]></literal>
    <justification jstring="[hyper(63,a,4413,a(flip),b,6629,a)].">
      <j1 rule="hyper" parents="63 4413 6629"/>
    </justification>
  </clause>

  <clause id="6746">
    <literal><![CDATA[
      T((1 / ((x * y) \ x)) * K(y,z),y) = ((1 / ((x * y) \ x)) / y) * T(y,z)
    ]]></literal>
    <justification jstring="[para(4653(a,1),6664(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4653 6664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6747">
    <literal><![CDATA[
      (T(x * y,y) / y) * T(y,z) = T(x * T(y,z),y)
    ]]></literal>
    <justification jstring="[para(5984(a,1),6664(a,2,1))].">
      <j1 rule="para" parents="5984 6664"/>
    </justification>
  </clause>

  <clause id="6748">
    <literal><![CDATA[
      T((x / y) * K(y,z),y) != u * K(y,z)
    ]]></literal>
    <literal><![CDATA[
      y \ x = u
    ]]></literal>
    <justification jstring="[para(6666(a,2),44(a,1))].">
      <j1 rule="para" parents="6666 44"/>
    </justification>
  </clause>

  <clause id="6749">
    <literal><![CDATA[
      x \ ((y / x) * T(x,z)) = ((x \ y) / x) * T(x,z)
    ]]></literal>
    <justification jstring="[para(113(a,1),6673(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="113 6673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6753">
    <literal><![CDATA[
      ((x \ T(y,x)) \ y) \ y = T(T(x,y) \ y,x)
    ]]></literal>
    <justification jstring="[para(3655(a,1),6680(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="3655 6680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6754">
    <literal><![CDATA[
      K(x,T((y \ z) \ z,u)) = K(x,T(T(y,z),u))
    ]]></literal>
    <justification jstring="[para(23(a,1),6682(a,2,2))].">
      <j1 rule="para" parents="23 6682"/>
    </justification>
  </clause>

  <clause id="6755">
    <literal><![CDATA[
      K(x,T(T(y / z,u),y)) = K(x,T(z \ y,u))
    ]]></literal>
    <justification jstring="[para(79(a,1),6682(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="79 6682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6756">
    <literal><![CDATA[
      K(x,T(T(y,z),u * y)) = K(x,T(T(y,u),z))
    ]]></literal>
    <justification jstring="[para(3649(a,2),6682(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3649 6682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6757">
    <literal><![CDATA[
      T(x,T(T(y,z),y * u)) = T(x,T(T(y,z),u))
    ]]></literal>
    <justification jstring="[para(9(a,1),6686(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 6686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6759">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(4525,a,6727,a)].">
      <j1 rule="hyper" parents="4525 6727"/>
    </justification>
  </clause>

  <clause id="6760">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,y) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(5313,a,6759,a)].">
      <j1 rule="hyper" parents="5313 6759"/>
    </justification>
  </clause>

  <clause id="6761">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(333,a,6365,a,b,6759,a),flip(a)].">
      <j1 rule="hyper" parents="333 6365 6759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6762">
    <literal><![CDATA[
      K(x,K(y,z)) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(34,a,5295,a,b,6759,a)].">
      <j1 rule="hyper" parents="34 5295 6759"/>
    </justification>
  </clause>

  <clause id="6763">
    <literal><![CDATA[
      K(K(x,y),z) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(34,a,4222,a(flip),b,6759,a)].">
      <j1 rule="hyper" parents="34 4222 6759"/>
    </justification>
  </clause>

  <clause id="6764">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(6759(a,2),6691(a,1))].">
      <j1 rule="para" parents="6759 6691"/>
    </justification>
  </clause>

  <clause id="6765">
    <literal><![CDATA[
      K(x * y,K(y,z)) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(333,a,6609,a,b,6762,a)].">
      <j1 rule="hyper" parents="333 6609 6762"/>
    </justification>
  </clause>

  <clause id="6766">
    <literal><![CDATA[
      x * K(y,K(z,x)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(126,a,6762,a,b,4215,a(flip))].">
      <j1 rule="hyper" parents="126 6762 4215"/>
    </justification>
  </clause>

  <clause id="6767">
    <literal><![CDATA[
      K(x,K(y,z)) * z = T(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(125,a,6762,a,b,4261,a(flip))].">
      <j1 rule="hyper" parents="125 6762 4261"/>
    </justification>
  </clause>

  <clause id="6768">
    <literal><![CDATA[
      K(x,K(y,z)) \ K(y,x) = T(K(y,x),z)
    ]]></literal>
    <justification jstring="[para(6762(a,1),4233(a,2,1)),flip(a)].">
      <j1 rule="para" parents="6762 4233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6769">
    <literal><![CDATA[
      K(x,K(y,z)) \ K(y,x) != u
    ]]></literal>
    <literal><![CDATA[
      T(K(y,x),z) = u
    ]]></literal>
    <justification jstring="[para(6762(a,1),4254(a,1,1))].">
      <j1 rule="para" parents="6762 4254"/>
    </justification>
  </clause>

  <clause id="6770">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z,K(x,y)) = 1
    ]]></literal>
    <justification jstring="[para(6762(a,1),5297(a,1,1))].">
      <j1 rule="para" parents="6762 5297"/>
    </justification>
  </clause>

  <clause id="6771">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,y) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(6762(a,1),6376(a,1,1))].">
      <j1 rule="para" parents="6762 6376"/>
    </justification>
  </clause>

  <clause id="6772">
    <literal><![CDATA[
      K(x,K(y,z)) * T(z,y) = T(z,T(y,x))
    ]]></literal>
    <justification jstring="[para(6762(a,1),6728(a,1,1))].">
      <j1 rule="para" parents="6762 6728"/>
    </justification>
  </clause>

  <clause id="6773">
    <literal><![CDATA[
      R(K(K(x,y),z \ 1),u,w) = K(x,K(y,R(z,u,w) \ 1))
    ]]></literal>
    <justification jstring="[hyper(5672,a,6763,a)].">
      <j1 rule="hyper" parents="5672 6763"/>
    </justification>
  </clause>

  <clause id="6774">
    <literal><![CDATA[
      K(K(R(x \ 1,y,z) \ 1,u),w) = R(K(x,K(u,w)),y,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,5114,a(flip),b,6763,a),flip(a)].">
      <j1 rule="hyper" parents="333 5114 6763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6775">
    <literal><![CDATA[
      (x * K(y,z)) * K(y,K(z,u)) = x * T(K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(126,a,6763,a(flip),b,6005,a)].">
      <j1 rule="hyper" parents="126 6763 6005"/>
    </justification>
  </clause>

  <clause id="6776">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(K(x,y),z) = u
    ]]></literal>
    <justification jstring="[para(6763(a,1),4285(a,1,2))].">
      <j1 rule="para" parents="6763 4285"/>
    </justification>
  </clause>

  <clause id="6778">
    <literal><![CDATA[
      K(x,K(y,z)) * (z \ u) = T(z,K(x,y)) \ u
    ]]></literal>
    <justification jstring="[para(6763(a,1),4555(a,1,1))].">
      <j1 rule="para" parents="6763 4555"/>
    </justification>
  </clause>

  <clause id="6779">
    <literal><![CDATA[
      K(x,K(y,z)) * (z \ u) != w
    ]]></literal>
    <literal><![CDATA[
      T(z,K(x,y)) \ u = w
    ]]></literal>
    <justification jstring="[para(6763(a,1),4697(a,1,1))].">
      <j1 rule="para" parents="6763 4697"/>
    </justification>
  </clause>

  <clause id="6780">
    <literal><![CDATA[
      (K(x,y) / z) * K(x,K(y,1 / z)) = T(K(x,y),1 / z) / z
    ]]></literal>
    <justification jstring="[para(6763(a,1),5325(a,1,2))].">
      <j1 rule="para" parents="6763 5325"/>
    </justification>
  </clause>

  <clause id="6781">
    <literal><![CDATA[
      K(L(K(x,y),z,u) \ 1,w) = L(K(y,K(x,w)),z,u)
    ]]></literal>
    <justification jstring="[para(6763(a,1),5373(a,2,1))].">
      <j1 rule="para" parents="6763 5373"/>
    </justification>
  </clause>

  <clause id="6782">
    <literal><![CDATA[
      (x / y) * K(z,K(u,y)) != w
    ]]></literal>
    <literal><![CDATA[
      x / T(y,K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(6763(a,1),5466(a,1,2))].">
      <j1 rule="para" parents="6763 5466"/>
    </justification>
  </clause>

  <clause id="6783">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,K(y,x)) = u
    ]]></literal>
    <justification jstring="[para(6763(a,1),6234(a,1))].">
      <j1 rule="para" parents="6763 6234"/>
    </justification>
  </clause>

  <clause id="6784">
    <literal><![CDATA[
      K(x,K(y,z * y)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,6762,a,b,6765,a)].">
      <j1 rule="hyper" parents="63 6762 6765"/>
    </justification>
  </clause>

  <clause id="6785">
    <literal><![CDATA[
      K(x,K(y,z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(5301,a,6770,a)].">
      <j1 rule="hyper" parents="5301 6770"/>
    </justification>
  </clause>

  <clause id="6786">
    <literal><![CDATA[
      K(K(x,y),z) = K(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(4381,a,6770,a)].">
      <j1 rule="hyper" parents="4381 6770"/>
    </justification>
  </clause>

  <clause id="6787">
    <literal><![CDATA[
      K(K(x,y),z) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(333,a,6763,a,b,6785,a)].">
      <j1 rule="hyper" parents="333 6763 6785"/>
    </justification>
  </clause>

  <clause id="6788">
    <literal><![CDATA[
      K(x,K(y,z)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(333,a,6762,a,b,6785,a),flip(a)].">
      <j1 rule="hyper" parents="333 6762 6785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6789">
    <literal><![CDATA[
      x * K(y,K(x,z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(126,a,6785,a,b,4215,a(flip))].">
      <j1 rule="hyper" parents="126 6785 4215"/>
    </justification>
  </clause>

  <clause id="6790">
    <literal><![CDATA[
      K(x,K(y,z)) * (y * u) = T(y,K(x,z)) * u
    ]]></literal>
    <justification jstring="[hyper(125,a,6785,a,b,4259,a)].">
      <j1 rule="hyper" parents="125 6785 4259"/>
    </justification>
  </clause>

  <clause id="6791">
    <literal><![CDATA[
      K(x,K(y,z)) * y = T(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(125,a,6785,a,b,4261,a(flip))].">
      <j1 rule="hyper" parents="125 6785 4261"/>
    </justification>
  </clause>

  <clause id="6792">
    <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(6785(a,1),4656(a,1,2))].">
      <j1 rule="para" parents="6785 4656"/>
    </justification>
  </clause>

  <clause id="6793">
    <literal><![CDATA[
      K(x,y) * K(y,K(z,x)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(6785(a,1),5295(a,1,2))].">
      <j1 rule="para" parents="6785 5295"/>
    </justification>
  </clause>

  <clause id="6794">
    <literal><![CDATA[
      x * K(y,K(z,x)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(6785(a,1),6766(a,1,2))].">
      <j1 rule="para" parents="6785 6766"/>
    </justification>
  </clause>

  <clause id="6795">
    <literal><![CDATA[
      K(x,K(y,z)) * z = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(6785(a,1),6767(a,1,1))].">
      <j1 rule="para" parents="6785 6767"/>
    </justification>
  </clause>

  <clause id="6796">
    <literal><![CDATA[
      K(K(x,y),z) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(333,a,6762,a,b,6786,a),flip(a)].">
      <j1 rule="hyper" parents="333 6762 6786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6798">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,K(x,z)) = u
    ]]></literal>
    <justification jstring="[para(6786(a,1),6234(a,1))].">
      <j1 rule="para" parents="6786 6234"/>
    </justification>
  </clause>

  <clause id="6799">
    <literal><![CDATA[
      K(K(x,y),z) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(333,a,6762,a,b,6787,a),flip(a)].">
      <j1 rule="hyper" parents="333 6762 6787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6800">
    <literal><![CDATA[
      K(x,K(y,z)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,6786,a(flip),b,6787,a)].">
      <j1 rule="hyper" parents="63 6786 6787"/>
    </justification>
  </clause>

  <clause id="6801">
    <literal><![CDATA[
      K(x,K(y,z)) * (z * K(y,x)) = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(125,a,6787,a(flip),b,4200,a(flip))].">
      <j1 rule="hyper" parents="125 6787 4200"/>
    </justification>
  </clause>

  <clause id="6802">
    <literal><![CDATA[
      K(x,K(R(y \ 1,z,u) \ 1,w)) = K(R(K(y,x),z,u),w)
    ]]></literal>
    <justification jstring="[para(5114(a,1),6787(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5114 6787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6803">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,K(x,y)) = u
    ]]></literal>
    <justification jstring="[para(6787(a,1),6234(a,1))].">
      <j1 rule="para" parents="6787 6234"/>
    </justification>
  </clause>

  <clause id="6804">
    <literal><![CDATA[
      x * K(K(y,z),x) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(6787(a,2),6766(a,1,2))].">
      <j1 rule="para" parents="6787 6766"/>
    </justification>
  </clause>

  <clause id="6805">
    <literal><![CDATA[
      K(x,y) * K(y,T(x,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(333,a,6407,a,b,6788,a)].">
      <j1 rule="hyper" parents="333 6407 6788"/>
    </justification>
  </clause>

  <clause id="6806">
    <literal><![CDATA[
      K(x,K(y,T(z,x))) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(333,a,6438,a(flip),b,6788,a),flip(a)].">
      <j1 rule="hyper" parents="333 6438 6788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6807">
    <literal><![CDATA[
      (x * y) * K(z,K(u,y)) = x * T(y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(126,a,6788,a,b,6005,a)].">
      <j1 rule="hyper" parents="126 6788 6005"/>
    </justification>
  </clause>

  <clause id="6808">
    <literal><![CDATA[
      x \ T(x * y,K(z,u)) = y * K(z,K(u,(x \ 1) \ y))
    ]]></literal>
    <justification jstring="[hyper(126,a,6788,a,b,5904,a),flip(a)].">
      <j1 rule="hyper" parents="126 6788 5904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6809">
    <literal><![CDATA[
      x * T(x \ y,K(z,u)) = y * K(z,K(u,x \ y))
    ]]></literal>
    <justification jstring="[hyper(126,a,6788,a,b,5859,a),flip(a)].">
      <j1 rule="hyper" parents="126 6788 5859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6810">
    <literal><![CDATA[
      K(x,K(y,z)) * (z * u) = T(z,K(x,y)) * u
    ]]></literal>
    <justification jstring="[hyper(125,a,6788,a,b,4259,a)].">
      <j1 rule="hyper" parents="125 6788 4259"/>
    </justification>
  </clause>

  <clause id="6811">
    <literal><![CDATA[
      K(x,K(y,((1 / z) / (u / z)) \ 1)) * (u / z) = T(u,K(x,y)) / z
    ]]></literal>
    <justification jstring="[hyper(125,a,6788,a,b,5219,a(flip))].">
      <j1 rule="hyper" parents="125 6788 5219"/>
    </justification>
  </clause>

  <clause id="6812">
    <literal><![CDATA[
      (K(x,y) * K(x,K(y,z))) * z = z * K(x,y)
    ]]></literal>
    <justification jstring="[para(6788(a,2),4291(a,1,1,2))].">
      <j1 rule="para" parents="6788 4291"/>
    </justification>
  </clause>

  <clause id="6813">
    <literal><![CDATA[
      K(x,K(y,z)) * (z * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(z,K(x,y)) * u = w
    ]]></literal>
    <justification jstring="[para(6788(a,2),4539(a,1,1))].">
      <j1 rule="para" parents="6788 4539"/>
    </justification>
  </clause>

  <clause id="6814">
    <literal><![CDATA[
      K(x,y) * K(x,K(z,y)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(6788(a,1),5295(a,1,2))].">
      <j1 rule="para" parents="6788 5295"/>
    </justification>
  </clause>

  <clause id="6815">
    <literal><![CDATA[
      (x * K(y,K(z,u))) / K(y,z) = x / T(K(y,z),u)
    ]]></literal>
    <justification jstring="[para(6788(a,2),5460(a,1,1,2))].">
      <j1 rule="para" parents="6788 5460"/>
    </justification>
  </clause>

  <clause id="6816">
    <literal><![CDATA[
      (x * K(y,K(z,u \ x))) / u = T(x / u,K(y,z))
    ]]></literal>
    <justification jstring="[para(6788(a,2),5914(a,1,1,2))].">
      <j1 rule="para" parents="6788 5914"/>
    </justification>
  </clause>

  <clause id="6817">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) = K(z,K(x,T(y,u)))
    ]]></literal>
    <justification jstring="[para(6370(a,1),6788(a,1,2))].">
      <j1 rule="para" parents="6370 6788"/>
    </justification>
  </clause>

  <clause id="6818">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,x) = K(y,T(x,z))
    ]]></literal>
    <justification jstring="[para(6788(a,2),6376(a,1,1))].">
      <j1 rule="para" parents="6788 6376"/>
    </justification>
  </clause>

  <clause id="6819">
    <literal><![CDATA[
      K(x,y) * K(y,K(x,z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(6788(a,2),6377(a,1,2))].">
      <j1 rule="para" parents="6788 6377"/>
    </justification>
  </clause>

  <clause id="6820">
    <literal><![CDATA[
      K(x,y) * K(z,K(x,y)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(6788(a,1),6759(a,1,2))].">
      <j1 rule="para" parents="6788 6759"/>
    </justification>
  </clause>

  <clause id="6821">
    <literal><![CDATA[
      K(x,K(y,z)) * x = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(6788(a,1),6767(a,1,1))].">
      <j1 rule="para" parents="6788 6767"/>
    </justification>
  </clause>

  <clause id="6822">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(y,z)) = 1
    ]]></literal>
    <justification jstring="[para(6788(a,1),6770(a,1,1))].">
      <j1 rule="para" parents="6788 6770"/>
    </justification>
  </clause>

  <clause id="6823">
    <literal><![CDATA[
      K(x,K(y,z)) / y = 1 / T(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(123,a,6796,a(flip),b,4213,a(flip))].">
      <j1 rule="hyper" parents="123 6796 4213"/>
    </justification>
  </clause>

  <clause id="6824">
    <literal><![CDATA[
      K(x,K(y,z)) * (y \ u) = T(y,K(x,z)) \ u
    ]]></literal>
    <justification jstring="[para(6796(a,1),4555(a,1,1))].">
      <j1 rule="para" parents="6796 4555"/>
    </justification>
  </clause>

  <clause id="6825">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,K(z,x)) = u
    ]]></literal>
    <justification jstring="[para(6796(a,1),6234(a,1))].">
      <j1 rule="para" parents="6796 6234"/>
    </justification>
  </clause>

  <clause id="6827">
    <literal><![CDATA[
      x / K(y,K(z,u)) = x * K(y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(197,a,6799,a(flip),b,5990,a)].">
      <j1 rule="hyper" parents="197 6799 5990"/>
    </justification>
  </clause>

  <clause id="6828">
    <literal><![CDATA[
      (x / y) * K(y,K(z,u)) = x / T(y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(126,a,6799,a(flip),b,5465,a)].">
      <j1 rule="hyper" parents="126 6799 5465"/>
    </justification>
  </clause>

  <clause id="6829">
    <literal><![CDATA[
      K(x,K(y,z)) \ u = K(x,K(y,z)) * u
    ]]></literal>
    <justification jstring="[hyper(125,a,6799,a(flip),b,4564,a),flip(a)].">
      <j1 rule="hyper" parents="125 6799 4564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6830">
    <literal><![CDATA[
      K(x,K(y,z)) * (x \ u) = T(x,K(y,z)) \ u
    ]]></literal>
    <justification jstring="[para(6799(a,1),4555(a,1,1))].">
      <j1 rule="para" parents="6799 4555"/>
    </justification>
  </clause>

  <clause id="6831">
    <literal><![CDATA[
      K(x,K(y,z)) \ (x * u) = T(x,K(y,z)) * u
    ]]></literal>
    <justification jstring="[para(6799(a,1),4598(a,1,1))].">
      <j1 rule="para" parents="6799 4598"/>
    </justification>
  </clause>

  <clause id="6832">
    <literal><![CDATA[
      K(x,K(y,z)) * u != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) * w = u
    ]]></literal>
    <justification jstring="[para(6799(a,1),4577(a,1,1))].">
      <j1 rule="para" parents="6799 4577"/>
    </justification>
  </clause>

  <clause id="6833">
    <literal><![CDATA[
      K(x,K(y,z)) * u != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) \ u = w
    ]]></literal>
    <justification jstring="[para(6799(a,1),4585(a,1,1))].">
      <j1 rule="para" parents="6799 4585"/>
    </justification>
  </clause>

  <clause id="6834">
    <literal><![CDATA[
      K(x,K(y,z)) * (x \ u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) \ u = w
    ]]></literal>
    <justification jstring="[para(6799(a,1),4697(a,1,1))].">
      <j1 rule="para" parents="6799 4697"/>
    </justification>
  </clause>

  <clause id="6835">
    <literal><![CDATA[
      x * (K(y,x) * K(y,K(z,u))) = (y * x) / T(y,K(z,u))
    ]]></literal>
    <justification jstring="[para(6799(a,1),5471(a,1,2,2))].">
      <j1 rule="para" parents="6799 5471"/>
    </justification>
  </clause>

  <clause id="6836">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(6799(a,1),6234(a,1))].">
      <j1 rule="para" parents="6799 6234"/>
    </justification>
  </clause>

  <clause id="6837">
    <literal><![CDATA[
      K(x,y) * K(y,T(x,z)) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(333,a,6407,a,b,6800,a)].">
      <j1 rule="hyper" parents="333 6407 6800"/>
    </justification>
  </clause>

  <clause id="6838">
    <literal><![CDATA[
      K(x,K(y,T(z,x))) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(333,a,6404,a,b,6800,a)].">
      <j1 rule="hyper" parents="333 6404 6800"/>
    </justification>
  </clause>

  <clause id="6839">
    <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(333,a,4438,a,b,6800,a)].">
      <j1 rule="hyper" parents="333 4438 6800"/>
    </justification>
  </clause>

  <clause id="6840">
    <literal><![CDATA[
      T(x,K(y,z)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(124,a,6800,a,b,4837,a)].">
      <j1 rule="hyper" parents="124 6800 4837"/>
    </justification>
  </clause>

  <clause id="6841">
    <literal><![CDATA[
      K(x,K(y,((1 / z) / (u / z)) \ 1)) = K(x,(T(u,y) / z) / (u / z))
    ]]></literal>
    <justification jstring="[para(5219(a,1),6800(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5219 6800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6842">
    <literal><![CDATA[
      K(x,y) * K(z,K(x,y)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(6800(a,1),6377(a,1,2))].">
      <j1 rule="para" parents="6800 6377"/>
    </justification>
  </clause>

  <clause id="6843">
    <literal><![CDATA[
      K(x,K(y,L(z,z,u))) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(6707(a,2),6800(a,1,2))].">
      <j1 rule="para" parents="6707 6800"/>
    </justification>
  </clause>

  <clause id="6844">
    <literal><![CDATA[
      (K(x,y) * z) * K(y,x) = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(6113,a,6840,a)].">
      <j1 rule="hyper" parents="6113 6840"/>
    </justification>
  </clause>

  <clause id="6845">
    <literal><![CDATA[
      T(x * K(y,z),K(y,z)) = K(y,z) * x
    ]]></literal>
    <justification jstring="[hyper(6106,a,6840,a),flip(a)].">
      <j1 rule="hyper" parents="6106 6840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6846">
    <literal><![CDATA[
      T(K(x,y) * z,K(y,x)) = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6097,a,6840,a),flip(a)].">
      <j1 rule="hyper" parents="6097 6840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6847">
    <literal><![CDATA[
      T(K(x,y) \ z,K(x,y)) = z * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(6096,a,6840,a),flip(a)].">
      <j1 rule="hyper" parents="6096 6840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6848">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(5310,a,6840,a)].">
      <j1 rule="hyper" parents="5310 6840"/>
    </justification>
  </clause>

  <clause id="6849">
    <literal><![CDATA[
      K(x,y) * (z * K(y,x)) = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(4582,a,6840,a)].">
      <j1 rule="hyper" parents="4582 6840"/>
    </justification>
  </clause>

  <clause id="6850">
    <literal><![CDATA[
      T(T(x,K(y,z)),u) = T(T(x,u),K(z,y))
    ]]></literal>
    <justification jstring="[hyper(437,a,6840,a)].">
      <j1 rule="hyper" parents="437 6840"/>
    </justification>
  </clause>

  <clause id="6851">
    <literal><![CDATA[
      T(T(x,y),K(z,y)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(333,a,6191,a(flip),b,6840,a),flip(a)].">
      <j1 rule="hyper" parents="333 6191 6840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6852">
    <literal><![CDATA[
      K(x,y) * T(z,K(y,x)) = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(126,a,6840,a,b,22,a(flip))].">
      <j1 rule="hyper" parents="126 6840 22"/>
    </justification>
  </clause>

  <clause id="6853">
    <literal><![CDATA[
      K(x,y) \ T(z,K(x,y)) = z * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(121,a,6840,a,b,4565,a)].">
      <j1 rule="hyper" parents="121 6840 4565"/>
    </justification>
  </clause>

  <clause id="6854">
    <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(6840(a,1),437(a,1))].">
      <j1 rule="para" parents="6840 437"/>
    </justification>
  </clause>

  <clause id="6855">
    <literal><![CDATA[
      T(x,K(y,z)) * (T(K(z,y),x) * u) = x * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(6840(a,1),4613(a,1,1))].">
      <j1 rule="para" parents="6840 4613"/>
    </justification>
  </clause>

  <clause id="6856">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(6840(a,1),5306(a,1,1))].">
      <j1 rule="para" parents="6840 5306"/>
    </justification>
  </clause>

  <clause id="6857">
    <literal><![CDATA[
      T(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(u,K(y,z)) = x
    ]]></literal>
    <justification jstring="[para(6840(a,1),5310(a,1))].">
      <j1 rule="para" parents="6840 5310"/>
    </justification>
  </clause>

  <clause id="6858">
    <literal><![CDATA[
      T(x,K(y,z)) * K(y,z) = K(y,z) * x
    ]]></literal>
    <justification jstring="[para(6840(a,1),5304(a,1,1))].">
      <j1 rule="para" parents="6840 5304"/>
    </justification>
  </clause>

  <clause id="6859">
    <literal><![CDATA[
      T(T(x,K(y,z)),z) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(6840(a,1),6190(a,1,1))].">
      <j1 rule="para" parents="6840 6190"/>
    </justification>
  </clause>

  <clause id="6860">
    <literal><![CDATA[
      T(x * K(y,z),K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) * x = u
    ]]></literal>
    <justification jstring="[para(6840(a,1),6106(a,1))].">
      <j1 rule="para" parents="6840 6106"/>
    </justification>
  </clause>

  <clause id="6861">
    <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(843,a,6848,a)].">
      <j1 rule="hyper" parents="843 6848"/>
    </justification>
  </clause>

  <clause id="6862">
    <literal><![CDATA[
      (K(x,y) * z) / K(x,y) = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(742,a,6848,a),flip(a)].">
      <j1 rule="hyper" parents="742 6848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6863">
    <literal><![CDATA[
      T(T(x,T(y,z)),K(y,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,6194,a(flip),b,6848,a)].">
      <j1 rule="hyper" parents="63 6194 6848"/>
    </justification>
  </clause>

  <clause id="6864">
    <literal><![CDATA[
      T(x * (y * K(x,z)),K(x,z)) = T(x,z) * y
    ]]></literal>
    <justification jstring="[hyper(40,a,6174,a,b,6848,a),flip(a)].">
      <j1 rule="hyper" parents="40 6174 6848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6865">
    <literal><![CDATA[
      (x * K(y,z)) / x = T(K(y,z),x)
    ]]></literal>
    <justification jstring="[hyper(197,a,6848,a(flip),b,3800,a)].">
      <j1 rule="hyper" parents="197 6848 3800"/>
    </justification>
  </clause>

  <clause id="6866">
    <literal><![CDATA[
      T(K(x,y),z) * z = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(126,a,6848,a(flip),b,3800,a)].">
      <j1 rule="hyper" parents="126 6848 3800"/>
    </justification>
  </clause>

  <clause id="6867">
    <literal><![CDATA[
      (K(x,y) * z) / K(x,y) != u
    ]]></literal>
    <literal><![CDATA[
      T(z,K(x,y)) = u
    ]]></literal>
    <justification jstring="[para(6848(a,1),302(a,1,1,2)),flip(b)].">
      <j1 rule="para" parents="6848 302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6868">
    <literal><![CDATA[
      T(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(6848(a,1),5305(a,1,1)),flip(b)].">
      <j1 rule="para" parents="6848 5305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6869">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(y,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(6848(a,1),6190(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6848 6190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6870">
    <literal><![CDATA[
      K(x,K(y,z * y)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(333,a,6800,a,b,6784,a),flip(a)].">
      <j1 rule="hyper" parents="333 6800 6784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6871">
    <literal><![CDATA[
      K(x,K(y,z * y)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(333,a,6785,a,b,6784,a),flip(a)].">
      <j1 rule="hyper" parents="333 6785 6784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6872">
    <literal><![CDATA[
      K(x,K(y,z / y)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(12(a,1),6784(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 6784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6873">
    <literal><![CDATA[
      K(x,K(a(y,z,u),(y * z) * u)) = K(x,K(a(y,z,u),y * (z * u)))
    ]]></literal>
    <justification jstring="[para(84(a,1),6784(a,1,2,2))].">
      <j1 rule="para" parents="84 6784"/>
    </justification>
  </clause>

  <clause id="6874">
    <literal><![CDATA[
      K(x,K(y,y * z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(4636(a,1),6784(a,1,2))].">
      <j1 rule="para" parents="4636 6784"/>
    </justification>
  </clause>

  <clause id="6875">
    <literal><![CDATA[
      T(x / y,K(((x / y) \ (1 / y)) \ 1,z)) = T(x,K(z,x / y)) / y
    ]]></literal>
    <justification jstring="[hyper(63,a,4490,a(flip),b,6794,a),flip(a)].">
      <j1 rule="hyper" parents="63 4490 6794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6876">
    <literal><![CDATA[
      T(T(T(x,K(y,z)),u),K(y,z)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u) = w
    ]]></literal>
    <justification jstring="[para(6804(a,1),4424(a,1,1,1))].">
      <j1 rule="para" parents="6804 4424"/>
    </justification>
  </clause>

  <clause id="6877">
    <literal><![CDATA[
      T(T(x,y / z),K(y,y / z)) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(333,a,6466,a(flip),b,6851,a),flip(a)].">
      <j1 rule="hyper" parents="333 6466 6851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6878">
    <literal><![CDATA[
      T(x,K(y,z)) * z = z * T(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(126,a,6851,a(flip),b,115,a),flip(a)].">
      <j1 rule="hyper" parents="126 6851 115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6879">
    <literal><![CDATA[
      T(x,T(y,z)) * K(y,z) = K(y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(6851(a,1),5304(a,1,1))].">
      <j1 rule="para" parents="6851 5304"/>
    </justification>
  </clause>

  <clause id="6880">
    <literal><![CDATA[
      K(x,T(y,T(z,x))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(6851(a,1),6384(a,1,2))].">
      <j1 rule="para" parents="6851 6384"/>
    </justification>
  </clause>

  <clause id="6881">
    <literal><![CDATA[
      T((x * y) \ y,K(z,x)) = (x * y) \ y
    ]]></literal>
    <justification jstring="[hyper(40,a,5223,a(flip),b,6859,a),flip(a)].">
      <j1 rule="hyper" parents="40 5223 6859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6882">
    <literal><![CDATA[
      T(x,T(y,z)) != T(u,y)
    ]]></literal>
    <literal><![CDATA[
      T(u,K(y,z)) = x
    ]]></literal>
    <justification jstring="[para(6863(a,1),147(a,1)),flip(a)].">
      <j1 rule="para" parents="6863 147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6883">
    <literal><![CDATA[
      T(T(x,y),K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(6863(a,1),5305(a,1,1)),flip(b)].">
      <j1 rule="para" parents="6863 5305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6884">
    <literal><![CDATA[
      (x * K(y,z)) / x = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(333,a,6365,a,b,6865,a),flip(a)].">
      <j1 rule="hyper" parents="333 6365 6865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6885">
    <literal><![CDATA[
      x * ((x * K(y,z)) / x) = K(y,z) * x
    ]]></literal>
    <justification jstring="[hyper(126,a,6865,a,b,22,a(flip))].">
      <j1 rule="hyper" parents="126 6865 22"/>
    </justification>
  </clause>

  <clause id="6886">
    <literal><![CDATA[
      K(x,T(T(y,z),u)) * z = z * K(x,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(125,a,6394,a,b,6865,a)].">
      <j1 rule="hyper" parents="125 6394 6865"/>
    </justification>
  </clause>

  <clause id="6887">
    <literal><![CDATA[
      K(x,T(y,z)) * z = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(125,a,6365,a,b,6865,a)].">
      <j1 rule="hyper" parents="125 6365 6865"/>
    </justification>
  </clause>

  <clause id="6888">
    <literal><![CDATA[
      K(T(x,y),z) * y = y * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(125,a,6352,a,b,6865,a)].">
      <j1 rule="hyper" parents="125 6352 6865"/>
    </justification>
  </clause>

  <clause id="6889">
    <literal><![CDATA[
      K(x \ y,z) * y = y * K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(125,a,5910,a(flip),b,6865,a)].">
      <j1 rule="hyper" parents="125 5910 6865"/>
    </justification>
  </clause>

  <clause id="6890">
    <literal><![CDATA[
      K(x,y \ z) * z = z * K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(125,a,5773,a(flip),b,6865,a)].">
      <j1 rule="hyper" parents="125 5773 6865"/>
    </justification>
  </clause>

  <clause id="6891">
    <literal><![CDATA[
      T(T(K(x,y),z),z) = K(x,y)
    ]]></literal>
    <justification jstring="[para(6865(a,1),238(a,1,1))].">
      <j1 rule="para" parents="6865 238"/>
    </justification>
  </clause>

  <clause id="6892">
    <literal><![CDATA[
      L(T(K(x,y),z),u,w) * z = z * L(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(6865(a,1),669(a,1,1,1))].">
      <j1 rule="para" parents="6865 669"/>
    </justification>
  </clause>

  <clause id="6893">
    <literal><![CDATA[
      T(K(x,y \ z),z) = K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(5817,a,6891,a),flip(a)].">
      <j1 rule="hyper" parents="5817 6891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6894">
    <literal><![CDATA[
      T(K(1 / T(x,y),z),y) = K(1 / x,z)
    ]]></literal>
    <justification jstring="[hyper(5290,a,6891,a),flip(a)].">
      <j1 rule="hyper" parents="5290 6891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6896">
    <literal><![CDATA[
      T(K(x,T(y,z)),z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(40,a,6365,a(flip),b,6891,a),flip(a)].">
      <j1 rule="hyper" parents="40 6365 6891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6897">
    <literal><![CDATA[
      T(K(T(x,y),z),y) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(40,a,6352,a(flip),b,6891,a),flip(a)].">
      <j1 rule="hyper" parents="40 6352 6891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6898">
    <literal><![CDATA[
      R(T(K(x,y),z),u,w) * z = z * R(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(6891(a,1),252(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6891 252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6899">
    <literal><![CDATA[
      L(T(K(x,y),z),u,w) \ (z * L(K(x,y),u,w)) = z
    ]]></literal>
    <justification jstring="[para(6891(a,1),292(a,1,2,2,1))].">
      <j1 rule="para" parents="6891 292"/>
    </justification>
  </clause>

  <clause id="6900">
    <literal><![CDATA[
      K(x,T(T(y,z),z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6691,a,6896,a)].">
      <j1 rule="hyper" parents="6691 6896"/>
    </justification>
  </clause>

  <clause id="6901">
    <literal><![CDATA[
      K(T(x,y),T(z,y)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(6611,a,6896,a)].">
      <j1 rule="hyper" parents="6611 6896"/>
    </justification>
  </clause>

  <clause id="6902">
    <literal><![CDATA[
      K(x,T(y \ z,z)) = K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(5817,a,6896,a),flip(a)].">
      <j1 rule="hyper" parents="5817 6896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6904">
    <literal><![CDATA[
      K(x \ y,T(z,y)) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5910,a(flip),b,6896,a)].">
      <j1 rule="hyper" parents="63 5910 6896"/>
    </justification>
  </clause>

  <clause id="6905">
    <literal><![CDATA[
      K(x,T((y \ z) \ 1,y)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(40,a,5150,a,b,6896,a),flip(a)].">
      <j1 rule="hyper" parents="40 5150 6896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6906">
    <literal><![CDATA[
      T(K(x,y \ z),y) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(113(a,1),6896(a,1,1,2))].">
      <j1 rule="para" parents="113 6896"/>
    </justification>
  </clause>

  <clause id="6907">
    <literal><![CDATA[
      R(K(x,T(y,z)),u,w) * z = z * R(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(6896(a,1),252(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6896 252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6908">
    <literal><![CDATA[
      (K(x,T(y,z * u)) * z) * u = (z * u) * R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(6896(a,1),673(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6896 673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6909">
    <literal><![CDATA[
      (K(x,T(y,z)) * u) * (u \ z) = z * R(K(x,y),u,u \ z)
    ]]></literal>
    <justification jstring="[para(6896(a,1),776(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6896 776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6910">
    <literal><![CDATA[
      T(K(x \ y,z),x) = K(y / x,z)
    ]]></literal>
    <justification jstring="[para(6431(a,1),6896(a,1,1))].">
      <j1 rule="para" parents="6431 6896"/>
    </justification>
  </clause>

  <clause id="6911">
    <literal><![CDATA[
      T(T(x,y),T(z,y)) = K(x,z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(6896(a,1),6358(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6896 6358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6913">
    <literal><![CDATA[
      K(T(x,y),L(T(z,y),u,w)) = K(x,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,6396,a,b,6897,a)].">
      <j1 rule="hyper" parents="63 6396 6897"/>
    </justification>
  </clause>

  <clause id="6916">
    <literal><![CDATA[
      K(x,T(y,z)) \ z = z * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(126,a,6897,a(flip),b,4566,a),flip(a)].">
      <j1 rule="hyper" parents="126 6897 4566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6917">
    <literal><![CDATA[
      T(x,T(T(y,z),z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(124,a,6900,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 6900 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6918">
    <literal><![CDATA[
      K(R(T(x,y),z,u),T(w,y)) = K(R(x,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,6430,a,b,6900,a)].">
      <j1 rule="hyper" parents="63 6430 6900"/>
    </justification>
  </clause>

  <clause id="6919">
    <literal><![CDATA[
      K(L(T(x,y),z,u),T(w,y)) = K(L(x,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,6429,a,b,6900,a)].">
      <j1 rule="hyper" parents="63 6429 6900"/>
    </justification>
  </clause>

  <clause id="6920">
    <literal><![CDATA[
      K(L(x,y,x),z) = K(x,T(T(z,u),u * x))
    ]]></literal>
    <justification jstring="[hyper(63,a,6535,a(flip),b,6900,a),flip(a)].">
      <j1 rule="hyper" parents="63 6535 6900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6921">
    <literal><![CDATA[
      K((x * y) / x,z) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,6433,a(flip),b,6900,a),flip(a)].">
      <j1 rule="hyper" parents="63 6433 6900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6922">
    <literal><![CDATA[
      K(x \ y,T(z,x)) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,6431,a(flip),b,6900,a)].">
      <j1 rule="hyper" parents="63 6431 6900"/>
    </justification>
  </clause>

  <clause id="6923">
    <literal><![CDATA[
      K(x,T(y \ z,y)) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(113(a,1),6900(a,1,2,1))].">
      <j1 rule="para" parents="113 6900"/>
    </justification>
  </clause>

  <clause id="6924">
    <literal><![CDATA[
      K(x,(y * z) / y) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(238(a,1),6900(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="238 6900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6925">
    <literal><![CDATA[
      K(x,y * K(z,y)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(4239(a,1),6900(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4239 6900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6926">
    <literal><![CDATA[
      x * K(T(x,y),T(z,y)) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(126,a,6901,a,b,4215,a(flip))].">
      <j1 rule="hyper" parents="126 6901 4215"/>
    </justification>
  </clause>

  <clause id="6927">
    <literal><![CDATA[
      K(x / (x / y),z) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,6313,a(flip),b,6901,a),flip(a)].">
      <j1 rule="hyper" parents="63 6313 6901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6928">
    <literal><![CDATA[
      K(T(x,y),y \ z) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(113(a,1),6901(a,1,2))].">
      <j1 rule="para" parents="113 6901"/>
    </justification>
  </clause>

  <clause id="6929">
    <literal><![CDATA[
      K(x,(y * z) / y) = K(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(238(a,1),6901(a,1,2)),flip(a)].">
      <j1 rule="para" parents="238 6901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6930">
    <literal><![CDATA[
      K(x,((y * z) * u) / (y * u)) = K(T(x,y),R(z,y,u))
    ]]></literal>
    <justification jstring="[para(830(a,2),6901(a,1,2)),flip(a)].">
      <j1 rule="para" parents="830 6901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6932">
    <literal><![CDATA[
      K(x \ T(x * y,y),z) = K(y,T(z,x * y))
    ]]></literal>
    <justification jstring="[para(3446(a,1),6901(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3446 6901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6933">
    <literal><![CDATA[
      L(x,T(y,z) \ 1,K(y,u)) = x
    ]]></literal>
    <justification jstring="[para(6901(a,1),3566(a,1,3))].">
      <j1 rule="para" parents="6901 3566"/>
    </justification>
  </clause>

  <clause id="6934">
    <literal><![CDATA[
      K(T(x,y \ z),y) = K(x,z / (z / y))
    ]]></literal>
    <justification jstring="[para(3701(a,1),6901(a,1,2))].">
      <j1 rule="para" parents="3701 6901"/>
    </justification>
  </clause>

  <clause id="6935">
    <literal><![CDATA[
      K(x * K(y,x),z) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(4239(a,1),6901(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4239 6901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6936">
    <literal><![CDATA[
      K(x,y * K(z,y)) = K(T(x,z),y)
    ]]></literal>
    <justification jstring="[para(4239(a,1),6901(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4239 6901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6938">
    <literal><![CDATA[
      T(T(x,y),T(z,y)) \ x = K(z,x) * K(y,x)
    ]]></literal>
    <justification jstring="[para(6901(a,1),4553(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6901 4553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6939">
    <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(6901(a,1),5360(a,1,1))].">
      <j1 rule="para" parents="6901 5360"/>
    </justification>
  </clause>

  <clause id="6940">
    <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(6901(a,1),5654(a,1,1))].">
      <j1 rule="para" parents="6901 5654"/>
    </justification>
  </clause>

  <clause id="6941">
    <literal><![CDATA[
      R(x,K(y,z),T(y,u)) = x
    ]]></literal>
    <justification jstring="[para(6901(a,1),6059(a,1,2))].">
      <j1 rule="para" parents="6901 6059"/>
    </justification>
  </clause>

  <clause id="6942">
    <literal><![CDATA[
      K(x,T(y,L(z,u,x))) = K(x * K(z,x),y)
    ]]></literal>
    <justification jstring="[para(6308(a,1),6901(a,1,1))].">
      <j1 rule="para" parents="6308 6901"/>
    </justification>
  </clause>

  <clause id="6943">
    <literal><![CDATA[
      K(x,T(y,z)) * (z * K(y,x)) = z
    ]]></literal>
    <justification jstring="[para(6901(a,1),6483(a,1,2,2))].">
      <j1 rule="para" parents="6901 6483"/>
    </justification>
  </clause>

  <clause id="6944">
    <literal><![CDATA[
      T(T(x,y),T(z,y)) = K(x,y) * T(x,z)
    ]]></literal>
    <justification jstring="[hyper(126,a,6917,a(flip),b,6621,a),flip(a)].">
      <j1 rule="hyper" parents="126 6917 6621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6945">
    <literal><![CDATA[
      T(T(x,y),y) * T(z,x) = z * T(T(x,y),y)
    ]]></literal>
    <justification jstring="[hyper(126,a,6917,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="126 6917 22"/>
    </justification>
  </clause>

  <clause id="6946">
    <literal><![CDATA[
      T(x,T(y \ z,y)) = T(x,z / y)
    ]]></literal>
    <justification jstring="[para(113(a,1),6917(a,1,2,1))].">
      <j1 rule="para" parents="113 6917"/>
    </justification>
  </clause>

  <clause id="6947">
    <literal><![CDATA[
      T(x,(y * z) / y) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(238(a,1),6917(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="238 6917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6948">
    <literal><![CDATA[
      T(x,T(T(y \ z,u),y)) = T(x,T(z / y,u))
    ]]></literal>
    <justification jstring="[para(259(a,1),6917(a,1,2,1))].">
      <j1 rule="para" parents="259 6917"/>
    </justification>
  </clause>

  <clause id="6949">
    <literal><![CDATA[
      T(x,T(y \ T(z,y),y)) = T(x,z / T(y,z))
    ]]></literal>
    <justification jstring="[para(3622(a,1),6917(a,1,2,1))].">
      <j1 rule="para" parents="3622 6917"/>
    </justification>
  </clause>

  <clause id="6950">
    <literal><![CDATA[
      T(x,y * K(z,y)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(4239(a,1),6917(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4239 6917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6951">
    <literal><![CDATA[
      K(x,K(y,z * x)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,6785,a,b,6871,a)].">
      <j1 rule="hyper" parents="63 6785 6871"/>
    </justification>
  </clause>

  <clause id="6952">
    <literal><![CDATA[
      K(x,K(y,y * z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[para(4636(a,1),6871(a,1,2))].">
      <j1 rule="para" parents="4636 6871"/>
    </justification>
  </clause>

  <clause id="6953">
    <literal><![CDATA[
      T(x,K(y,z / y)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(124,a,6872,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 6872 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6954">
    <literal><![CDATA[
      K(x,K(y,y \ z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(4368(a,1),6872(a,1,2))].">
      <j1 rule="para" parents="4368 6872"/>
    </justification>
  </clause>

  <clause id="6955">
    <literal><![CDATA[
      K(x,K(y,z \ 1)) = K(x,K(y,z \ y))
    ]]></literal>
    <justification jstring="[para(5061(a,1),6872(a,1,2))].">
      <j1 rule="para" parents="5061 6872"/>
    </justification>
  </clause>

  <clause id="6956">
    <literal><![CDATA[
      T(x,K(y,y * z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(124,a,6874,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 6874 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6957">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y * z,y) = K(y * z,T(y,x))
    ]]></literal>
    <justification jstring="[para(6874(a,1),6376(a,1,1))].">
      <j1 rule="para" parents="6874 6376"/>
    </justification>
  </clause>

  <clause id="6958">
    <literal><![CDATA[
      K(x * y,T(z,T(x,y))) = K(x * y,T(z,x))
    ]]></literal>
    <justification jstring="[para(6464(a,1),6880(a,1,2))].">
      <j1 rule="para" parents="6464 6880"/>
    </justification>
  </clause>

  <clause id="6959">
    <literal><![CDATA[
      K(x,T(y \ x,T(z,y))) = K(x,T(y \ x,z))
    ]]></literal>
    <justification jstring="[para(6546(a,1),6880(a,1,2))].">
      <j1 rule="para" parents="6546 6880"/>
    </justification>
  </clause>

  <clause id="6960">
    <literal><![CDATA[
      T(K(x,T(y,z)),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(6884(a,1),350(a,1,1)),flip(b)].">
      <j1 rule="para" parents="6884 350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6961">
    <literal><![CDATA[
      K(x,T(y,z)) * z != z * u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(6884(a,1),132(a,1,1))].">
      <j1 rule="para" parents="6884 132"/>
    </justification>
  </clause>

  <clause id="6962">
    <literal><![CDATA[
      K(x,T(y,z)) * z != u * w
    ]]></literal>
    <literal><![CDATA[
      (z * K(x,y)) / w = u
    ]]></literal>
    <justification jstring="[para(6884(a,1),410(a,1,1))].">
      <j1 rule="para" parents="6884 410"/>
    </justification>
  </clause>

  <clause id="6963">
    <literal><![CDATA[
      (x * L(K(y,z),u,w)) / x = L(K(y,T(z,x)),u,w)
    ]]></literal>
    <justification jstring="[para(6884(a,1),891(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6884 891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6965">
    <literal><![CDATA[
      (x * (y * K(z,u))) / (x * y) = L(K(z,T(u,x * y)),y,x)
    ]]></literal>
    <justification jstring="[para(6884(a,1),892(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6884 892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6966">
    <literal><![CDATA[
      (x * K(y,T(z,u))) * u = (x * K(y,z)) * T(u,K(y,z))
    ]]></literal>
    <justification jstring="[para(6884(a,1),6050(a,1,1,2))].">
      <j1 rule="para" parents="6884 6050"/>
    </justification>
  </clause>

  <clause id="6967">
    <literal><![CDATA[
      x * T(x \ y,T(z,y)) = y * K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,4243,a(flip),b,6887,a)].">
      <j1 rule="hyper" parents="63 4243 6887"/>
    </justification>
  </clause>

  <clause id="6968">
    <literal><![CDATA[
      x / (x * K(y,z)) = K(z,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(197,a,6887,a(flip),b,6427,a)].">
      <j1 rule="hyper" parents="197 6887 6427"/>
    </justification>
  </clause>

  <clause id="6969">
    <literal><![CDATA[
      R(x / K(y,T(z,u)),K(y,T(z,u)),u) = (x * u) / (u * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(197,a,6887,a(flip),b,530,a),flip(a)].">
      <j1 rule="hyper" parents="197 6887 530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6970">
    <literal><![CDATA[
      T(x,T(y,z)) * z = x * (z * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(126,a,6887,a(flip),b,4515,a),flip(a)].">
      <j1 rule="hyper" parents="126 6887 4515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6971">
    <literal><![CDATA[
      K(x,y \ z) * y = y * K(x,z / y)
    ]]></literal>
    <justification jstring="[para(113(a,1),6887(a,1,1,2))].">
      <j1 rule="para" parents="113 6887"/>
    </justification>
  </clause>

  <clause id="6972">
    <literal><![CDATA[
      (x * K(y,z)) * a(K(y,T(z,x)),u,u \ x) = (K(y,T(z,x)) * u) * (u \ x)
    ]]></literal>
    <justification jstring="[para(6887(a,1),749(a,1,1))].">
      <j1 rule="para" parents="6887 749"/>
    </justification>
  </clause>

  <clause id="6973">
    <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(6887(a,1),4574(a,1,1,3)),flip(a)].">
      <j1 rule="para" parents="6887 4574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6974">
    <literal><![CDATA[
      K(K(x,y) * z,u) * z = z * K(z * K(x,y),u)
    ]]></literal>
    <justification jstring="[para(6470(a,1),6888(a,1,1))].">
      <j1 rule="para" parents="6470 6888"/>
    </justification>
  </clause>

  <clause id="6976">
    <literal><![CDATA[
      K(x,T(y \ (x * z),z)) = K(x,(x * z) / y)
    ]]></literal>
    <justification jstring="[hyper(63,a,6421,a(flip),b,6893,a)].">
      <j1 rule="hyper" parents="63 6421 6893"/>
    </justification>
  </clause>

  <clause id="6977">
    <literal><![CDATA[
      T(x,T(y \ z,z)) = T(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(124,a,6902,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 6902 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6979">
    <literal><![CDATA[
      K(x,y / (y / z)) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(79(a,1),6902(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="79 6902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6982">
    <literal><![CDATA[
      L(x,K(y / z,u),z \ y) = x
    ]]></literal>
    <justification jstring="[para(6904(a,1),3867(a,1,2))].">
      <j1 rule="para" parents="6904 3867"/>
    </justification>
  </clause>

  <clause id="6983">
    <literal><![CDATA[
      K(x / (x / y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(6904(a,1),4739(a,1))].">
      <j1 rule="para" parents="6904 4739"/>
    </justification>
  </clause>

  <clause id="6984">
    <literal><![CDATA[
      K(x,y \ z) * (z * K(z / y,x)) = z
    ]]></literal>
    <justification jstring="[para(6904(a,1),6483(a,1,2,2))].">
      <j1 rule="para" parents="6904 6483"/>
    </justification>
  </clause>

  <clause id="6985">
    <literal><![CDATA[
      L(x,K(y \ 1,z),u \ (y \ u)) = x
    ]]></literal>
    <justification jstring="[para(4972(a,1),6982(a,1,2))].">
      <j1 rule="para" parents="4972 6982"/>
    </justification>
  </clause>

  <clause id="6987">
    <literal><![CDATA[
      T(K(x \ y,z),x) = K((x / y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,4965,a,b,6910,a),flip(a)].">
      <j1 rule="hyper" parents="333 4965 6910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6988">
    <literal><![CDATA[
      K(x \ y,T(T(z,x),u)) = K(y / x,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,6394,a,b,6910,a)].">
      <j1 rule="hyper" parents="63 6394 6910"/>
    </justification>
  </clause>

  <clause id="6989">
    <literal><![CDATA[
      K(x / ((y * z) \ y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(((y * z) \ y) \ x,z) = u
    ]]></literal>
    <justification jstring="[para(6910(a,1),6554(a,1))].">
      <j1 rule="para" parents="6910 6554"/>
    </justification>
  </clause>

  <clause id="6991">
    <literal><![CDATA[
      K(x,T(y,z)) \ (z / x) = (z / x) * K(y,x)
    ]]></literal>
    <justification jstring="[para(6536(a,1),6916(a,1,1))].">
      <j1 rule="para" parents="6536 6916"/>
    </justification>
  </clause>

  <clause id="6992">
    <literal><![CDATA[
      K(((x * y) * z) / (x * (y * z)),u) = K(a(x,y,z),T(u,x * (y * z)))
    ]]></literal>
    <justification jstring="[para(84(a,1),6921(a,1,1,1))].">
      <j1 rule="para" parents="84 6921"/>
    </justification>
  </clause>

  <clause id="6993">
    <literal><![CDATA[
      K(R((x * y) / x,z,u),w) = K(R(y,z,u),T(w,x))
    ]]></literal>
    <justification jstring="[para(902(a,2),6921(a,1,1))].">
      <j1 rule="para" parents="902 6921"/>
    </justification>
  </clause>

  <clause id="6994">
    <literal><![CDATA[
      x \ (T((y * x) / y,z) * u) = K(y,x) * (K(x,T(z,y)) * u)
    ]]></literal>
    <justification jstring="[para(6921(a,1),4816(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6921 4816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6995">
    <literal><![CDATA[
      K(((x \ y) * z) / (x \ y),T(x,y)) = K(z,(x \ T(y,x)) \ y)
    ]]></literal>
    <justification jstring="[para(6685(a,1),6921(a,2,2))].">
      <j1 rule="para" parents="6685 6921"/>
    </justification>
  </clause>

  <clause id="6996">
    <literal><![CDATA[
      K((x \ y) \ 1,T(z,y)) = K(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5852,a,b,6922,a)].">
      <j1 rule="hyper" parents="63 5852 6922"/>
    </justification>
  </clause>

  <clause id="6997">
    <literal><![CDATA[
      K(x / y,y * K(z,u)) = K(y \ x,K(z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,6481,a(flip),b,6922,a),flip(a)].">
      <j1 rule="hyper" parents="63 6481 6922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6998">
    <literal><![CDATA[
      x * T(x \ y,T(z,x)) = y * K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(126,a,6922,a(flip),b,5859,a),flip(a)].">
      <j1 rule="hyper" parents="126 6922 5859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6999">
    <literal><![CDATA[
      K(x \ y,T(z,x)) / (x \ y) = (1 / (x \ y)) * K(y / x,z)
    ]]></literal>
    <justification jstring="[para(6922(a,1),3561(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6922 3561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7000">
    <literal><![CDATA[
      K(x / (y \ z),z / (z / y)) = K((y \ z) \ x,y)
    ]]></literal>
    <justification jstring="[para(3701(a,1),6922(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3701 6922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7001">
    <literal><![CDATA[
      K((x * y) / x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(6922(a,1),4614(a,1))].">
      <j1 rule="para" parents="6922 4614"/>
    </justification>
  </clause>

  <clause id="7002">
    <literal><![CDATA[
      (x * K(x / y,z)) / y = T(x / y,T(z,y))
    ]]></literal>
    <justification jstring="[para(6922(a,1),5914(a,1,1,2))].">
      <j1 rule="para" parents="6922 5914"/>
    </justification>
  </clause>

  <clause id="7003">
    <literal><![CDATA[
      K(x,((y * z) * u) / (y * (z * u))) = K(x,T(a(y,z,u),y * (z * u)))
    ]]></literal>
    <justification jstring="[para(14(a,2),6923(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14 6923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7004">
    <literal><![CDATA[
      K(x,(y * (z * u)) / (y * z)) = K(x,T(L(u,z,y),y * z))
    ]]></literal>
    <justification jstring="[para(18(a,2),6923(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="18 6923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7006">
    <literal><![CDATA[
      K(x,T((y * z) \ (y * u),z)) = K(x,L(u / z,z,y))
    ]]></literal>
    <justification jstring="[para(897(a,1),6924(a,1,2)),flip(a)].">
      <j1 rule="para" parents="897 6924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7007">
    <literal><![CDATA[
      K(x,T(T(y,z),u / y)) = K(x,T(u / (u / y),z))
    ]]></literal>
    <justification jstring="[para(477(a,1),6924(a,1,2)),flip(a)].">
      <j1 rule="para" parents="477 6924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7008">
    <literal><![CDATA[
      K(x,y * K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(T(x,z),y) = u
    ]]></literal>
    <justification jstring="[para(6925(a,2),6610(a,1))].">
      <j1 rule="para" parents="6925 6610"/>
    </justification>
  </clause>

  <clause id="7009">
    <literal><![CDATA[
      K(T(x,x \ y),((x \ 1) * y) \ z) = K(x,z / ((x \ 1) * y))
    ]]></literal>
    <justification jstring="[para(3930(a,1),6928(a,1,1))].">
      <j1 rule="para" parents="3930 6928"/>
    </justification>
  </clause>

  <clause id="7010">
    <literal><![CDATA[
      ((x * ((y * z) / y)) / x) / ((x * z) / x) = K(T(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,4441,a,b,6929,a)].">
      <j1 rule="hyper" parents="63 4441 6929"/>
    </justification>
  </clause>

  <clause id="7011">
    <literal><![CDATA[
      K(x,(y * z) / y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y)) = u
    ]]></literal>
    <justification jstring="[para(6929(a,2),6695(a,1))].">
      <j1 rule="para" parents="6929 6695"/>
    </justification>
  </clause>

  <clause id="7012">
    <literal><![CDATA[
      x / (K(T(y,z),x) * K(x * K(z,x),z)) = T(x * K(z,x),y)
    ]]></literal>
    <justification jstring="[para(6936(a,1),4841(a,1,2,1))].">
      <j1 rule="para" parents="6936 4841"/>
    </justification>
  </clause>

  <clause id="7013">
    <literal><![CDATA[
      K(x,y * K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(6936(a,2),6695(a,1))].">
      <j1 rule="para" parents="6936 6695"/>
    </justification>
  </clause>

  <clause id="7014">
    <literal><![CDATA[
      T(x,((y \ z) \ z) \ z) = T(x,z / y)
    ]]></literal>
    <justification jstring="[para(3674(a,1),6946(a,1,2))].">
      <j1 rule="para" parents="3674 6946"/>
    </justification>
  </clause>

  <clause id="7015">
    <literal><![CDATA[
      T(x,T(y * z,u) / y) = T(x,y \ T(z * y,u))
    ]]></literal>
    <justification jstring="[para(4112(a,1),6946(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4112 6946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7016">
    <literal><![CDATA[
      T(x * (y \ z),K(y \ z,y)) = (y \ z) * T(x,z / y)
    ]]></literal>
    <justification jstring="[para(6946(a,1),6167(a,2,2))].">
      <j1 rule="para" parents="6946 6167"/>
    </justification>
  </clause>

  <clause id="7017">
    <literal><![CDATA[
      T(x,L(y * K(z,y),u,w)) = T(x,T(L(y,u,w),z))
    ]]></literal>
    <justification jstring="[para(4426(a,2),6947(a,1,2))].">
      <j1 rule="para" parents="4426 6947"/>
    </justification>
  </clause>

  <clause id="7018">
    <literal><![CDATA[
      T(x,T(T(y \ (z \ y),T(z,u)),y)) = T(x,(((z \ 1) \ 1) \ y) / y)
    ]]></literal>
    <justification jstring="[para(5217(a,1),6947(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5217 6947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7019">
    <literal><![CDATA[
      L(x,y,x) \ (T(x * y,T(x,y)) \ z) = ((y * x) / y) \ ((x * y) \ z)
    ]]></literal>
    <justification jstring="[para(6947(a,1),4855(a,1,2,1))].">
      <j1 rule="para" parents="6947 4855"/>
    </justification>
  </clause>

  <clause id="7020">
    <literal><![CDATA[
      ((x \ 1) \ K(y,x)) \ K(y,x) = T(x \ 1,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,3935,a(flip),b,6950,a)].">
      <j1 rule="hyper" parents="63 3935 6950"/>
    </justification>
  </clause>

  <clause id="7021">
    <literal><![CDATA[
      T(x,K(y,1 / z) / z) = T(x,T(1 / z,y))
    ]]></literal>
    <justification jstring="[para(4885(a,1),6950(a,1,2))].">
      <j1 rule="para" parents="4885 6950"/>
    </justification>
  </clause>

  <clause id="7022">
    <literal><![CDATA[
      K(x,K(y,z * x)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(333,a,6800,a,b,6951,a),flip(a)].">
      <j1 rule="hyper" parents="333 6800 6951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7023">
    <literal><![CDATA[
      T(x,K(y,z * x)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(124,a,6951,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 6951 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7024">
    <literal><![CDATA[
      K(x,K(y,x * z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,6785,a,b,6952,a)].">
      <j1 rule="hyper" parents="63 6785 6952"/>
    </justification>
  </clause>

  <clause id="7025">
    <literal><![CDATA[
      T(x,K(y,y \ z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(4368(a,1),6953(a,1,2))].">
      <j1 rule="para" parents="4368 6953"/>
    </justification>
  </clause>

  <clause id="7026">
    <literal><![CDATA[
      K(x,K(y,y \ z)) = K(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(333,a,6788,a,b,6954,a),flip(a)].">
      <j1 rule="hyper" parents="333 6788 6954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7027">
    <literal><![CDATA[
      T(x,K(y,z / y)) = T(x,K(y,y * z))
    ]]></literal>
    <justification jstring="[hyper(333,a,6953,a,b,6956,a)].">
      <j1 rule="hyper" parents="333 6953 6956"/>
    </justification>
  </clause>

  <clause id="7028">
    <literal><![CDATA[
      T(x,K(y,y * z)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(333,a,6840,a,b,6956,a),flip(a)].">
      <j1 rule="hyper" parents="333 6840 6956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7029">
    <literal><![CDATA[
      x * T(x \ y,K(x,z)) = T(y,K(x,x * z))
    ]]></literal>
    <justification jstring="[hyper(126,a,6956,a(flip),b,6181,a(flip))].">
      <j1 rule="hyper" parents="126 6956 6181"/>
    </justification>
  </clause>

  <clause id="7030">
    <literal><![CDATA[
      T(x,y / (y / z)) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(79(a,1),6977(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="79 6977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7031">
    <literal><![CDATA[
      K(x / y,x / (x / z)) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,6382,a(flip),b,6979,a),flip(a)].">
      <j1 rule="hyper" parents="333 6382 6979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7032">
    <literal><![CDATA[
      K(x,y / (y / z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(T(x,y),z) = u
    ]]></literal>
    <justification jstring="[para(6979(a,2),6610(a,1))].">
      <j1 rule="para" parents="6979 6610"/>
    </justification>
  </clause>

  <clause id="7033">
    <literal><![CDATA[
      T(x,K(y,z * x)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(124,a,7022,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 7022 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7034">
    <literal><![CDATA[
      T(x \ y,K(z,y)) = T(x \ y,K(z,x))
    ]]></literal>
    <justification jstring="[para(10(a,1),7023(a,1,2,2))].">
      <j1 rule="para" parents="10 7023"/>
    </justification>
  </clause>

  <clause id="7035">
    <literal><![CDATA[
      T(x,K(y,z / x)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(12(a,1),7023(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 7023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7036">
    <literal><![CDATA[
      K(x,K(y,x \ z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(10(a,1),7024(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 7024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7037">
    <literal><![CDATA[
      K(x,K(x \ y,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,6788,a,b,7026,a)].">
      <j1 rule="hyper" parents="63 6788 7026"/>
    </justification>
  </clause>

  <clause id="7038">
    <literal><![CDATA[
      T(T(x,K(y,z)),z * y) = T(x,T(z * y,z))
    ]]></literal>
    <justification jstring="[para(7028(a,1),6859(a,1,1))].">
      <j1 rule="para" parents="7028 6859"/>
    </justification>
  </clause>

  <clause id="7039">
    <literal><![CDATA[
      T(x,K(y * x,z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,6840,a,b,7033,a)].">
      <j1 rule="hyper" parents="63 6840 7033"/>
    </justification>
  </clause>

  <clause id="7040">
    <literal><![CDATA[
      T(x,K(y,z / x)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(333,a,6840,a,b,7035,a),flip(a)].">
      <j1 rule="hyper" parents="333 6840 7035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7041">
    <literal><![CDATA[
      T(x,K(y,x \ z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,6502,a(flip),b,7035,a)].">
      <j1 rule="hyper" parents="63 6502 7035"/>
    </justification>
  </clause>

  <clause id="7042">
    <literal><![CDATA[
      K(x,K(y,x \ z)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(333,a,6788,a(flip),b,7036,a),flip(a)].">
      <j1 rule="hyper" parents="333 6788 7036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7043">
    <literal><![CDATA[
      K(x,K(x * y,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(9(a,1),7037(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 7037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7044">
    <literal><![CDATA[
      K(K(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(5296(a,2),6783(a,1))].">
      <j1 rule="para" parents="5296 6783"/>
    </justification>
  </clause>

  <clause id="7045">
    <literal><![CDATA[
      K(K(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,K(x,y)) = u
    ]]></literal>
    <justification jstring="[para(6787(a,2),6783(a,1))].">
      <j1 rule="para" parents="6787 6783"/>
    </justification>
  </clause>

  <clause id="7047">
    <literal><![CDATA[
      K(x,K(y,z * y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,K(x,y * z)) = u
    ]]></literal>
    <justification jstring="[para(4636(a,2),6798(a,1,2))].">
      <j1 rule="para" parents="4636 6798"/>
    </justification>
  </clause>

  <clause id="7048">
    <literal><![CDATA[
      K(x,K(y,x \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(7042(a,2),6798(a,1))].">
      <j1 rule="para" parents="7042 6798"/>
    </justification>
  </clause>

  <clause id="7049">
    <literal><![CDATA[
      K(x,K(y,y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7026(a,2),6803(a,1))].">
      <j1 rule="para" parents="7026 6803"/>
    </justification>
  </clause>

  <clause id="7050">
    <literal><![CDATA[
      K(x,y) * K(y,T(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(6407(a,2),6825(a,1))].">
      <j1 rule="para" parents="6407 6825"/>
    </justification>
  </clause>

  <clause id="7051">
    <literal><![CDATA[
      K(x,K(y,z * y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(6871(a,2),6825(a,1))].">
      <j1 rule="para" parents="6871 6825"/>
    </justification>
  </clause>

  <clause id="7052">
    <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(4438(a,2),6836(a,1))].">
      <j1 rule="para" parents="4438 6836"/>
    </justification>
  </clause>

  <clause id="7053">
    <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(6370(a,1),6836(a,1,2))].">
      <j1 rule="para" parents="6370 6836"/>
    </justification>
  </clause>

  <clause id="7056">
    <literal><![CDATA[
      T(T(x,y),K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(6863(a,1),6856(a,1,1))].">
      <j1 rule="para" parents="6863 6856"/>
    </justification>
  </clause>

  <clause id="7057">
    <literal><![CDATA[
      K(x,y) * (z * K(y,x)) != u
    ]]></literal>
    <literal><![CDATA[
      T(z,K(x,y)) = u
    ]]></literal>
    <justification jstring="[para(4565(a,2),6868(a,1))].">
      <j1 rule="para" parents="4565 6868"/>
    </justification>
  </clause>

  <clause id="7058">
    <literal><![CDATA[
      x * T(y,T(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(y * x,K(z,x)) = u
    ]]></literal>
    <justification jstring="[para(6167(a,1),6868(a,1))].">
      <j1 rule="para" parents="6167 6868"/>
    </justification>
  </clause>

  <clause id="7059">
    <literal><![CDATA[
      T(x,K(y,y * z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7028(a,2),6868(a,1))].">
      <j1 rule="para" parents="7028 6868"/>
    </justification>
  </clause>

  <clause id="7060">
    <literal><![CDATA[
      T(x,K(y,z / x)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7040(a,2),6868(a,1))].">
      <j1 rule="para" parents="7040 6868"/>
    </justification>
  </clause>

  <clause id="7061">
    <literal><![CDATA[
      K(x \ y,T(z,y / x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,z) = u
    ]]></literal>
    <justification jstring="[para(3381(a,1),6960(a,1))].">
      <j1 rule="para" parents="3381 6960"/>
    </justification>
  </clause>

  <clause id="7062">
    <literal><![CDATA[
      K(x \ y,T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(5910(a,1),6960(a,1))].">
      <j1 rule="para" parents="5910 6960"/>
    </justification>
  </clause>

  <clause id="7063">
    <literal><![CDATA[
      K(T(x,y),T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(6352(a,2),6960(a,1))].">
      <j1 rule="para" parents="6352 6960"/>
    </justification>
  </clause>

  <clause id="7064">
    <literal><![CDATA[
      K(x,T(T(y,z),z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(6365(a,2),6960(a,1))].">
      <j1 rule="para" parents="6365 6960"/>
    </justification>
  </clause>

  <clause id="7065">
    <literal><![CDATA[
      T(K(x \ y,z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(6382(a,1),6960(a,1,1))].">
      <j1 rule="para" parents="6382 6960"/>
    </justification>
  </clause>

  <clause id="7066">
    <literal><![CDATA[
      T(K(x \ y,z),x) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(6431(a,1),6960(a,1,1))].">
      <j1 rule="para" parents="6431 6960"/>
    </justification>
  </clause>

  <clause id="7067">
    <literal><![CDATA[
      K(x / y,T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(6910(a,1),6960(a,1))].">
      <j1 rule="para" parents="6910 6960"/>
    </justification>
  </clause>

  <clause id="7068">
    <literal><![CDATA[
      L(x,K(y \ 1,z),u \ (y \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(6985(a,1),50(a,2))].">
      <j1 rule="para" parents="6985 50"/>
    </justification>
  </clause>

  <clause id="7069">
    <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(23(a,1),7063(a,1,2))].">
      <j1 rule="para" parents="23 7063"/>
    </justification>
  </clause>

  <clause id="7070">
    <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(25(a,2),7063(a,1,1))].">
      <j1 rule="para" parents="25 7063"/>
    </justification>
  </clause>

  <clause id="7071">
    <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(27(a,2),7063(a,1,2))].">
      <j1 rule="para" parents="27 7063"/>
    </justification>
  </clause>

  <clause id="7072">
    <literal><![CDATA[
      K(x \ y,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(113(a,1),7063(a,1,1))].">
      <j1 rule="para" parents="113 7063"/>
    </justification>
  </clause>

  <clause id="7073">
    <literal><![CDATA[
      K(T(x,y),y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(113(a,1),7063(a,1,2))].">
      <j1 rule="para" parents="113 7063"/>
    </justification>
  </clause>

  <clause id="7074">
    <literal><![CDATA[
      K(x,T(y,R(T(x,z),u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(219(a,1),7063(a,1,1))].">
      <j1 rule="para" parents="219 7063"/>
    </justification>
  </clause>

  <clause id="7075">
    <literal><![CDATA[
      K(x,T(y,K(z,z \ x))) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(4670(a,1),7063(a,1,1))].">
      <j1 rule="para" parents="4670 7063"/>
    </justification>
  </clause>

  <clause id="7076">
    <literal><![CDATA[
      K(x,T(y \ z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(113(a,1),7064(a,1,2,1))].">
      <j1 rule="para" parents="113 7064"/>
    </justification>
  </clause>

  <clause id="7077">
    <literal><![CDATA[
      T(K(x,y),T(z,K(y,u))) = K(x,K(y,z)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(6384(a,1),6760(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6384 6760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7080">
    <literal><![CDATA[
      K(x,T(y,z)) * K(y,x) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(34,a,4573,a,b,6761,a)].">
      <j1 rule="hyper" parents="34 4573 6761"/>
    </justification>
  </clause>

  <clause id="7081">
    <literal><![CDATA[
      K(x,T(y,z)) != K(x,y) * u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(6761(a,1),43(a,1))].">
      <j1 rule="para" parents="6761 43"/>
    </justification>
  </clause>

  <clause id="7082">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) \ K(y,x) = T(K(y,x),T(z,y \ u))
    ]]></literal>
    <justification jstring="[para(6508(a,1),6768(a,1,1,2))].">
      <j1 rule="para" parents="6508 6768"/>
    </justification>
  </clause>

  <clause id="7083">
    <literal><![CDATA[
      K(x,T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(6771(a,1),5313(a,1))].">
      <j1 rule="para" parents="6771 5313"/>
    </justification>
  </clause>

  <clause id="7084">
    <literal><![CDATA[
      K(x,T(y,z)) \ K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = u
    ]]></literal>
    <justification jstring="[para(6771(a,1),6024(a,1,1))].">
      <j1 rule="para" parents="6771 6024"/>
    </justification>
  </clause>

  <clause id="7085">
    <literal><![CDATA[
      K(x,y) * K(y,K(z,T(x,u))) = T(K(x,y),T(z,u))
    ]]></literal>
    <justification jstring="[para(6370(a,1),6793(a,1,2,2))].">
      <j1 rule="para" parents="6370 6793"/>
    </justification>
  </clause>

  <clause id="7086">
    <literal><![CDATA[
      K(x,T(y,z)) * K(y,x) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(2011,a,6805,a)].">
      <j1 rule="hyper" parents="2011 6805"/>
    </justification>
  </clause>

  <clause id="7088">
    <literal><![CDATA[
      K(x,y / z) * K(x,K(y,y / z)) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(333,a,5773,a(flip),b,6814,a),flip(a)].">
      <j1 rule="hyper" parents="333 5773 6814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7089">
    <literal><![CDATA[
      K(x,K(y,T(z,u / x))) = K(z,K(x,T(y,u)))
    ]]></literal>
    <justification jstring="[para(6536(a,1),6817(a,2,2))].">
      <j1 rule="para" parents="6536 6817"/>
    </justification>
  </clause>

  <clause id="7090">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(z,K(y,T(x,u))) = w
    ]]></literal>
    <justification jstring="[para(6817(a,1),6798(a,1))].">
      <j1 rule="para" parents="6817 6798"/>
    </justification>
  </clause>

  <clause id="7091">
    <literal><![CDATA[
      T(x,y) * K(y,T(x,z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(126,a,6818,a(flip),b,4842,a)].">
      <j1 rule="hyper" parents="126 6818 4842"/>
    </justification>
  </clause>

  <clause id="7092">
    <literal><![CDATA[
      K(x * y,x) * K(x,K(y,z)) = K(x * y,T(x,z))
    ]]></literal>
    <justification jstring="[para(7043(a,1),6819(a,1,2))].">
      <j1 rule="para" parents="7043 6819"/>
    </justification>
  </clause>

  <clause id="7093">
    <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(6820(a,1),4950(a,1,2,1))].">
      <j1 rule="para" parents="6820 4950"/>
    </justification>
  </clause>

  <clause id="7094">
    <literal><![CDATA[
      x / y != K(z,u) * K(w,K(z,u))
    ]]></literal>
    <literal><![CDATA[
      K(z,T(u,w)) * y = x
    ]]></literal>
    <justification jstring="[para(6837(a,1),4596(a,2,2))].">
      <j1 rule="para" parents="6837 4596"/>
    </justification>
  </clause>

  <clause id="7095">
    <literal><![CDATA[
      K(x,y) * (z / K(x,y)) = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(12(a,1),6845(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12 6845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7096">
    <literal><![CDATA[
      T(x / T(y,z),K(z,y)) = K(z,y) * (x / y)
    ]]></literal>
    <justification jstring="[para(5450(a,1),6845(a,1,1))].">
      <j1 rule="para" parents="5450 6845"/>
    </justification>
  </clause>

  <clause id="7097">
    <literal><![CDATA[
      T(x * T(y,z),K(y,z)) = K(y,z) * (x * y)
    ]]></literal>
    <justification jstring="[para(5984(a,1),6845(a,1,1))].">
      <j1 rule="para" parents="5984 6845"/>
    </justification>
  </clause>

  <clause id="7098">
    <literal><![CDATA[
      T(K(x,y) * z,u) * K(y,x) = K(y,x) * T(z * K(x,y),u)
    ]]></literal>
    <justification jstring="[para(6846(a,1),250(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6846 250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7099">
    <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(126,a,6849,a(flip),b,4295,a)].">
      <j1 rule="hyper" parents="126 6849 4295"/>
    </justification>
  </clause>

  <clause id="7100">
    <literal><![CDATA[
      L(x,(K(y,z) \ 1) * (u * K(z,y)),w) = L(x,T(u,K(y,z)),w)
    ]]></literal>
    <justification jstring="[para(6849(a,1),2955(a,2,2))].">
      <j1 rule="para" parents="6849 2955"/>
    </justification>
  </clause>

  <clause id="7101">
    <literal><![CDATA[
      K(x,T(y,z)) * (u * K(y,T(x,z))) = T(u,K(x,T(y,z)))
    ]]></literal>
    <justification jstring="[para(6370(a,1),6849(a,1,2,2))].">
      <j1 rule="para" parents="6370 6849"/>
    </justification>
  </clause>

  <clause id="7102">
    <literal><![CDATA[
      K(x,y) \ z != u * K(y,x)
    ]]></literal>
    <literal><![CDATA[
      T(u,K(x,y)) = z
    ]]></literal>
    <justification jstring="[para(6853(a,1),47(a,1)),flip(a)].">
      <j1 rule="para" parents="6853 47"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7103">
    <literal><![CDATA[
      T(x,K(y,z)) * K(y,z * x) = K(y,z * x) * x
    ]]></literal>
    <justification jstring="[para(7023(a,1),6858(a,1,1))].">
      <j1 rule="para" parents="7023 6858"/>
    </justification>
  </clause>

  <clause id="7104">
    <literal><![CDATA[
      T(x * K(y,z),u) / x = x \ T(K(y,z) * x,u)
    ]]></literal>
    <justification jstring="[para(6885(a,1),4082(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6885 4082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7105">
    <literal><![CDATA[
      K(x \ y,z) \ (y * K(y / x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      u = y
    ]]></literal>
    <justification jstring="[para(6889(a,1),344(a,1,2))].">
      <j1 rule="para" parents="6889 344"/>
    </justification>
  </clause>

  <clause id="7106">
    <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(6889(a,2),5479(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="6889 5479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7107">
    <literal><![CDATA[
      K(1 / T(T(x,y),y),z) = K(1 / x,z)
    ]]></literal>
    <justification jstring="[hyper(5290,a,6894,a),flip(a)].">
      <j1 rule="hyper" parents="5290 6894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7108">
    <literal><![CDATA[
      K(x,T(y \ 1,z)) = K(x,z / (z * y))
    ]]></literal>
    <justification jstring="[para(9(a,1),6905(a,1,2,1,1))].">
      <j1 rule="para" parents="9 6905"/>
    </justification>
  </clause>

  <clause id="7109">
    <literal><![CDATA[
      x * (K(y,z) * T(y,x)) = T(y,T(z,x)) * x
    ]]></literal>
    <justification jstring="[hyper(126,a,6911,a(flip),b,115,a)].">
      <j1 rule="hyper" parents="126 6911 115"/>
    </justification>
  </clause>

  <clause id="7110">
    <literal><![CDATA[
      (x * K(T(y,z),T(u,z))) / T(u,z) = x / (K(u,y) * T(u,z))
    ]]></literal>
    <justification jstring="[para(6911(a,1),5460(a,2,2))].">
      <j1 rule="para" parents="6911 5460"/>
    </justification>
  </clause>

  <clause id="7111">
    <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(6944(a,2),247(a,1,1,1))].">
      <j1 rule="para" parents="6944 247"/>
    </justification>
  </clause>

  <clause id="7112">
    <literal><![CDATA[
      R(K(x,y),T(y,T(z,u)) * u,w) = K(x,R(y,u * K(y,z),w))
    ]]></literal>
    <justification jstring="[para(6970(a,2),5654(a,1,2))].">
      <j1 rule="para" parents="6970 5654"/>
    </justification>
  </clause>

  <clause id="7113">
    <literal><![CDATA[
      (T(x,T(y,z)) * z) * x = (x * z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(6970(a,2),6144(a,1,1))].">
      <j1 rule="para" parents="6970 6144"/>
    </justification>
  </clause>

  <clause id="7114">
    <literal><![CDATA[
      (x * y) \ ((x * K(z,u / x)) * y) = R(T(K(z,x \ u),x * y),x,y)
    ]]></literal>
    <justification jstring="[para(6971(a,1),674(a,1,2,1))].">
      <j1 rule="para" parents="6971 674"/>
    </justification>
  </clause>

  <clause id="7115">
    <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(444,a,2259,a,b,6984,a)].">
      <j1 rule="hyper" parents="444 2259 6984"/>
    </justification>
  </clause>

  <clause id="7117">
    <literal><![CDATA[
      L(x,y \ z,K(y / z,u)) = x
    ]]></literal>
    <justification jstring="[para(6996(a,1),3565(a,1,3))].">
      <j1 rule="para" parents="6996 3565"/>
    </justification>
  </clause>

  <clause id="7118">
    <literal><![CDATA[
      R(x,y \ z,K(y / z,u)) = x
    ]]></literal>
    <justification jstring="[para(6996(a,1),6124(a,1,3))].">
      <j1 rule="para" parents="6996 6124"/>
    </justification>
  </clause>

  <clause id="7119">
    <literal><![CDATA[
      L(x,(y * z) \ z,K(y,u)) = x
    ]]></literal>
    <justification jstring="[para(11(a,1),7117(a,1,3,1))].">
      <j1 rule="para" parents="11 7117"/>
    </justification>
  </clause>

  <clause id="7120">
    <literal><![CDATA[
      x \ (y * K(x / y,z)) = (x \ y) * K(x / y,z)
    ]]></literal>
    <justification jstring="[para(7118(a,1),529(a,1,1))].">
      <j1 rule="para" parents="7118 529"/>
    </justification>
  </clause>

  <clause id="7123">
    <literal><![CDATA[
      K(x,K(y \ z,y)) = K(x,K(z / y,z))
    ]]></literal>
    <justification jstring="[para(7031(a,1),6872(a,1,2))].">
      <j1 rule="para" parents="7031 6872"/>
    </justification>
  </clause>

  <clause id="7124">
    <literal><![CDATA[
      K(x,T(y,z)) \ K(x,y) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,6427,a,b,7086,a)].">
      <j1 rule="hyper" parents="63 6427 7086"/>
    </justification>
  </clause>

  <clause id="7125">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(x,z)) = u
    ]]></literal>
    <justification jstring="[para(7086(a,1),5998(a,1,1))].">
      <j1 rule="para" parents="7086 5998"/>
    </justification>
  </clause>

  <clause id="7126">
    <literal><![CDATA[
      T(x * K(y,T(x,z)),y) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,6650,a,b,7091,a)].">
      <j1 rule="hyper" parents="63 6650 7091"/>
    </justification>
  </clause>

  <clause id="7127">
    <literal><![CDATA[
      x * T(y,T(x,z)) = y * T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(126,a,7091,a(flip),b,6663,a),flip(a)].">
      <j1 rule="hyper" parents="126 7091 6663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7128">
    <literal><![CDATA[
      T(x,1 / T(T(y,z),z)) = x / K(1 / y,x)
    ]]></literal>
    <justification jstring="[hyper(197,a,7107,a(flip),b,4205,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="197 7107 4205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7129">
    <literal><![CDATA[
      K(1 / T(x,y / x),z) = K(1 / (y / (y / x)),z)
    ]]></literal>
    <justification jstring="[para(258(a,1),7107(a,1,1,2,1))].">
      <j1 rule="para" parents="258 7107"/>
    </justification>
  </clause>

  <clause id="7130">
    <literal><![CDATA[
      K(1 / T(T(x,x * y),y),z) = K(1 / L(x,y,x),z)
    ]]></literal>
    <justification jstring="[para(635(a,1),7107(a,1,1,2,1))].">
      <j1 rule="para" parents="635 7107"/>
    </justification>
  </clause>

  <clause id="7131">
    <literal><![CDATA[
      K(x,T(1 / y,z)) = K(x,z / (z * y))
    ]]></literal>
    <justification jstring="[hyper(5850,a,7108,a)].">
      <j1 rule="hyper" parents="5850 7108"/>
    </justification>
  </clause>

  <clause id="7132">
    <literal><![CDATA[
      K(x,y / (y * z)) = K(x,y \ (z \ y))
    ]]></literal>
    <justification jstring="[hyper(63,a,6736,a(flip),b,7108,a),flip(a)].">
      <j1 rule="hyper" parents="63 6736 7108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7133">
    <literal><![CDATA[
      K(x,K(y / z,y)) = K(x,K(z,z \ y))
    ]]></literal>
    <justification jstring="[hyper(6836,a,7123,a),flip(a)].">
      <j1 rule="hyper" parents="6836 7123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7134">
    <literal><![CDATA[
      T(x * K(y,x),K(y,z)) = x * K(y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(4652,a,7126,a)].">
      <j1 rule="hyper" parents="4652 7126"/>
    </justification>
  </clause>

  <clause id="7135">
    <literal><![CDATA[
      T(x * K(y / z,x),z \ y) = T(x,K(z \ y,y))
    ]]></literal>
    <justification jstring="[para(6904(a,1),7126(a,1,1,2))].">
      <j1 rule="para" parents="6904 7126"/>
    </justification>
  </clause>

  <clause id="7136">
    <literal><![CDATA[
      T(x * T(y,K(x,z)),y) = T(x * y,T(y,z))
    ]]></literal>
    <justification jstring="[para(7127(a,1),6202(a,1,1))].">
      <j1 rule="para" parents="7127 6202"/>
    </justification>
  </clause>

  <clause id="7138">
    <literal><![CDATA[
      T(x,y / (y * z)) = T(x,y \ (z \ y))
    ]]></literal>
    <justification jstring="[hyper(124,a,7132,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 7132 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7139">
    <literal><![CDATA[
      K(x,K(y / z,y)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(333,a,6954,a(flip),b,7133,a),flip(a)].">
      <j1 rule="hyper" parents="333 6954 7133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7140">
    <literal><![CDATA[
      K(x,K(y \ z,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(76(a,1),7139(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="76 7139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7141">
    <literal><![CDATA[
      K(x,K(y,z \ y)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(6836,a,7140,a)].">
      <j1 rule="hyper" parents="6836 7140"/>
    </justification>
  </clause>

  <clause id="7142">
    <literal><![CDATA[
      K(x,K(y \ z,z)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(333,a,6788,a(flip),b,7140,a),flip(a)].">
      <j1 rule="hyper" parents="333 6788 7140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7143">
    <literal><![CDATA[
      K(x,K(y,z \ y)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(333,a,6800,a,b,7141,a),flip(a)].">
      <j1 rule="hyper" parents="333 6800 7141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7144">
    <literal><![CDATA[
      K(x,K(y,z \ 1)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,6955,a,b,7141,a)].">
      <j1 rule="hyper" parents="63 6955 7141"/>
    </justification>
  </clause>

  <clause id="7145">
    <literal><![CDATA[
      K(x,K(y,z \ x)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(6803,a,7142,a)].">
      <j1 rule="hyper" parents="6803 7142"/>
    </justification>
  </clause>

  <clause id="7146">
    <literal><![CDATA[
      K(x,K(y \ z,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7142(a,2),6825(a,1))].">
      <j1 rule="para" parents="7142 6825"/>
    </justification>
  </clause>

  <clause id="7147">
    <literal><![CDATA[
      T(x,K(y,z \ y)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(124,a,7143,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 7143 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7148">
    <literal><![CDATA[
      K(x,K(y,z \ 1)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,6955,a,b,7143,a)].">
      <j1 rule="hyper" parents="63 6955 7143"/>
    </justification>
  </clause>

  <clause id="7149">
    <literal><![CDATA[
      K(x,K(y,y / z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(79(a,1),7143(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="79 7143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7150">
    <literal><![CDATA[
      K(x,K(y \ 1,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(6836,a,7144,a)].">
      <j1 rule="hyper" parents="6836 7144"/>
    </justification>
  </clause>

  <clause id="7151">
    <literal><![CDATA[
      K(x \ 1,K(y,z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(6803,a,7144,a)].">
      <j1 rule="hyper" parents="6803 7144"/>
    </justification>
  </clause>

  <clause id="7152">
    <literal><![CDATA[
      K(x,K(y,z \ 1)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(333,a,6785,a,b,7144,a),flip(a)].">
      <j1 rule="hyper" parents="333 6785 7144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7153">
    <literal><![CDATA[
      T(x,K(y,z \ 1)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(124,a,7144,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 7144 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7154">
    <literal><![CDATA[
      K(x,K(y,1 / z)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(4615(a,2),7144(a,1,2))].">
      <j1 rule="para" parents="4615 7144"/>
    </justification>
  </clause>

  <clause id="7155">
    <literal><![CDATA[
      K(x,K(y \ 1,z)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(4621(a,1),7144(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4621 7144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7156">
    <literal><![CDATA[
      K(x,K(y \ z,u)) = K(x,K(u,z \ y))
    ]]></literal>
    <justification jstring="[para(5766(a,1),7144(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5766 7144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7157">
    <literal><![CDATA[
      K(x,K(y,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7144(a,2),6836(a,1))].">
      <j1 rule="para" parents="7144 6836"/>
    </justification>
  </clause>

  <clause id="7158">
    <literal><![CDATA[
      K(x,K(y,x / z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(5820,a,7145,a)].">
      <j1 rule="hyper" parents="5820 7145"/>
    </justification>
  </clause>

  <clause id="7159">
    <literal><![CDATA[
      K(x,K(y,z \ x)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(333,a,6788,a(flip),b,7145,a),flip(a)].">
      <j1 rule="hyper" parents="333 6788 7145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7160">
    <literal><![CDATA[
      T(x,K(y,z \ x)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(124,a,7145,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 7145 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7161">
    <literal><![CDATA[
      T(x,K(y \ z,z)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(6868,a,7147,a)].">
      <j1 rule="hyper" parents="6868 7147"/>
    </justification>
  </clause>

  <clause id="7162">
    <literal><![CDATA[
      K(x,K(y \ 1,z)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(6825,a,7148,a)].">
      <j1 rule="hyper" parents="6825 7148"/>
    </justification>
  </clause>

  <clause id="7163">
    <literal><![CDATA[
      K(x \ 1,K(y,z)) = K(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(6803,a,7148,a)].">
      <j1 rule="hyper" parents="6803 7148"/>
    </justification>
  </clause>

  <clause id="7164">
    <literal><![CDATA[
      T(x,K(y,z \ 1)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(124,a,7148,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 7148 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7165">
    <literal><![CDATA[
      K(x,K(y,1 / z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(79(a,1),7148(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="79 7148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7166">
    <literal><![CDATA[
      K(x,K(y,z / u)) = K(x,K(y,u / z))
    ]]></literal>
    <justification jstring="[para(5055(a,1),7148(a,1,2))].">
      <j1 rule="para" parents="5055 7148"/>
    </justification>
  </clause>

  <clause id="7167">
    <literal><![CDATA[
      K(x,K(y,z \ u)) = K(x,K(y,u \ z))
    ]]></literal>
    <justification jstring="[para(5766(a,1),7148(a,1,2))].">
      <j1 rule="para" parents="5766 7148"/>
    </justification>
  </clause>

  <clause id="7168">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z)) = T(K(x,y),z \ 1)
    ]]></literal>
    <justification jstring="[para(7148(a,1),6759(a,1,2))].">
      <j1 rule="para" parents="7148 6759"/>
    </justification>
  </clause>

  <clause id="7169">
    <literal><![CDATA[
      K(x,K(y,z)) * (z \ 1) = T(z \ 1,K(x,y))
    ]]></literal>
    <justification jstring="[para(7148(a,1),6795(a,1,1))].">
      <j1 rule="para" parents="7148 6795"/>
    </justification>
  </clause>

  <clause id="7170">
    <literal><![CDATA[
      K(x,K(y,1 / z)) = K(x,K(y,z * y))
    ]]></literal>
    <justification jstring="[para(5064(a,1),7149(a,1,2))].">
      <j1 rule="para" parents="5064 7149"/>
    </justification>
  </clause>

  <clause id="7171">
    <literal><![CDATA[
      (x * K(y \ 1,z)) \ K(x,K(y,z)) = (K(y \ 1,z) * x) \ 1
    ]]></literal>
    <justification jstring="[hyper(121,a,7150,a(flip),b,4997,a(flip))].">
      <j1 rule="hyper" parents="121 7150 4997"/>
    </justification>
  </clause>

  <clause id="7172">
    <literal><![CDATA[
      K(x,y * ((z \ (y \ 1)) * z)) = K(x,K(y * z,z))
    ]]></literal>
    <justification jstring="[para(5119(a,2),7150(a,1,2))].">
      <j1 rule="para" parents="5119 7150"/>
    </justification>
  </clause>

  <clause id="7173">
    <literal><![CDATA[
      K(1 / x,K(y,z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(3400,a,7151,a)].">
      <j1 rule="hyper" parents="3400 7151"/>
    </justification>
  </clause>

  <clause id="7174">
    <literal><![CDATA[
      K(x \ 1,K(y,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(333,a,6785,a,b,7151,a),flip(a)].">
      <j1 rule="hyper" parents="333 6785 7151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7175">
    <literal><![CDATA[
      K(x \ 1,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,K(z,x)) = u
    ]]></literal>
    <justification jstring="[para(7151(a,2),6836(a,1))].">
      <j1 rule="para" parents="7151 6836"/>
    </justification>
  </clause>

  <clause id="7176">
    <literal><![CDATA[
      K(1 / x,K(y,z)) = K(y,K(z,x))
    ]]></literal>
    <justification jstring="[para(79(a,1),7152(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="79 7152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7177">
    <literal><![CDATA[
      T(x,K(y \ 1,z)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(4621(a,1),7153(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4621 7153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7178">
    <literal><![CDATA[
      T(x,K(y \ z,u)) = T(x,K(u,z \ y))
    ]]></literal>
    <justification jstring="[para(5766(a,1),7153(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5766 7153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7180">
    <literal><![CDATA[
      K(x,K(y,1 / z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7154(a,2),6836(a,1))].">
      <j1 rule="para" parents="7154 6836"/>
    </justification>
  </clause>

  <clause id="7181">
    <literal><![CDATA[
      K(x,K(y \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7155(a,2),6836(a,1))].">
      <j1 rule="para" parents="7155 6836"/>
    </justification>
  </clause>

  <clause id="7182">
    <literal><![CDATA[
      T(x,K(y,x / z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(124,a,7158,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 7158 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7183">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x / z,y) = K(z \ x,y)
    ]]></literal>
    <justification jstring="[para(7158(a,1),5923(a,1,1))].">
      <j1 rule="para" parents="7158 5923"/>
    </justification>
  </clause>

  <clause id="7184">
    <literal><![CDATA[
      K(x,K(y,z)) * (x \ y) = T(x \ y,K(y,z))
    ]]></literal>
    <justification jstring="[para(7159(a,1),6795(a,1,1))].">
      <j1 rule="para" parents="7159 6795"/>
    </justification>
  </clause>

  <clause id="7185">
    <literal><![CDATA[
      T(x,K(y,z)) * K(y,z \ x) = K(y,z \ x) * x
    ]]></literal>
    <justification jstring="[hyper(125,a,7160,a(flip),b,6862,a)].">
      <j1 rule="hyper" parents="125 7160 6862"/>
    </justification>
  </clause>

  <clause id="7186">
    <literal><![CDATA[
      T(x,K(y,y / z)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(79(a,1),7161(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="79 7161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7187">
    <literal><![CDATA[
      K(x,K(y,(z \ 1) / (u / z))) = K(y,(T(u,x) / z) / (u / z))
    ]]></literal>
    <justification jstring="[para(5129(a,1),7162(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5129 7162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7188">
    <literal><![CDATA[
      K(x,y \ 1) * T(z,K(x,y)) = z * K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(126,a,7164,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="126 7164 22"/>
    </justification>
  </clause>

  <clause id="7189">
    <literal><![CDATA[
      T(x,K(y,1 / z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(79(a,1),7164(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="79 7164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7190">
    <literal><![CDATA[
      K(x,K(y,1 / z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(7165(a,2),6836(a,1))].">
      <j1 rule="para" parents="7165 6836"/>
    </justification>
  </clause>

  <clause id="7191">
    <literal><![CDATA[
      K(x,K(y,z)) / y != u
    ]]></literal>
    <literal><![CDATA[
      T(1 / y,K(x,z)) = u
    ]]></literal>
    <justification jstring="[para(7173(a,1),4602(a,1,1))].">
      <j1 rule="para" parents="7173 4602"/>
    </justification>
  </clause>

  <clause id="7192">
    <literal><![CDATA[
      (T(x * y,K(z,u)) / y) / x = K(z,K(u,(1 / y) / x))
    ]]></literal>
    <justification jstring="[hyper(63,a,4980,a(flip),b,7176,a)].">
      <j1 rule="hyper" parents="63 4980 7176"/>
    </justification>
  </clause>

  <clause id="7193">
    <literal><![CDATA[
      K(1 / x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,K(x,z)) = u
    ]]></literal>
    <justification jstring="[para(7176(a,2),6836(a,1))].">
      <j1 rule="para" parents="7176 6836"/>
    </justification>
  </clause>

  <clause id="7194">
    <literal><![CDATA[
      K(1 / ((1 / x) / y),K(z,(y * x) / u)) = (T(y * x,K(z,u)) / x) / y
    ]]></literal>
    <justification jstring="[para(7182(a,1),4980(a,2,1,1))].">
      <j1 rule="para" parents="7182 4980"/>
    </justification>
  </clause>

  <clause id="7195">
    <literal><![CDATA[
      K(x,K(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u \ z)) = w
    ]]></literal>
    <justification jstring="[para(7156(a,1),6836(a,1))].">
      <j1 rule="para" parents="7156 6836"/>
    </justification>
  </clause>

  <clause id="7196">
    <literal><![CDATA[
      T(x,K(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,u \ z)) = w
    ]]></literal>
    <justification jstring="[para(7178(a,1),6868(a,1))].">
      <j1 rule="para" parents="7178 6868"/>
    </justification>
  </clause>

  <clause id="7197">
    <literal><![CDATA[
      T(T(x,y),K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z \ 1)) = u
    ]]></literal>
    <justification jstring="[para(7177(a,1),6883(a,1))].">
      <j1 rule="para" parents="7177 6883"/>
    </justification>
  </clause>

  <clause id="7198">
    <literal><![CDATA[
      K(x,T(y,L(z,u,x))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(333,a,6935,a(flip),b,6942,a),flip(a)].">
      <j1 rule="hyper" parents="333 6935 6942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7199">
    <literal><![CDATA[
      K(x,T(y,(x \ z) \ u)) = K(x,T(y,z \ (x * u)))
    ]]></literal>
    <justification jstring="[para(515(a,1),7198(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="515 7198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7200">
    <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(898(a,2),7001(a,1,1))].">
      <j1 rule="para" parents="898 7001"/>
    </justification>
  </clause>

  <clause id="7201">
    <literal><![CDATA[
      K(T(x,y \ z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(T(x,z),y) = u
    ]]></literal>
    <justification jstring="[para(6934(a,2),7032(a,1))].">
      <j1 rule="para" parents="6934 7032"/>
    </justification>
  </clause>

  <clause id="7202">
    <literal><![CDATA[
      K(x,K(x \ y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(6800(a,1),7048(a,1))].">
      <j1 rule="para" parents="6800 7048"/>
    </justification>
  </clause>

  <clause id="7203">
    <literal><![CDATA[
      T(x,K(y,z / y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7027(a,2),7059(a,1))].">
      <j1 rule="para" parents="7027 7059"/>
    </justification>
  </clause>

  <clause id="7204">
    <literal><![CDATA[
      K(((x \ y) \ y) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(6373(a,2),7062(a,1))].">
      <j1 rule="para" parents="6373 7062"/>
    </justification>
  </clause>

  <clause id="7205">
    <literal><![CDATA[
      K(R(x / y,y,z),T(u,y * z)) != w
    ]]></literal>
    <literal><![CDATA[
      K((y * z) \ (x * z),u) = w
    ]]></literal>
    <justification jstring="[para(108(a,2),7067(a,1,1))].">
      <j1 rule="para" parents="108 7067"/>
    </justification>
  </clause>

  <clause id="7206">
    <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(4085(a,1),7067(a,1,1))].">
      <j1 rule="para" parents="4085 7067"/>
    </justification>
  </clause>

  <clause id="7207">
    <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(4419(a,2),7067(a,1,1))].">
      <j1 rule="para" parents="4419 7067"/>
    </justification>
  </clause>

  <clause id="7208">
    <literal><![CDATA[
      K(x / (y \ z),T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K((y \ z) \ x,y) = u
    ]]></literal>
    <justification jstring="[para(6341(a,1),7067(a,1))].">
      <j1 rule="para" parents="6341 7067"/>
    </justification>
  </clause>

  <clause id="7209">
    <literal><![CDATA[
      K((x / y) \ z,y \ x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z / (x / y),y \ x) = u
    ]]></literal>
    <justification jstring="[para(295(a,1),7072(a,1,2))].">
      <j1 rule="para" parents="295 7072"/>
    </justification>
  </clause>

  <clause id="7210">
    <literal><![CDATA[
      K(L(x \ y,x,z),T(u,z * x)) != w
    ]]></literal>
    <literal><![CDATA[
      K((z * y) / (z * x),u) = w
    ]]></literal>
    <justification jstring="[para(99(a,2),7072(a,1,1))].">
      <j1 rule="para" parents="99 7072"/>
    </justification>
  </clause>

  <clause id="7211">
    <literal><![CDATA[
      K(x,K(y \ x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z * K(y \ x,y)) = u
    ]]></literal>
    <justification jstring="[para(6035(a,1),7075(a,1,2))].">
      <j1 rule="para" parents="6035 7075"/>
    </justification>
  </clause>

  <clause id="7212">
    <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(1258(a,1),7076(a,1,2,1))].">
      <j1 rule="para" parents="1258 7076"/>
    </justification>
  </clause>

  <clause id="7213">
    <literal><![CDATA[
      K(x,y \ T(z * y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y * z,u) / y) = w
    ]]></literal>
    <justification jstring="[para(4112(a,1),7076(a,1,2))].">
      <j1 rule="para" parents="4112 7076"/>
    </justification>
  </clause>

  <clause id="7214">
    <literal><![CDATA[
      K(x,K(y,z / u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u / z)) = w
    ]]></literal>
    <justification jstring="[para(5055(a,1),7157(a,1,2))].">
      <j1 rule="para" parents="5055 7157"/>
    </justification>
  </clause>

  <clause id="7215">
    <literal><![CDATA[
      T(x,K(y,y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(4368(a,1),7203(a,1,2))].">
      <j1 rule="para" parents="4368 7203"/>
    </justification>
  </clause>

  <clause id="7216">
    <literal><![CDATA[
      T(x,K(y \ z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(6840(a,1),7215(a,1))].">
      <j1 rule="para" parents="6840 7215"/>
    </justification>
  </clause>

  <clause id="7217">
    <literal><![CDATA[
      T(x,K(y \ z,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(7178(a,2),7215(a,1))].">
      <j1 rule="para" parents="7178 7215"/>
    </justification>
  </clause>

  <clause id="7218">
    <literal><![CDATA[
      K((x \ 1) \ (y \ z),y) = K((x \ y) \ z,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,5006,a(flip),b,6731,a),flip(a)].">
      <j1 rule="hyper" parents="63 5006 6731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7219">
    <literal><![CDATA[
      K(x,(y * z) \ z) = K(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(34,a,4222,a(flip),b,6741,a)].">
      <j1 rule="hyper" parents="34 4222 6741"/>
    </justification>
  </clause>

  <clause id="7220">
    <literal><![CDATA[
      K(x,T(y \ 1,z)) = K(x,(y * z) \ z)
    ]]></literal>
    <justification jstring="[hyper(333,a,6736,a,b,7219,a)].">
      <j1 rule="hyper" parents="333 6736 7219"/>
    </justification>
  </clause>

  <clause id="7221">
    <literal><![CDATA[
      K(x,y) \ ((x \ z) * x) = (x \ (K(x,y) \ z)) * x
    ]]></literal>
    <justification jstring="[para(4531(a,2),6743(a,2,1))].">
      <j1 rule="para" parents="4531 6743"/>
    </justification>
  </clause>

  <clause id="7222">
    <literal><![CDATA[
      K(x,T(y,z)) \ ((R(z,u,w) * T(y,z)) / T(y,z)) = (T(T(y,z),x) * R(T(z,y),u,w)) / T(y,z)
    ]]></literal>
    <justification jstring="[para(3638(a,1),6744(a,1,2,1))].">
      <j1 rule="para" parents="3638 6744"/>
    </justification>
  </clause>

  <clause id="7223">
    <literal><![CDATA[
      x * (K(y,x) * K(y,x)) = (T(y,x) * x) / y
    ]]></literal>
    <justification jstring="[hyper(4887,a,6745,a)].">
      <j1 rule="hyper" parents="4887 6745"/>
    </justification>
  </clause>

  <clause id="7224">
    <literal><![CDATA[
      K(x,T(R(y \ z,y,u),z * u)) = K(x,T((y * u) \ (z * u),y))
    ]]></literal>
    <justification jstring="[para(688(a,1),6755(a,1,2,1))].">
      <j1 rule="para" parents="688 6755"/>
    </justification>
  </clause>

  <clause id="7225">
    <literal><![CDATA[
      K(x,T(y \ z,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(6755(a,1),7064(a,1))].">
      <j1 rule="para" parents="6755 7064"/>
    </justification>
  </clause>

  <clause id="7226">
    <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(6434(a,1),7225(a,1))].">
      <j1 rule="para" parents="6434 7225"/>
    </justification>
  </clause>

  <clause id="7227">
    <literal><![CDATA[
      K(x,T(T(y,z),u * y)) = K(x,T(T(y,z),u))
    ]]></literal>
    <justification jstring="[para(23(a,1),6756(a,2,2))].">
      <j1 rule="para" parents="23 6756"/>
    </justification>
  </clause>

  <clause id="7228">
    <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(121,a,4556,a(flip),b,6790,a)].">
      <j1 rule="hyper" parents="121 4556 6790"/>
    </justification>
  </clause>

  <clause id="7229">
    <literal><![CDATA[
      K(x,K(y,z)) * (z / K(x,y)) = K(y,x) * z
    ]]></literal>
    <justification jstring="[para(5994(a,2),6801(a,1,2))].">
      <j1 rule="para" parents="5994 6801"/>
    </justification>
  </clause>

  <clause id="7230">
    <literal><![CDATA[
      K(x,K(y,z)) * (T(z,y) * u) = T(T(z,y),K(x,y)) * u
    ]]></literal>
    <justification jstring="[para(4370(a,1),6810(a,1,1,2))].">
      <j1 rule="para" parents="4370 6810"/>
    </justification>
  </clause>

  <clause id="7231">
    <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(121,a,4434,a(flip),b,6824,a)].">
      <j1 rule="hyper" parents="121 4434 6824"/>
    </justification>
  </clause>

  <clause id="7234">
    <literal><![CDATA[
      T(T(x,y),x / z) = T(T(x,y),z \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,3343,a(flip),b,6877,a)].">
      <j1 rule="hyper" parents="63 3343 6877"/>
    </justification>
  </clause>

  <clause id="7235">
    <literal><![CDATA[
      T(x,y / z) * K(z \ y,z) = K(z \ y,z) * T(x,z \ y)
    ]]></literal>
    <justification jstring="[para(6946(a,1),6879(a,1,1))].">
      <j1 rule="para" parents="6946 6879"/>
    </justification>
  </clause>

  <clause id="7236">
    <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(1487(a,1),6913(a,1,2))].">
      <j1 rule="para" parents="1487 6913"/>
    </justification>
  </clause>

  <clause id="7237">
    <literal><![CDATA[
      K(R(x / (x / y),z,u),w) = K(R(y,z,u),T(w,y \ x))
    ]]></literal>
    <justification jstring="[para(3701(a,1),6918(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="3701 6918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7238">
    <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(63,a,6297,a(flip),b,6919,a)].">
      <j1 rule="hyper" parents="63 6297 6919"/>
    </justification>
  </clause>

  <clause id="7239">
    <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(1487(a,1),6919(a,1,1))].">
      <j1 rule="para" parents="1487 6919"/>
    </justification>
  </clause>

  <clause id="7240">
    <literal><![CDATA[
      K(T(x * y,y) / x,z) = K(y,T(T(z,x),x * y))
    ]]></literal>
    <justification jstring="[hyper(7072,a,6932,a)].">
      <j1 rule="hyper" parents="7072 6932"/>
    </justification>
  </clause>

  <clause id="7241">
    <literal><![CDATA[
      (K(x,y) * T(x,z)) \ x = K(z,x) * K(y,x)
    ]]></literal>
    <justification jstring="[para(6944(a,1),6938(a,1,1))].">
      <j1 rule="para" parents="6944 6938"/>
    </justification>
  </clause>

  <clause id="7242">
    <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(6624(a,1),6948(a,1,2,1,1))].">
      <j1 rule="para" parents="6624 6948"/>
    </justification>
  </clause>

  <clause id="7243">
    <literal><![CDATA[
      T(x,T(y,z) / z) = T(x,y / T(z,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,6946,a(flip),b,6949,a)].">
      <j1 rule="hyper" parents="63 6946 6949"/>
    </justification>
  </clause>

  <clause id="7244">
    <literal><![CDATA[
      T(x,y) * K(x * y,T(z,x)) = K(x * y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(6958(a,1),6390(a,1,2))].">
      <j1 rule="para" parents="6958 6390"/>
    </justification>
  </clause>

  <clause id="7245">
    <literal><![CDATA[
      T(x,y) * K(x * y,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * y,z) * T(x,y) = u
    ]]></literal>
    <justification jstring="[para(6958(a,1),6397(a,1,2))].">
      <j1 rule="para" parents="6958 6397"/>
    </justification>
  </clause>

  <clause id="7246">
    <literal><![CDATA[
      K(x,T(y \ x,z / y)) = K(x,T(y \ x,y \ z))
    ]]></literal>
    <justification jstring="[para(113(a,1),6959(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="113 6959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7247">
    <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(3625(a,1),6967(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="3625 6967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7248">
    <literal><![CDATA[
      K(x,T(y \ (x * z),z)) = K(x,(y / z) \ x)
    ]]></literal>
    <justification jstring="[hyper(333,a,5661,a(flip),b,6976,a),flip(a)].">
      <j1 rule="hyper" parents="333 5661 6976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7249">
    <literal><![CDATA[
      T(x * K(x / K(y,z),u),K(z,y)) = K(z,y) \ T(x / K(y,z),T(u,K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(6025,a,7002,a)].">
      <j1 rule="hyper" parents="6025 7002"/>
    </justification>
  </clause>

  <clause id="7250">
    <literal><![CDATA[
      T(x,K(y,z / y) / (z \ y)) = T(x,T(1 / (z \ y),y))
    ]]></literal>
    <justification jstring="[para(4724(a,1),7021(a,1,2,1))].">
      <j1 rule="para" parents="4724 7021"/>
    </justification>
  </clause>

  <clause id="7251">
    <literal><![CDATA[
      K(x,K(y,T(z,u / x))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,T(y,u))) = w
    ]]></literal>
    <justification jstring="[para(7089(a,2),6798(a,1))].">
      <j1 rule="para" parents="7089 6798"/>
    </justification>
  </clause>

  <clause id="7252">
    <literal><![CDATA[
      T(x * T(y,z),K(y,z)) = T(y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,4520,a(flip),b,7097,a),flip(a)].">
      <j1 rule="hyper" parents="333 4520 7097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7253">
    <literal><![CDATA[
      K(x * T(y,z),T(u,K(y,z))) = K(K(y,z) * (x * y),u)
    ]]></literal>
    <justification jstring="[para(7097(a,1),6370(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7097 6370"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7254">
    <literal><![CDATA[
      ((T(x,T(y,z / T(x,y))) * (z / T(x,y))) * x) / z = R(x,z / T(x,y),T(x,y))
    ]]></literal>
    <justification jstring="[hyper(123,a,7113,a,b,540,a)].">
      <j1 rule="hyper" parents="123 7113 540"/>
    </justification>
  </clause>

  <clause id="7255">
    <literal><![CDATA[
      T(x,1 / T(T(y,z),z)) = T(x,1 / y)
    ]]></literal>
    <justification jstring="[hyper(333,a,4206,a,b,7128,a),flip(a)].">
      <j1 rule="hyper" parents="333 4206 7128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7256">
    <literal><![CDATA[
      T(x,1 / T(y \ z,y)) = T(x,1 / (z / y))
    ]]></literal>
    <justification jstring="[para(113(a,1),7255(a,1,2,2,1))].">
      <j1 rule="para" parents="113 7255"/>
    </justification>
  </clause>

  <clause id="7257">
    <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(7134(a,2),43(a,1))].">
      <j1 rule="para" parents="7134 43"/>
    </justification>
  </clause>

  <clause id="7258">
    <literal><![CDATA[
      T(x * K(y,T(x,z)),y) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7134(a,1),4424(a,1,1))].">
      <j1 rule="para" parents="7134 4424"/>
    </justification>
  </clause>

  <clause id="7259">
    <literal><![CDATA[
      K(T(x * y,T(y,z)) \ ((x * T(y,K(x,z))) * u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(K(x * T(y,K(x,z)),y) \ u,w) = v5
    ]]></literal>
    <justification jstring="[para(7136(a,1),4740(a,1,1,1))].">
      <j1 rule="para" parents="7136 4740"/>
    </justification>
  </clause>

  <clause id="7260">
    <literal><![CDATA[
      T(K(x,y),z \ 1) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,6761,a(flip),b,7168,a),flip(a)].">
      <j1 rule="hyper" parents="63 6761 7168"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7261">
    <literal><![CDATA[
      K(x,T(y,z \ 1)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(6691,a,7260,a)].">
      <j1 rule="hyper" parents="6691 7260"/>
    </justification>
  </clause>

  <clause id="7262">
    <literal><![CDATA[
      T(x,T(y,z \ 1)) = x * K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7260(a,1),6393(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7260 6393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7263">
    <literal><![CDATA[
      T(K(x,y),z \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      T(K(x,y),z) = u
    ]]></literal>
    <justification jstring="[para(7260(a,2),6552(a,1))].">
      <j1 rule="para" parents="7260 6552"/>
    </justification>
  </clause>

  <clause id="7264">
    <literal><![CDATA[
      T(x,T(y,z \ 1)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(124,a,7261,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 7261 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7265">
    <literal><![CDATA[
      K(x * y,T(z,y)) = K(x * y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,6544,a(flip),b,7261,a)].">
      <j1 rule="hyper" parents="63 6544 7261"/>
    </justification>
  </clause>

  <clause id="7266">
    <literal><![CDATA[
      K(x,T(y,z \ x)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,6543,a(flip),b,7261,a)].">
      <j1 rule="hyper" parents="63 6543 7261"/>
    </justification>
  </clause>

  <clause id="7267">
    <literal><![CDATA[
      K(x,T(y * z,z)) = K(x,T(y * z,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,6479,a(flip),b,7261,a)].">
      <j1 rule="hyper" parents="63 6479 7261"/>
    </justification>
  </clause>

  <clause id="7268">
    <literal><![CDATA[
      K(x,T(y,1 / z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(79(a,1),7261(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="79 7261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7269">
    <literal><![CDATA[
      K(x,T(y / (z \ 1),z)) = K(x,(z \ 1) \ y)
    ]]></literal>
    <justification jstring="[para(113(a,1),7261(a,1,2)),flip(a)].">
      <j1 rule="para" parents="113 7261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7270">
    <literal><![CDATA[
      K(x,T(y,z / u)) = K(x,T(y,u / z))
    ]]></literal>
    <justification jstring="[para(3760(a,1),7261(a,1,2))].">
      <j1 rule="para" parents="3760 7261"/>
    </justification>
  </clause>

  <clause id="7271">
    <literal><![CDATA[
      K(x,T(y,z \ u)) = K(x,T(y,u \ z))
    ]]></literal>
    <justification jstring="[para(5772(a,1),7261(a,1,2))].">
      <j1 rule="para" parents="5772 7261"/>
    </justification>
  </clause>

  <clause id="7272">
    <literal><![CDATA[
      K(x,T(y,z)) * (z \ x) = (z \ x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(125,a,7266,a(flip),b,6884,a)].">
      <j1 rule="hyper" parents="125 7266 6884"/>
    </justification>
  </clause>

  <clause id="7273">
    <literal><![CDATA[
      T(x,T(y,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7262(a,2),4285(a,1))].">
      <j1 rule="para" parents="7262 4285"/>
    </justification>
  </clause>

  <clause id="7274">
    <literal><![CDATA[
      T(x * y,T(z,y)) = T(x * y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(124,a,7265,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 7265 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7275">
    <literal><![CDATA[
      K(x * R(y,z,u),T(y,x)) = K(x * R(y,z,u),y)
    ]]></literal>
    <justification jstring="[para(177(a,1),7265(a,1,2)),flip(a)].">
      <j1 rule="para" parents="177 7265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7276">
    <literal><![CDATA[
      K(x,T(y,z \ y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7271(a,1),6364(a,1))].">
      <j1 rule="para" parents="7271 6364"/>
    </justification>
  </clause>

  <clause id="7277">
    <literal><![CDATA[
      K(x,T(y,z \ x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7271(a,1),6697(a,1))].">
      <j1 rule="para" parents="7271 6697"/>
    </justification>
  </clause>

  <clause id="7278">
    <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(221(a,1),7274(a,1,2)),flip(a)].">
      <j1 rule="para" parents="221 7274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7279">
    <literal><![CDATA[
      K(T(x,y \ 1) \ 1,z) = T(K(x \ 1,z),y)
    ]]></literal>
    <justification jstring="[hyper(7263,a,5284,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="7263 5284"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7280">
    <literal><![CDATA[
      T(x,T(y,z \ y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(6467(a,1),7273(a,1))].">
      <j1 rule="para" parents="6467 7273"/>
    </justification>
  </clause>

  <clause id="7281">
    <literal><![CDATA[
      K((x \ y) \ z,T(y,x)) = K(z / (x \ y),y)
    ]]></literal>
    <justification jstring="[hyper(7276,a,6922,a)].">
      <j1 rule="hyper" parents="7276 6922"/>
    </justification>
  </clause>

  <clause id="7282">
    <literal><![CDATA[
      K(x,T(y,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(6369(a,2),7276(a,1))].">
      <j1 rule="para" parents="6369 7276"/>
    </justification>
  </clause>

  <clause id="7283">
    <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(7267(a,1),7277(a,1))].">
      <j1 rule="para" parents="7267 7277"/>
    </justification>
  </clause>

  <clause id="7284">
    <literal><![CDATA[
      K(x,T(y,1 / z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(2986(a,2),7282(a,1,2))].">
      <j1 rule="para" parents="2986 7282"/>
    </justification>
  </clause>

  <clause id="7285">
    <literal><![CDATA[
      K(x,T(y,z / u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u / z)) = w
    ]]></literal>
    <justification jstring="[para(3760(a,1),7282(a,1,2))].">
      <j1 rule="para" parents="3760 7282"/>
    </justification>
  </clause>

  <clause id="7286">
    <literal><![CDATA[
      K(x,T(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u \ z)) = w
    ]]></literal>
    <justification jstring="[para(5772(a,1),7282(a,1,2))].">
      <j1 rule="para" parents="5772 7282"/>
    </justification>
  </clause>

  <clause id="7287">
    <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(6738(a,1),7282(a,1,2))].">
      <j1 rule="para" parents="6738 7282"/>
    </justification>
  </clause>

  <clause id="7288">
    <literal><![CDATA[
      T(x \ 1,K(y,z)) = T(x,K(y,z)) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,6778,a(flip),b,7169,a),flip(a)].">
      <j1 rule="hyper" parents="63 6778 7169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7289">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y / x,z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(6788(a,1),7183(a,1,1))].">
      <j1 rule="para" parents="6788 7183"/>
    </justification>
  </clause>

  <clause id="7290">
    <literal><![CDATA[
      T(x \ y,K(y,z)) = T(x,K(y,z)) \ y
    ]]></literal>
    <justification jstring="[hyper(63,a,6830,a(flip),b,7184,a),flip(a)].">
      <j1 rule="hyper" parents="63 6830 7184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7291">
    <literal><![CDATA[
      K(x,T(T(y,z),u \ 1)) = K(x,T(T(y,z),u \ y))
    ]]></literal>
    <justification jstring="[para(3808(a,1),7227(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3808 7227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7292">
    <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(5209(a,1),7229(a,1,1,2))].">
      <j1 rule="para" parents="5209 7229"/>
    </justification>
  </clause>

  <clause id="7293">
    <literal><![CDATA[
      (K(x,y) * T(x,K(z,u))) \ x = K(z,K(u,x)) * K(y,x)
    ]]></literal>
    <justification jstring="[para(6763(a,1),7241(a,2,1))].">
      <j1 rule="para" parents="6763 7241"/>
    </justification>
  </clause>

  <clause id="7294">
    <literal><![CDATA[
      K(x,T(y \ (x * z),z)) * u = u * K(x,T((y / z) \ x,u))
    ]]></literal>
    <justification jstring="[para(7248(a,2),6390(a,2,1)),flip(a)].">
      <j1 rule="para" parents="7248 6390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7295">
    <literal><![CDATA[
      T(T(x,y) * T(z,x),T(x,y)) = T(z * T(x,y),x)
    ]]></literal>
    <justification jstring="[para(7252(a,1),6869(a,1,1))].">
      <j1 rule="para" parents="7252 6869"/>
    </justification>
  </clause>

  <clause id="7296">
    <literal><![CDATA[
      T(x,1 / (((y \ z) \ z) \ z)) = T(x,1 / (z / y))
    ]]></literal>
    <justification jstring="[para(3674(a,1),7256(a,1,2,2))].">
      <j1 rule="para" parents="3674 7256"/>
    </justification>
  </clause>

  <clause id="7297">
    <literal><![CDATA[
      K(T(x,y \ 1) \ 1,z) = K(T(x,y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,5284,a,b,7279,a),flip(a)].">
      <j1 rule="hyper" parents="333 5284 7279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7298">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x \ y,z) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(126,a,7289,a(flip),b,6829,a)].">
      <j1 rule="hyper" parents="126 7289 6829"/>
    </justification>
  </clause>

  <clause id="7299">
    <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(4368(a,1),7289(a,1,2))].">
      <j1 rule="para" parents="4368 7289"/>
    </justification>
  </clause>

  <clause id="7300">
    <literal><![CDATA[
      L(K(x \ y,z),y,x \ 1) = K((x \ 1) * y,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,4762,a(flip),b,6290,a),flip(a)].">
      <j1 rule="hyper" parents="333 4762 6290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7301">
    <literal><![CDATA[
      (x * (y * z)) * K(z,L(y,z,x)) = x * (z * y)
    ]]></literal>
    <justification jstring="[hyper(5999,a,6304,a)].">
      <j1 rule="hyper" parents="5999 6304"/>
    </justification>
  </clause>

  <clause id="7302">
    <literal><![CDATA[
      (x * (y * z)) * u != x * (z * y)
    ]]></literal>
    <literal><![CDATA[
      K(L(z,y,x),y) = u
    ]]></literal>
    <justification jstring="[para(6304(a,1),131(a,1,1))].">
      <j1 rule="para" parents="6304 131"/>
    </justification>
  </clause>

  <clause id="7303">
    <literal><![CDATA[
      K(x / y,T(z,x \ y)) = K(y \ x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(6439,a,6988,a),flip(a)].">
      <j1 rule="hyper" parents="6439 6988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7304">
    <literal><![CDATA[
      K(x / y,T(z,x \ y)) = K(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,6922,a(flip),b,7303,a),flip(a)].">
      <j1 rule="hyper" parents="333 6922 7303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7305">
    <literal><![CDATA[
      T(x / y,T(z,x \ y)) = T(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(124,a,7304,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 7304 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7306">
    <literal><![CDATA[
      K(T(x,y),z) * u != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y)) * u = w
    ]]></literal>
    <justification jstring="[para(4567(a,1),6447(a,1))].">
      <j1 rule="para" parents="4567 6447"/>
    </justification>
  </clause>

  <clause id="7307">
    <literal><![CDATA[
      x * K(T(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      x * K(y,T(u,z)) = w
    ]]></literal>
    <justification jstring="[para(5994(a,1),6455(a,1))].">
      <j1 rule="para" parents="5994 6455"/>
    </justification>
  </clause>

  <clause id="7309">
    <literal><![CDATA[
      (x * y) \ (T(x,z) * y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y)) = u
    ]]></literal>
    <justification jstring="[para(6726(a,1),372(a,1)),flip(b)].">
      <j1 rule="para" parents="6726 372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7310">
    <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(6609(a,1),6764(a,1,2))].">
      <j1 rule="para" parents="6609 6764"/>
    </justification>
  </clause>

  <clause id="7311">
    <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(6817(a,2),6776(a,1,2))].">
      <j1 rule="para" parents="6817 6776"/>
    </justification>
  </clause>

  <clause id="7312">
    <literal><![CDATA[
      K(x,K(y,1 / z)) = K(y,K(x,y * z))
    ]]></literal>
    <justification jstring="[hyper(7047,a,7170,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="7047 7170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7313">
    <literal><![CDATA[
      T(x * y,K(z,y)) = T(x,K(z,y)) * y
    ]]></literal>
    <justification jstring="[hyper(7058,a,6878,a(flip))].">
      <j1 rule="hyper" parents="7058 6878"/>
    </justification>
  </clause>

  <clause id="7314">
    <literal><![CDATA[
      T(x \ y,K(z,x)) = x \ T(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(35,a,4105,a(flip),b,7313,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="35 4105 7313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7315">
    <literal><![CDATA[
      T(T(x,y) * z,K(y,z)) = T(x,T(y,z)) * z
    ]]></literal>
    <justification jstring="[para(6191(a,1),7313(a,2,1))].">
      <j1 rule="para" parents="6191 7313"/>
    </justification>
  </clause>

  <clause id="7316">
    <literal><![CDATA[
      x * T(x \ y,K(z,x)) = T(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(126,a,7314,a,b,xx)].">
      <j1 rule="hyper" parents="126 7314"/>
    </justification>
  </clause>

  <clause id="7318">
    <literal><![CDATA[
      T(x,K(y,z)) / z = T(x / z,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(123,a,7316,a(flip),b,471,a)].">
      <j1 rule="hyper" parents="123 7316 471"/>
    </justification>
  </clause>

  <clause id="7319">
    <literal><![CDATA[
      T(T(x,y) / z,K(y,z)) = T(x,T(y,z)) / z
    ]]></literal>
    <justification jstring="[para(6191(a,1),7318(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6191 7318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7320">
    <literal><![CDATA[
      K(x,K(y \ z,T(y,u))) = K(y,K(z,T(x,u)))
    ]]></literal>
    <justification jstring="[hyper(7090,a,7037,a)].">
      <j1 rule="hyper" parents="7090 7037"/>
    </justification>
  </clause>

  <clause id="7321">
    <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(7320(a,2),7053(a,1))].">
      <j1 rule="para" parents="7320 7053"/>
    </justification>
  </clause>

  <clause id="7322">
    <literal><![CDATA[
      1 / T(x,K(y,z)) = T(1 / x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(7191,a,6823,a),flip(a)].">
      <j1 rule="hyper" parents="7191 6823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7323">
    <literal><![CDATA[
      T(1 / (x * K(y,z)),K(z,y)) = 1 / (K(y,z) * x)
    ]]></literal>
    <justification jstring="[para(6035(a,1),7322(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6035 7322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7324">
    <literal><![CDATA[
      K(x,T(y,T(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u \ (z \ u))) = w
    ]]></literal>
    <justification jstring="[para(6465(a,1),7286(a,1,2))].">
      <j1 rule="para" parents="6465 7286"/>
    </justification>
  </clause>

  <clause id="7326">
    <literal><![CDATA[
      K(L(x,y,z),y) = K(x,L(y,x,z))
    ]]></literal>
    <justification jstring="[hyper(34,a,6305,a,b,7301,a)].">
      <j1 rule="hyper" parents="34 6305 7301"/>
    </justification>
  </clause>

  <clause id="7327">
    <literal><![CDATA[
      (x * (y * z)) * u != x * (z * y)
    ]]></literal>
    <literal><![CDATA[
      K(z,L(y,z,x)) = u
    ]]></literal>
    <justification jstring="[para(7301(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="7301 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7328">
    <literal><![CDATA[
      T(K(x,y),z) * u != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) * u = w
    ]]></literal>
    <justification jstring="[para(6352(a,1),7306(a,1,1))].">
      <j1 rule="para" parents="6352 7306"/>
    </justification>
  </clause>

  <clause id="7329">
    <literal><![CDATA[
      x * T(K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      x * K(y,T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(6352(a,1),7307(a,1,2))].">
      <j1 rule="para" parents="6352 7307"/>
    </justification>
  </clause>

  <clause id="7330">
    <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(5299(a,2),7328(a,1))].">
      <j1 rule="para" parents="5299 7328"/>
    </justification>
  </clause>

  <clause id="7332">
    <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(6627(a,2),7329(a,1))].">
      <j1 rule="para" parents="6627 7329"/>
    </justification>
  </clause>

  <clause id="7333">
    <literal><![CDATA[
      L(x \ 1,y,K(x,z)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(2942,a,6347,a)].">
      <j1 rule="hyper" parents="2942 6347"/>
    </justification>
  </clause>

  <clause id="7334">
    <literal><![CDATA[
      (K(x,y) * (z * x)) \ (K(x,y) * z) = L(x \ 1,x,z)
    ]]></literal>
    <justification jstring="[para(7333(a,1),928(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7333 928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7335">
    <literal><![CDATA[
      R(T(K(x,y),z),y * u,w) = K(x,R(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(27(a,2),6375(a,2,2))].">
      <j1 rule="para" parents="27 6375"/>
    </justification>
  </clause>

  <clause id="7336">
    <literal><![CDATA[
      L(K(x,y),z,u) * (u * z) != w
    ]]></literal>
    <literal><![CDATA[
      u * (z * K(x,T(y,u * z))) = w
    ]]></literal>
    <justification jstring="[para(6399(a,1),306(a,1))].">
      <j1 rule="para" parents="6399 306"/>
    </justification>
  </clause>

  <clause id="7337">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(x,y) * u) = K(x,T(y,z)) * u
    ]]></literal>
    <justification jstring="[para(6762(a,1),6409(a,1,1))].">
      <j1 rule="para" parents="6762 6409"/>
    </justification>
  </clause>

  <clause id="7338">
    <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(1522,a,6414,a),flip(a)].">
      <j1 rule="hyper" parents="1522 6414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7339">
    <literal><![CDATA[
      (x \ y) * K(z,T(x,y)) = T(x,z) \ y
    ]]></literal>
    <justification jstring="[hyper(39,a,6668,a(flip),b,6480,a),flip(a)].">
      <j1 rule="hyper" parents="39 6668 6480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7340">
    <literal><![CDATA[
      (x \ y) \ (T(x,z) \ y) = K(z,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(129,a,7339,a)].">
      <j1 rule="hyper" parents="129 7339"/>
    </justification>
  </clause>

  <clause id="7341">
    <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(222(a,1),7339(a,1,2,2))].">
      <j1 rule="para" parents="222 7339"/>
    </justification>
  </clause>

  <clause id="7342">
    <literal><![CDATA[
      x * K(y,(1 / x) * (z * x)) = K(y,L(z,x,x \ 1)) * x
    ]]></literal>
    <justification jstring="[para(2654(a,1),6495(a,1,2,2))].">
      <j1 rule="para" parents="2654 6495"/>
    </justification>
  </clause>

  <clause id="7343">
    <literal><![CDATA[
      T(x,T((y \ 1) / z,y)) = T(x,(y * y) \ (z \ y))
    ]]></literal>
    <justification jstring="[para(442(a,1),6529(a,2,2))].">
      <j1 rule="para" parents="442 6529"/>
    </justification>
  </clause>

  <clause id="7344">
    <literal><![CDATA[
      T(x,y) * (L(T(x,y),z,x) \ u) = x * (L(x,z,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(126,a,6550,a(flip),b,4550,a)].">
      <j1 rule="hyper" parents="126 6550 4550"/>
    </justification>
  </clause>

  <clause id="7345">
    <literal><![CDATA[
      (x * K((y \ 1) \ (z \ x),z)) * y = (z \ (x * y)) * z
    ]]></literal>
    <justification jstring="[hyper(125,a,6559,a,b,4161,a(flip))].">
      <j1 rule="hyper" parents="125 6559 4161"/>
    </justification>
  </clause>

  <clause id="7346">
    <literal><![CDATA[
      (x * ((y \ (x \ z)) * y)) \ z = K(y,x \ (y \ z))
    ]]></literal>
    <justification jstring="[para(6559(a,1),5990(a,1,1))].">
      <j1 rule="para" parents="6559 5990"/>
    </justification>
  </clause>

  <clause id="7348">
    <literal><![CDATA[
      T(x,K(y,x) * z) = z \ (x * z)
    ]]></literal>
    <justification jstring="[para(4513(a,1),6585(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4513 6585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7349">
    <literal><![CDATA[
      T(x,K(y,x) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,22,a,b,7348,a),flip(a)].">
      <j1 rule="hyper" parents="333 22 7348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7350">
    <literal><![CDATA[
      T(x,K(y,x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z) = u
    ]]></literal>
    <justification jstring="[para(7348(a,2),347(a,1))].">
      <j1 rule="para" parents="7348 347"/>
    </justification>
  </clause>

  <clause id="7352">
    <literal><![CDATA[
      K(K(x,y) * z,y) = y / T(y,z)
    ]]></literal>
    <justification jstring="[hyper(197,a,7349,a(flip),b,4233,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="197 7349 4233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7353">
    <literal><![CDATA[
      T(((K(x,y) * z) \ y) \ T(y,z),y) = ((K(x,y) * z) \ y) \ y
    ]]></literal>
    <justification jstring="[para(7349(a,1),1098(a,1,1,2))].">
      <j1 rule="para" parents="7349 1098"/>
    </justification>
  </clause>

  <clause id="7354">
    <literal><![CDATA[
      T(x,K(x,y) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[para(4558(a,1),7349(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4558 7349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7355">
    <literal><![CDATA[
      T(x,T(x,y) * z) = T(x,x * z)
    ]]></literal>
    <justification jstring="[para(4557(a,1),7349(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4557 7349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7357">
    <literal><![CDATA[
      T(x,(y / (y / x)) * z) = T(x,x * z)
    ]]></literal>
    <justification jstring="[para(4876(a,1),7349(a,1,2))].">
      <j1 rule="para" parents="4876 7349"/>
    </justification>
  </clause>

  <clause id="7359">
    <literal><![CDATA[
      T(x,y * T(z,x)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(4967(a,1),7349(a,1,2))].">
      <j1 rule="para" parents="4967 7349"/>
    </justification>
  </clause>

  <clause id="7360">
    <literal><![CDATA[
      T(x,y \ T(z,x)) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(4963(a,1),7349(a,1,2))].">
      <j1 rule="para" parents="4963 7349"/>
    </justification>
  </clause>

  <clause id="7361">
    <literal><![CDATA[
      T(x,y * K(z,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(6888(a,1),7349(a,1,2))].">
      <j1 rule="para" parents="6888 7349"/>
    </justification>
  </clause>

  <clause id="7362">
    <literal><![CDATA[
      T(x,K(x,y) * L(K(z,x),u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(333,a,2751,a(flip),b,7354,a),flip(a)].">
      <j1 rule="hyper" parents="333 2751 7354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7363">
    <literal><![CDATA[
      K(x,K(x,y) * z) = x \ T(x,z)
    ]]></literal>
    <justification jstring="[hyper(121,a,7354,a(flip),b,4222,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="121 7354 4222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7364">
    <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(7354(a,1),4649(a,1,1))].">
      <j1 rule="para" parents="7354 4649"/>
    </justification>
  </clause>

  <clause id="7366">
    <literal><![CDATA[
      K(x,T(y,K(x,z) * u)) = K(T(x,u),y)
    ]]></literal>
    <justification jstring="[para(7354(a,1),6370(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7354 6370"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7367">
    <literal><![CDATA[
      T(x,y * K(x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(6887(a,1),7354(a,1,2))].">
      <j1 rule="para" parents="6887 7354"/>
    </justification>
  </clause>

  <clause id="7368">
    <literal><![CDATA[
      K(x \ (K(y,z) * u),T(y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K((K(y,z) * u) / x,y) = w
    ]]></literal>
    <justification jstring="[para(7354(a,1),7062(a,1,2))].">
      <j1 rule="para" parents="7354 7062"/>
    </justification>
  </clause>

  <clause id="7369">
    <literal><![CDATA[
      T(T(x,y),z * K(u,x)) = T(T(x,z),y)
    ]]></literal>
    <justification jstring="[para(7361(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7361 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7370">
    <literal><![CDATA[
      T((x \ y) * x,z * K(u,y)) = (x \ T(y,z)) * x
    ]]></literal>
    <justification jstring="[para(7361(a,1),4105(a,2,1,2))].">
      <j1 rule="para" parents="7361 4105"/>
    </justification>
  </clause>

  <clause id="7371">
    <literal><![CDATA[
      T(x,y / T(x,z)) = T(x,y / x)
    ]]></literal>
    <justification jstring="[para(5450(a,1),7361(a,1,2))].">
      <j1 rule="para" parents="5450 7361"/>
    </justification>
  </clause>

  <clause id="7372">
    <literal><![CDATA[
      K(T(x,y),(y * K(z,x)) \ u) = K(x,u / (y * K(z,x)))
    ]]></literal>
    <justification jstring="[para(7361(a,1),6928(a,1,1))].">
      <j1 rule="para" parents="7361 6928"/>
    </justification>
  </clause>

  <clause id="7373">
    <literal><![CDATA[
      T(x,y * (z * x)) = T(x,y * (x * z))
    ]]></literal>
    <justification jstring="[para(6305(a,1),7361(a,1,2))].">
      <j1 rule="para" parents="6305 7361"/>
    </justification>
  </clause>

  <clause id="7376">
    <literal><![CDATA[
      (x * K(y,z)) * L(T(y,x),u,w) = L(y,u,w) * (x * K(y,z))
    ]]></literal>
    <justification jstring="[para(7367(a,1),251(a,1,2,1))].">
      <j1 rule="para" parents="7367 251"/>
    </justification>
  </clause>

  <clause id="7377">
    <literal><![CDATA[
      T(x * K(y,z),L(T(y,x),u,w)) = T(x * K(y,z),L(y,u,w))
    ]]></literal>
    <justification jstring="[para(7367(a,1),3632(a,1,2,1))].">
      <j1 rule="para" parents="7367 3632"/>
    </justification>
  </clause>

  <clause id="7380">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,T(y,x)) = K(u / (x * K(y,z)),y)
    ]]></literal>
    <justification jstring="[para(7367(a,1),6922(a,1,2))].">
      <j1 rule="para" parents="7367 6922"/>
    </justification>
  </clause>

  <clause id="7381">
    <literal><![CDATA[
      T(x,y * T(z,K(x,u))) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(6807(a,1),7367(a,1,2))].">
      <j1 rule="para" parents="6807 7367"/>
    </justification>
  </clause>

  <clause id="7382">
    <literal><![CDATA[
      K(K(x,y) * z,y) = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,4212,a,b,7352,a),flip(a)].">
      <j1 rule="hyper" parents="333 4212 7352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7383">
    <literal><![CDATA[
      K(K(x,y) * z,y) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) = u
    ]]></literal>
    <justification jstring="[para(7352(a,2),4313(a,1))].">
      <j1 rule="para" parents="7352 4313"/>
    </justification>
  </clause>

  <clause id="7384">
    <literal><![CDATA[
      K(K(x,y) * z,x) = K(z,x)
    ]]></literal>
    <justification jstring="[para(4558(a,1),7382(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4558 7382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7385">
    <literal><![CDATA[
      K(K(x,y) \ z,x) = K(z,x)
    ]]></literal>
    <justification jstring="[para(4567(a,2),7382(a,1,1))].">
      <j1 rule="para" parents="4567 7382"/>
    </justification>
  </clause>

  <clause id="7386">
    <literal><![CDATA[
      K(T(x,y) \ z,x) = K(x \ z,x)
    ]]></literal>
    <justification jstring="[para(4555(a,1),7382(a,1,1))].">
      <j1 rule="para" parents="4555 7382"/>
    </justification>
  </clause>

  <clause id="7387">
    <literal><![CDATA[
      K(T(x,y) * z,x) = K(x * z,x)
    ]]></literal>
    <justification jstring="[para(4557(a,1),7382(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4557 7382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7388">
    <literal><![CDATA[
      K(x * T(y,z),z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(4967(a,1),7382(a,1,1))].">
      <j1 rule="para" parents="4967 7382"/>
    </justification>
  </clause>

  <clause id="7389">
    <literal><![CDATA[
      K(x \ T(y,z),z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(4963(a,1),7382(a,1,1))].">
      <j1 rule="para" parents="4963 7382"/>
    </justification>
  </clause>

  <clause id="7390">
    <literal><![CDATA[
      K(K(x,y) * z,T(y,u)) = K(z,T(y,u))
    ]]></literal>
    <justification jstring="[para(6433(a,1),7382(a,1,1,1))].">
      <j1 rule="para" parents="6433 7382"/>
    </justification>
  </clause>

  <clause id="7391">
    <literal><![CDATA[
      K(x * K(y,z),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(6888(a,1),7382(a,1,1))].">
      <j1 rule="para" parents="6888 7382"/>
    </justification>
  </clause>

  <clause id="7393">
    <literal><![CDATA[
      K(R(K(x,y),z,u) * w,x) = K(w,x)
    ]]></literal>
    <justification jstring="[para(5632(a,1),7384(a,1,1,1))].">
      <j1 rule="para" parents="5632 7384"/>
    </justification>
  </clause>

  <clause id="7394">
    <literal><![CDATA[
      L(K(x,y),K(y,z) * x,u) = K(K(y,z) * x,y)
    ]]></literal>
    <justification jstring="[para(7384(a,1),6123(a,1,1))].">
      <j1 rule="para" parents="7384 6123"/>
    </justification>
  </clause>

  <clause id="7395">
    <literal><![CDATA[
      K(x * K(y,z),y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(6887(a,1),7384(a,1,1))].">
      <j1 rule="para" parents="6887 7384"/>
    </justification>
  </clause>

  <clause id="7396">
    <literal><![CDATA[
      K(K(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(K(y,w) * x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7384(a,1),7044(a,1,1))].">
      <j1 rule="para" parents="7384 7044"/>
    </justification>
  </clause>

  <clause id="7397">
    <literal><![CDATA[
      K(K(x,y) * z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,x) = u
    ]]></literal>
    <justification jstring="[para(7385(a,1),4614(a,1))].">
      <j1 rule="para" parents="7385 4614"/>
    </justification>
  </clause>

  <clause id="7398">
    <literal><![CDATA[
      K(T(x,T(y,z)) * u,y) = K(x * u,y)
    ]]></literal>
    <justification jstring="[para(6445(a,1),7385(a,1,1))].">
      <j1 rule="para" parents="6445 7385"/>
    </justification>
  </clause>

  <clause id="7399">
    <literal><![CDATA[
      K(x * K(y,z),z) = 1 / K(z,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,4371,a,b,7391,a),flip(a)].">
      <j1 rule="hyper" parents="333 4371 7391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7400">
    <literal><![CDATA[
      K(x * T(y,z),y) = K(x * y,y)
    ]]></literal>
    <justification jstring="[para(5455(a,1),7391(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5455 7391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7401">
    <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(7395(a,1),4952(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7395 4952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7402">
    <literal><![CDATA[
      T(T(x,y),T(x,z) * u) = T(T(x,x * u),y)
    ]]></literal>
    <justification jstring="[para(7355(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7355 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7404">
    <literal><![CDATA[
      T(x,y) / T(y,y \ x) = y \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(197,a,7360,a(flip),b,112,a(flip))].">
      <j1 rule="hyper" parents="197 7360 112"/>
    </justification>
  </clause>

  <clause id="7405">
    <literal><![CDATA[
      T(x,y \ (z / x)) = T(x,y \ (x \ z))
    ]]></literal>
    <justification jstring="[para(113(a,1),7360(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="113 7360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7406">
    <literal><![CDATA[
      K(x,K(x,y) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,4215,a,b,7363,a),flip(a)].">
      <j1 rule="hyper" parents="333 4215 7363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7407">
    <literal><![CDATA[
      K(x,K(x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(7363(a,2),4306(a,1))].">
      <j1 rule="para" parents="7363 4306"/>
    </justification>
  </clause>

  <clause id="7408">
    <literal><![CDATA[
      K(x,K(y,x) \ z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(4567(a,2),7406(a,1,2))].">
      <j1 rule="para" parents="4567 7406"/>
    </justification>
  </clause>

  <clause id="7409">
    <literal><![CDATA[
      K(x,T(x,y) * z) = K(x,x * z)
    ]]></literal>
    <justification jstring="[para(4273(a,1),7406(a,1,2))].">
      <j1 rule="para" parents="4273 7406"/>
    </justification>
  </clause>

  <clause id="7410">
    <literal><![CDATA[
      K(x,T(x,y) \ z) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[para(4518(a,1),7406(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4518 7406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7411">
    <literal><![CDATA[
      K(x,T(y,x) \ z) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(4555(a,1),7406(a,1,2))].">
      <j1 rule="para" parents="4555 7406"/>
    </justification>
  </clause>

  <clause id="7412">
    <literal><![CDATA[
      K(x,y \ T(y * z,x)) = K(x,z)
    ]]></literal>
    <justification jstring="[para(4839(a,1),7406(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4839 7406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7413">
    <literal><![CDATA[
      K(x,R(K(x,y),z,u) * w) = K(x,w)
    ]]></literal>
    <justification jstring="[para(5632(a,1),7406(a,1,2,1))].">
      <j1 rule="para" parents="5632 7406"/>
    </justification>
  </clause>

  <clause id="7414">
    <literal><![CDATA[
      K(x,y * K(x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(6887(a,1),7406(a,1,2))].">
      <j1 rule="para" parents="6887 7406"/>
    </justification>
  </clause>

  <clause id="7415">
    <literal><![CDATA[
      K(x,y * K(z,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(6943(a,1),7406(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6943 7406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7416">
    <literal><![CDATA[
      K(x,y / K(z,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,6459,a,b,7408,a)].">
      <j1 rule="hyper" parents="63 6459 7408"/>
    </justification>
  </clause>

  <clause id="7417">
    <literal><![CDATA[
      T(K(x,y),K(z,y) \ u) = K(x,y) * K(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(7408(a,1),6759(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7408 6759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7418">
    <literal><![CDATA[
      K(x,K(y,x * K(y,z))) = 1
    ]]></literal>
    <justification jstring="[para(7414(a,2),2724(a,1,2))].">
      <j1 rule="para" parents="7414 2724"/>
    </justification>
  </clause>

  <clause id="7419">
    <literal><![CDATA[
      K(x,y * T(z,x)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(5455(a,1),7414(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5455 7414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7420">
    <literal><![CDATA[
      K(x,y / (z / x)) = K(x,y / (x \ z))
    ]]></literal>
    <justification jstring="[para(5520(a,1),7414(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5520 7414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7421">
    <literal><![CDATA[
      K(x,y / T(x,z)) = K(x,y / x)
    ]]></literal>
    <justification jstring="[para(5975(a,1),7414(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5975 7414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7422">
    <literal><![CDATA[
      K(x \ y,z / (y / x)) = K(x \ y,z / (x \ y))
    ]]></literal>
    <justification jstring="[para(6012(a,1),7414(a,1,2))].">
      <j1 rule="para" parents="6012 7414"/>
    </justification>
  </clause>

  <clause id="7423">
    <literal><![CDATA[
      K(x,(y * z) * (z \ K(u,x))) = K(x,R(y,z,z \ K(u,x)))
    ]]></literal>
    <justification jstring="[para(367(a,1),7415(a,1,2))].">
      <j1 rule="para" parents="367 7415"/>
    </justification>
  </clause>

  <clause id="7424">
    <literal><![CDATA[
      R(K(x,y),y * K(z,x),u) = K(x,y * K(z,x))
    ]]></literal>
    <justification jstring="[para(7415(a,1),4889(a,1,1))].">
      <j1 rule="para" parents="7415 4889"/>
    </justification>
  </clause>

  <clause id="7425">
    <literal><![CDATA[
      K(x,y \ R(T(z,x),u,w)) = K(x,y \ R(z,u,w))
    ]]></literal>
    <justification jstring="[para(5189(a,1),7415(a,1,2))].">
      <j1 rule="para" parents="5189 7415"/>
    </justification>
  </clause>

  <clause id="7426">
    <literal><![CDATA[
      K(x,y \ K(z,x)) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(5072,a,7416,a),flip(a)].">
      <j1 rule="hyper" parents="5072 7416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7428">
    <literal><![CDATA[
      K(x,T(y,z / T(y,u))) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(7371(a,2),5843(a,1,2))].">
      <j1 rule="para" parents="7371 5843"/>
    </justification>
  </clause>

  <clause id="7429">
    <literal><![CDATA[
      K(x / T(y,z),y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,5094,a,b,7386,a)].">
      <j1 rule="hyper" parents="63 5094 7386"/>
    </justification>
  </clause>

  <clause id="7430">
    <literal><![CDATA[
      (T(x,y) * z) * K(x * z,x) = T(T(x,y) * z,x)
    ]]></literal>
    <justification jstring="[hyper(126,a,7387,a(flip),b,4215,a(flip))].">
      <j1 rule="hyper" parents="126 7387 4215"/>
    </justification>
  </clause>

  <clause id="7431">
    <literal><![CDATA[
      K(x * (y / R(z,u,z)),z) = K(x * (R(z,u,z) \ y),z)
    ]]></literal>
    <justification jstring="[para(6342(a,1),7388(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6342 7388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7432">
    <literal><![CDATA[
      K(x \ (y \ (z * y)),y) = K(x \ z,y)
    ]]></literal>
    <justification jstring="[para(22(a,1),7389(a,1,1,2))].">
      <j1 rule="para" parents="22 7389"/>
    </justification>
  </clause>

  <clause id="7433">
    <literal><![CDATA[
      K(x * K(y,z),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(7399(a,2),4388(a,1))].">
      <j1 rule="para" parents="7399 4388"/>
    </justification>
  </clause>

  <clause id="7434">
    <literal><![CDATA[
      K(x * T(y,z),y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,4543,a(flip),b,7400,a),flip(a)].">
      <j1 rule="hyper" parents="333 4543 7400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7435">
    <literal><![CDATA[
      K(x,T(x * K(y,z),y)) = K(x,x * K(y,z))
    ]]></literal>
    <justification jstring="[para(6650(a,2),7409(a,1,2))].">
      <j1 rule="para" parents="6650 7409"/>
    </justification>
  </clause>

  <clause id="7436">
    <literal><![CDATA[
      K(x,y / T(x,z)) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,4640,a,b,7410,a)].">
      <j1 rule="hyper" parents="63 4640 7410"/>
    </justification>
  </clause>

  <clause id="7438">
    <literal><![CDATA[
      K(x / y,(x / y) \ z) = K(x / y,(y \ x) \ z)
    ]]></literal>
    <justification jstring="[para(113(a,1),7410(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="113 7410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7439">
    <literal><![CDATA[
      K(x,R(y / x,z,u) \ w) = K(x,R(x \ y,z,u) \ w)
    ]]></literal>
    <justification jstring="[para(261(a,1),7411(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="261 7411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7440">
    <literal><![CDATA[
      T(x,K(y,z / T(y,u))) = T(x,K(y,y * z))
    ]]></literal>
    <justification jstring="[para(7421(a,2),7027(a,1,2))].">
      <j1 rule="para" parents="7421 7027"/>
    </justification>
  </clause>

  <clause id="7442">
    <literal><![CDATA[
      (x / T(y,z)) * K(y \ x,y) = T(x / T(y,z),y)
    ]]></literal>
    <justification jstring="[hyper(126,a,7429,a(flip),b,4215,a(flip))].">
      <j1 rule="hyper" parents="126 7429 4215"/>
    </justification>
  </clause>

  <clause id="7443">
    <literal><![CDATA[
      K(x * (y / T(x,z)),x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(12(a,1),7434(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12 7434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7445">
    <literal><![CDATA[
      (x / T(y,x)) * ((y \ T(x,y)) \ z) = K(y,y \ x) * z
    ]]></literal>
    <justification jstring="[para(7436(a,1),4710(a,2,1))].">
      <j1 rule="para" parents="7436 4710"/>
    </justification>
  </clause>

  <clause id="7446">
    <literal><![CDATA[
      T(x,(x \ y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,(y / x) * z) = u
    ]]></literal>
    <justification jstring="[para(5049(a,1),7350(a,1,2))].">
      <j1 rule="para" parents="5049 7350"/>
    </justification>
  </clause>

  <clause id="7447">
    <literal><![CDATA[
      K(x * y,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y * x,y) = z
    ]]></literal>
    <justification jstring="[para(4201(a,1),7383(a,1,1))].">
      <j1 rule="para" parents="4201 7383"/>
    </justification>
  </clause>

  <clause id="7448">
    <literal><![CDATA[
      K((x \ y) \ z,x \ y) != u
    ]]></literal>
    <literal><![CDATA[
      K((y / x) \ z,x \ y) = u
    ]]></literal>
    <justification jstring="[para(4981(a,1),7383(a,1,1))].">
      <j1 rule="para" parents="4981 7383"/>
    </justification>
  </clause>

  <clause id="7449">
    <literal><![CDATA[
      K(x * T(y,z),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(4967(a,1),7383(a,1,1))].">
      <j1 rule="para" parents="4967 7383"/>
    </justification>
  </clause>

  <clause id="7450">
    <literal><![CDATA[
      K((K(x,y) * z) * u,x) = K(z * u,x)
    ]]></literal>
    <justification jstring="[para(107(a,1),7393(a,1,1))].">
      <j1 rule="para" parents="107 7393"/>
    </justification>
  </clause>

  <clause id="7451">
    <literal><![CDATA[
      K(K(R(x,y,z),u) * w,x) = K(w,x)
    ]]></literal>
    <justification jstring="[para(5562(a,1),7393(a,1,1,1))].">
      <j1 rule="para" parents="5562 7393"/>
    </justification>
  </clause>

  <clause id="7452">
    <literal><![CDATA[
      K(x * y,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y * x,x) = z
    ]]></literal>
    <justification jstring="[para(4201(a,1),7397(a,1,1))].">
      <j1 rule="para" parents="4201 7397"/>
    </justification>
  </clause>

  <clause id="7453">
    <literal><![CDATA[
      K(x * K(y,z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(6887(a,1),7397(a,1,1))].">
      <j1 rule="para" parents="6887 7397"/>
    </justification>
  </clause>

  <clause id="7455">
    <literal><![CDATA[
      K(x,T(y,x) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(4555(a,1),7407(a,1,2))].">
      <j1 rule="para" parents="4555 7407"/>
    </justification>
  </clause>

  <clause id="7456">
    <literal><![CDATA[
      K(x,y * K(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(6887(a,1),7407(a,1,2))].">
      <j1 rule="para" parents="6887 7407"/>
    </justification>
  </clause>

  <clause id="7457">
    <literal><![CDATA[
      K(x,(K(x,y) * z) * u) = K(x,z * u)
    ]]></literal>
    <justification jstring="[para(107(a,1),7413(a,1,2))].">
      <j1 rule="para" parents="107 7413"/>
    </justification>
  </clause>

  <clause id="7458">
    <literal><![CDATA[
      K(x,K(R(x,y,z),u) * w) = K(x,w)
    ]]></literal>
    <justification jstring="[para(5562(a,1),7413(a,1,2,1))].">
      <j1 rule="para" parents="5562 7413"/>
    </justification>
  </clause>

  <clause id="7459">
    <literal><![CDATA[
      K(x * (y * z),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * (z * y),z) = u
    ]]></literal>
    <justification jstring="[para(6305(a,1),7433(a,1,1))].">
      <j1 rule="para" parents="6305 7433"/>
    </justification>
  </clause>

  <clause id="7460">
    <literal><![CDATA[
      K(R(x,y,z) * u,x) = K(u * R(x,y,z),x)
    ]]></literal>
    <justification jstring="[para(4201(a,1),7451(a,1,1))].">
      <j1 rule="para" parents="4201 7451"/>
    </justification>
  </clause>

  <clause id="7461">
    <literal><![CDATA[
      K(T(x,R(y,z,u)) * w,y) = K(x * w,y)
    ]]></literal>
    <justification jstring="[para(4557(a,1),7451(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4557 7451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7462">
    <literal><![CDATA[
      K(K(R(x,y,z),u) * w,T(x,v5)) = K(w,T(x,v5))
    ]]></literal>
    <justification jstring="[para(6918(a,1),7451(a,1,1,1))].">
      <j1 rule="para" parents="6918 7451"/>
    </justification>
  </clause>

  <clause id="7463">
    <literal><![CDATA[
      K((x \ 1) \ y,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x * y,y) = z
    ]]></literal>
    <justification jstring="[para(5938(a,2),7452(a,1))].">
      <j1 rule="para" parents="5938 7452"/>
    </justification>
  </clause>

  <clause id="7465">
    <literal><![CDATA[
      K(x,y / (x \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (z / x)) = u
    ]]></literal>
    <justification jstring="[para(5520(a,1),7456(a,1,2))].">
      <j1 rule="para" parents="5520 7456"/>
    </justification>
  </clause>

  <clause id="7466">
    <literal><![CDATA[
      K(x,y * (x * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z * x)) = u
    ]]></literal>
    <justification jstring="[para(7301(a,1),7456(a,1,2))].">
      <j1 rule="para" parents="7301 7456"/>
    </justification>
  </clause>

  <clause id="7467">
    <literal><![CDATA[
      K(x,R(x,y,z) * u) = K(x,u * R(x,y,z))
    ]]></literal>
    <justification jstring="[para(4201(a,1),7458(a,1,2))].">
      <j1 rule="para" parents="4201 7458"/>
    </justification>
  </clause>

  <clause id="7469">
    <literal><![CDATA[
      K(x,T(R(x,y,z),u) \ w) = K(x,R(x,y,z) \ w)
    ]]></literal>
    <justification jstring="[para(4518(a,1),7458(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4518 7458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7470">
    <literal><![CDATA[
      K(x,(y / R(x,z,u)) \ w) = K(x,(R(x,z,u) \ y) \ w)
    ]]></literal>
    <justification jstring="[para(4981(a,1),7458(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4981 7458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7471">
    <literal><![CDATA[
      K(x,y * K(z,R(x,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(6943(a,1),7458(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6943 7458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7472">
    <literal><![CDATA[
      K(x,T(y,T(z,R(x,u,w)))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(6772(a,1),7458(a,1,2))].">
      <j1 rule="para" parents="6772 7458"/>
    </justification>
  </clause>

  <clause id="7473">
    <literal><![CDATA[
      K(x,y / (z / R(x,u,w))) = K(x,y / (R(x,u,w) \ z))
    ]]></literal>
    <justification jstring="[para(6012(a,1),7471(a,1,2))].">
      <j1 rule="para" parents="6012 7471"/>
    </justification>
  </clause>

  <clause id="7474">
    <literal><![CDATA[
      T(T(x,x * y) * ((x \ y) * x),x) = x * ((x \ y) * x)
    ]]></literal>
    <justification jstring="[para(7357(a,1),3810(a,1,1,1))].">
      <j1 rule="para" parents="7357 3810"/>
    </justification>
  </clause>

  <clause id="7475">
    <literal><![CDATA[
      K(x,T(y,K(x,z) * u)) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(333,a,6370,a(flip),b,7366,a),flip(a)].">
      <j1 rule="hyper" parents="333 6370 7366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7476">
    <literal><![CDATA[
      T(T(x / y,z),u * K(w,y \ x)) = T(T(x / y,u),z)
    ]]></literal>
    <justification jstring="[para(6353(a,1),7369(a,1,2,2))].">
      <j1 rule="para" parents="6353 7369"/>
    </justification>
  </clause>

  <clause id="7477">
    <literal><![CDATA[
      T(x * K(y,T(x,z * (u * x))),y) = T(x,K(y,z * (x * u)))
    ]]></literal>
    <justification jstring="[para(7373(a,2),7126(a,1,1,2,2))].">
      <j1 rule="para" parents="7373 7126"/>
    </justification>
  </clause>

  <clause id="7478">
    <literal><![CDATA[
      (K(x,y) * z) * K(z,T(y,u)) = T(K(x,y) * z,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(126,a,7390,a(flip),b,4215,a(flip))].">
      <j1 rule="hyper" parents="126 7390 4215"/>
    </justification>
  </clause>

  <clause id="7479">
    <literal><![CDATA[
      K(T(x,y) * z,T(x,u)) = K(x * z,T(x,u))
    ]]></literal>
    <justification jstring="[para(4557(a,1),7390(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4557 7390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7480">
    <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(7398(a,1),5582(a,1,1,2))].">
      <j1 rule="para" parents="7398 5582"/>
    </justification>
  </clause>

  <clause id="7481">
    <literal><![CDATA[
      T(x * y,x) / T(x,y) = x \ T(x * y,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),7404(a,1,2,2))].">
      <j1 rule="para" parents="9 7404"/>
    </justification>
  </clause>

  <clause id="7482">
    <literal><![CDATA[
      K(x,(y * x) / z) = K(x,y / (x \ z))
    ]]></literal>
    <justification jstring="[hyper(63,a,6327,a,b,7420,a)].">
      <j1 rule="hyper" parents="63 6327 7420"/>
    </justification>
  </clause>

  <clause id="7483">
    <literal><![CDATA[
      T(K(x,y),z * T(y,u)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(11(a,1),7428(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11 7428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7484">
    <literal><![CDATA[
      K((x * y) \ (z * y),y) = K(x \ z,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,6555,a,b,7432,a)].">
      <j1 rule="hyper" parents="63 6555 7432"/>
    </justification>
  </clause>

  <clause id="7485">
    <literal><![CDATA[
      K((x \ y) \ (z * y),y) = K((x \ 1) \ z,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,7218,a(flip),b,7432,a)].">
      <j1 rule="hyper" parents="63 7218 7432"/>
    </justification>
  </clause>

  <clause id="7486">
    <literal><![CDATA[
      K(x,(y * x) * z) = K(x,(x * y) * z)
    ]]></literal>
    <justification jstring="[para(4201(a,1),7457(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4201 7457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7487">
    <literal><![CDATA[
      K(x,(K(y,x) * z) * u) = K(x,z * u)
    ]]></literal>
    <justification jstring="[para(4558(a,1),7457(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4558 7457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7488">
    <literal><![CDATA[
      K(x,(T(y,x) * z) * u) = K(x,(y * z) * u)
    ]]></literal>
    <justification jstring="[para(4557(a,1),7457(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4557 7457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7489">
    <literal><![CDATA[
      K(x,(y \ T(z,x)) * u) = K(x,(y \ z) * u)
    ]]></literal>
    <justification jstring="[para(4840(a,1),7457(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4840 7457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7490">
    <literal><![CDATA[
      K(x,T(y,K(z,x) * u)) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[para(4558(a,1),7475(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4558 7475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7492">
    <literal><![CDATA[
      K(x,T(y,T(z,K(u,x)))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(6767(a,1),7475(a,1,2,2))].">
      <j1 rule="para" parents="6767 7475"/>
    </justification>
  </clause>

  <clause id="7493">
    <literal><![CDATA[
      K(x,T(y,z * K(x,u))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(6887(a,1),7475(a,1,2,2))].">
      <j1 rule="para" parents="6887 7475"/>
    </justification>
  </clause>

  <clause id="7494">
    <literal><![CDATA[
      K(x \ (y * T(z,u)),T(z,y)) = K((y * T(z,u)) / x,z)
    ]]></literal>
    <justification jstring="[hyper(7065,a,7483,a),flip(a)].">
      <j1 rule="hyper" parents="7065 7483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7495">
    <literal><![CDATA[
      K(x,(T(y,x) / z) * u) = K(x,(y / z) * u)
    ]]></literal>
    <justification jstring="[para(5220(a,1),7487(a,1,2,1))].">
      <j1 rule="para" parents="5220 7487"/>
    </justification>
  </clause>

  <clause id="7496">
    <literal><![CDATA[
      K(x,T(y,K(z,x) * u)) = T(K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(333,a,6365,a(flip),b,7490,a),flip(a)].">
      <j1 rule="hyper" parents="333 6365 7490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7497">
    <literal><![CDATA[
      T(K(x,y),T(z,K(u,x))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(6552,a,7492,a)].">
      <j1 rule="hyper" parents="6552 7492"/>
    </justification>
  </clause>

  <clause id="7498">
    <literal><![CDATA[
      K(x,T(y,z * (u * x))) = K(x,T(y,z * (x * u)))
    ]]></literal>
    <justification jstring="[para(7301(a,1),7493(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7301 7493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7499">
    <literal><![CDATA[
      T(K(x,y),K(z,x) * u) = T(K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(6552,a,7496,a)].">
      <j1 rule="hyper" parents="6552 7496"/>
    </justification>
  </clause>

  <clause id="7500">
    <literal><![CDATA[
      T(K(x,y),R(K(z,x),u,w) * v5) = T(K(x,y),v5)
    ]]></literal>
    <justification jstring="[para(5113(a,1),7499(a,1,2,1))].">
      <j1 rule="para" parents="5113 7499"/>
    </justification>
  </clause>

  <clause id="7501">
    <literal><![CDATA[
      T(K(x,y),z * K(u,x)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(6888(a,1),7499(a,1,2))].">
      <j1 rule="para" parents="6888 7499"/>
    </justification>
  </clause>

  <clause id="7502">
    <literal><![CDATA[
      T(K(x,y),z * L(K(u,x),w,v5)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(5372(a,1),7501(a,1,2,2))].">
      <j1 rule="para" parents="5372 7501"/>
    </justification>
  </clause>

  <clause id="7503">
    <literal><![CDATA[
      K(x,T(y,z / R(x,u,w))) = K(x,T(y,R(x,u,w) \ z))
    ]]></literal>
    <justification jstring="[para(113(a,1),7472(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="113 7472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7504">
    <literal><![CDATA[
      T(x,K(y,z / T(y,u))) != w * v5
    ]]></literal>
    <literal><![CDATA[
      w \ T(x,K(y,y * z)) = v5
    ]]></literal>
    <justification jstring="[para(7440(a,2),827(a,1))].">
      <j1 rule="para" parents="7440 827"/>
    </justification>
  </clause>

  <clause id="7505">
    <literal><![CDATA[
      K(T(x,y) * z,T(T(x,u),w)) = T(T(x,u),w) \ T(T(x,u) * K(x * z,T(x,u)),w)
    ]]></literal>
    <justification jstring="[para(7479(a,1),4812(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="7479 4812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7506">
    <literal><![CDATA[
      T(x * y,x) / T(x,y) = y * K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,5479,a(flip),b,7481,a),flip(a)].">
      <j1 rule="hyper" parents="333 5479 7481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7507">
    <literal><![CDATA[
      T(x,(y \ x) \ (z * x)) = 1 / (x \ K((y \ 1) \ z,x))
    ]]></literal>
    <justification jstring="[para(7485(a,1),4403(a,2,2,2))].">
      <j1 rule="para" parents="7485 4403"/>
    </justification>
  </clause>

  <clause id="7508">
    <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(3095(a,2),7488(a,1,2,1))].">
      <j1 rule="para" parents="3095 7488"/>
    </justification>
  </clause>

  <clause id="7509">
    <literal><![CDATA[
      K(x,(y \ (z / x)) * u) = K(x,(y \ (x \ z)) * u)
    ]]></literal>
    <justification jstring="[para(113(a,1),7489(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="113 7489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7510">
    <literal><![CDATA[
      K(x,(T(T(y,x),z) / u) * w) = K(x,(T(y,z) / u) * w)
    ]]></literal>
    <justification jstring="[para(23(a,1),7495(a,1,2,1,1))].">
      <j1 rule="para" parents="23 7495"/>
    </justification>
  </clause>

  <clause id="7511">
    <literal><![CDATA[
      K(x / y,((x / (x / y)) / z) * u) = K(x / y,(y / z) * u)
    ]]></literal>
    <justification jstring="[para(258(a,1),7495(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="258 7495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7512">
    <literal><![CDATA[
      L(K(x * y,x) * K(z * y,K(x * y,x)),y,z) = (z * (T(x * y,x) / T(x,y))) / (z * y)
    ]]></literal>
    <justification jstring="[para(7506(a,2),4429(a,2,1,2))].">
      <j1 rule="para" parents="7506 4429"/>
    </justification>
  </clause>

  <clause id="7513">
    <literal><![CDATA[
      K(L(x,K(y,z),u),y) = K(K(y,z) * x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,6298,a(flip),b,7394,a)].">
      <j1 rule="hyper" parents="63 6298 7394"/>
    </justification>
  </clause>

  <clause id="7514">
    <literal><![CDATA[
      K(L(x,K(y,z),u),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,7384,a(flip),b,7513,a),flip(a)].">
      <j1 rule="hyper" parents="333 7384 7513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7516">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,y) = K(K(y,z) \ (x \ u),y)
    ]]></literal>
    <justification jstring="[para(311(a,1),7514(a,1,1))].">
      <j1 rule="para" parents="311 7514"/>
    </justification>
  </clause>

  <clause id="7517">
    <literal><![CDATA[
      K(K(x,y) * z,K(x,u)) = K(x,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(7396,a,6786,a)].">
      <j1 rule="hyper" parents="7396 6786"/>
    </justification>
  </clause>

  <clause id="7518">
    <literal><![CDATA[
      K(K(x,y) * z,K(x,u)) = K(z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(7396,a,6763,a)].">
      <j1 rule="hyper" parents="7396 6763"/>
    </justification>
  </clause>

  <clause id="7519">
    <literal><![CDATA[
      K(x,K(y,K(x,z) * u)) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(6825,a,7517,a)].">
      <j1 rule="hyper" parents="6825 7517"/>
    </justification>
  </clause>

  <clause id="7520">
    <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(7517(a,1),6830(a,1,1))].">
      <j1 rule="para" parents="7517 6830"/>
    </justification>
  </clause>

  <clause id="7521">
    <literal><![CDATA[
      R(x,K(y,z) * u,K(u,K(y,w))) = x
    ]]></literal>
    <justification jstring="[para(7518(a,1),6122(a,1,3))].">
      <j1 rule="para" parents="7518 6122"/>
    </justification>
  </clause>

  <clause id="7522">
    <literal><![CDATA[
      K(x,K(y,T(x,z) * u)) = K(x,K(y,x * u))
    ]]></literal>
    <justification jstring="[para(4273(a,1),7519(a,1,2,2))].">
      <j1 rule="para" parents="4273 7519"/>
    </justification>
  </clause>

  <clause id="7523">
    <literal><![CDATA[
      K(x,K(y,(z / x) \ u)) = K(x,K(y,(x \ z) \ u))
    ]]></literal>
    <justification jstring="[para(4981(a,1),7519(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4981 7519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7524">
    <literal><![CDATA[
      K(x,K(y,T(x,z) * u)) = K(y,K(x,1 / u))
    ]]></literal>
    <justification jstring="[hyper(333,a,7312,a,b,7522,a),flip(a)].">
      <j1 rule="hyper" parents="333 7312 7522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7525">
    <literal><![CDATA[
      K(x,K(y,T(x,z) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,1 / u)) = w
    ]]></literal>
    <justification jstring="[para(7524(a,2),6798(a,1))].">
      <j1 rule="para" parents="7524 6798"/>
    </justification>
  </clause>

  <clause id="7526">
    <literal><![CDATA[
      K(x,R(y,K(z,x),u)) = K(x,y * K(z,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,5654,a(flip),b,7424,a)].">
      <j1 rule="hyper" parents="63 5654 7424"/>
    </justification>
  </clause>

  <clause id="7527">
    <literal><![CDATA[
      K(x,y * K(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(7424(a,1),547(a,1))].">
      <j1 rule="para" parents="7424 547"/>
    </justification>
  </clause>

  <clause id="7528">
    <literal><![CDATA[
      K(x,y \ T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(2086(a,1),7527(a,1,2))].">
      <j1 rule="para" parents="2086 7527"/>
    </justification>
  </clause>

  <clause id="7529">
    <literal><![CDATA[
      K(x,T(y,x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(4959(a,1),7527(a,1,2))].">
      <j1 rule="para" parents="4959 7527"/>
    </justification>
  </clause>

  <clause id="7530">
    <literal><![CDATA[
      K(x,y / (z / x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (x \ z)) = u
    ]]></literal>
    <justification jstring="[para(6012(a,1),7527(a,1,2))].">
      <j1 rule="para" parents="6012 7527"/>
    </justification>
  </clause>

  <clause id="7531">
    <literal><![CDATA[
      K(x,K(x,y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(6356(a,1),7527(a,1,2))].">
      <j1 rule="para" parents="6356 7527"/>
    </justification>
  </clause>

  <clause id="7533">
    <literal><![CDATA[
      K(x,R(y,K(z,x),u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,7415,a(flip),b,7526,a),flip(a)].">
      <j1 rule="hyper" parents="333 7415 7526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7535">
    <literal><![CDATA[
      K(x,R(R(y,K(z,x),u),w,v5)) = K(x,R(y,w,v5))
    ]]></literal>
    <justification jstring="[para(31(a,1),7533(a,1,2))].">
      <j1 rule="para" parents="31 7533"/>
    </justification>
  </clause>

  <clause id="7536">
    <literal><![CDATA[
      T(K(x,y),z * (u * K(w,x))) = T(K(x,y),z * u)
    ]]></literal>
    <justification jstring="[para(97(a,1),7502(a,1,2))].">
      <j1 rule="para" parents="97 7502"/>
    </justification>
  </clause>

  <clause id="7537">
    <literal><![CDATA[
      K(x,(y * x) / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (x \ z)) = u
    ]]></literal>
    <justification jstring="[para(6327(a,2),7530(a,1))].">
      <j1 rule="para" parents="6327 7530"/>
    </justification>
  </clause>

  <clause id="7538">
    <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(6606(a,1),1044(a,1,1,2))].">
      <j1 rule="para" parents="6606 1044"/>
    </justification>
  </clause>

  <clause id="7539">
    <literal><![CDATA[
      T(K(x,y) * (z * K(y,u)),K(y,u)) = K(y,u) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(6606(a,1),6845(a,1,1))].">
      <j1 rule="para" parents="6606 6845"/>
    </justification>
  </clause>

  <clause id="7540">
    <literal><![CDATA[
      x / (x * (y * K(z,y \ 1))) = T(x / (x * y),z)
    ]]></literal>
    <justification jstring="[para(5751(a,1),6656(a,1,2))].">
      <j1 rule="para" parents="5751 6656"/>
    </justification>
  </clause>

  <clause id="7541">
    <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(6683(a,1),639(a,1,2))].">
      <j1 rule="para" parents="6683 639"/>
    </justification>
  </clause>

  <clause id="7542">
    <literal><![CDATA[
      T(x,y) * K(y * L(x,z,u),x) = R(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(6729(a,1),5587(a,1,2))].">
      <j1 rule="para" parents="6729 5587"/>
    </justification>
  </clause>

  <clause id="7543">
    <literal><![CDATA[
      K(T(L(x,y,z) * u,u),x) = K(L(x,y,z) * u,x)
    ]]></literal>
    <justification jstring="[hyper(6610,a,6730,a)].">
      <j1 rule="hyper" parents="6610 6730"/>
    </justification>
  </clause>

  <clause id="7544">
    <literal><![CDATA[
      T((x \ y) * T(x,z),x) = (x \ T(y,x)) * T(x,z)
    ]]></literal>
    <justification jstring="[para(1398(a,1),6747(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1398 6747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7545">
    <literal><![CDATA[
      (x * K(y,z)) * T(K(z,y),u) = x * K(z,K(y,u))
    ]]></literal>
    <justification jstring="[para(5995(a,1),6775(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5995 6775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7546">
    <literal><![CDATA[
      T(x,K(y,z \ x)) / z = T(x / z,K(x,y))
    ]]></literal>
    <justification jstring="[para(4222(a,2),6816(a,1,1))].">
      <j1 rule="para" parents="4222 6816"/>
    </justification>
  </clause>

  <clause id="7547">
    <literal><![CDATA[
      ((1 / x) * (K(y,z) * x)) * x = x * L(K(y,z),x,x \ 1)
    ]]></literal>
    <justification jstring="[para(2654(a,1),6892(a,1,1))].">
      <j1 rule="para" parents="2654 6892"/>
    </justification>
  </clause>

  <clause id="7548">
    <literal><![CDATA[
      T(R(K(x,y),z,u),w) * w = w * R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(27(a,1),6898(a,1,1))].">
      <j1 rule="para" parents="27 6898"/>
    </justification>
  </clause>

  <clause id="7549">
    <literal><![CDATA[
      T(T(x,L(K(y,z),u,w)),L(K(y,z),u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(3890,a,6899,a)].">
      <j1 rule="hyper" parents="3890 6899"/>
    </justification>
  </clause>

  <clause id="7551">
    <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(740,a,7549,a)].">
      <j1 rule="hyper" parents="740 7549"/>
    </justification>
  </clause>

  <clause id="7552">
    <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(7367(a,1),6907(a,1,1,1,2))].">
      <j1 rule="para" parents="7367 6907"/>
    </justification>
  </clause>

  <clause id="7553">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) * K(x * T(y,u),x) = K(x * T(y,u),T(x,z))
    ]]></literal>
    <justification jstring="[para(6817(a,2),6957(a,1,1))].">
      <j1 rule="para" parents="6817 6957"/>
    </justification>
  </clause>

  <clause id="7554">
    <literal><![CDATA[
      K(x * K(y,z),(x / u) \ 1) = K(K(y,z) * x,x \ u)
    ]]></literal>
    <justification jstring="[hyper(35,a,6618,a,b,6974,a)].">
      <j1 rule="hyper" parents="35 6618 6974"/>
    </justification>
  </clause>

  <clause id="7555">
    <literal><![CDATA[
      K((x / y) \ 1,x * K(z,u)) = K(x \ y,K(z,u) * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,4965,a,b,6997,a)].">
      <j1 rule="hyper" parents="63 4965 6997"/>
    </justification>
  </clause>

  <clause id="7556">
    <literal><![CDATA[
      K(x / ((y \ 1) * z),L(z,y \ 1,y) / (L(z,y \ 1,y) / y)) = K((y \ L(z,y \ 1,y)) \ x,y)
    ]]></literal>
    <justification jstring="[para(439(a,1),7000(a,1,1,2))].">
      <j1 rule="para" parents="439 7000"/>
    </justification>
  </clause>

  <clause id="7557">
    <literal><![CDATA[
      K(x,T(y / (y / z),u)) = K(x,T((z \ y) \ y,u))
    ]]></literal>
    <justification jstring="[para(3673(a,1),7007(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3673 7007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7558">
    <literal><![CDATA[
      T(x,L(y * K(z,y),u,w)) = T(x,L(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(25(a,2),7017(a,2,2))].">
      <j1 rule="para" parents="25 7017"/>
    </justification>
  </clause>

  <clause id="7559">
    <literal><![CDATA[
      ((x \ 1) \ K(y,x)) \ K(y,x) = T(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,3374,a(flip),b,7020,a),flip(a)].">
      <j1 rule="hyper" parents="333 3374 7020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7561">
    <literal><![CDATA[
      T(K(x,y),T(z,K(y,u))) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(333,a,6760,a(flip),b,7077,a),flip(a)].">
      <j1 rule="hyper" parents="333 6760 7077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7562">
    <literal><![CDATA[
      T(K(x,y),z / K(u,y)) = T(K(x,y),K(u,y) \ z)
    ]]></literal>
    <justification jstring="[para(5302(a,1),7561(a,1,2))].">
      <j1 rule="para" parents="5302 7561"/>
    </justification>
  </clause>

  <clause id="7563">
    <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(3678(a,1),7085(a,1,2,2,2))].">
      <j1 rule="para" parents="3678 7085"/>
    </justification>
  </clause>

  <clause id="7564">
    <literal><![CDATA[
      K(x,y / z) * K(x,K(y,z)) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[para(7149(a,1),7088(a,1,2))].">
      <j1 rule="para" parents="7149 7088"/>
    </justification>
  </clause>

  <clause id="7565">
    <literal><![CDATA[
      K(x,y \ z) * K(x,K(z,y)) = K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(125,a,7564,a(flip),b,6827,a)].">
      <j1 rule="hyper" parents="125 7564 6827"/>
    </justification>
  </clause>

  <clause id="7567">
    <literal><![CDATA[
      (x \ y) * K(x / y,y) = (y * (x / y)) \ y
    ]]></literal>
    <justification jstring="[hyper(63,a,1309,a(flip),b,7120,a),flip(a)].">
      <j1 rule="hyper" parents="63 1309 7120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7568">
    <literal><![CDATA[
      T(x * K(y / z,x),z \ y) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(333,a,7161,a(flip),b,7135,a),flip(a)].">
      <j1 rule="hyper" parents="333 7161 7135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7569">
    <literal><![CDATA[
      T(x / (y / z),z \ y) = T((y / z) \ x,K(y,z))
    ]]></literal>
    <justification jstring="[para(4292(a,1),7568(a,1,1))].">
      <j1 rule="para" parents="4292 7568"/>
    </justification>
  </clause>

  <clause id="7570">
    <literal><![CDATA[
      T(T(x,K(y,z)),y / z) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[para(7568(a,1),4320(a,1,1))].">
      <j1 rule="para" parents="7568 4320"/>
    </justification>
  </clause>

  <clause id="7571">
    <literal><![CDATA[
      T(x * (y / x),z / y) = T(x * (y / x),y \ z)
    ]]></literal>
    <justification jstring="[para(4098(a,1),7570(a,1,1))].">
      <j1 rule="para" parents="4098 7570"/>
    </justification>
  </clause>

  <clause id="7572">
    <literal><![CDATA[
      T(T(x,K(y,z)),z / y) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(6840(a,1),7570(a,1,1))].">
      <j1 rule="para" parents="6840 7570"/>
    </justification>
  </clause>

  <clause id="7573">
    <literal><![CDATA[
      T(T(x,K(y,z)),z \ y) = T(x,y / z)
    ]]></literal>
    <justification jstring="[para(6848(a,1),7570(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6848 7570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7574">
    <literal><![CDATA[
      T(T(x,y \ z),K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(7572(a,1),6876(a,1,1))].">
      <j1 rule="para" parents="7572 6876"/>
    </justification>
  </clause>

  <clause id="7575">
    <literal><![CDATA[
      T(T(x,y \ z),K(y,z)) = T(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(63,a,6850,a(flip),b,7573,a)].">
      <j1 rule="hyper" parents="63 6850 7573"/>
    </justification>
  </clause>

  <clause id="7576">
    <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(4795(a,1),7573(a,1,1,2))].">
      <j1 rule="para" parents="4795 7573"/>
    </justification>
  </clause>

  <clause id="7577">
    <literal><![CDATA[
      T(T(x,K(y,z)),y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(23(a,1),7574(a,1))].">
      <j1 rule="para" parents="23 7574"/>
    </justification>
  </clause>

  <clause id="7578">
    <literal><![CDATA[
      T(T(x,K(y,z)),z \ y) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y / z) = u
    ]]></literal>
    <justification jstring="[para(6850(a,2),7574(a,1))].">
      <j1 rule="para" parents="6850 7574"/>
    </justification>
  </clause>

  <clause id="7579">
    <literal><![CDATA[
      K(x,(1 / y) * ((z \ ((1 / y) \ 1)) * z)) = K(x,K(y \ z,z))
    ]]></literal>
    <justification jstring="[para(5944(a,1),7172(a,2,2))].">
      <j1 rule="para" parents="5944 7172"/>
    </justification>
  </clause>

  <clause id="7580">
    <literal><![CDATA[
      T(x,K(y,z)) * K(y,z \ x) = x * K(y,x / z)
    ]]></literal>
    <justification jstring="[hyper(333,a,6890,a(flip),b,7185,a),flip(a)].">
      <j1 rule="hyper" parents="333 6890 7185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7581">
    <literal><![CDATA[
      K(L(x,y,x),z) = K(T(u * x,x) / u,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,6920,a,b,7240,a)].">
      <j1 rule="hyper" parents="333 6920 7240"/>
    </justification>
  </clause>

  <clause id="7582">
    <literal><![CDATA[
      K(T(x * y,y) / x,z) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(6478,a,7581,a),flip(a)].">
      <j1 rule="hyper" parents="6478 7581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7584">
    <literal><![CDATA[
      K(T(x,y \ x) / y,z) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),7582(a,1,1,1,1))].">
      <j1 rule="para" parents="10 7582"/>
    </justification>
  </clause>

  <clause id="7585">
    <literal><![CDATA[
      K(T(x,y) / (x / y),z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(12(a,1),7582(a,1,1,1,1))].">
      <j1 rule="para" parents="12 7582"/>
    </justification>
  </clause>

  <clause id="7586">
    <literal><![CDATA[
      T(x,y) * K(y * R(x,z,u),x) = R(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[para(7275(a,1),5584(a,1,2))].">
      <j1 rule="para" parents="7275 5584"/>
    </justification>
  </clause>

  <clause id="7587">
    <literal><![CDATA[
      K(x,T(T(y,z),u \ y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(T(y,z),u)) = w
    ]]></literal>
    <justification jstring="[para(7291(a,1),7282(a,1))].">
      <j1 rule="para" parents="7291 7282"/>
    </justification>
  </clause>

  <clause id="7588">
    <literal><![CDATA[
      T(T(x,y) * T((x \ z) / x,x),T(x,y)) = T(x \ ((z / x) * T(x,y)),x)
    ]]></literal>
    <justification jstring="[para(6749(a,2),7295(a,2,1))].">
      <j1 rule="para" parents="6749 7295"/>
    </justification>
  </clause>

  <clause id="7589">
    <literal><![CDATA[
      R(K(x,T(y,z)),y * u,w) = K(x,R(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(6365(a,2),7335(a,1,1))].">
      <j1 rule="para" parents="6365 7335"/>
    </justification>
  </clause>

  <clause id="7590">
    <literal><![CDATA[
      K(x,y) \ (K(x,K(y,z)) \ u) = K(x,T(y,z)) \ u
    ]]></literal>
    <justification jstring="[hyper(629,a,7337,a),flip(a)].">
      <j1 rule="hyper" parents="629 7337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7591">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(x,x \ y) * u) = K(x,T(x \ y,z)) * u
    ]]></literal>
    <justification jstring="[para(7037(a,1),7337(a,1,1))].">
      <j1 rule="para" parents="7037 7337"/>
    </justification>
  </clause>

  <clause id="7592">
    <literal><![CDATA[
      K(x,(y * (z * x)) \ u) = K(x,(y * z) \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,5612,a(flip),b,7346,a)].">
      <j1 rule="hyper" parents="63 5612 7346"/>
    </justification>
  </clause>

  <clause id="7593">
    <literal><![CDATA[
      T((x \ y) * x,z * K(u,y)) = T((x \ y) * x,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,4105,a,b,7370,a),flip(a)].">
      <j1 rule="hyper" parents="333 4105 7370"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7594">
    <literal><![CDATA[
      T(K(x,y),K(z,y) \ u) = T(K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(333,a,6759,a(flip),b,7417,a),flip(a)].">
      <j1 rule="hyper" parents="333 6759 7417"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7595">
    <literal><![CDATA[
      x * K(y \ z,x / (z / y)) = (y \ z) * (x / (y \ z))
    ]]></literal>
    <justification jstring="[hyper(126,a,7422,a,b,91,a)].">
      <j1 rule="hyper" parents="126 7422 91"/>
    </justification>
  </clause>

  <clause id="7596">
    <literal><![CDATA[
      T((x \ R(T(y,z),u,w)) * K(z,x \ R(y,u,w)),z) = x \ R(T(y,z),u,w)
    ]]></literal>
    <justification jstring="[para(7425(a,1),4239(a,1,1,2))].">
      <j1 rule="para" parents="7425 4239"/>
    </justification>
  </clause>

  <clause id="7597">
    <literal><![CDATA[
      T(x,y) * (z * K(x * z,x)) = T(T(x,y) * z,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,6221,a(flip),b,7430,a)].">
      <j1 rule="hyper" parents="63 6221 7430"/>
    </justification>
  </clause>

  <clause id="7598">
    <literal><![CDATA[
      x * K(y / z,(z \ y) \ x) = (y / z) * (x / (y / z))
    ]]></literal>
    <justification jstring="[hyper(126,a,7438,a(flip),b,4460,a)].">
      <j1 rule="hyper" parents="126 7438 4460"/>
    </justification>
  </clause>

  <clause id="7599">
    <literal><![CDATA[
      K(x,R(T(x,y),z,u) \ w) = K(x,R(x,z,u) \ w)
    ]]></literal>
    <justification jstring="[para(27(a,2),7469(a,1,2,1))].">
      <j1 rule="para" parents="27 7469"/>
    </justification>
  </clause>

  <clause id="7600">
    <literal><![CDATA[
      K(x,R(x,y,z) \ (R(x,y,z) * (T(R(x,y,z),u) * w))) = K(x,R(x,y,z) * w)
    ]]></literal>
    <justification jstring="[para(1060(a,1),7469(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1060 7469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7601">
    <literal><![CDATA[
      T(x * K(y,T(x,z * (u * y))),y) = T(x,K(y,z * (y * u)))
    ]]></literal>
    <justification jstring="[para(7498(a,2),7126(a,1,1,2))].">
      <j1 rule="para" parents="7498 7126"/>
    </justification>
  </clause>

  <clause id="7602">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,y) = K(x \ u,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,7385,a(flip),b,7516,a),flip(a)].">
      <j1 rule="hyper" parents="333 7385 7516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7604">
    <literal><![CDATA[
      K((x * T(y,z)) \ u,z) = K((x * y) \ u,z)
    ]]></literal>
    <justification jstring="[para(5455(a,1),7602(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5455 7602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7605">
    <literal><![CDATA[
      K((x * (y / z)) \ u,z) = K((x * (z \ y)) \ u,z)
    ]]></literal>
    <justification jstring="[para(5523(a,1),7602(a,1,1,1))].">
      <j1 rule="para" parents="5523 7602"/>
    </justification>
  </clause>

  <clause id="7606">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,z) = K(x \ u,z)
    ]]></literal>
    <justification jstring="[para(5995(a,1),7602(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5995 7602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7607">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,T(y,w)) = K(x \ u,T(y,w))
    ]]></literal>
    <justification jstring="[para(6901(a,1),7602(a,1,1,1,2))].">
      <j1 rule="para" parents="6901 7602"/>
    </justification>
  </clause>

  <clause id="7608">
    <literal><![CDATA[
      K((x * (y * z)) \ u,z) = K((x * (z * y)) \ u,z)
    ]]></literal>
    <justification jstring="[para(7301(a,1),7602(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7301 7602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7609">
    <literal><![CDATA[
      K(x,(y * K(z,x)) \ u) = (w * K(y \ u,x)) \ w
    ]]></literal>
    <justification jstring="[para(7606(a,1),5990(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7606 5990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7610">
    <literal><![CDATA[
      K((K(x,y) * z) \ u,y) = K(z \ u,y)
    ]]></literal>
    <justification jstring="[para(6357(a,1),7606(a,1,1,1))].">
      <j1 rule="para" parents="6357 7606"/>
    </justification>
  </clause>

  <clause id="7611">
    <literal><![CDATA[
      K(x \ K(y,z),y) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,5867,a(flip),b,7610,a)].">
      <j1 rule="hyper" parents="63 5867 7610"/>
    </justification>
  </clause>

  <clause id="7613">
    <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(4928(a,1),7545(a,1,1))].">
      <j1 rule="para" parents="4928 7545"/>
    </justification>
  </clause>

  <clause id="7614">
    <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(253,a,7548,a(flip),b,3355,a(flip))].">
      <j1 rule="hyper" parents="253 7548 3355"/>
    </justification>
  </clause>

  <clause id="7615">
    <literal><![CDATA[
      K(x,T(((y \ z) \ z) \ z,u)) = K(x,T(z / y,u))
    ]]></literal>
    <justification jstring="[para(76(a,1),7557(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="76 7557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7616">
    <literal><![CDATA[
      T(K(x,y),z / K(u,y)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(333,a,7594,a(flip),b,7562,a),flip(a)].">
      <j1 rule="hyper" parents="333 7594 7562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7618">
    <literal><![CDATA[
      T(K(x,y),z * K(y,u)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(5994(a,1),7616(a,1,2))].">
      <j1 rule="para" parents="5994 7616"/>
    </justification>
  </clause>

  <clause id="7619">
    <literal><![CDATA[
      T(x * (y / x),(y / z) \ 1) = T(x * (y / x),y \ z)
    ]]></literal>
    <justification jstring="[hyper(3795,a,7571,a)].">
      <j1 rule="hyper" parents="3795 7571"/>
    </justification>
  </clause>

  <clause id="7620">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,z \ x) = K(y,x / z)
    ]]></literal>
    <justification jstring="[hyper(4525,a,7580,a)].">
      <j1 rule="hyper" parents="4525 7580"/>
    </justification>
  </clause>

  <clause id="7621">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,y \ z) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(6788(a,2),7620(a,1,1))].">
      <j1 rule="para" parents="6788 7620"/>
    </justification>
  </clause>

  <clause id="7622">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,z / y) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(6832,a,7621,a)].">
      <j1 rule="hyper" parents="6832 7621"/>
    </justification>
  </clause>

  <clause id="7623">
    <literal><![CDATA[
      K(x,y / z) * K(z \ y,x) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(5997,a,7621,a)].">
      <j1 rule="hyper" parents="5997 7621"/>
    </justification>
  </clause>

  <clause id="7624">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,y \ (z \ y)) = K(x,(z \ y) / y)
    ]]></literal>
    <justification jstring="[para(7143(a,1),7621(a,1,1))].">
      <j1 rule="para" parents="7143 7621"/>
    </justification>
  </clause>

  <clause id="7625">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z,y / x) = K(z,x \ y)
    ]]></literal>
    <justification jstring="[para(6788(a,2),7622(a,1,1))].">
      <j1 rule="para" parents="6788 7622"/>
    </justification>
  </clause>

  <clause id="7626">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,(y / z) / y) = K(x,y \ (y / z))
    ]]></literal>
    <justification jstring="[para(7149(a,1),7622(a,1,1))].">
      <j1 rule="para" parents="7149 7622"/>
    </justification>
  </clause>

  <clause id="7627">
    <literal><![CDATA[
      K(x / y,z) * K(z,K(y,x)) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(4577,a,7623,a)].">
      <j1 rule="hyper" parents="4577 7623"/>
    </justification>
  </clause>

  <clause id="7628">
    <literal><![CDATA[
      K(x,y \ z) * K(z / y,x) = K(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(5997,a,7625,a)].">
      <j1 rule="hyper" parents="5997 7625"/>
    </justification>
  </clause>

  <clause id="7629">
    <literal><![CDATA[
      K(x / y,z) * K(x,K(y,z)) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[para(6762(a,1),7627(a,1,2))].">
      <j1 rule="para" parents="6762 7627"/>
    </justification>
  </clause>

  <clause id="7630">
    <literal><![CDATA[
      K(x \ y,z) * K(x,K(y,z)) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(4577,a,7628,a)].">
      <j1 rule="hyper" parents="4577 7628"/>
    </justification>
  </clause>

  <clause id="7631">
    <literal><![CDATA[
      K(x,R(T(y,z),y \ u,w)) = R(K(x,T(y,z)),u,w)
    ]]></literal>
    <justification jstring="[para(10(a,1),7589(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 7589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7632">
    <literal><![CDATA[
      T(x,(y * (z * x)) \ u) = T(x,(y * z) \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(124,a,7592,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 7592 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7633">
    <literal><![CDATA[
      K(x,(y * (z / x)) \ (x \ u)) = K(x,(y * z) \ u)
    ]]></literal>
    <justification jstring="[para(12(a,1),7592(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="12 7592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7634">
    <literal><![CDATA[
      K(x,((1 / y) * y) \ (x \ z)) = K(x,L(x,y,y \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(2652(a,1),7592(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2652 7592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7635">
    <literal><![CDATA[
      (x * K(y,(z * u) \ (y \ w))) \ x = K((z * (u * y)) \ w,y)
    ]]></literal>
    <justification jstring="[para(7592(a,1),5990(a,1,1,2))].">
      <j1 rule="para" parents="7592 5990"/>
    </justification>
  </clause>

  <clause id="7636">
    <literal><![CDATA[
      T((x \ y) * x,z \ T(u,y)) = T((x \ y) * x,z \ u)
    ]]></literal>
    <justification jstring="[para(2086(a,1),7593(a,1,2))].">
      <j1 rule="para" parents="2086 7593"/>
    </justification>
  </clause>

  <clause id="7637">
    <literal><![CDATA[
      T(x,y) * (x \ T(x * z,x)) = T(T(x,y) * z,x)
    ]]></literal>
    <justification jstring="[para(5479(a,2),7597(a,1,2))].">
      <j1 rule="para" parents="5479 7597"/>
    </justification>
  </clause>

  <clause id="7638">
    <literal><![CDATA[
      K(((x \ 1) * (y * x)) \ z,x) = K(L(y,x,x \ 1) \ z,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,5130,a(flip),b,7608,a),flip(a)].">
      <j1 rule="hyper" parents="333 5130 7608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7639">
    <literal><![CDATA[
      K(x,(y * K(z,x)) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[hyper(333,a,5990,a(flip),b,7609,a),flip(a)].">
      <j1 rule="hyper" parents="333 5990 7609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7640">
    <literal><![CDATA[
      K(x,(y * K(z,x)) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ u) = w
    ]]></literal>
    <justification jstring="[para(7609(a,2),6024(a,1))].">
      <j1 rule="para" parents="7609 6024"/>
    </justification>
  </clause>

  <clause id="7642">
    <literal><![CDATA[
      K(x,(y * L(K(z,x),u,w)) \ v5) = K(x,y \ v5)
    ]]></literal>
    <justification jstring="[para(5372(a,1),7639(a,1,2,1,2))].">
      <j1 rule="para" parents="5372 7639"/>
    </justification>
  </clause>

  <clause id="7643">
    <literal><![CDATA[
      K(x,(y * K(x,z)) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(5995(a,1),7639(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5995 7639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7644">
    <literal><![CDATA[
      K(x,(K(x,y) * z) \ u) = K(x,z \ u)
    ]]></literal>
    <justification jstring="[para(6355(a,1),7639(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6355 7639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7647">
    <literal><![CDATA[
      K(x,y \ K(x,z)) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(5949,a,7644,a),flip(a)].">
      <j1 rule="hyper" parents="5949 7644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7648">
    <literal><![CDATA[
      K(x,(y * z) \ ((K(x,u) * y) * z)) = K(x,a(K(x,u),y,z))
    ]]></literal>
    <justification jstring="[para(14(a,2),7644(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14 7644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7649">
    <literal><![CDATA[
      T(x,y \ K(x,z)) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(124,a,7647,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 7647 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7650">
    <literal><![CDATA[
      T(T(x,y),z \ K(x,u)) = T(T(x,z \ 1),y)
    ]]></literal>
    <justification jstring="[para(7649(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7649 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7651">
    <literal><![CDATA[
      K(x,(T(y,x) * z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * z) \ u) = w
    ]]></literal>
    <justification jstring="[para(4959(a,1),7640(a,1,2,1))].">
      <j1 rule="para" parents="4959 7640"/>
    </justification>
  </clause>

  <clause id="7652">
    <literal><![CDATA[
      K(x,(y * (x \ z)) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * (z / x)) \ u) = w
    ]]></literal>
    <justification jstring="[para(6011(a,1),7640(a,1,2,1))].">
      <j1 rule="para" parents="6011 7640"/>
    </justification>
  </clause>

  <clause id="7653">
    <literal><![CDATA[
      K(x,(K(y,x) * z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ u) = w
    ]]></literal>
    <justification jstring="[para(6357(a,1),7640(a,1,2,1))].">
      <j1 rule="para" parents="6357 7640"/>
    </justification>
  </clause>

  <clause id="7654">
    <literal><![CDATA[
      K(T(x,y),(z * K(u,x)) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(T(x,y),z \ w) = v5
    ]]></literal>
    <justification jstring="[para(6433(a,1),7640(a,1,2,1,2))].">
      <j1 rule="para" parents="6433 7640"/>
    </justification>
  </clause>

  <clause id="7655">
    <literal><![CDATA[
      K(x,(y * (z * K(u,x))) \ w) = K(x,(y * z) \ w)
    ]]></literal>
    <justification jstring="[para(97(a,1),7642(a,1,2,1))].">
      <j1 rule="para" parents="97 7642"/>
    </justification>
  </clause>

  <clause id="7656">
    <literal><![CDATA[
      K(x,T(T(y \ z,u),z)) = K(x,T(z / y,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,6682,a(flip),b,7615,a)].">
      <j1 rule="hyper" parents="63 6682 7615"/>
    </justification>
  </clause>

  <clause id="7657">
    <literal><![CDATA[
      K(x,R(T(y,z),y \ 1,u)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(333,a,549,a(flip),b,7631,a),flip(a)].">
      <j1 rule="hyper" parents="333 549 7631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7658">
    <literal><![CDATA[
      K(x,R(T(y,z),y \ 1,u)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(333,a,6365,a(flip),b,7657,a),flip(a)].">
      <j1 rule="hyper" parents="333 6365 7657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7659">
    <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(1592(a,1),7637(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1592 7637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7660">
    <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(1634(a,1),7637(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1634 7637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7661">
    <literal><![CDATA[
      K(x,(y * (K(x,z) * u)) \ w) = K(x,(y * u) \ w)
    ]]></literal>
    <justification jstring="[para(6355(a,1),7655(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="6355 7655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7662">
    <literal><![CDATA[
      (x * y) / ((z * y) / z) = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(5418,a,6033,a),flip(a)].">
      <j1 rule="hyper" parents="5418 6033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7663">
    <literal><![CDATA[
      (x * y) * ((y * x) / y) = (y * x) * x
    ]]></literal>
    <justification jstring="[hyper(580,a,7662,a)].">
      <j1 rule="hyper" parents="580 7662"/>
    </justification>
  </clause>

  <clause id="7664">
    <literal><![CDATA[
      x / ((y * z) / y) = (x / z) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(422,a,7662,a)].">
      <j1 rule="hyper" parents="422 7662"/>
    </justification>
  </clause>

  <clause id="7666">
    <literal><![CDATA[
      (x / ((y * z) / y)) * z = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,1453,a(flip),b,7662,a)].">
      <j1 rule="hyper" parents="63 1453 7662"/>
    </justification>
  </clause>

  <clause id="7669">
    <literal><![CDATA[
      (x * y) / (y * K(z,y)) = x * K(y,z)
    ]]></literal>
    <justification jstring="[para(4238(a,1),7662(a,1,2))].">
      <j1 rule="para" parents="4238 7662"/>
    </justification>
  </clause>

  <clause id="7670">
    <literal><![CDATA[
      x / ((x * y) / x) = K(y,x) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(333,a,5478,a,b,7664,a),flip(a)].">
      <j1 rule="hyper" parents="333 5478 7664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7672">
    <literal><![CDATA[
      x / (y / (y / z)) = (x / z) * K(z,z \ y)
    ]]></literal>
    <justification jstring="[para(3697(a,1),7664(a,1,2))].">
      <j1 rule="para" parents="3697 7664"/>
    </justification>
  </clause>

  <clause id="7673">
    <literal><![CDATA[
      x / (y * K(z,y)) = (x / y) * K(y,z)
    ]]></literal>
    <justification jstring="[para(4238(a,1),7664(a,1,2))].">
      <j1 rule="para" parents="4238 7664"/>
    </justification>
  </clause>

  <clause id="7674">
    <literal><![CDATA[
      x * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x / ((z * y) / z),y) = y \ u
    ]]></literal>
    <justification jstring="[para(7666(a,1),296(a,1))].">
      <j1 rule="para" parents="7666 296"/>
    </justification>
  </clause>

  <clause id="7679">
    <literal><![CDATA[
      a(x,T(y,z),T(z,y)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(752,a,6119,a),flip(a)].">
      <j1 rule="hyper" parents="752 6119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7680">
    <literal><![CDATA[
      T(L(x \ 1,x,y) \ 1,x * L(x \ 1,z,u)) = ((y * x) \ y) \ 1
    ]]></literal>
    <justification jstring="[para(1607(a,1),6248(a,2,2))].">
      <j1 rule="para" parents="1607 6248"/>
    </justification>
  </clause>

  <clause id="7681">
    <literal><![CDATA[
      R(x,y / z,z) * (u * (u \ y)) = (x * (z \ y)) * T(z,z \ y)
    ]]></literal>
    <justification jstring="[hyper(333,a,154,a,b,6260,a)].">
      <j1 rule="hyper" parents="333 154 6260"/>
    </justification>
  </clause>

  <clause id="7682">
    <literal><![CDATA[
      x * ((x \ y) * K(z \ (x \ y),u)) = y * K((x * z) \ y,u)
    ]]></literal>
    <justification jstring="[hyper(126,a,6283,a(flip),b,98,a),flip(a)].">
      <j1 rule="hyper" parents="126 6283 98"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7683">
    <literal><![CDATA[
      K((x * y) \ 1,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y \ (x \ 1),x) = z
    ]]></literal>
    <justification jstring="[para(6283(a,1),5762(a,1))].">
      <j1 rule="para" parents="6283 5762"/>
    </justification>
  </clause>

  <clause id="7684">
    <literal><![CDATA[
      L(K((x \ y) \ (z \ u),y),z \ u,z) = K((z * (y / x)) \ u,y)
    ]]></literal>
    <justification jstring="[para(6268(a,1),6283(a,1,1))].">
      <j1 rule="para" parents="6268 6283"/>
    </justification>
  </clause>

  <clause id="7685">
    <literal><![CDATA[
      K(x / ((y * z) * x),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(z \ (y \ 1),y) = u
    ]]></literal>
    <justification jstring="[para(4970(a,2),7683(a,1))].">
      <j1 rule="para" parents="4970 7683"/>
    </justification>
  </clause>

  <clause id="7686">
    <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(25(a,2),6962(a,1,1,2))].">
      <j1 rule="para" parents="25 6962"/>
    </justification>
  </clause>

  <clause id="7687">
    <literal><![CDATA[
      K(1 / T(T(x,y),y * x),z) = K(1 / L(x,y,x),z)
    ]]></literal>
    <justification jstring="[para(3685(a,1),7130(a,1,1,2))].">
      <j1 rule="para" parents="3685 7130"/>
    </justification>
  </clause>

  <clause id="7688">
    <literal><![CDATA[
      K(x,y) * K(y * L(x,z,u),x) = x \ R(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(121,a,7542,a(flip),b,4241,a),flip(a)].">
      <j1 rule="hyper" parents="121 7542 4241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7689">
    <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(7542(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="7542 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7690">
    <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(7586(a,1),3546(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7586 3546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7691">
    <literal><![CDATA[
      K(1 / T(x,y),T(z,y * x)) = K(1 / L(x,y,x),z)
    ]]></literal>
    <justification jstring="[hyper(6693,a,7687,a)].">
      <j1 rule="hyper" parents="6693 7687"/>
    </justification>
  </clause>

  <clause id="7692">
    <literal><![CDATA[
      K(1 / x,T(T(y,z * x),z)) = K(1 / L(x,z,x),y)
    ]]></literal>
    <justification jstring="[hyper(6693,a,7691,a)].">
      <j1 rule="hyper" parents="6693 7691"/>
    </justification>
  </clause>

  <clause id="7693">
    <literal><![CDATA[
      K(1 / x,T(T(y,z),z * x)) = K(1 / L(x,z,x),y)
    ]]></literal>
    <justification jstring="[para(23(a,1),7692(a,1,2))].">
      <j1 rule="para" parents="23 7692"/>
    </justification>
  </clause>

  <clause id="7694">
    <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(2298(a,2),5778(a,1,2))].">
      <j1 rule="para" parents="2298 5778"/>
    </justification>
  </clause>

  <clause id="7695">
    <literal><![CDATA[
      K(x,(T(y,z) * u) \ y) = K(x,u \ K(z,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,5964,a(flip),b,5779,a),flip(a)].">
      <j1 rule="hyper" parents="63 5964 5779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7696">
    <literal><![CDATA[
      K(x,(T(y,z) \ u) \ K(z,y)) = K(x,u \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),7695(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 7695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7697">
    <literal><![CDATA[
      K(x,((y / z) \ y) \ 1) \ (y / z) = T(y \ (y / z),x) * T(y,z \ 1)
    ]]></literal>
    <justification jstring="[para(5813(a,1),5787(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5813 5787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7698">
    <literal><![CDATA[
      K((1 / ((x * y) \ x)) * z,y) = K(z * (1 / ((x * y) \ x)),y)
    ]]></literal>
    <justification jstring="[para(5835(a,1),7388(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5835 7388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7699">
    <literal><![CDATA[
      (1 / x) * K(y \ (x \ 1),z) = K((y * x) \ 1,z) / x
    ]]></literal>
    <justification jstring="[para(4766(a,1),5875(a,1,2))].">
      <j1 rule="para" parents="4766 5875"/>
    </justification>
  </clause>

  <clause id="7700">
    <literal><![CDATA[
      x \ T(x * K(y \ x,z),x) = K(T(y,x) \ x,z)
    ]]></literal>
    <justification jstring="[hyper(121,a,5915,a(flip),b,5860,a(flip))].">
      <j1 rule="hyper" parents="121 5915 5860"/>
    </justification>
  </clause>

  <clause id="7701">
    <literal><![CDATA[
      K(T(x / y,x) \ x,z) = x \ T(x * K(y,z),x)
    ]]></literal>
    <justification jstring="[para(79(a,1),7700(a,1,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="79 7700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7702">
    <literal><![CDATA[
      K(T(x / y,x) \ x,z) = K(y,T(x / z,x) \ x)
    ]]></literal>
    <justification jstring="[hyper(333,a,5569,a,b,7701,a),flip(a)].">
      <j1 rule="hyper" parents="333 5569 7701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7703">
    <literal><![CDATA[
      T(K(x \ K(x,y),z),y) = K(x \ 1,z)
    ]]></literal>
    <justification jstring="[para(4327(a,1),5967(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4327 5967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7704">
    <literal><![CDATA[
      K(x \ K(x,y),z) = K(x \ 1,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(6960,a,7703,a)].">
      <j1 rule="hyper" parents="6960 7703"/>
    </justification>
  </clause>

  <clause id="7705">
    <literal><![CDATA[
      K(x \ K(x,y),z) * y = y * K(x \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(126,a,7703,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="126 7703 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7706">
    <literal><![CDATA[
      K(T(x,y) \ 1,z) = K(x \ K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(333,a,6378,a,b,7704,a)].">
      <j1 rule="hyper" parents="333 6378 7704"/>
    </justification>
  </clause>

  <clause id="7707">
    <literal><![CDATA[
      K(((x * y) / x) \ 1,z) = K(T(y,x) \ 1,z)
    ]]></literal>
    <justification jstring="[para(4355(a,2),7706(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4355 7706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7708">
    <literal><![CDATA[
      K(L(x / (y \ 1),y \ 1,y) \ 1,z) = K(T(y * x,y \ 1) \ 1,z)
    ]]></literal>
    <justification jstring="[para(900(a,1),7707(a,1,1,1))].">
      <j1 rule="para" parents="900 7707"/>
    </justification>
  </clause>

  <clause id="7709">
    <literal><![CDATA[
      (x * y) * K(T(y,x),z) = T(y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(3624(a,1),6074(a,1,1))].">
      <j1 rule="para" parents="3624 6074"/>
    </justification>
  </clause>

  <clause id="7710">
    <literal><![CDATA[
      (x * y) * K(y,T(z,x)) = T(y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(7307,a,7709,a)].">
      <j1 rule="hyper" parents="7307 7709"/>
    </justification>
  </clause>

  <clause id="7711">
    <literal><![CDATA[
      ((x * y) / R(x,y,x)) * x = T(x,y * x) * T(y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,5353,a,b,7709,a)].">
      <j1 rule="hyper" parents="63 5353 7709"/>
    </justification>
  </clause>

  <clause id="7712">
    <literal><![CDATA[
      T(x,y) * T(z,x) = z * T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(6089,a,7710,a),flip(a)].">
      <j1 rule="hyper" parents="6089 7710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7713">
    <literal><![CDATA[
      T(T(x,y) * K(z,x),z) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(6066,a,7712,a)].">
      <j1 rule="hyper" parents="6066 7712"/>
    </justification>
  </clause>

  <clause id="7714">
    <literal><![CDATA[
      K(x,y) * (z * x) = z * T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(4610,a,7712,a)].">
      <j1 rule="hyper" parents="4610 7712"/>
    </justification>
  </clause>

  <clause id="7716">
    <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(7714(a,1),99(a,2,1))].">
      <j1 rule="para" parents="7714 99"/>
    </justification>
  </clause>

  <clause id="7717">
    <literal><![CDATA[
      K(x,T(y,z)) * (z * x) = z * T(x,y)
    ]]></literal>
    <justification jstring="[para(6917(a,1),7714(a,2,2))].">
      <j1 rule="para" parents="6917 7714"/>
    </justification>
  </clause>

  <clause id="7718">
    <literal><![CDATA[
      K(x,T(y,z)) \ (z * y) = z * T(y,x)
    ]]></literal>
    <justification jstring="[hyper(6448,a,7717,a)].">
      <j1 rule="hyper" parents="6448 7717"/>
    </justification>
  </clause>

  <clause id="7719">
    <literal><![CDATA[
      (x * T(y,z)) / (x * y) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(7717(a,1),268(a,1,1)),flip(b)].">
      <j1 rule="para" parents="7717 268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7720">
    <literal><![CDATA[
      K(x,y) * (y * T(x,z)) = T(x,T(z,y)) * y
    ]]></literal>
    <justification jstring="[para(7717(a,1),5669(a,1,2))].">
      <j1 rule="para" parents="7717 5669"/>
    </justification>
  </clause>

  <clause id="7722">
    <literal><![CDATA[
      K(T(x,y),z) * (y * x) = y * T(x,z)
    ]]></literal>
    <justification jstring="[para(6370(a,2),7717(a,1,1))].">
      <j1 rule="para" parents="6370 7717"/>
    </justification>
  </clause>

  <clause id="7723">
    <literal><![CDATA[
      K(x,T(y,z)) * ((z * y) * x) = (z * y) * T(x,y)
    ]]></literal>
    <justification jstring="[para(6383(a,1),7717(a,1,1))].">
      <j1 rule="para" parents="6383 7717"/>
    </justification>
  </clause>

  <clause id="7724">
    <literal><![CDATA[
      T(K(x,y),z) * ((x \ z) * x) = (x \ z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(6423(a,1),7717(a,1,1))].">
      <j1 rule="para" parents="6423 7717"/>
    </justification>
  </clause>

  <clause id="7725">
    <literal><![CDATA[
      ((x \ 1) * x) \ (y * x) = y * T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(3443(a,1),7718(a,1,1))].">
      <j1 rule="para" parents="3443 7718"/>
    </justification>
  </clause>

  <clause id="7726">
    <literal><![CDATA[
      K(x,T(y,K(y * T(x,y),z))) * ((K(y * T(x,y),z) * y) * x) = (x * y) * R(K(x * y,z),y,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(333,a,3552,a,b,7723,a),flip(a)].">
      <j1 rule="hyper" parents="333 3552 7723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7727">
    <literal><![CDATA[
      T(x,(x \ y) * x) * T(x \ y,x) = (y / R(x,x \ y,x)) * x
    ]]></literal>
    <justification jstring="[para(10(a,1),7711(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 7711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7728">
    <literal><![CDATA[
      T((x \ K(y,x)) \ L((x \ 1) * (z / (x \ 1)),u,w),K(x,y)) = (L(z,u,w) / (x \ 1)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(2544(a,1),6105(a,2,1))].">
      <j1 rule="para" parents="2544 6105"/>
    </justification>
  </clause>

  <clause id="7729">
    <literal><![CDATA[
      T(L(K(x,y),z,u),K(y,x) * w) = T(L(K(x,y),z,u),w)
    ]]></literal>
    <justification jstring="[para(4558(a,1),6108(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4558 6108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7730">
    <literal><![CDATA[
      (x * T(y,L(z,y,x))) \ (x * (y * z)) = L(T(z,y),y,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,25,a,b,6116,a),flip(a)].">
      <j1 rule="hyper" parents="333 25 6116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7734">
    <literal><![CDATA[
      L(K(x,y),z,L(x,u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(2942,a,6151,a)].">
      <j1 rule="hyper" parents="2942 6151"/>
    </justification>
  </clause>

  <clause id="7735">
    <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(6151(a,1),6024(a,1,1))].">
      <j1 rule="para" parents="6151 6024"/>
    </justification>
  </clause>

  <clause id="7736">
    <literal><![CDATA[
      K(L(x,y,L(x,z,u)),w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,6298,a(flip),b,7734,a)].">
      <j1 rule="hyper" parents="63 6298 7734"/>
    </justification>
  </clause>

  <clause id="7737">
    <literal><![CDATA[
      x * K(L(x,y,L(x,z,u)),w) = T(x,w)
    ]]></literal>
    <justification jstring="[hyper(126,a,7736,a,b,4215,a(flip))].">
      <j1 rule="hyper" parents="126 7736 4215"/>
    </justification>
  </clause>

  <clause id="7740">
    <literal><![CDATA[
      R(x,y,y \ 1) * K(y,x) = (y * x) * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,4422,a(flip),b,6349,a),flip(a)].">
      <j1 rule="hyper" parents="63 4422 6349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7741">
    <literal><![CDATA[
      K(x,y) * ((y * x) * (y \ 1)) = R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(7740(a,1),4572(a,1,2))].">
      <j1 rule="para" parents="7740 4572"/>
    </justification>
  </clause>

  <clause id="7742">
    <literal><![CDATA[
      K(x,y / R(T(x,z),u,w)) = K(x,R(x,u,w) \ y)
    ]]></literal>
    <justification jstring="[hyper(333,a,7599,a(flip),b,6515,a),flip(a)].">
      <j1 rule="hyper" parents="333 7599 6515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7744">
    <literal><![CDATA[
      K(R(x,y,z),T(u,x \ w)) = K(R(x,y,z),T(u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,5562,a(flip),b,6539,a),flip(a)].">
      <j1 rule="hyper" parents="63 5562 6539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7745">
    <literal><![CDATA[
      K(R(x,y,z),T(u,x * w)) = K(R(x,y,z),T(u,w))
    ]]></literal>
    <justification jstring="[para(9(a,1),7744(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 7744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7746">
    <literal><![CDATA[
      R(K(x,y),z,R(x,u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(543,a,6572,a)].">
      <j1 rule="hyper" parents="543 6572"/>
    </justification>
  </clause>

  <clause id="7747">
    <literal><![CDATA[
      (x * (K(y,x) * z)) * R(y,u,w) = K(y,x) * ((x * z) * R(y,u,w))
    ]]></literal>
    <justification jstring="[para(4712(a,1),6572(a,1,1))].">
      <j1 rule="para" parents="4712 6572"/>
    </justification>
  </clause>

  <clause id="7748">
    <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(6572(a,1),4524(a,1,1,2))].">
      <j1 rule="para" parents="6572 4524"/>
    </justification>
  </clause>

  <clause id="7749">
    <literal><![CDATA[
      K(x,R(y,z,R(x,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,5654,a(flip),b,7746,a)].">
      <j1 rule="hyper" parents="63 5654 7746"/>
    </justification>
  </clause>

  <clause id="7750">
    <literal><![CDATA[
      K(x,(y * R(x,z,u)) / w) = K(x,y / (w / R(x,z,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,5647,a(flip),b,7746,a)].">
      <j1 rule="hyper" parents="63 5647 7746"/>
    </justification>
  </clause>

  <clause id="7751">
    <literal><![CDATA[
      K(R(x,y,R(x,z,u)),w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,5562,a(flip),b,7746,a)].">
      <j1 rule="hyper" parents="63 5562 7746"/>
    </justification>
  </clause>

  <clause id="7752">
    <literal><![CDATA[
      K(x,T((y * R(x,z,u)) / w,w / R(x,z,u))) = K(x,(w / R(x,z,u)) \ y)
    ]]></literal>
    <justification jstring="[para(807(a,1),7749(a,1,2))].">
      <j1 rule="para" parents="807 7749"/>
    </justification>
  </clause>

  <clause id="7753">
    <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(125,a,7751,a(flip),b,4334,a)].">
      <j1 rule="hyper" parents="125 7751 4334"/>
    </justification>
  </clause>

  <clause id="7755">
    <literal><![CDATA[
      T(L(x / y,z,x / y),y) = L(y \ x,z,T(y \ x,u))
    ]]></literal>
    <justification jstring="[para(6582(a,2),6580(a,1,1))].">
      <j1 rule="para" parents="6582 6580"/>
    </justification>
  </clause>

  <clause id="7756">
    <literal><![CDATA[
      K(x,y) * ((y * R(x,z,u)) * x) = (x * y) * R(x,z,u)
    ]]></literal>
    <justification jstring="[para(1575(a,2),6592(a,1,2))].">
      <j1 rule="para" parents="1575 6592"/>
    </justification>
  </clause>

  <clause id="7757">
    <literal><![CDATA[
      T(T(x,1 / y),K(1 / y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,1 / T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(6620(a,2),4285(a,1))].">
      <j1 rule="para" parents="6620 4285"/>
    </justification>
  </clause>

  <clause id="7758">
    <literal><![CDATA[
      T(K(x,y) * (z / T(y,u)),y) = (T(y,x) \ z) * K(u,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,6228,a(flip),b,6637,a),flip(a)].">
      <j1 rule="hyper" parents="333 6228 6637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7760">
    <literal><![CDATA[
      T(x,y) / T(R(x,z,u),w) = R(T(x,w),z,u) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(27(a,2),6670(a,2,1))].">
      <j1 rule="para" parents="27 6670"/>
    </justification>
  </clause>

  <clause id="7761">
    <literal><![CDATA[
      R(K(x,K(y,z \ 1)),u,w) = K(x,K(y,R(z,u,w) \ 1))
    ]]></literal>
    <justification jstring="[para(6763(a,1),6773(a,1,1))].">
      <j1 rule="para" parents="6763 6773"/>
    </justification>
  </clause>

  <clause id="7762">
    <literal><![CDATA[
      R(K(x,K(y,z)),u,w) = K(R(K(x,y),u,w),z)
    ]]></literal>
    <justification jstring="[para(5114(a,1),6774(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5114 6774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7763">
    <literal><![CDATA[
      K(R(K(x,y),z,u),w) = K(y,R(K(x,w),z,u))
    ]]></literal>
    <justification jstring="[para(5114(a,1),6802(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5114 6802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7764">
    <literal><![CDATA[
      R(K(x,K(y,z)),u,w) = K(y,R(K(x,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,7762,a,b,7763,a)].">
      <j1 rule="hyper" parents="63 7762 7763"/>
    </justification>
  </clause>

  <clause id="7765">
    <literal><![CDATA[
      R(K(x,K(y,z)),u,w) = K(x,R(K(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(6785(a,1),7764(a,1,1))].">
      <j1 rule="para" parents="6785 7764"/>
    </justification>
  </clause>

  <clause id="7766">
    <literal><![CDATA[
      (x / y) \ T(x,K(z,u)) = y * K(z,K(u,((x / y) \ 1) \ y))
    ]]></literal>
    <justification jstring="[para(12(a,1),6808(a,1,2,1))].">
      <j1 rule="para" parents="12 6808"/>
    </justification>
  </clause>

  <clause id="7767">
    <literal><![CDATA[
      T(x,K(y,z)) * (K(z,T(y,x)) * u) = x * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(6365(a,2),6855(a,1,2,1))].">
      <j1 rule="para" parents="6365 6855"/>
    </justification>
  </clause>

  <clause id="7768">
    <literal><![CDATA[
      R(K(x,y),T(y,z) * u,w) = K(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(7071,a,6940,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="7071 6940"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7769">
    <literal><![CDATA[
      ((x * (y * K(z,y))) / x) / ((x * y) / x) = K(T(z,x),y)
    ]]></literal>
    <justification jstring="[para(4238(a,1),7010(a,1,1,1,2))].">
      <j1 rule="para" parents="4238 7010"/>
    </justification>
  </clause>

  <clause id="7770">
    <literal><![CDATA[
      T(x * (y \ z),K(y,z)) = (y \ z) * T(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(7216,a,7016,a)].">
      <j1 rule="hyper" parents="7216 7016"/>
    </justification>
  </clause>

  <clause id="7772">
    <literal><![CDATA[
      K(x \ y,x) * (z * (y / x)) = T(z * (x \ y),K(x,y))
    ]]></literal>
    <justification jstring="[hyper(5081,a,7770,a(flip))].">
      <j1 rule="hyper" parents="5081 7770"/>
    </justification>
  </clause>

  <clause id="7773">
    <literal><![CDATA[
      T(K(x,y),T(z,x \ u)) = T(K(x,y),T(z,u))
    ]]></literal>
    <justification jstring="[hyper(6769,a,7082,a),flip(a)].">
      <j1 rule="hyper" parents="6769 7082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7774">
    <literal><![CDATA[
      T(K(x,y),T(z,x * u)) = T(K(x,y),T(z,u))
    ]]></literal>
    <justification jstring="[para(9(a,1),7773(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 7773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7775">
    <literal><![CDATA[
      K(x,K(y,z)) * (T(z,y) * u) = T(z,T(y,x)) * u
    ]]></literal>
    <justification jstring="[para(6851(a,1),7230(a,2,1))].">
      <j1 rule="para" parents="6851 7230"/>
    </justification>
  </clause>

  <clause id="7776">
    <literal><![CDATA[
      K(R(x / (x / y),z,u),w) = K(R(y,z,u),T(w,x))
    ]]></literal>
    <justification jstring="[hyper(333,a,7744,a(flip),b,7237,a),flip(a)].">
      <j1 rule="hyper" parents="333 7744 7237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7777">
    <literal><![CDATA[
      K(R(x,y / x,z),T(u,y)) = K((y * z) / ((y / x) * z),u)
    ]]></literal>
    <justification jstring="[para(108(a,1),7776(a,1,1)),flip(a)].">
      <j1 rule="para" parents="108 7776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7778">
    <literal><![CDATA[
      K(L(x,y / T(x,z),u),w) = L(K(x,w),y,u)
    ]]></literal>
    <justification jstring="[para(6901(a,1),7238(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6901 7238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7779">
    <literal><![CDATA[
      L(K(x,y),x * z,u) = K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(191(a,1),7778(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="191 7778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7780">
    <literal><![CDATA[
      K(L(x,x \ y,z),u) = L(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(281(a,1),7778(a,1,1,2))].">
      <j1 rule="para" parents="281 7778"/>
    </justification>
  </clause>

  <clause id="7782">
    <literal><![CDATA[
      K(L(x,y,z),x * y) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(5761,a,7779,a),flip(a)].">
      <j1 rule="hyper" parents="5761 7779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7783">
    <literal><![CDATA[
      L(K(x,y),K(z,x) * u,w) = K(L(x,T(x,z) \ u,w),y)
    ]]></literal>
    <justification jstring="[para(4556(a,1),7779(a,1,2))].">
      <j1 rule="para" parents="4556 7779"/>
    </justification>
  </clause>

  <clause id="7784">
    <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(6901(a,1),7779(a,1,1))].">
      <j1 rule="para" parents="6901 7779"/>
    </justification>
  </clause>

  <clause id="7785">
    <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(333,a,7462,a(flip),b,7253,a),flip(a)].">
      <j1 rule="hyper" parents="333 7462 7253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7786">
    <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(6786(a,1),7293(a,2,2))].">
      <j1 rule="para" parents="6786 7293"/>
    </justification>
  </clause>

  <clause id="7787">
    <literal><![CDATA[
      (x * K((y \ z) \ x,z)) * y = (z \ (x * y)) * z
    ]]></literal>
    <justification jstring="[para(7218(a,1),7345(a,1,1,2))].">
      <j1 rule="para" parents="7218 7345"/>
    </justification>
  </clause>

  <clause id="7788">
    <literal><![CDATA[
      K(x \ y,T(z,x)) = K(y / (x * K(z,u)),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,7607,a(flip),b,7380,a)].">
      <j1 rule="hyper" parents="63 7607 7380"/>
    </justification>
  </clause>

  <clause id="7789">
    <literal><![CDATA[
      K(x / (y * K(z,u)),z) = K(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(7072,a,7788,a),flip(a)].">
      <j1 rule="hyper" parents="7072 7788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7791">
    <literal><![CDATA[
      K(x / (y * z),z) = K(x / (z * y),z)
    ]]></literal>
    <justification jstring="[para(88(a,1),7789(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="88 7789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7792">
    <literal><![CDATA[
      K(x,x \ y) * ((x \ y) * (K(y,x) * z)) = (y / T(x,y)) * L(z,K(y,x),x \ y)
    ]]></literal>
    <justification jstring="[para(5480(a,1),7445(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5480 7445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7794">
    <literal><![CDATA[
      (x * ((x \ y) * x)) * K(x,x * ((x \ y) * x)) = T(x,x * y) * ((x \ y) * x)
    ]]></literal>
    <justification jstring="[hyper(4321,a,7474,a)].">
      <j1 rule="hyper" parents="4321 7474"/>
    </justification>
  </clause>

  <clause id="7796">
    <literal><![CDATA[
      T(K(x,y) * z,T(y,u)) = K(x,y) * T(z,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(6089,a,7478,a),flip(a)].">
      <j1 rule="hyper" parents="6089 7478"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7797">
    <literal><![CDATA[
      K(T(K(x,y) * z,T(y,u)) \ 1,w) = K(T(z,T(y,u)) \ K(y,x),w)
    ]]></literal>
    <justification jstring="[para(7796(a,2),5867(a,1,1,1))].">
      <j1 rule="para" parents="7796 5867"/>
    </justification>
  </clause>

  <clause id="7798">
    <literal><![CDATA[
      T(x,(y \ x) \ (z * x)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,(y \ 1) \ z) = u
    ]]></literal>
    <justification jstring="[para(7507(a,2),4404(a,1))].">
      <j1 rule="para" parents="7507 4404"/>
    </justification>
  </clause>

  <clause id="7799">
    <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(5824(a,1),7510(a,2,2,1,1))].">
      <j1 rule="para" parents="5824 7510"/>
    </justification>
  </clause>

  <clause id="7800">
    <literal><![CDATA[
      (((x * (y * x)) / x) / y) * (z / (((x * (y * x)) / x) / y)) = z * K(((x * (y * x)) / x) / y,T(x,y * x) \ z)
    ]]></literal>
    <justification jstring="[para(859(a,1),7598(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="859 7598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7801">
    <literal><![CDATA[
      x / T(x * (y / x),y \ x) = L((y / x) \ 1,y / x,x)
    ]]></literal>
    <justification jstring="[para(7619(a,1),5898(a,1,2))].">
      <j1 rule="para" parents="7619 5898"/>
    </justification>
  </clause>

  <clause id="7802">
    <literal><![CDATA[
      K(x,y \ (y / z)) = K(x,K(u,z)) * K(x,u \ (z \ u))
    ]]></literal>
    <justification jstring="[hyper(333,a,5822,a,b,7624,a)].">
      <j1 rule="hyper" parents="333 5822 7624"/>
    </justification>
  </clause>

  <clause id="7803">
    <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(4239(a,1),7730(a,2,1))].">
      <j1 rule="para" parents="4239 7730"/>
    </justification>
  </clause>

  <clause id="7807">
    <literal><![CDATA[
      K(x,(y * R(x,z,u)) / w) = K(x,y / (R(x,z,u) \ w))
    ]]></literal>
    <justification jstring="[hyper(333,a,7473,a(flip),b,7750,a),flip(a)].">
      <j1 rule="hyper" parents="333 7473 7750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7808">
    <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(121,a,7753,a(flip),b,4532,a),flip(a)].">
      <j1 rule="hyper" parents="121 7753 4532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7809">
    <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(7753(a,1),6331(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7753 6331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7810">
    <literal><![CDATA[
      L(x \ y,z,T(x \ y,u)) = L(x \ y,z,y / x)
    ]]></literal>
    <justification jstring="[hyper(896,a,7755,a),flip(a)].">
      <j1 rule="hyper" parents="896 7755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7811">
    <literal><![CDATA[
      L(x \ y,z,y / x) = L(x \ y,z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,6575,a(flip),b,7810,a),flip(a)].">
      <j1 rule="hyper" parents="63 6575 7810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7812">
    <literal><![CDATA[
      R(K(x,K(y,z \ 1)),u,w) = K(x,K(y,R(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(333,a,7148,a(flip),b,7761,a),flip(a)].">
      <j1 rule="hyper" parents="333 7148 7761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7813">
    <literal><![CDATA[
      R(K(x,K(y,z)),u,w) = K(x,K(y,R(z,u,w)))
    ]]></literal>
    <justification jstring="[para(7148(a,1),7812(a,1,1))].">
      <j1 rule="para" parents="7148 7812"/>
    </justification>
  </clause>

  <clause id="7814">
    <literal><![CDATA[
      R(K(x,K(y,z)),u,w) = K(y,K(z,R(x,u,w)))
    ]]></literal>
    <justification jstring="[para(7152(a,1),7812(a,1,1))].">
      <j1 rule="para" parents="7152 7812"/>
    </justification>
  </clause>

  <clause id="7815">
    <literal><![CDATA[
      K(x,R(K(y,z),u,w)) = K(x,K(y,R(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,7765,a(flip),b,7813,a)].">
      <j1 rule="hyper" parents="63 7765 7813"/>
    </justification>
  </clause>

  <clause id="7816">
    <literal><![CDATA[
      K(x,K(y,R(z,u,w))) = K(z,K(x,R(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,7813,a(flip),b,7814,a),flip(a)].">
      <j1 rule="hyper" parents="63 7813 7814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7817">
    <literal><![CDATA[
      K(x,R(K(y,z),u,w)) = K(x,K(z,R(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,7764,a(flip),b,7814,a)].">
      <j1 rule="hyper" parents="63 7764 7814"/>
    </justification>
  </clause>

  <clause id="7818">
    <literal><![CDATA[
      T(x,R(K(y,z),u,w)) = T(x,K(y,R(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(124,a,7815,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 7815 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7819">
    <literal><![CDATA[
      K(x,K(y,R(z,y,u))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(3556(a,1),7815(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3556 7815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7820">
    <literal><![CDATA[
      T(x,R(K(y,z),u,w)) = T(x,K(z,R(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(124,a,7817,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 7817 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7821">
    <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(5649(a,1),7817(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5649 7817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7822">
    <literal><![CDATA[
      T(x,K(y,R(z,u,w))) = T(x,K(z,R(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,7818,a(flip),b,7820,a)].">
      <j1 rule="hyper" parents="63 7818 7820"/>
    </justification>
  </clause>

  <clause id="7824">
    <literal><![CDATA[
      K(T(x,y),z) * ((y * z) / y) = (y * (z * K(x,z))) / y
    ]]></literal>
    <justification jstring="[hyper(140,a,7769,a)].">
      <j1 rule="hyper" parents="140 7769"/>
    </justification>
  </clause>

  <clause id="7826">
    <literal><![CDATA[
      L(K(x,y),T(x,z) * u,w) = K(L(x,u,w),y)
    ]]></literal>
    <justification jstring="[hyper(333,a,6919,a(flip),b,7784,a),flip(a)].">
      <j1 rule="hyper" parents="333 6919 7784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7827">
    <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(7784(a,2),7070(a,1))].">
      <j1 rule="para" parents="7784 7070"/>
    </justification>
  </clause>

  <clause id="7829">
    <literal><![CDATA[
      K(L(x,T(x,y) \ z,u),w) = L(K(x,w),z,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),7826(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 7826"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7830">
    <literal><![CDATA[
      L(K(x,y),K(z,x) * u,w) = L(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,7783,a,b,7829,a)].">
      <j1 rule="hyper" parents="63 7783 7829"/>
    </justification>
  </clause>

  <clause id="7831">
    <literal><![CDATA[
      L(K(x,y),K(z,x),u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(509,a,7830,a),flip(a)].">
      <j1 rule="hyper" parents="509 7830"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7833">
    <literal><![CDATA[
      L(K(x,y),K(x,z) * u,w) = L(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(4558(a,1),7830(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4558 7830"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7834">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,u) = x * (K(y,z) * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(126,a,7831,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="126 7831 18"/>
    </justification>
  </clause>

  <clause id="7835">
    <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(7831(a,1),462(a,1,2,1))].">
      <j1 rule="para" parents="7831 462"/>
    </justification>
  </clause>

  <clause id="7836">
    <literal><![CDATA[
      L(K(x,y),L(K(z,x),u,w),v5) = K(x,y)
    ]]></literal>
    <justification jstring="[para(5372(a,1),7831(a,1,2))].">
      <j1 rule="para" parents="5372 7831"/>
    </justification>
  </clause>

  <clause id="7837">
    <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(126,a,7836,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="126 7836 18"/>
    </justification>
  </clause>

  <clause id="7838">
    <literal><![CDATA[
      (x * (K(y,z) * K(z,u))) * K(u,z) = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(5997,a,7834,a)].">
      <j1 rule="hyper" parents="5997 7834"/>
    </justification>
  </clause>

  <clause id="7839">
    <literal><![CDATA[
      R(x,K(y,z),K(z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(543,a,7834,a)].">
      <j1 rule="hyper" parents="543 7834"/>
    </justification>
  </clause>

  <clause id="7840">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,u) = x * (K(z,u) * K(y,z))
    ]]></literal>
    <justification jstring="[para(2005(a,2),7834(a,2,2))].">
      <j1 rule="para" parents="2005 7834"/>
    </justification>
  </clause>

  <clause id="7841">
    <literal><![CDATA[
      R(x,T(K(y,z),u),K(z,w)) = x
    ]]></literal>
    <justification jstring="[para(2078(a,1),7839(a,1,2))].">
      <j1 rule="para" parents="2078 7839"/>
    </justification>
  </clause>

  <clause id="7842">
    <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(7839(a,1),2347(a,1,1,1))].">
      <j1 rule="para" parents="7839 2347"/>
    </justification>
  </clause>

  <clause id="7843">
    <literal><![CDATA[
      R(x,L(K(y,z),u,w),K(z,v5)) = x
    ]]></literal>
    <justification jstring="[para(5372(a,1),7839(a,1,2))].">
      <j1 rule="para" parents="5372 7839"/>
    </justification>
  </clause>

  <clause id="7844">
    <literal><![CDATA[
      (x * y) \ ((x * (y * K(z,u))) * K(u,w)) = L(K(z,u),y,x) * K(u,w)
    ]]></literal>
    <justification jstring="[para(7843(a,1),568(a,1,1))].">
      <j1 rule="para" parents="7843 568"/>
    </justification>
  </clause>

  <clause id="7845">
    <literal><![CDATA[
      (x * (K(y,z) * K(u,y))) * K(z,y) = x * K(u,y)
    ]]></literal>
    <justification jstring="[para(2005(a,2),7838(a,1,1,2))].">
      <j1 rule="para" parents="2005 7838"/>
    </justification>
  </clause>

  <clause id="7846">
    <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(253,a,7840,a,b,664,a)].">
      <j1 rule="hyper" parents="253 7840 664"/>
    </justification>
  </clause>

  <clause id="7847">
    <literal><![CDATA[
      (x / y) * (K(y,z) * K(u,y)) = (x / T(y,u)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(5450(a,1),7840(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5450 7840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7848">
    <literal><![CDATA[
      (x * (K(y,z) * K(u,y))) * (K(z,y) * K(y,u)) = x
    ]]></literal>
    <justification jstring="[hyper(35,a,7838,a,b,7845,a(flip))].">
      <j1 rule="hyper" parents="35 7838 7845"/>
    </justification>
  </clause>

  <clause id="7849">
    <literal><![CDATA[
      x / (K(y,z) * K(z,u)) = x * (K(z,y) * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(138,a,7848,a)].">
      <j1 rule="hyper" parents="138 7848"/>
    </justification>
  </clause>

  <clause id="7850">
    <literal><![CDATA[
      x / (K(y,z) * K(z,u)) = x * (K(u,z) * K(z,y))
    ]]></literal>
    <justification jstring="[para(2005(a,1),7849(a,2,2))].">
      <j1 rule="para" parents="2005 7849"/>
    </justification>
  </clause>

  <clause id="7852">
    <literal><![CDATA[
      K(x,(y / z) / y) = K(x,y \ (z \ y))
    ]]></literal>
    <justification jstring="[hyper(34,a,7626,a,b,7802,a(flip))].">
      <j1 rule="hyper" parents="34 7626 7802"/>
    </justification>
  </clause>

  <clause id="7853">
    <literal><![CDATA[
      K(x,(y / z) / y) = K(x,y / (y * z))
    ]]></literal>
    <justification jstring="[hyper(333,a,7132,a,b,7852,a),flip(a)].">
      <j1 rule="hyper" parents="333 7132 7852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7855">
    <literal><![CDATA[
      ((x * y) / x) / ((x * (y * K(z,y))) / x) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(197,a,7824,a(flip),b,4567,a)].">
      <j1 rule="hyper" parents="197 7824 4567"/>
    </justification>
  </clause>

  <clause id="7856">
    <literal><![CDATA[
      ((x * y) / x) / ((x * (y * K(z,y))) / x) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(7824(a,1),4579(a,1,2))].">
      <j1 rule="para" parents="7824 4579"/>
    </justification>
  </clause>

  <clause id="7857">
    <literal><![CDATA[
      K(x,T((y \ z) / z,u)) = ((u * x) / u) / ((u * (x * K(y \ 1,x))) / u)
    ]]></literal>
    <justification jstring="[para(4972(a,1),7855(a,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4972 7855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7858">
    <literal><![CDATA[
      K(x,L(y \ L(y,z,u),y,u * z)) = K(x,a(u,z,y) \ 1)
    ]]></literal>
    <justification jstring="[para(525(a,2),5775(a,1,2))].">
      <j1 rule="para" parents="525 5775"/>
    </justification>
  </clause>

  <clause id="7865">
    <literal><![CDATA[
      R(x,T(y,z) \ 1,y) / y = (x * (1 / T(y,z))) * K(y,z)
    ]]></literal>
    <justification jstring="[para(1937(a,1),6058(a,1,1))].">
      <j1 rule="para" parents="1937 6058"/>
    </justification>
  </clause>

  <clause id="7866">
    <literal><![CDATA[
      R(x,y,z * K(y,z)) = R(x,T(y,z),z)
    ]]></literal>
    <justification jstring="[hyper(544,a,6173,a),flip(a)].">
      <j1 rule="hyper" parents="544 6173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7867">
    <literal><![CDATA[
      R(x,T(y,z),z) = R(x,y,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(4561,a,7866,a),flip(a)].">
      <j1 rule="hyper" parents="4561 7866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7868">
    <literal><![CDATA[
      T((x \ 1) * y,K(x,z)) = (x \ 1) * T(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,570,a(flip),b,6189,a),flip(a)].">
      <j1 rule="hyper" parents="63 570 6189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7869">
    <literal><![CDATA[
      T((x \ 1) * (x * y),K(x,y)) = (x \ 1) * (x * y)
    ]]></literal>
    <justification jstring="[para(4463(a,1),7868(a,2,2))].">
      <j1 rule="para" parents="4463 7868"/>
    </justification>
  </clause>

  <clause id="7870">
    <literal><![CDATA[
      K(x,y) * T((x \ 1) * z,K(x,y)) = (x \ 1) * (z * K(x,y))
    ]]></literal>
    <justification jstring="[para(7868(a,2),5340(a,1,2))].">
      <j1 rule="para" parents="7868 5340"/>
    </justification>
  </clause>

  <clause id="7871">
    <literal><![CDATA[
      T(((x \ 1) \ 1) * ((x \ 1) * y),K(x \ 1,y)) = x * ((1 / x) * y)
    ]]></literal>
    <justification jstring="[hyper(333,a,5146,a(flip),b,7869,a),flip(a)].">
      <j1 rule="hyper" parents="333 5146 7869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7872">
    <literal><![CDATA[
      L(T(K(x,y \ z),u),y \ z,w) = K(x,T((z \ y) \ 1,u))
    ]]></literal>
    <justification jstring="[hyper(333,a,6365,a,b,6231,a),flip(a)].">
      <j1 rule="hyper" parents="333 6365 6231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7874">
    <literal><![CDATA[
      K(x,(y * x) \ z) = K(x,y \ (x \ z))
    ]]></literal>
    <justification jstring="[hyper(6247,a,7346,a)].">
      <j1 rule="hyper" parents="6247 7346"/>
    </justification>
  </clause>

  <clause id="7875">
    <literal><![CDATA[
      T(x,(y * x) \ z) = T(x,y \ (x \ z))
    ]]></literal>
    <justification jstring="[hyper(124,a,7874,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 7874 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7876">
    <literal><![CDATA[
      x * (y * ((x \ 1) / y)) = K(y,x \ (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,5195,a,b,7874,a)].">
      <j1 rule="hyper" parents="63 5195 7874"/>
    </justification>
  </clause>

  <clause id="7877">
    <literal><![CDATA[
      T(x,L(x \ y,x,z)) = T(x,z \ (x \ (z * y)))
    ]]></literal>
    <justification jstring="[para(99(a,2),7875(a,1,2))].">
      <j1 rule="para" parents="99 7875"/>
    </justification>
  </clause>

  <clause id="7878">
    <literal><![CDATA[
      (x * y) * (z * (((x * y) \ x) / z)) = x * K(z,y \ (z \ 1))
    ]]></literal>
    <justification jstring="[para(7876(a,1),5694(a,2,2))].">
      <j1 rule="para" parents="7876 5694"/>
    </justification>
  </clause>

  <clause id="7879">
    <literal><![CDATA[
      L(x,T(y,K(x,z)),x) = T(x,x * y) * K(y,x)
    ]]></literal>
    <justification jstring="[para(7381(a,1),6362(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7381 6362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7880">
    <literal><![CDATA[
      L(x,T(y,K(x,z)),x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,4733,a(flip),b,7879,a),flip(a)].">
      <j1 rule="hyper" parents="333 4733 7879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7882">
    <literal><![CDATA[
      L(x,T(y,T(x,z)),x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,6198,a(flip),b,7880,a)].">
      <j1 rule="hyper" parents="63 6198 7880"/>
    </justification>
  </clause>

  <clause id="7884">
    <literal><![CDATA[
      L(x,y / T(x,z),x) = L(x,T(x,z) \ y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,4845,a(flip),b,7882,a)].">
      <j1 rule="hyper" parents="63 4845 7882"/>
    </justification>
  </clause>

  <clause id="7885">
    <literal><![CDATA[
      T(x / T(y,T(z,x)),y) = T(y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(6451,a,6491,a)].">
      <j1 rule="hyper" parents="6451 6491"/>
    </justification>
  </clause>

  <clause id="7886">
    <literal><![CDATA[
      T(x / T(y,z),y) = T(y,T(z,x)) \ x
    ]]></literal>
    <justification jstring="[para(6917(a,1),7885(a,1,1,2))].">
      <j1 rule="para" parents="6917 7885"/>
    </justification>
  </clause>

  <clause id="7887">
    <literal><![CDATA[
      K(T(x,y),z) * (y / z) = y / T(z,x)
    ]]></literal>
    <justification jstring="[hyper(6651,a,7886,a)].">
      <j1 rule="hyper" parents="6651 7886"/>
    </justification>
  </clause>

  <clause id="7888">
    <literal><![CDATA[
      K(x,T(y,z)) * (z / y) = z / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(7306,a,7887,a)].">
      <j1 rule="hyper" parents="7306 7887"/>
    </justification>
  </clause>

  <clause id="7889">
    <literal><![CDATA[
      T(x,T(y,z)) \ (x * (z / x)) = z / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(4916,a,7887,a)].">
      <j1 rule="hyper" parents="4916 7887"/>
    </justification>
  </clause>

  <clause id="7890">
    <literal><![CDATA[
      K(x,y \ z) * (z / (z / y)) = z / T(z / y,x)
    ]]></literal>
    <justification jstring="[para(6353(a,1),7887(a,1,1))].">
      <j1 rule="para" parents="6353 7887"/>
    </justification>
  </clause>

  <clause id="7891">
    <literal><![CDATA[
      K(x,y) * (z / T(y,z)) = z / T(T(y,z),x)
    ]]></literal>
    <justification jstring="[para(6901(a,1),7887(a,1,1))].">
      <j1 rule="para" parents="6901 7887"/>
    </justification>
  </clause>

  <clause id="7892">
    <literal><![CDATA[
      K(x,(y / T(z,x)) * u) = K(x,(y / z) * u)
    ]]></literal>
    <justification jstring="[para(7888(a,1),7457(a,1,2,1))].">
      <j1 rule="para" parents="7888 7457"/>
    </justification>
  </clause>

  <clause id="7893">
    <literal><![CDATA[
      T(x,y) \ (x * (z / x)) = z / T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(6917(a,1),7889(a,1,1))].">
      <j1 rule="para" parents="6917 7889"/>
    </justification>
  </clause>

  <clause id="7894">
    <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(7891(a,2),1936(a,2,1,2))].">
      <j1 rule="para" parents="7891 1936"/>
    </justification>
  </clause>

  <clause id="7895">
    <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(7891(a,2),5969(a,1,2,1,2))].">
      <j1 rule="para" parents="7891 5969"/>
    </justification>
  </clause>

  <clause id="7896">
    <literal><![CDATA[
      K(x,R(T(y,z * u),y \ z,u)) = K(x,((y \ z) * u) \ (z * u))
    ]]></literal>
    <justification jstring="[para(76(a,1),6482(a,1,2,1,1))].">
      <j1 rule="para" parents="76 6482"/>
    </justification>
  </clause>

  <clause id="7897">
    <literal><![CDATA[
      K(x * y,z) * (y * x) = K(y,x) * T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(6617,a,5988,a(flip))].">
      <j1 rule="hyper" parents="6617 5988"/>
    </justification>
  </clause>

  <clause id="7898">
    <literal><![CDATA[
      (x * K(y * z,u)) * (z * y) = x * (K(z,y) * T(y * z,u))
    ]]></literal>
    <justification jstring="[para(7897(a,1),5440(a,2,2))].">
      <j1 rule="para" parents="7897 5440"/>
    </justification>
  </clause>

  <clause id="7899">
    <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(333,a,6370,a(flip),b,6722,a),flip(a)].">
      <j1 rule="hyper" parents="333 6370 6722"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7900">
    <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(5309(a,1),6909(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5309 6909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7901">
    <literal><![CDATA[
      L(K(x,T(T(y,z),u * z)),z,u) = (u * (K(x,y) * z)) / (u * z)
    ]]></literal>
    <justification jstring="[para(6390(a,1),6965(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6390 6965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7903">
    <literal><![CDATA[
      x / y != K(z,u) * K(z,K(u,w))
    ]]></literal>
    <literal><![CDATA[
      K(z,T(u,w)) * y = x
    ]]></literal>
    <justification jstring="[para(6788(a,2),7094(a,2,2))].">
      <j1 rule="para" parents="6788 7094"/>
    </justification>
  </clause>

  <clause id="7904">
    <literal><![CDATA[
      K(L(x,y,L(x,z,u)),T(w,L(x,z,u) * y)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(w,y)) = v5
    ]]></literal>
    <justification jstring="[para(7239(a,1),7069(a,1))].">
      <j1 rule="para" parents="7239 7069"/>
    </justification>
  </clause>

  <clause id="7905">
    <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(6762(a,1),7330(a,1,1))].">
      <j1 rule="para" parents="6762 7330"/>
    </justification>
  </clause>

  <clause id="7906">
    <literal><![CDATA[
      x * K(y,(x \ 1) * (z * x)) = K(y,L(z,x,x \ 1)) * x
    ]]></literal>
    <justification jstring="[para(4791(a,1),7342(a,1,2))].">
      <j1 rule="para" parents="4791 7342"/>
    </justification>
  </clause>

  <clause id="7907">
    <literal><![CDATA[
      K(x,L(x,y,y \ 1) \ z) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[para(167(a,1),7634(a,1,2)),flip(a)].">
      <j1 rule="para" parents="167 7634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7909">
    <literal><![CDATA[
      K((x \ 1) \ y,((x \ 1) \ y) \ z) = K((x \ 1) \ y,(x * y) \ z)
    ]]></literal>
    <justification jstring="[para(2660(a,1),7907(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2660 7907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7910">
    <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(674(a,1),7648(a,1,2))].">
      <j1 rule="para" parents="674 7648"/>
    </justification>
  </clause>

  <clause id="7911">
    <literal><![CDATA[
      K(x,a(K(x,y),z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(63,a,4940,a(flip),b,7910,a),flip(a)].">
      <j1 rule="hyper" parents="63 4940 7910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7913">
    <literal><![CDATA[
      T(x,a(K(x,y),z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(56,a,7911,a)].">
      <j1 rule="hyper" parents="56 7911"/>
    </justification>
  </clause>

  <clause id="7914">
    <literal><![CDATA[
      T(a(K(x,y),z,u),x) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(54,a,7913,a)].">
      <j1 rule="hyper" parents="54 7913"/>
    </justification>
  </clause>

  <clause id="7915">
    <literal><![CDATA[
      T(T(x,y),a(K(x,z),u,w)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(7913(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7913 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7916">
    <literal><![CDATA[
      K(x,y) * a(K(x,z),u,w) = a(K(x,z),u,w) * K(x,y)
    ]]></literal>
    <justification jstring="[para(7913(a,1),6357(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7913 6357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7917">
    <literal><![CDATA[
      K(a(K(x,y),z,u),w) * x = x * K(a(K(x,y),z,u),w)
    ]]></literal>
    <justification jstring="[para(7914(a,1),6357(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7914 6357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7918">
    <literal><![CDATA[
      K(T(x,y),y \ z) = K(x,z / (y * K(u,x)))
    ]]></literal>
    <justification jstring="[hyper(7654,a,7372,a)].">
      <j1 rule="hyper" parents="7654 7372"/>
    </justification>
  </clause>

  <clause id="7919">
    <literal><![CDATA[
      K(x,y / (z * K(u,x))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(7073,a,7918,a),flip(a)].">
      <j1 rule="hyper" parents="7073 7918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7920">
    <literal><![CDATA[
      K(x,y / (z * x)) = K(x,y / (x * z))
    ]]></literal>
    <justification jstring="[para(88(a,1),7919(a,1,2,2))].">
      <j1 rule="para" parents="88 7919"/>
    </justification>
  </clause>

  <clause id="7921">
    <literal><![CDATA[
      K(x,y / (z * T(u,x))) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[para(2087(a,1),7919(a,1,2,2))].">
      <j1 rule="para" parents="2087 7919"/>
    </justification>
  </clause>

  <clause id="7922">
    <literal><![CDATA[
      K(x,y / (T(z,x) / u)) = K(x,y / (z / u))
    ]]></literal>
    <justification jstring="[para(2170(a,1),7919(a,1,2,2))].">
      <j1 rule="para" parents="2170 7919"/>
    </justification>
  </clause>

  <clause id="7923">
    <literal><![CDATA[
      K(x,y / K(z,z \ K(u,x))) = K(x,y / (z * (K(u,x) / z)))
    ]]></literal>
    <justification jstring="[para(4297(a,1),7919(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4297 7919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7924">
    <literal><![CDATA[
      K(x,y / (T(z,x) * u)) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[para(4959(a,1),7919(a,1,2,2))].">
      <j1 rule="para" parents="4959 7919"/>
    </justification>
  </clause>

  <clause id="7925">
    <literal><![CDATA[
      K(x,y / (z * K(x,u))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(5995(a,1),7919(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5995 7919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7926">
    <literal><![CDATA[
      K(x,y / (K(x,z) * u)) = K(x,y / u)
    ]]></literal>
    <justification jstring="[para(6355(a,1),7919(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6355 7919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7927">
    <literal><![CDATA[
      K(x,R(y / x,x,z)) = K(x,(y * z) / (z * x))
    ]]></literal>
    <justification jstring="[para(108(a,2),7920(a,2,2)),flip(a)].">
      <j1 rule="para" parents="108 7920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7928">
    <literal><![CDATA[
      K(x,y / ((z / x) * u)) = K(x,y / ((x \ z) * u))
    ]]></literal>
    <justification jstring="[para(5966(a,1),7925(a,1,2,2))].">
      <j1 rule="para" parents="5966 7925"/>
    </justification>
  </clause>

  <clause id="7929">
    <literal><![CDATA[
      K(x,((y * K(x,z)) * u) / u) = K(x,R(y,K(x,z),u))
    ]]></literal>
    <justification jstring="[para(20(a,2),7926(a,1,2)),flip(a)].">
      <j1 rule="para" parents="20 7926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7930">
    <literal><![CDATA[
      K(x,y / (T(z \ T(u,z),x) / w)) = K(x,y / ((T(z,u) \ u) / w))
    ]]></literal>
    <justification jstring="[para(3770(a,1),7922(a,1,2,2,1))].">
      <j1 rule="para" parents="3770 7922"/>
    </justification>
  </clause>

  <clause id="7931">
    <literal><![CDATA[
      K(x,R(x \ y,x,z)) = K(x,(y * z) / (z * x))
    ]]></literal>
    <justification jstring="[hyper(63,a,4398,a(flip),b,7927,a)].">
      <j1 rule="hyper" parents="63 4398 7927"/>
    </justification>
  </clause>

  <clause id="7932">
    <literal><![CDATA[
      K(x,R(y,K(x,z),u)) = K(x,y * K(x,z))
    ]]></literal>
    <justification jstring="[para(11(a,1),7929(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11 7929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7933">
    <literal><![CDATA[
      K(x,R(y,K(x,z),u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,7414,a(flip),b,7932,a),flip(a)].">
      <j1 rule="hyper" parents="333 7414 7932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7936">
    <literal><![CDATA[
      K(x,R(R(y,K(x,z),u),w,v5)) = K(x,R(y,w,v5))
    ]]></literal>
    <justification jstring="[para(31(a,1),7933(a,1,2))].">
      <j1 rule="para" parents="31 7933"/>
    </justification>
  </clause>

  <clause id="7937">
    <literal><![CDATA[
      T(T(x,1 / y),K(z,1 / y)) = T(x,1 / T(y,z))
    ]]></literal>
    <justification jstring="[hyper(7757,a,6840,a),flip(a)].">
      <j1 rule="hyper" parents="7757 6840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7938">
    <literal><![CDATA[
      T(T(x,1 / (y / z)),K(u,z / y)) = T(x,1 / T(y / z,u))
    ]]></literal>
    <justification jstring="[para(5058(a,1),7937(a,1,2))].">
      <j1 rule="para" parents="5058 7937"/>
    </justification>
  </clause>

  <clause id="7939">
    <literal><![CDATA[
      T(x,1 / T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(1 / y,z)) = u
    ]]></literal>
    <justification jstring="[para(7937(a,1),6883(a,1))].">
      <j1 rule="para" parents="7937 6883"/>
    </justification>
  </clause>

  <clause id="7940">
    <literal><![CDATA[
      K(R(x,y / x,z),u) = K((y * z) / ((y / x) * z),T(u,y))
    ]]></literal>
    <justification jstring="[hyper(7064,a,7777,a)].">
      <j1 rule="hyper" parents="7064 7777"/>
    </justification>
  </clause>

  <clause id="7941">
    <literal><![CDATA[
      L(((x / y) / x) \ 1,(x / y) / x,x) = x / T(x * ((x / y) / x),y)
    ]]></literal>
    <justification jstring="[para(79(a,1),7801(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="79 7801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7942">
    <literal><![CDATA[
      L(K(x,T(y \ z,u)),y \ z,w) = K(x,T((z \ y) \ 1,u))
    ]]></literal>
    <justification jstring="[para(6365(a,2),7872(a,1,1))].">
      <j1 rule="para" parents="6365 7872"/>
    </justification>
  </clause>

  <clause id="7943">
    <literal><![CDATA[
      K(x,T(y,z * R(x,u,w))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,7751,a(flip),b,7899,a)].">
      <j1 rule="hyper" parents="63 7751 7899"/>
    </justification>
  </clause>

  <clause id="7945">
    <literal><![CDATA[
      K(x,T(y,z / R(x,u,w))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(12(a,1),7943(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 7943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7946">
    <literal><![CDATA[
      K(x,T(y,R(x,z,u) \ w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,7503,a(flip),b,7945,a)].">
      <j1 rule="hyper" parents="63 7503 7945"/>
    </justification>
  </clause>

  <clause id="7948">
    <literal><![CDATA[
      K(x,T(y,R(x,z,u) * w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[para(9(a,1),7946(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 7946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7949">
    <literal><![CDATA[
      K(x,T(y,(x * z) * u)) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(187(a,1),7946(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="187 7946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7950">
    <literal><![CDATA[
      K(x,T(y \ (R(x,z,u) * w),w)) = K(x,(R(x,z,u) * w) / y)
    ]]></literal>
    <justification jstring="[hyper(7225,a,7948,a),flip(a)].">
      <j1 rule="hyper" parents="7225 7948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7951">
    <literal><![CDATA[
      K(x,T(y,R(x,z,u) * w)) = K(x,y) * K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(333,a,6761,a,b,7948,a),flip(a)].">
      <j1 rule="hyper" parents="333 6761 7948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7952">
    <literal><![CDATA[
      K(x,K(y,R(x,z,u) * w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(7081,a,7951,a)].">
      <j1 rule="hyper" parents="7081 7951"/>
    </justification>
  </clause>

  <clause id="7953">
    <literal><![CDATA[
      K(x,K(y,(x * z) * u)) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[para(107(a,1),7952(a,1,2,2))].">
      <j1 rule="para" parents="107 7952"/>
    </justification>
  </clause>

  <clause id="7954">
    <literal><![CDATA[
      K(x,K(y,(y * z) * u)) = K(y,K(x,z * u))
    ]]></literal>
    <justification jstring="[hyper(6798,a,7953,a)].">
      <j1 rule="hyper" parents="6798 7953"/>
    </justification>
  </clause>

  <clause id="7955">
    <literal><![CDATA[
      K(x,K(y,z * u)) * K(y,x) = K(y,T(x,(x * z) * u))
    ]]></literal>
    <justification jstring="[para(7953(a,1),6818(a,1,1))].">
      <j1 rule="para" parents="7953 6818"/>
    </justification>
  </clause>

  <clause id="7956">
    <literal><![CDATA[
      K(x,T(y,(y * z) * u)) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(7125,a,7955,a),flip(a)].">
      <j1 rule="hyper" parents="7125 7955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7957">
    <literal><![CDATA[
      K(x,T(y,(y \ z) * u)) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(10(a,1),7956(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10 7956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7958">
    <literal><![CDATA[
      K(x \ y,T(x,y * z)) = K(x \ y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(6699,a,7957,a),flip(a)].">
      <j1 rule="hyper" parents="6699 7957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7959">
    <literal><![CDATA[
      K(x \ (y / z),T(x,z)) = K(x \ (y / z),T(x,y))
    ]]></literal>
    <justification jstring="[para(12(a,1),7958(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 7958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7960">
    <literal><![CDATA[
      K(x,T((y \ 1) * (z * y),y)) = K(x,L(z,y,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(35,a,6887,a,b,7906,a(flip))].">
      <j1 rule="hyper" parents="35 6887 7906"/>
    </justification>
  </clause>

  <clause id="7961">
    <literal><![CDATA[
      R(K((x / y) \ x,z),x,u) = K(R(y,x / y,u),z)
    ]]></literal>
    <justification jstring="[hyper(333,a,6487,a(flip),b,7940,a)].">
      <j1 rule="hyper" parents="333 6487 7940"/>
    </justification>
  </clause>

  <clause id="7962">
    <literal><![CDATA[
      K(R(x,y / x,z),u) = R(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(79(a,1),7961(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="79 7961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7963">
    <literal><![CDATA[
      R(K(x,y),z * x,u) = K(R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(11(a,1),7962(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="11 7962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7965">
    <literal><![CDATA[
      K(R(x,y,z),y) = K(x,R(y,x,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,5654,a(flip),b,7963,a),flip(a)].">
      <j1 rule="hyper" parents="63 5654 7963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7966">
    <literal><![CDATA[
      K(x,T((y \ z) \ 1,u)) = K(x,T(z \ y,u))
    ]]></literal>
    <justification jstring="[hyper(6638,a,7942,a),flip(a)].">
      <j1 rule="hyper" parents="6638 7942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7967">
    <literal><![CDATA[
      K(x,T((y \ z) \ 1,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z \ y,u)) = w
    ]]></literal>
    <justification jstring="[para(7942(a,1),372(a,1)),flip(b)].">
      <j1 rule="para" parents="7942 372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7968">
    <literal><![CDATA[
      K(x * ((y \ z) \ 1),T((y \ z) \ 1,u)) = K(((y \ z) \ 1) * x,T(z \ y,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,5207,a,b,7966,a)].">
      <j1 rule="hyper" parents="63 5207 7966"/>
    </justification>
  </clause>

  <clause id="7969">
    <literal><![CDATA[
      K(x,y \ ((z \ u) \ y)) = K(x,T(u \ z,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,6736,a(flip),b,7966,a)].">
      <j1 rule="hyper" parents="63 6736 7966"/>
    </justification>
  </clause>

  <clause id="7971">
    <literal><![CDATA[
      T(x,y \ ((z \ u) \ y)) = T(x,T(u \ z,y))
    ]]></literal>
    <justification jstring="[hyper(124,a,7969,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 7969 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7972">
    <literal><![CDATA[
      T(x,((y \ z) * u) \ u) = T(x,T(z \ y,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,6740,a,b,7971,a)].">
      <j1 rule="hyper" parents="63 6740 7971"/>
    </justification>
  </clause>

  <clause id="7973">
    <literal><![CDATA[
      T(x,T(y \ z,u) \ 1) = T(x,T(z \ y,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,6738,a,b,7971,a)].">
      <j1 rule="hyper" parents="63 6738 7971"/>
    </justification>
  </clause>

  <clause id="7974">
    <literal><![CDATA[
      T(x,y \ T(z,z \ y)) = T(x,T(y \ z,z))
    ]]></literal>
    <justification jstring="[para(5040(a,1),7972(a,1,2))].">
      <j1 rule="para" parents="5040 7972"/>
    </justification>
  </clause>

  <clause id="7975">
    <literal><![CDATA[
      T(x,y \ T(z,z \ y)) = T(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(333,a,6977,a(flip),b,7974,a),flip(a)].">
      <j1 rule="hyper" parents="333 6977 7974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7976">
    <literal><![CDATA[
      K(x,y \ ((z \ u) \ y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(u \ z,y)) = w
    ]]></literal>
    <justification jstring="[para(6736(a,1),7967(a,1))].">
      <j1 rule="para" parents="6736 7967"/>
    </justification>
  </clause>

  <clause id="7977">
    <literal><![CDATA[
      K(x,y \ (z \ y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z \ 1,y)) = u
    ]]></literal>
    <justification jstring="[para(65(a,1),7976(a,1,2,2,1))].">
      <j1 rule="para" parents="65 7976"/>
    </justification>
  </clause>

  <clause id="7978">
    <literal><![CDATA[
      ((x \ y) * K(z,y \ x)) * u = K(z,y \ x) * ((x \ y) * u)
    ]]></literal>
    <justification jstring="[para(2049(a,1),5793(a,1,1))].">
      <j1 rule="para" parents="2049 5793"/>
    </justification>
  </clause>

  <clause id="7979">
    <literal><![CDATA[
      (x * K((x \ y) \ 1,z)) / K((y / x) \ 1,z) = T(x,K(z,y \ x))
    ]]></literal>
    <justification jstring="[para(4486(a,1),5968(a,1,1))].">
      <j1 rule="para" parents="4486 5968"/>
    </justification>
  </clause>

  <clause id="7980">
    <literal><![CDATA[
      ((x * K(y,z)) * u) * K(z,((x / y) * u) \ (x * u)) = x * u
    ]]></literal>
    <justification jstring="[hyper(126,a,5991,a,b,xx)].">
      <j1 rule="hyper" parents="126 5991"/>
    </justification>
  </clause>

  <clause id="7981">
    <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(5432(a,1),5991(a,2,1))].">
      <j1 rule="para" parents="5432 5991"/>
    </justification>
  </clause>

  <clause id="7982">
    <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(4207(a,1),6027(a,1,1,1))].">
      <j1 rule="para" parents="4207 6027"/>
    </justification>
  </clause>

  <clause id="7983">
    <literal><![CDATA[
      T(x,y) / ((y \ 1) * K(x,y)) = x / (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(7982,a,5745,a)].">
      <j1 rule="hyper" parents="7982 5745"/>
    </justification>
  </clause>

  <clause id="7984">
    <literal><![CDATA[
      T(x,y) / (T(y,x) \ 1) = x / (y \ 1)
    ]]></literal>
    <justification jstring="[para(4219(a,1),7983(a,1,2))].">
      <j1 rule="para" parents="4219 7983"/>
    </justification>
  </clause>

  <clause id="7985">
    <literal><![CDATA[
      (x / (y \ 1)) \ T(x,y) = T(y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(192,a,7984,a)].">
      <j1 rule="hyper" parents="192 7984"/>
    </justification>
  </clause>

  <clause id="7986">
    <literal><![CDATA[
      (x / (y \ 1)) \ T(x,y) != z \ u
    ]]></literal>
    <literal><![CDATA[
      u / (T(y,x) \ 1) = z
    ]]></literal>
    <justification jstring="[para(7984(a,1),467(a,1,1))].">
      <j1 rule="para" parents="7984 467"/>
    </justification>
  </clause>

  <clause id="7987">
    <literal><![CDATA[
      T(x,y) / ((y \ 1) \ x) = (x / (y \ 1)) \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,5244,a,b,7985,a)].">
      <j1 rule="hyper" parents="333 5244 7985"/>
    </justification>
  </clause>

  <clause id="7988">
    <literal><![CDATA[
      ((x \ y) / (x \ 1)) \ T(x \ y,x) = (x \ y) / ((x \ 1) \ (y / x))
    ]]></literal>
    <justification jstring="[hyper(63,a,5351,a(flip),b,7987,a),flip(a)].">
      <j1 rule="hyper" parents="63 5351 7987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7989">
    <literal><![CDATA[
      ((x / y) / (y \ 1)) \ T(x / y,y) = (y \ x) / ((y \ 1) \ (x / y))
    ]]></literal>
    <justification jstring="[para(113(a,1),7987(a,1,1)),flip(a)].">
      <j1 rule="para" parents="113 7987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7990">
    <literal><![CDATA[
      x / (K(y,z) * T(y,u)) = (x / T(y,u)) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(6028,a,6941,a)].">
      <j1 rule="hyper" parents="6028 6941"/>
    </justification>
  </clause>

  <clause id="7992">
    <literal><![CDATA[
      x / (K(y,z) * T(z,u)) = (x / T(z,u)) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(6028,a,5442,a)].">
      <j1 rule="hyper" parents="6028 5442"/>
    </justification>
  </clause>

  <clause id="7993">
    <literal><![CDATA[
      (x / T(y,z)) * K(T(u,w),T(y,w)) = x / (K(y,u) * T(y,z))
    ]]></literal>
    <justification jstring="[para(6901(a,2),7990(a,2,2)),flip(a)].">
      <j1 rule="para" parents="6901 7990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7994">
    <literal><![CDATA[
      (x / T(y,y * z)) * K(y,z) = x / L(y,z,y)
    ]]></literal>
    <justification jstring="[para(4522(a,1),7992(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4522 7992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7995">
    <literal><![CDATA[
      (x / T(y,z)) * K(y,y * z) = x / R(y,z,y)
    ]]></literal>
    <justification jstring="[para(4523(a,1),7992(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4523 7992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7996">
    <literal><![CDATA[
      (x / y) * (K(y,z) * K(y * z,y)) = x / L(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,7847,a,b,7994,a)].">
      <j1 rule="hyper" parents="63 7847 7994"/>
    </justification>
  </clause>

  <clause id="7997">
    <literal><![CDATA[
      (x / T(y,z)) * T(y,y * z) = (x / R(y,z,y)) * y
    ]]></literal>
    <justification jstring="[hyper(125,a,7995,a(flip),b,5979,a),flip(a)].">
      <j1 rule="hyper" parents="125 7995 5979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7998">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,z * y) = (x / R(z,y,z)) * z
    ]]></literal>
    <justification jstring="[hyper(63,a,5989,a(flip),b,7997,a)].">
      <j1 rule="hyper" parents="63 5989 7997"/>
    </justification>
  </clause>

  <clause id="7999">
    <literal><![CDATA[
      x * (K(y,z) * K(z,z * y)) = (x / R(z,y,z)) * z
    ]]></literal>
    <justification jstring="[hyper(63,a,7834,a(flip),b,7998,a)].">
      <j1 rule="hyper" parents="63 7834 7998"/>
    </justification>
  </clause>

  <clause id="8000">
    <literal><![CDATA[
      (x / R(y,z,y)) * y = x * (y \ L(y,z,y))
    ]]></literal>
    <justification jstring="[para(4919(a,1),7999(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4919 7999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8001">
    <literal><![CDATA[
      R(x,y,x) \ x = x \ L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(6734,a,8000,a)].">
      <j1 rule="hyper" parents="6734 8000"/>
    </justification>
  </clause>

  <clause id="8002">
    <literal><![CDATA[
      x \ (x \ L(x,y,x)) = R(x,y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(121,a,8001,a(flip),b,1515,a)].">
      <j1 rule="hyper" parents="121 8001 1515"/>
    </justification>
  </clause>

  <clause id="8003">
    <literal><![CDATA[
      L(x \ 1,y,x) = R(x,y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(2591,a,8002,a)].">
      <j1 rule="hyper" parents="2591 8002"/>
    </justification>
  </clause>

  <clause id="8004">
    <literal><![CDATA[
      x \ ((x \ L(x,y,x)) * T(x,z)) = T(x,z) * (R(x,y,x) \ 1)
    ]]></literal>
    <justification jstring="[para(8002(a,1),2530(a,2,2))].">
      <j1 rule="para" parents="8002 2530"/>
    </justification>
  </clause>

  <clause id="8005">
    <literal><![CDATA[
      ((x * (y * z)) / L(T(z,u),y,x)) \ (x * y) = K(L(z,y,x),u)
    ]]></literal>
    <justification jstring="[para(25(a,2),6040(a,1,1,2))].">
      <j1 rule="para" parents="25 6040"/>
    </justification>
  </clause>

  <clause id="8006">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,y \ x) = K((x \ y) \ z,y \ x)
    ]]></literal>
    <justification jstring="[hyper(333,a,5766,a(flip),b,6162,a),flip(a)].">
      <j1 rule="hyper" parents="333 5766 6162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8007">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,y \ x) = K(z / (x \ y),y \ x)
    ]]></literal>
    <justification jstring="[hyper(333,a,6615,a,b,8006,a),flip(a)].">
      <j1 rule="hyper" parents="333 6615 8006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8008">
    <literal><![CDATA[
      K((((x * y) \ x) \ 1) * z,x \ (x * y)) = K(z / ((x * y) \ x),y)
    ]]></literal>
    <justification jstring="[para(9(a,1),8007(a,2,2))].">
      <j1 rule="para" parents="9 8007"/>
    </justification>
  </clause>

  <clause id="8012">
    <literal><![CDATA[
      K((x * y) \ T(x,z),u) = K(y \ K(x,z),u)
    ]]></literal>
    <justification jstring="[hyper(333,a,4688,a(flip),b,6238,a),flip(a)].">
      <j1 rule="hyper" parents="333 4688 6238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8013">
    <literal><![CDATA[
      K((x * y) \ T(x,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(y \ K(x,z),u) = w
    ]]></literal>
    <justification jstring="[para(6238(a,2),4730(a,1))].">
      <j1 rule="para" parents="6238 4730"/>
    </justification>
  </clause>

  <clause id="8014">
    <literal><![CDATA[
      K((x \ y) \ K(x,z),u) = K(y \ T(x,z),u)
    ]]></literal>
    <justification jstring="[para(10(a,1),8012(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 8012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8015">
    <literal><![CDATA[
      K(T(x / y,T(y,x)) \ K(y,z),u) = K(x \ T(y,z),u)
    ]]></literal>
    <justification jstring="[para(3383(a,2),8014(a,1,1,1))].">
      <j1 rule="para" parents="3383 8014"/>
    </justification>
  </clause>

  <clause id="8017">
    <literal><![CDATA[
      K(x \ (y * z),z) * K(z,z \ T(z * ((y \ x) \ 1),z)) = (y \ x) * (T(z * ((y \ x) \ 1),z) / z)
    ]]></literal>
    <justification jstring="[para(6296(a,1),5521(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6296 5521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8018">
    <literal><![CDATA[
      K(L(x,y,z),R(z,u,w)) = K(x,R(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(333,a,4950,a(flip),b,6309,a),flip(a)].">
      <j1 rule="hyper" parents="333 4950 6309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8019">
    <literal><![CDATA[
      K((x \ 1) \ y,R(x,z,u)) = K(x * y,R(x,z,u))
    ]]></literal>
    <justification jstring="[para(514(a,1),8018(a,1,1)),flip(a)].">
      <j1 rule="para" parents="514 8018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8020">
    <literal><![CDATA[
      K((x \ 1) * y,R(x \ 1,z,u)) = K(x \ y,R(x \ 1,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,4764,a(flip),b,8019,a),flip(a)].">
      <j1 rule="hyper" parents="63 4764 8019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8021">
    <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(6410(a,2),7321(a,1))].">
      <j1 rule="para" parents="6410 7321"/>
    </justification>
  </clause>

  <clause id="8022">
    <literal><![CDATA[
      K(x,y / z) * K(z \ y,z) = z \ (y / T(y / z,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,5475,a(flip),b,6498,a),flip(a)].">
      <j1 rule="hyper" parents="63 5475 6498"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8023">
    <literal><![CDATA[
      R(K(x,y),T(T(y,z),u),w) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(1924,a,6522,a)].">
      <j1 rule="hyper" parents="1924 6522"/>
    </justification>
  </clause>

  <clause id="8024">
    <literal><![CDATA[
      T(T(x,y),K(z,x)) * ((T(x,y) * K(z,x)) \ u) = K(z,x) \ u
    ]]></literal>
    <justification jstring="[para(8023(a,1),796(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8023 796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8025">
    <literal><![CDATA[
      K(x,y) * T(x * K(y,x),z) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(35,a,7720,a(flip),b,6601,a),flip(a)].">
      <j1 rule="hyper" parents="35 7720 6601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8027">
    <literal><![CDATA[
      K(x,y) \ T(x,T(z,y)) = T(x * K(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(129,a,8025,a)].">
      <j1 rule="hyper" parents="129 8025"/>
    </justification>
  </clause>

  <clause id="8028">
    <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(8027(a,1),273(a,1,2)),flip(b)].">
      <j1 rule="para" parents="8027 273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8029">
    <literal><![CDATA[
      K(x,(y \ K(x,z)) \ u) = (y \ T(y * u,x)) \ u
    ]]></literal>
    <justification jstring="[para(6660(a,1),5485(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6660 5485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8030">
    <literal><![CDATA[
      K(x,(y \ K(x,z)) \ u) = K(x,(y \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(333,a,5500,a(flip),b,8029,a),flip(a)].">
      <j1 rule="hyper" parents="333 5500 8029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8031">
    <literal><![CDATA[
      K(x,((y \ 1) \ K(x,z)) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[hyper(333,a,4795,a(flip),b,8030,a),flip(a)].">
      <j1 rule="hyper" parents="333 4795 8030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8033">
    <literal><![CDATA[
      K(x,y / (x / ((z * y) \ 1))) = y / (K(z \ (x \ 1),x) * y)
    ]]></literal>
    <justification jstring="[para(6732(a,1),5136(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6732 5136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8034">
    <literal><![CDATA[
      K((x \ y) \ ((x \ y) * z),x) = K(z,(x \ T(y,x)) \ y)
    ]]></literal>
    <justification jstring="[hyper(7208,a,6995,a)].">
      <j1 rule="hyper" parents="7208 6995"/>
    </justification>
  </clause>

  <clause id="8035">
    <literal><![CDATA[
      K(x,(y \ T(z,y)) \ z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(4614,a,8034,a),flip(a)].">
      <j1 rule="hyper" parents="4614 8034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8037">
    <literal><![CDATA[
      (1 / (x \ y)) * K(y / x,z) = K(y / x,z) / (x \ y)
    ]]></literal>
    <justification jstring="[para(6922(a,1),6999(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6922 6999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8038">
    <literal><![CDATA[
      K(1 / x,y) / (x \ 1) = x * K(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(351,a,8037,a),flip(a)].">
      <j1 rule="hyper" parents="351 8037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8039">
    <literal><![CDATA[
      1 / (x \ K(y,1 / x)) = x * K(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,5193,a(flip),b,8038,a)].">
      <j1 rule="hyper" parents="63 5193 8038"/>
    </justification>
  </clause>

  <clause id="8040">
    <literal><![CDATA[
      1 / ((x * (y \ 1)) / x) = y * K(1 / y,x)
    ]]></literal>
    <justification jstring="[para(4444(a,1),8039(a,1,2))].">
      <j1 rule="para" parents="4444 8039"/>
    </justification>
  </clause>

  <clause id="8041">
    <literal><![CDATA[
      1 / ((x * ((y / z) \ 1)) / x) = (y / z) * K(z / y,x)
    ]]></literal>
    <justification jstring="[para(4968(a,1),8040(a,2,2))].">
      <j1 rule="para" parents="4968 8040"/>
    </justification>
  </clause>

  <clause id="8042">
    <literal><![CDATA[
      K(T(x,y),((x \ 1) * y) \ z) = K(x,z / ((x \ 1) * y))
    ]]></literal>
    <justification jstring="[hyper(6613,a,7009,a)].">
      <j1 rule="hyper" parents="6613 7009"/>
    </justification>
  </clause>

  <clause id="8043">
    <literal><![CDATA[
      K(T(x,T(y,x)),((T(x,y) \ 1) * y) \ z) = K(x,z / ((x \ 1) * T(y,x)))
    ]]></literal>
    <justification jstring="[para(6049(a,2),8042(a,1,2,1))].">
      <j1 rule="para" parents="6049 8042"/>
    </justification>
  </clause>

  <clause id="8044">
    <literal><![CDATA[
      x / (K(T(y,z),x) * K(x,z)) = T(x * K(z,x),y)
    ]]></literal>
    <justification jstring="[para(4384(a,1),7012(a,1,2,2))].">
      <j1 rule="para" parents="4384 7012"/>
    </justification>
  </clause>

  <clause id="8045">
    <literal><![CDATA[
      T(x * K(y,x),z) \ x = K(T(z,y),x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(192,a,8044,a)].">
      <j1 rule="hyper" parents="192 8044"/>
    </justification>
  </clause>

  <clause id="8047">
    <literal><![CDATA[
      T((x * y) / x,z) \ y = K(T(z,x),y) * K(y,x)
    ]]></literal>
    <justification jstring="[para(4238(a,2),8045(a,1,1,1))].">
      <j1 rule="para" parents="4238 8045"/>
    </justification>
  </clause>

  <clause id="8048">
    <literal><![CDATA[
      T((x * y) / x,z) \ y = K(y,x) * K(T(z,x),y)
    ]]></literal>
    <justification jstring="[hyper(333,a,2005,a,b,8047,a),flip(a)].">
      <j1 rule="hyper" parents="333 2005 8047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8049">
    <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(1485(a,1),8048(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1485 8048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8050">
    <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="[hyper(35,a,3686,a(flip),b,7098,a),flip(a)].">
      <j1 rule="hyper" parents="35 3686 7098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8051">
    <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(7098(a,1),7714(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7098 7714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8052">
    <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(6799(a,1),7099(a,1,1))].">
      <j1 rule="para" parents="6799 7099"/>
    </justification>
  </clause>

  <clause id="8053">
    <literal><![CDATA[
      L(x,K(y,z) * (u * K(y,z)),w) = L(x,T(u,K(z,y)),w)
    ]]></literal>
    <justification jstring="[para(4367(a,1),7100(a,1,2,1))].">
      <j1 rule="para" parents="4367 7100"/>
    </justification>
  </clause>

  <clause id="8054">
    <literal><![CDATA[
      (x * K(y,z)) / T(z,u) = x / (K(z,y) * T(z,u))
    ]]></literal>
    <justification jstring="[para(6901(a,1),7110(a,1,1,2))].">
      <j1 rule="para" parents="6901 7110"/>
    </justification>
  </clause>

  <clause id="8055">
    <literal><![CDATA[
      (x * K(y,z)) / T(z,u) = (x / T(z,u)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,7990,a(flip),b,8054,a),flip(a)].">
      <j1 rule="hyper" parents="333 7990 8054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8056">
    <literal><![CDATA[
      1 / (K(x,y) * T(x,z)) = K(y,x) / T(x,z)
    ]]></literal>
    <justification jstring="[hyper(303,a,8054,a),flip(a)].">
      <j1 rule="hyper" parents="303 8054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8058">
    <literal><![CDATA[
      K(x,R(y,z * K(y,u),w)) = K(x,R(y,z,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,7768,a(flip),b,7112,a),flip(a)].">
      <j1 rule="hyper" parents="63 7768 7112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8060">
    <literal><![CDATA[
      K(x,R(y,T(z,y),u)) = K(x,R(y,z,u))
    ]]></literal>
    <justification jstring="[para(4207(a,1),8058(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4207 8058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8061">
    <literal><![CDATA[
      K(x,R(y,K(y,z) * u,w)) = K(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[para(6390(a,1),8058(a,1,2,2))].">
      <j1 rule="para" parents="6390 8058"/>
    </justification>
  </clause>

  <clause id="8062">
    <literal><![CDATA[
      R(K(x,y),z * y,u) = K(x,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,5655,a,b,8060,a)].">
      <j1 rule="hyper" parents="63 5655 8060"/>
    </justification>
  </clause>

  <clause id="8063">
    <literal><![CDATA[
      R(K(x,y \ z),z,u) = K(x,R(y \ z,y,u))
    ]]></literal>
    <justification jstring="[para(10(a,1),8062(a,1,2))].">
      <j1 rule="para" parents="10 8062"/>
    </justification>
  </clause>

  <clause id="8064">
    <literal><![CDATA[
      R(K(x,y),z * K(u,y),w) = K(x,R(y,z / T(y,u),w))
    ]]></literal>
    <justification jstring="[para(5444(a,1),8062(a,1,2))].">
      <j1 rule="para" parents="5444 8062"/>
    </justification>
  </clause>

  <clause id="8065">
    <literal><![CDATA[
      R(K(x,y),z * T(y,u),w) = K(x,R(y,z * K(y,u),w))
    ]]></literal>
    <justification jstring="[para(5982(a,1),8062(a,1,2))].">
      <j1 rule="para" parents="5982 8062"/>
    </justification>
  </clause>

  <clause id="8066">
    <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(7415(a,1),8062(a,1,1))].">
      <j1 rule="para" parents="7415 8062"/>
    </justification>
  </clause>

  <clause id="8067">
    <literal><![CDATA[
      K(R(x,K(x,y) * z,u),w) = (v5 * K(w,R(x,z,u))) \ v5
    ]]></literal>
    <justification jstring="[para(8061(a,1),5990(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="8061 5990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8068">
    <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(3033(a,1),8063(a,2,2))].">
      <j1 rule="para" parents="3033 8063"/>
    </justification>
  </clause>

  <clause id="8069">
    <literal><![CDATA[
      R(K(x,y),z * T(y,u),w) = K(x,R(y,z,w))
    ]]></literal>
    <justification jstring="[hyper(333,a,8058,a(flip),b,8065,a),flip(a)].">
      <j1 rule="hyper" parents="333 8058 8065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8071">
    <literal><![CDATA[
      K(x,R(y,z / T(y,u),w)) = R(K(x,y),z,w)
    ]]></literal>
    <justification jstring="[para(12(a,1),8069(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12 8069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8072">
    <literal><![CDATA[
      R(K(x,y),z * K(u,y),w) = R(K(x,y),z,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,8064,a,b,8071,a)].">
      <j1 rule="hyper" parents="63 8064 8071"/>
    </justification>
  </clause>

  <clause id="8073">
    <literal><![CDATA[
      R(K(x,y),K(z,y),u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(550,a,8072,a),flip(a)].">
      <j1 rule="hyper" parents="550 8072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8075">
    <literal><![CDATA[
      R(K(x,y),y \ K(y,z),u) = R(K(x,y),y \ 1,u)
    ]]></literal>
    <justification jstring="[para(6016(a,1),8072(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6016 8072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8076">
    <literal><![CDATA[
      R(K(x,y),K(z,y),u) = w / (K(y,x) * w)
    ]]></literal>
    <justification jstring="[hyper(333,a,4569,a,b,8073,a),flip(a)].">
      <j1 rule="hyper" parents="333 4569 8073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8077">
    <literal><![CDATA[
      (K(x,y) * K(z,x)) * u = K(x,y) * (K(z,x) * u)
    ]]></literal>
    <justification jstring="[hyper(36,a,5636,a,b,8076,a(flip))].">
      <j1 rule="hyper" parents="36 5636 8076"/>
    </justification>
  </clause>

  <clause id="8078">
    <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(8075(a,2),1627(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="8075 1627"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8079">
    <literal><![CDATA[
      L(x,K(y,z),K(z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(501,a,8077,a)].">
      <j1 rule="hyper" parents="501 8077"/>
    </justification>
  </clause>

  <clause id="8080">
    <literal><![CDATA[
      (K(x,y) * K(y,z)) * u = K(y,z) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[para(2005(a,1),8077(a,1,1))].">
      <j1 rule="para" parents="2005 8077"/>
    </justification>
  </clause>

  <clause id="8081">
    <literal><![CDATA[
      L(x,K(y,z),K(y,u)) = x
    ]]></literal>
    <justification jstring="[hyper(4391,a,8079,a)].">
      <j1 rule="hyper" parents="4391 8079"/>
    </justification>
  </clause>

  <clause id="8082">
    <literal><![CDATA[
      L(x,L(K(y,z),u,w),K(z,v5)) = x
    ]]></literal>
    <justification jstring="[para(5372(a,1),8079(a,1,2))].">
      <j1 rule="para" parents="5372 8079"/>
    </justification>
  </clause>

  <clause id="8083">
    <literal><![CDATA[
      L(x,K(y,z),K(u,K(z,w))) = x
    ]]></literal>
    <justification jstring="[para(6785(a,1),8079(a,1,3))].">
      <j1 rule="para" parents="6785 8079"/>
    </justification>
  </clause>

  <clause id="8084">
    <literal><![CDATA[
      (K(x,y) * K(x,z)) * u = K(x,y) * (K(x,z) * u)
    ]]></literal>
    <justification jstring="[hyper(1170,a,8081,a),flip(a)].">
      <j1 rule="hyper" parents="1170 8081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8085">
    <literal><![CDATA[
      (K(x,K(y,z)) * K(u,y)) * w = K(x,K(y,z)) * (K(u,y) * w)
    ]]></literal>
    <justification jstring="[hyper(1170,a,8083,a),flip(a)].">
      <j1 rule="hyper" parents="1170 8083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8086">
    <literal><![CDATA[
      (K(x,y) * L(K(z,x),u,w)) * v5 = K(x,y) * (L(K(z,x),u,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(1170,a,8082,a),flip(a)].">
      <j1 rule="hyper" parents="1170 8082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8087">
    <literal><![CDATA[
      K(x,y) * (K(x,K(y,z)) * u) = K(x,T(y,z)) * u
    ]]></literal>
    <justification jstring="[para(6761(a,1),8084(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6761 8084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8088">
    <literal><![CDATA[
      K(x,y) * (K(y,T(x,z)) * u) = K(y,K(x,z)) * u
    ]]></literal>
    <justification jstring="[hyper(4577,a,8087,a)].">
      <j1 rule="hyper" parents="4577 8087"/>
    </justification>
  </clause>

  <clause id="8089">
    <literal><![CDATA[
      T(K(x,y) \ T(K(x,T(y,z)) * u,w),K(x,y)) = K(x,y) \ T((K(x,K(y,z)) * u) * K(x,y),w)
    ]]></literal>
    <justification jstring="[para(8087(a,1),4112(a,1,1,2,1))].">
      <j1 rule="para" parents="8087 4112"/>
    </justification>
  </clause>

  <clause id="8090">
    <literal><![CDATA[
      K(R(x,K(x,y) * z,u),w) = K(R(x,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(333,a,5990,a(flip),b,8067,a),flip(a)].">
      <j1 rule="hyper" parents="333 5990 8067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8091">
    <literal><![CDATA[
      R(K(x,y),K(x,z) * u,w) = K(R(x,x \ u,w),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,5563,a(flip),b,8090,a)].">
      <j1 rule="hyper" parents="63 5563 8090"/>
    </justification>
  </clause>

  <clause id="8092">
    <literal><![CDATA[
      K(R(x,K(y,x) * z,u),w) = K(R(x,z,u),w)
    ]]></literal>
    <justification jstring="[para(4558(a,1),8090(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4558 8090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8094">
    <literal><![CDATA[
      R(K(x,y),K(x,z) * u,w) = R(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(333,a,5560,a(flip),b,8091,a),flip(a)].">
      <j1 rule="hyper" parents="333 5560 8091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8095">
    <literal><![CDATA[
      R(K(x,y),z / x,u) = R(K(x,y),x \ z,u)
    ]]></literal>
    <justification jstring="[para(4312(a,1),8094(a,1,2))].">
      <j1 rule="para" parents="4312 8094"/>
    </justification>
  </clause>

  <clause id="8096">
    <literal><![CDATA[
      R(K(x,y),z * (K(u,x) * w),v5) = R(K(x,y),z * w,v5)
    ]]></literal>
    <justification jstring="[para(5354(a,1),8094(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5354 8094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8097">
    <literal><![CDATA[
      R(K(x,y),x \ y,z) * ((y / T(x,y)) * z) = (y / x) * z
    ]]></literal>
    <justification jstring="[para(8095(a,1),5639(a,1,1))].">
      <j1 rule="para" parents="8095 5639"/>
    </justification>
  </clause>

  <clause id="8098">
    <literal><![CDATA[
      R(K(x,y),z * (u * K(w,x)),v5) = R(K(x,y),z * u,v5)
    ]]></literal>
    <justification jstring="[para(6888(a,1),8096(a,1,2,2))].">
      <j1 rule="para" parents="6888 8096"/>
    </justification>
  </clause>

  <clause id="8099">
    <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(8097(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="8097 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8101">
    <literal><![CDATA[
      T(x,y / z) * K(z \ y,z) = (y / z) \ (x * (z \ y))
    ]]></literal>
    <justification jstring="[hyper(333,a,5034,a(flip),b,7235,a),flip(a)].">
      <j1 rule="hyper" parents="333 5034 7235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8102">
    <literal><![CDATA[
      x \ ((y / z) \ (x * (z \ y))) = K(x,y / z) * K(z \ y,z)
    ]]></literal>
    <justification jstring="[hyper(121,a,8101,a(flip),b,4241,a)].">
      <j1 rule="hyper" parents="121 8101 4241"/>
    </justification>
  </clause>

  <clause id="8103">
    <literal><![CDATA[
      x * (K(y,z) * L(T(y,x),u,w)) = L(y,u,w) * (x * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(5441,a,7376,a)].">
      <j1 rule="hyper" parents="5441 7376"/>
    </justification>
  </clause>

  <clause id="8104">
    <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(6101(a,1),7539(a,1,1,2))].">
      <j1 rule="para" parents="6101 7539"/>
    </justification>
  </clause>

  <clause id="8105">
    <literal><![CDATA[
      T(K(x,y),T(z,u * x)) = T(K(x,y),T(z,x * u))
    ]]></literal>
    <justification jstring="[hyper(7311,a,7563,a),flip(a)].">
      <j1 rule="hyper" parents="7311 7563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8106">
    <literal><![CDATA[
      T(K(x,y \ (z * x)),T(y,x * z)) = T(K(x,y \ (z * x)),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,6462,a(flip),b,8105,a),flip(a)].">
      <j1 rule="hyper" parents="63 6462 8105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8107">
    <literal><![CDATA[
      K(x,(1 / y) * ((z \ ((1 / y) \ 1)) * z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(333,a,7140,a(flip),b,7579,a),flip(a)].">
      <j1 rule="hyper" parents="333 7140 7579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8108">
    <literal><![CDATA[
      K(x,(1 / y) * ((z \ y) * z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(79(a,1),8107(a,1,2,2,1,2))].">
      <j1 rule="para" parents="79 8107"/>
    </justification>
  </clause>

  <clause id="8109">
    <literal><![CDATA[
      K(x,(y \ 1) * ((z \ y) * z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,4791,a(flip),b,8108,a)].">
      <j1 rule="hyper" parents="63 4791 8108"/>
    </justification>
  </clause>

  <clause id="8110">
    <literal><![CDATA[
      K(x,T(x \ y,z)) * (K(y,z) * x) = T(x,x \ y) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5669,a(flip),b,7591,a),flip(a)].">
      <j1 rule="hyper" parents="63 5669 7591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8111">
    <literal><![CDATA[
      K((x * (y * z)) \ u,z) = K((x * y) \ (z \ u),z)
    ]]></literal>
    <justification jstring="[hyper(6024,a,7635,a),flip(a)].">
      <j1 rule="hyper" parents="6024 7635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8112">
    <literal><![CDATA[
      K((x * (y * z)) \ u,y) = K((x * z) \ (y \ u),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,7608,a(flip),b,8111,a)].">
      <j1 rule="hyper" parents="63 7608 8111"/>
    </justification>
  </clause>

  <clause id="8114">
    <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(7682(a,2),6024(a,1,1))].">
      <j1 rule="para" parents="7682 6024"/>
    </justification>
  </clause>

  <clause id="8115">
    <literal><![CDATA[
      K((((x * y) \ x) \ 1) * z,y) = K(z * (1 / ((x * y) \ x)),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,4762,a(flip),b,7698,a)].">
      <j1 rule="hyper" parents="63 4762 7698"/>
    </justification>
  </clause>

  <clause id="8116">
    <literal><![CDATA[
      ((x \ 1) * y) * K(x,z) = (x \ 1) * (y * K(x,z))
    ]]></literal>
    <justification jstring="[hyper(300,a,7870,a)].">
      <j1 rule="hyper" parents="300 7870"/>
    </justification>
  </clause>

  <clause id="8117">
    <literal><![CDATA[
      L(K(x,y),z,x \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(2942,a,8116,a)].">
      <j1 rule="hyper" parents="2942 8116"/>
    </justification>
  </clause>

  <clause id="8118">
    <literal><![CDATA[
      ((x \ 1) * (y * K(x,z))) \ ((x \ 1) * y) = K(z,x)
    ]]></literal>
    <justification jstring="[para(8116(a,1),5990(a,1,1))].">
      <j1 rule="para" parents="8116 5990"/>
    </justification>
  </clause>

  <clause id="8120">
    <literal><![CDATA[
      L(K(x \ 1,y),z,x) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3144,a(flip),b,8117,a)].">
      <j1 rule="hyper" parents="63 3144 8117"/>
    </justification>
  </clause>

  <clause id="8121">
    <literal><![CDATA[
      (x * y) * K(x \ 1,z) = x * (y * K(x \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(126,a,8120,a(flip),b,3220,a(flip))].">
      <j1 rule="hyper" parents="126 8120 3220"/>
    </justification>
  </clause>

  <clause id="8122">
    <literal><![CDATA[
      R(x,y,K(x \ 1,z)) = x
    ]]></literal>
    <justification jstring="[hyper(543,a,8121,a)].">
      <j1 rule="hyper" parents="543 8121"/>
    </justification>
  </clause>

  <clause id="8123">
    <literal><![CDATA[
      R(T(x,y),z,K(x \ 1,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(8122(a,1),27(a,2,1))].">
      <j1 rule="para" parents="8122 27"/>
    </justification>
  </clause>

  <clause id="8124">
    <literal><![CDATA[
      (K(x,y) * K(x * y,z)) * (y * x) = T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,4558,a(flip),b,7898,a),flip(a)].">
      <j1 rule="hyper" parents="333 4558 7898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8125">
    <literal><![CDATA[
      K(x,y / (z * (K(u,x) / z))) = K(x,y * K(z \ K(u,x),z))
    ]]></literal>
    <justification jstring="[para(5994(a,1),7923(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5994 7923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8126">
    <literal><![CDATA[
      T(T(x,1 / (y / z)),K(y,z)) = T(x,1 / T(y / z,y))
    ]]></literal>
    <justification jstring="[hyper(7203,a,7938,a)].">
      <j1 rule="hyper" parents="7203 7938"/>
    </justification>
  </clause>

  <clause id="8127">
    <literal><![CDATA[
      T(T(x,1 / (y / z)),K(z,z / y)) = T(x,1 / (z \ y))
    ]]></literal>
    <justification jstring="[para(113(a,1),7938(a,2,2,2))].">
      <j1 rule="para" parents="113 7938"/>
    </justification>
  </clause>

  <clause id="8128">
    <literal><![CDATA[
      T(T(x,1 / (y / z)),K(y,z)) = T(x,1 / (z \ y))
    ]]></literal>
    <justification jstring="[hyper(63,a,7186,a(flip),b,8127,a)].">
      <j1 rule="hyper" parents="63 7186 8127"/>
    </justification>
  </clause>

  <clause id="8129">
    <literal><![CDATA[
      T(x,1 / T(y / z,y)) = T(x,1 / (z \ y))
    ]]></literal>
    <justification jstring="[hyper(63,a,8126,a(flip),b,8128,a)].">
      <j1 rule="hyper" parents="63 8126 8128"/>
    </justification>
  </clause>

  <clause id="8130">
    <literal><![CDATA[
      T(x,T(1 / (y / z),y)) = T(x,1 / (z \ y))
    ]]></literal>
    <justification jstring="[hyper(7939,a,8129,a)].">
      <j1 rule="hyper" parents="7939 8129"/>
    </justification>
  </clause>

  <clause id="8131">
    <literal><![CDATA[
      T(x,1 / ((y \ z) \ z)) = T(x,T(1 / y,z))
    ]]></literal>
    <justification jstring="[para(76(a,1),8130(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="76 8130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8132">
    <literal><![CDATA[
      T(x,T(1 / (y \ z),z)) = T(x,1 / (z / y))
    ]]></literal>
    <justification jstring="[hyper(63,a,7296,a(flip),b,8131,a),flip(a)].">
      <j1 rule="hyper" parents="63 7296 8131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8133">
    <literal><![CDATA[
      T(x,K(y,z / y) / (z \ y)) = T(x,1 / (y / z))
    ]]></literal>
    <justification jstring="[hyper(63,a,7250,a,b,8132,a)].">
      <j1 rule="hyper" parents="63 7250 8132"/>
    </justification>
  </clause>

  <clause id="8134">
    <literal><![CDATA[
      ((x * K(y,z)) * K(y,u)) * K(z,y) = x * K(y,u)
    ]]></literal>
    <justification jstring="[para(6062(a,1),7980(a,1,2,2))].">
      <j1 rule="para" parents="6062 7980"/>
    </justification>
  </clause>

  <clause id="8135">
    <literal><![CDATA[
      K(x,T(y,(z * K(u,x)) * w)) = K(x,T(y,z * w))
    ]]></literal>
    <justification jstring="[para(7980(a,1),7493(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7980 7493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8136">
    <literal><![CDATA[
      K(x,((y * K(z,x)) * u) \ w) = K(x,(y * u) \ w)
    ]]></literal>
    <justification jstring="[para(7980(a,1),7643(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7980 7643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8137">
    <literal><![CDATA[
      K(x / ((y * K(z,u)) * w),u) = K(x / (y * w),u)
    ]]></literal>
    <justification jstring="[para(7980(a,1),7789(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7980 7789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8138">
    <literal><![CDATA[
      K(x,y / ((z * K(u,x)) * w)) = K(x,y / (z * w))
    ]]></literal>
    <justification jstring="[para(7980(a,1),7925(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7980 7925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8140">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,y) = (x * K(u,y)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(5995(a,1),8134(a,1,1,1))].">
      <j1 rule="para" parents="5995 8134"/>
    </justification>
  </clause>

  <clause id="8141">
    <literal><![CDATA[
      K(x,T(y,(z * x) * u)) = K(x,T(y,(x * z) * u))
    ]]></literal>
    <justification jstring="[para(88(a,1),8135(a,1,2,2,1))].">
      <j1 rule="para" parents="88 8135"/>
    </justification>
  </clause>

  <clause id="8142">
    <literal><![CDATA[
      K(x,(((x \ y) * x) * z) \ u) = K(x,(y * z) \ u)
    ]]></literal>
    <justification jstring="[para(317(a,1),8136(a,1,2,1,1))].">
      <j1 rule="para" parents="317 8136"/>
    </justification>
  </clause>

  <clause id="8143">
    <literal><![CDATA[
      K(x / ((T(y,z) \ 1) * u),y) = K(x / ((y \ 1) * u),y)
    ]]></literal>
    <justification jstring="[para(4219(a,1),8137(a,1,1,2,1))].">
      <j1 rule="para" parents="4219 8137"/>
    </justification>
  </clause>

  <clause id="8144">
    <literal><![CDATA[
      K(x / ((K(y,z) * u) * w),y) = K(x / (u * w),y)
    ]]></literal>
    <justification jstring="[para(6355(a,1),8137(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6355 8137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8145">
    <literal><![CDATA[
      K(x,y / ((z * x) * u)) = K(x,y / ((x * z) * u))
    ]]></literal>
    <justification jstring="[para(88(a,1),8138(a,1,2,2,1))].">
      <j1 rule="para" parents="88 8138"/>
    </justification>
  </clause>

  <clause id="8146">
    <literal><![CDATA[
      K(x,y / (((x \ z) * x) * u)) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[para(317(a,1),8138(a,1,2,2,1))].">
      <j1 rule="para" parents="317 8138"/>
    </justification>
  </clause>

  <clause id="8147">
    <literal><![CDATA[
      K(x,y / ((K(x,z) * u) * w)) = K(x,y / (u * w))
    ]]></literal>
    <justification jstring="[para(6355(a,1),8138(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="6355 8138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8148">
    <literal><![CDATA[
      K(x,y / ((K(z,x) * u) * w)) = K(x,y / (u * w))
    ]]></literal>
    <justification jstring="[para(6357(a,1),8138(a,1,2,2,1))].">
      <j1 rule="para" parents="6357 8138"/>
    </justification>
  </clause>

  <clause id="8149">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,y) = x * (K(y,z) * K(u,y))
    ]]></literal>
    <justification jstring="[hyper(333,a,7840,a(flip),b,8140,a),flip(a)].">
      <j1 rule="hyper" parents="333 7840 8140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8151">
    <literal><![CDATA[
      ((x * K(y,z)) * K(z,u)) / z = (x * K(z,u)) / T(z,y)
    ]]></literal>
    <justification jstring="[hyper(123,a,8140,a(flip),b,5444,a)].">
      <j1 rule="hyper" parents="123 8140 5444"/>
    </justification>
  </clause>

  <clause id="8152">
    <literal><![CDATA[
      K(x,T(y,(z * x) * u)) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(333,a,7949,a(flip),b,8141,a),flip(a)].">
      <j1 rule="hyper" parents="333 7949 8141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8153">
    <literal><![CDATA[
      K(x,T(y / ((z * x) * u),z * u)) = K(x,((z * x) * u) \ y)
    ]]></literal>
    <justification jstring="[para(113(a,1),8152(a,1,2)),flip(a)].">
      <j1 rule="para" parents="113 8152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8155">
    <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(8144(a,1),7855(a,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8144 7855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8156">
    <literal><![CDATA[
      K(x,y / ((z * (K(u,x) * w)) * v5)) = K(x,y / ((z * w) * v5))
    ]]></literal>
    <justification jstring="[para(5354(a,1),8147(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5354 8147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8157">
    <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(541(a,1),8148(a,1,2))].">
      <j1 rule="para" parents="541 8148"/>
    </justification>
  </clause>

  <clause id="8158">
    <literal><![CDATA[
      L(K(x,y),K(y,z),u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(501,a,8149,a)].">
      <j1 rule="hyper" parents="501 8149"/>
    </justification>
  </clause>

  <clause id="8159">
    <literal><![CDATA[
      (x * K(y,z)) \ (x * K(y,u)) = K(y,u) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(121,a,8134,a(flip),b,8149,a(flip))].">
      <j1 rule="hyper" parents="121 8134 8149"/>
    </justification>
  </clause>

  <clause id="8160">
    <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(2836(a,1),8149(a,1,1))].">
      <j1 rule="para" parents="2836 8149"/>
    </justification>
  </clause>

  <clause id="8161">
    <literal><![CDATA[
      L(K(x,y),K(z,y),u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(4391,a,8158,a)].">
      <j1 rule="hyper" parents="4391 8158"/>
    </justification>
  </clause>

  <clause id="8162">
    <literal><![CDATA[
      L(L(K(x,y),z,u),K(y,w),v5) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(8158(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8158 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8163">
    <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(8158(a,1),306(a,1,2))].">
      <j1 rule="para" parents="8158 306"/>
    </justification>
  </clause>

  <clause id="8165">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,z) = x * (K(y,z) * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(126,a,8161,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="126 8161 18"/>
    </justification>
  </clause>

  <clause id="8167">
    <literal><![CDATA[
      ((x * K(y,z)) / z) * K(z,u) = (x * K(z,u)) / T(z,y)
    ]]></literal>
    <justification jstring="[hyper(6120,a,8151,a)].">
      <j1 rule="hyper" parents="6120 8151"/>
    </justification>
  </clause>

  <clause id="8168">
    <literal><![CDATA[
      (x * K(y,z)) / T(y,u) = (x / T(y,u)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(5460(a,1),8167(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5460 8167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8169">
    <literal><![CDATA[
      (1 / T(x,y)) * K(x,z) = K(x,z) / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(303,a,8168,a),flip(a)].">
      <j1 rule="hyper" parents="303 8168"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8170">
    <literal><![CDATA[
      ((x / T(y,z)) * K(y,u)) \ (x * K(y,u)) = T(y,z)
    ]]></literal>
    <justification jstring="[hyper(192,a,8168,a)].">
      <j1 rule="hyper" parents="192 8168"/>
    </justification>
  </clause>

  <clause id="8171">
    <literal><![CDATA[
      ((x \ y) * K(x,z)) \ (y * K(x,z)) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(281(a,1),8170(a,1,1,1))].">
      <j1 rule="para" parents="281 8170"/>
    </justification>
  </clause>

  <clause id="8172">
    <literal><![CDATA[
      x \ ((x \ L(x,y,x)) * T(x,z)) = R(x,y,x) \ T(x,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,1791,a(flip),b,8004,a),flip(a)].">
      <j1 rule="hyper" parents="333 1791 8004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8173">
    <literal><![CDATA[
      x \ (K(x,y) * L(x,z,x)) = R(x,z,x) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(4534(a,1),8172(a,1,2))].">
      <j1 rule="para" parents="4534 8172"/>
    </justification>
  </clause>

  <clause id="8174">
    <literal><![CDATA[
      R(x,y,x) \ T(x,z) = x \ L(T(x,z),y,x)
    ]]></literal>
    <justification jstring="[para(6317(a,1),8173(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6317 8173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8175">
    <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(8174(a,1),6229(a,2,1))].">
      <j1 rule="para" parents="8174 6229"/>
    </justification>
  </clause>

  <clause id="8176">
    <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(8174(a,1),7442(a,1,2,1))].">
      <j1 rule="para" parents="8174 7442"/>
    </justification>
  </clause>

  <clause id="8177">
    <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(690(a,1),8020(a,1,2)),flip(a)].">
      <j1 rule="para" parents="690 8020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8178">
    <literal><![CDATA[
      T(T(x,y),K(z,x)) * ((T(x,y) * K(z,x)) \ u) = K(x,z) * u
    ]]></literal>
    <justification jstring="[hyper(333,a,4567,a(flip),b,8024,a),flip(a)].">
      <j1 rule="hyper" parents="333 4567 8024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8179">
    <literal><![CDATA[
      K(x,y / (x / ((z * y) \ 1))) = K(x,z \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(333,a,4569,a(flip),b,8033,a),flip(a)].">
      <j1 rule="hyper" parents="333 4569 8033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8181">
    <literal><![CDATA[
      K(x,y / (x * (z * y))) = K(x,z \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,5221,a(flip),b,8179,a)].">
      <j1 rule="hyper" parents="63 5221 8179"/>
    </justification>
  </clause>

  <clause id="8182">
    <literal><![CDATA[
      K(x,y / ((z * y) * x)) = K(x,z \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,7920,a,b,8181,a)].">
      <j1 rule="hyper" parents="63 7920 8181"/>
    </justification>
  </clause>

  <clause id="8183">
    <literal><![CDATA[
      K(x,(y / z) \ (x \ 1)) = K(x,z / (y * x))
    ]]></literal>
    <justification jstring="[para(12(a,1),8182(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="12 8182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8184">
    <literal><![CDATA[
      K(x,(y * (z / y)) / ((z / y) * x)) = K(x,((y \ z) / z) \ (x \ 1))
    ]]></literal>
    <justification jstring="[para(3814(a,1),8182(a,1,2,2,1))].">
      <j1 rule="para" parents="3814 8182"/>
    </justification>
  </clause>

  <clause id="8185">
    <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(63,a,6632,a,b,8052,a)].">
      <j1 rule="hyper" parents="63 6632 8052"/>
    </justification>
  </clause>

  <clause id="8186">
    <literal><![CDATA[
      R(K(x,y),z * y,u) = K(x,R(y * K(w,x),z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,8098,a(flip),b,8066,a)].">
      <j1 rule="hyper" parents="63 8098 8066"/>
    </justification>
  </clause>

  <clause id="8188">
    <literal><![CDATA[
      K(x,R(y * K(z,x),u,w)) = K(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,8062,a(flip),b,8186,a),flip(a)].">
      <j1 rule="hyper" parents="63 8062 8186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8189">
    <literal><![CDATA[
      K(x,R(y * K(x,z),u,w)) = K(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[para(5995(a,1),8188(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5995 8188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8190">
    <literal><![CDATA[
      R(x,T(K(y,z),x),T(K(u,K(z,w)),K(y,z) * x)) \ ((K(u,K(z,w)) * K(y,z)) * x) = T(K(y,z),x) * T(K(u,K(z,w)),K(y,z) * x)
    ]]></literal>
    <justification jstring="[para(8085(a,2),946(a,1,2))].">
      <j1 rule="para" parents="8085 946"/>
    </justification>
  </clause>

  <clause id="8191">
    <literal><![CDATA[
      x \ ((y / z) \ (x * (z \ y))) = z \ (y / T(y / z,x))
    ]]></literal>
    <justification jstring="[hyper(333,a,8022,a(flip),b,8102,a),flip(a)].">
      <j1 rule="hyper" parents="333 8022 8102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8192">
    <literal><![CDATA[
      L(L(T(x,y),z,u),K(x,w),y) \ (L(x,z,u) * (y * K(x,w))) = T(y * K(x,w),L(L(T(x,y),z,u),K(x,w),y))
    ]]></literal>
    <justification jstring="[hyper(507,a,8103,a),flip(a)].">
      <j1 rule="hyper" parents="507 8103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8193">
    <literal><![CDATA[
      T(K(x,y \ (z * x)),T(y,z)) = T(K(x,y \ (z * x)),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,7774,a(flip),b,8106,a)].">
      <j1 rule="hyper" parents="63 7774 8106"/>
    </justification>
  </clause>

  <clause id="8194">
    <literal><![CDATA[
      K(x,T(y \ (z * x),T(y,z))) = T(K(x,y \ (z * x)),y)
    ]]></literal>
    <justification jstring="[hyper(6691,a,8193,a)].">
      <j1 rule="hyper" parents="6691 8193"/>
    </justification>
  </clause>

  <clause id="8195">
    <literal><![CDATA[
      K((((x * y) \ x) \ 1) * z,y) = K(z * (((x * y) \ x) \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(333,a,4757,a(flip),b,8115,a),flip(a)].">
      <j1 rule="hyper" parents="333 4757 8115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8196">
    <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(63,a,5027,a(flip),b,8125,a),flip(a)].">
      <j1 rule="hyper" parents="63 5027 8125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8197">
    <literal><![CDATA[
      T(T(x,K(y,x)),z * x) * ((T(x,x * z) * K(y,x)) \ u) = K(x,y) * u
    ]]></literal>
    <justification jstring="[para(3685(a,1),8178(a,1,1))].">
      <j1 rule="para" parents="3685 8178"/>
    </justification>
  </clause>

  <clause id="8198">
    <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(7328,a,8185,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="7328 8185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8199">
    <literal><![CDATA[
      (x * K(y,z)) * (K(z,y) * L(K(u,z),w,v5)) = x * L(K(u,z),w,v5)
    ]]></literal>
    <justification jstring="[para(8162(a,1),6036(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8162 6036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8200">
    <literal><![CDATA[
      (x * y) \ (y * T(x,z)) = K(y,x) * K(x,z)
    ]]></literal>
    <justification jstring="[para(7839(a,1),6081(a,1,1))].">
      <j1 rule="para" parents="7839 6081"/>
    </justification>
  </clause>

  <clause id="8201">
    <literal><![CDATA[
      (x * y) \ (y * T(x,z)) = K(x,z) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,2005,a,b,8200,a),flip(a)].">
      <j1 rule="hyper" parents="333 2005 8200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8202">
    <literal><![CDATA[
      K(x,y) * K(y,y \ x) = a(y,x / y,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3772,a(flip),b,8200,a),flip(a)].">
      <j1 rule="hyper" parents="63 3772 8200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8203">
    <literal><![CDATA[
      (x * y) \ (y * T(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) * K(y,x) = u
    ]]></literal>
    <justification jstring="[para(8200(a,2),2011(a,1))].">
      <j1 rule="para" parents="8200 2011"/>
    </justification>
  </clause>

  <clause id="8205">
    <literal><![CDATA[
      x \ R(x,x \ y,x) = a(x,y / x,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,4926,a,b,8202,a)].">
      <j1 rule="hyper" parents="63 4926 8202"/>
    </justification>
  </clause>

  <clause id="8206">
    <literal><![CDATA[
      a(x,y / x,x) \ K(y,x) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[para(8202(a,1),5990(a,1,1))].">
      <j1 rule="para" parents="8202 5990"/>
    </justification>
  </clause>

  <clause id="8207">
    <literal><![CDATA[
      a(x,y / x,x) * K(x,y) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(8202(a,1),6018(a,1,1))].">
      <j1 rule="para" parents="8202 6018"/>
    </justification>
  </clause>

  <clause id="8208">
    <literal><![CDATA[
      a(x,(x * y) / x,x) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),8205(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 8205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8209">
    <literal><![CDATA[
      x \ R(x,T(y,x),x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[para(239(a,1),8208(a,1,2)),flip(a)].">
      <j1 rule="para" parents="239 8208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8210">
    <literal><![CDATA[
      x \ R(x,y,x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[para(3858(a,1),8209(a,1,2))].">
      <j1 rule="para" parents="3858 8209"/>
    </justification>
  </clause>

  <clause id="8211">
    <literal><![CDATA[
      K(x,y) * K(x * y,x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(4927,a,8210,a)].">
      <j1 rule="hyper" parents="4927 8210"/>
    </justification>
  </clause>

  <clause id="8212">
    <literal><![CDATA[
      K(x * y,x) * K(x,y) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(4922,a,8210,a)].">
      <j1 rule="hyper" parents="4922 8210"/>
    </justification>
  </clause>

  <clause id="8213">
    <literal><![CDATA[
      R(x,y,x) / x = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(3034,a,8210,a)].">
      <j1 rule="hyper" parents="3034 8210"/>
    </justification>
  </clause>

  <clause id="8214">
    <literal><![CDATA[
      x * a(x,y,x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(142,a,8210,a)].">
      <j1 rule="hyper" parents="142 8210"/>
    </justification>
  </clause>

  <clause id="8215">
    <literal><![CDATA[
      L(x,y,x) \ x = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,6689,a,b,8210,a)].">
      <j1 rule="hyper" parents="63 6689 8210"/>
    </justification>
  </clause>

  <clause id="8216">
    <literal><![CDATA[
      T(x,y) \ R(T(x,y),z,x) = a(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,6561,a,b,8210,a)].">
      <j1 rule="hyper" parents="63 6561 8210"/>
    </justification>
  </clause>

  <clause id="8217">
    <literal><![CDATA[
      K(x,y) * K(y * x,x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,4923,a,b,8210,a)].">
      <j1 rule="hyper" parents="63 4923 8210"/>
    </justification>
  </clause>

  <clause id="8219">
    <literal><![CDATA[
      K(x,y) * K(y,y \ x) = a(y,y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,4926,a(flip),b,8210,a)].">
      <j1 rule="hyper" parents="63 4926 8210"/>
    </justification>
  </clause>

  <clause id="8221">
    <literal><![CDATA[
      T(x,y) * a(x,z,x) = R(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[hyper(126,a,8210,a(flip),b,6561,a)].">
      <j1 rule="hyper" parents="126 8210 6561"/>
    </justification>
  </clause>

  <clause id="8222">
    <literal><![CDATA[
      a(x,y,x) * x = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(125,a,8210,a(flip),b,3022,a)].">
      <j1 rule="hyper" parents="125 8210 3022"/>
    </justification>
  </clause>

  <clause id="8223">
    <literal><![CDATA[
      a(x,y,x) != x \ z
    ]]></literal>
    <literal><![CDATA[
      R(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(8210(a,1),47(a,1))].">
      <j1 rule="para" parents="8210 47"/>
    </justification>
  </clause>

  <clause id="8224">
    <literal><![CDATA[
      a(x,y,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * K(x * y,x) = z
    ]]></literal>
    <justification jstring="[para(8210(a,1),4927(a,1))].">
      <j1 rule="para" parents="8210 4927"/>
    </justification>
  </clause>

  <clause id="8225">
    <literal><![CDATA[
      T(x * y,x) / x = y * a(x,y,x)
    ]]></literal>
    <justification jstring="[para(8210(a,1),5524(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8210 5524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8226">
    <literal><![CDATA[
      a(x,y,x) \ K(x * y,x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(8210(a,1),6002(a,1,1))].">
      <j1 rule="para" parents="8210 6002"/>
    </justification>
  </clause>

  <clause id="8227">
    <literal><![CDATA[
      a(x,x \ (y \ x),x) = x \ R(x,y \ 1,x)
    ]]></literal>
    <justification jstring="[para(6232(a,1),8210(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6232 8210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8228">
    <literal><![CDATA[
      L(x,y,x) \ 1 = x \ a(x,y,x)
    ]]></literal>
    <justification jstring="[para(8210(a,1),6688(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8210 6688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8229">
    <literal><![CDATA[
      T(x,T(y,z)) \ R(x,u,x) = K(y,T(x,z)) * a(x,u,x)
    ]]></literal>
    <justification jstring="[para(8210(a,1),6444(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8210 6444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8230">
    <literal><![CDATA[
      x \ R(T(x,y),z,x) = K(x,y) * a(x,z,x)
    ]]></literal>
    <justification jstring="[para(8210(a,1),6563(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8210 6563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8231">
    <literal><![CDATA[
      x \ a(x,x,x) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(121,a,8213,a(flip),b,1188,a(flip))].">
      <j1 rule="hyper" parents="121 8213 1188"/>
    </justification>
  </clause>

  <clause id="8232">
    <literal><![CDATA[
      K(x,x \ 1) = a(x,x,x)
    ]]></literal>
    <justification jstring="[hyper(2127,a,8231,a)].">
      <j1 rule="hyper" parents="2127 8231"/>
    </justification>
  </clause>

  <clause id="8233">
    <literal><![CDATA[
      L(x,x,x) \ 1 = 1 / x
    ]]></literal>
    <justification jstring="[hyper(63,a,4731,a,b,8231,a)].">
      <j1 rule="hyper" parents="63 4731 8231"/>
    </justification>
  </clause>

  <clause id="8234">
    <literal><![CDATA[
      (x \ 1) * a(x,x,x) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(126,a,8232,a(flip),b,4445,a)].">
      <j1 rule="hyper" parents="126 8232 4445"/>
    </justification>
  </clause>

  <clause id="8235">
    <literal><![CDATA[
      L(T((1 / x) \ y,z),L(x,x,x) \ 1,L(x,x,x)) = T(1 \ (L(x,x,x) * y),z)
    ]]></literal>
    <justification jstring="[para(8233(a,1),791(a,1,1,1,1))].">
      <j1 rule="para" parents="8233 791"/>
    </justification>
  </clause>

  <clause id="8236">
    <literal><![CDATA[
      L(L(x \ 1,y,z),L(x,y,z),L(x \ 1,y,z)) \ 1 = 1 / L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(2619(a,1),8233(a,1,1))].">
      <j1 rule="para" parents="2619 8233"/>
    </justification>
  </clause>

  <clause id="8237">
    <literal><![CDATA[
      x \ R(x,y,x) != z
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(8214(a,1),342(a,1,2))].">
      <j1 rule="para" parents="8214 342"/>
    </justification>
  </clause>

  <clause id="8238">
    <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(8214(a,1),246(a,1,1))].">
      <j1 rule="para" parents="8214 246"/>
    </justification>
  </clause>

  <clause id="8239">
    <literal><![CDATA[
      a(x,y,x) \ x = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(8215(a,1),2559(a,1,1))].">
      <j1 rule="para" parents="8215 2559"/>
    </justification>
  </clause>

  <clause id="8240">
    <literal><![CDATA[
      a(x,y,x) \ (x * L(x \ a(x,y,x),z,u)) = L(x,y,x) \ L(a(x,y,x) \ x,z,u)
    ]]></literal>
    <justification jstring="[para(8239(a,1),2586(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8239 2586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8241">
    <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(8228(a,1),5561(a,1,1,2))].">
      <j1 rule="para" parents="8228 5561"/>
    </justification>
  </clause>

  <clause id="8242">
    <literal><![CDATA[
      a(x,y,x) * K(x,x * y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(5997,a,8211,a)].">
      <j1 rule="hyper" parents="5997 8211"/>
    </justification>
  </clause>

  <clause id="8243">
    <literal><![CDATA[
      K(x,y) * a(y,x,y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(4577,a,8211,a)].">
      <j1 rule="hyper" parents="4577 8211"/>
    </justification>
  </clause>

  <clause id="8244">
    <literal><![CDATA[
      K(x,x * y) * a(x,y,x) = K(x,y)
    ]]></literal>
    <justification jstring="[para(8211(a,1),4573(a,1,2))].">
      <j1 rule="para" parents="8211 4573"/>
    </justification>
  </clause>

  <clause id="8245">
    <literal><![CDATA[
      a(x,y,x) \ K(x,y) = K(x,x * y)
    ]]></literal>
    <justification jstring="[para(8211(a,1),5990(a,1,1))].">
      <j1 rule="para" parents="8211 5990"/>
    </justification>
  </clause>

  <clause id="8246">
    <literal><![CDATA[
      a(x,y,x) \ K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,x * y) = z
    ]]></literal>
    <justification jstring="[para(8211(a,1),6024(a,1,1))].">
      <j1 rule="para" parents="8211 6024"/>
    </justification>
  </clause>

  <clause id="8247">
    <literal><![CDATA[
      (x / y) * a(y,z,y) = x / L(y,z,y)
    ]]></literal>
    <justification jstring="[para(8211(a,1),7996(a,1,2))].">
      <j1 rule="para" parents="8211 7996"/>
    </justification>
  </clause>

  <clause id="8248">
    <literal><![CDATA[
      a(x,y,x) * (y * x) = T(x * y,x)
    ]]></literal>
    <justification jstring="[para(8211(a,1),8124(a,1,1))].">
      <j1 rule="para" parents="8211 8124"/>
    </justification>
  </clause>

  <clause id="8249">
    <literal><![CDATA[
      a(x,y,x) * K(y,x) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(5997,a,8212,a)].">
      <j1 rule="hyper" parents="5997 8212"/>
    </justification>
  </clause>

  <clause id="8250">
    <literal><![CDATA[
      K(x,y) \ K(x * y,y) = a(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(4585,a,8217,a)].">
      <j1 rule="hyper" parents="4585 8217"/>
    </justification>
  </clause>

  <clause id="8251">
    <literal><![CDATA[
      (x \ y) * a(x,x \ y,x) = T(y,x) / x
    ]]></literal>
    <justification jstring="[para(10(a,1),8225(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 8225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8252">
    <literal><![CDATA[
      T(x * a(y,x,y),y) = y \ T(y * x,y)
    ]]></literal>
    <justification jstring="[para(8225(a,1),113(a,1,1))].">
      <j1 rule="para" parents="8225 113"/>
    </justification>
  </clause>

  <clause id="8253">
    <literal><![CDATA[
      R(x * a(y,x,y),z,u) * y = y * R(y \ T(y * x,y),z,u)
    ]]></literal>
    <justification jstring="[para(8225(a,1),675(a,1,1,1))].">
      <j1 rule="para" parents="8225 675"/>
    </justification>
  </clause>

  <clause id="8254">
    <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(8225(a,2),245(a,1,2,2))].">
      <j1 rule="para" parents="8225 245"/>
    </justification>
  </clause>

  <clause id="8255">
    <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(8225(a,2),497(a,1,2,2))].">
      <j1 rule="para" parents="8225 497"/>
    </justification>
  </clause>

  <clause id="8256">
    <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(8225(a,2),877(a,1,2,2,2))].">
      <j1 rule="para" parents="8225 877"/>
    </justification>
  </clause>

  <clause id="8257">
    <literal><![CDATA[
      a(T(x,y * z),z,T(x,y * z)) * K(z,T(x,y)) = K(T(x,y * z) * z,T(x,y * z))
    ]]></literal>
    <justification jstring="[hyper(126,a,6506,a(flip),b,8226,a)].">
      <j1 rule="hyper" parents="126 6506 8226"/>
    </justification>
  </clause>

  <clause id="8258">
    <literal><![CDATA[
      a(x,y \ 1,x) \ K(y \ x,x) = K(y \ 1,x)
    ]]></literal>
    <justification jstring="[para(5939(a,1),8226(a,1,2))].">
      <j1 rule="para" parents="5939 8226"/>
    </justification>
  </clause>

  <clause id="8260">
    <literal><![CDATA[
      K(x * y,x) * K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(4920(a,2),8237(a,1))].">
      <j1 rule="para" parents="4920 8237"/>
    </justification>
  </clause>

  <clause id="8261">
    <literal><![CDATA[
      a(x,x \ y,x) * K(x,y) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),8242(a,1,2,2))].">
      <j1 rule="para" parents="10 8242"/>
    </justification>
  </clause>

  <clause id="8263">
    <literal><![CDATA[
      K(x,y) * a(x,x \ y,x) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),8244(a,1,1,2))].">
      <j1 rule="para" parents="10 8244"/>
    </justification>
  </clause>

  <clause id="8264">
    <literal><![CDATA[
      L(a(x,y,x),K(x,x * y),z) = (z * K(x,x * y)) \ (z * K(x,y))
    ]]></literal>
    <justification jstring="[para(8244(a,1),18(a,2,2,2))].">
      <j1 rule="para" parents="8244 18"/>
    </justification>
  </clause>

  <clause id="8265">
    <literal><![CDATA[
      a(x,y,x) * K(y,x) = K(y * x,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,4543,a,b,8249,a),flip(a)].">
      <j1 rule="hyper" parents="333 4543 8249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8266">
    <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(5835(a,1),8249(a,2,1))].">
      <j1 rule="para" parents="5835 8249"/>
    </justification>
  </clause>

  <clause id="8267">
    <literal><![CDATA[
      a(x,y,x) * T(x,z) = R(T(x,z),y,x)
    ]]></literal>
    <justification jstring="[hyper(125,a,8216,a(flip),b,3022,a)].">
      <j1 rule="hyper" parents="125 8216 3022"/>
    </justification>
  </clause>

  <clause id="8268">
    <literal><![CDATA[
      a(x,x \ y,x) = T(x,y) \ ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[para(3721(a,1),8216(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3721 8216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8269">
    <literal><![CDATA[
      (x / y) \ (x / L(y,z,y)) = a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(129,a,8247,a)].">
      <j1 rule="hyper" parents="129 8247"/>
    </justification>
  </clause>

  <clause id="8270">
    <literal><![CDATA[
      (x * y) / L(y,z,y) = x * a(y,z,y)
    ]]></literal>
    <justification jstring="[para(11(a,1),8247(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 8247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8271">
    <literal><![CDATA[
      R(T(x / y,K(y,x)),z,x / y) = a(x / y,z,x / y) * (x / y)
    ]]></literal>
    <justification jstring="[para(5477(a,1),8267(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5477 8267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8272">
    <literal><![CDATA[
      (x / L(y,z,y)) * y = x * a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(1828,a,8270,a)].">
      <j1 rule="hyper" parents="1828 8270"/>
    </justification>
  </clause>

  <clause id="8273">
    <literal><![CDATA[
      (x * a(y,z,y)) \ (x * y) = L(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(192,a,8270,a)].">
      <j1 rule="hyper" parents="192 8270"/>
    </justification>
  </clause>

  <clause id="8274">
    <literal><![CDATA[
      (x * L(y,z,y)) * a(y,z,y) = x * y
    ]]></literal>
    <justification jstring="[para(11(a,1),8272(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 8272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8275">
    <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(968(a,1),8273(a,1,2))].">
      <j1 rule="para" parents="968 8273"/>
    </justification>
  </clause>

  <clause id="8276">
    <literal><![CDATA[
      (T(x * y,x) / x) \ (y * x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(8225(a,2),8273(a,1,1))].">
      <j1 rule="para" parents="8225 8273"/>
    </justification>
  </clause>

  <clause id="8277">
    <literal><![CDATA[
      K(x,x \ y) * (K(y,x) * z) = a(x,x \ y,x) * z
    ]]></literal>
    <justification jstring="[para(8219(a,1),8080(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8219 8080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8278">
    <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(6889(a,1),8276(a,1,2))].">
      <j1 rule="para" parents="6889 8276"/>
    </justification>
  </clause>

  <clause id="8279">
    <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(333,a,7688,a(flip),b,8201,a),flip(a)].">
      <j1 rule="hyper" parents="333 7688 8201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8281">
    <literal><![CDATA[
      a(x,x \ (y \ x),x) = a(x,y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,8210,a(flip),b,8227,a),flip(a)].">
      <j1 rule="hyper" parents="333 8210 8227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8282">
    <literal><![CDATA[
      T(x,y \ x) \ ((x \ (y \ x)) \ (y \ x)) = a(x,y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,8268,a(flip),b,8281,a)].">
      <j1 rule="hyper" parents="63 8268 8281"/>
    </justification>
  </clause>

  <clause id="8283">
    <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(8230(a,1),98(a,1,2,2,1))].">
      <j1 rule="para" parents="8230 98"/>
    </justification>
  </clause>

  <clause id="8284">
    <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(8230(a,1),3385(a,1,1,1))].">
      <j1 rule="para" parents="8230 3385"/>
    </justification>
  </clause>

  <clause id="8285">
    <literal><![CDATA[
      (x \ y) * (a(x,x \ y,x) * z) = (y / x) * (K(y,x) * z)
    ]]></literal>
    <justification jstring="[para(8277(a,1),4624(a,1,2))].">
      <j1 rule="para" parents="8277 4624"/>
    </justification>
  </clause>

  <clause id="8286">
    <literal><![CDATA[
      T(1 / (x \ (x / y)),z) \ 1 = K(y,z) \ (x \ (x / y))
    ]]></literal>
    <justification jstring="[para(371(a,1),6161(a,1,1)),flip(a)].">
      <j1 rule="para" parents="371 6161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8287">
    <literal><![CDATA[
      R(K(x,T((y / z) \ x,u)),x,z) = K(x,T((y / (x * z)) \ 1,u))
    ]]></literal>
    <justification jstring="[para(6365(a,2),6374(a,1,1))].">
      <j1 rule="para" parents="6365 6374"/>
    </justification>
  </clause>

  <clause id="8288">
    <literal><![CDATA[
      K(R(T(x,y),x \ z,z \ y),u) = K(((x \ z) * (z \ y)) \ y,u)
    ]]></literal>
    <justification jstring="[para(27(a,2),6469(a,1,1))].">
      <j1 rule="para" parents="27 6469"/>
    </justification>
  </clause>

  <clause id="8289">
    <literal><![CDATA[
      K(L(x,y,z),T(u,x \ w)) = K(L(x,y,z),T(u,w))
    ]]></literal>
    <justification jstring="[hyper(4472,a,6545,a),flip(a)].">
      <j1 rule="hyper" parents="4472 6545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8290">
    <literal><![CDATA[
      K(T(x,y \ z),L(y,u,w)) = 1 / K(L(y,u,w),T(x,z))
    ]]></literal>
    <justification jstring="[hyper(197,a,8289,a(flip),b,4367,a),flip(a)].">
      <j1 rule="hyper" parents="197 8289 4367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8291">
    <literal><![CDATA[
      K(T(x,y \ z),L(y,u,w)) = K(x,T(L(y,u,w),z))
    ]]></literal>
    <justification jstring="[hyper(119,a,6424,a(flip),b,8290,a),flip(a)].">
      <j1 rule="hyper" parents="119 6424 8290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8292">
    <literal><![CDATA[
      K(T(x,y \ z),L(y,u,w)) = K(x,L(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(25(a,2),8291(a,2,2))].">
      <j1 rule="para" parents="25 8291"/>
    </justification>
  </clause>

  <clause id="8293">
    <literal><![CDATA[
      K(x,T(L(y,z,u),y \ w)) = K(x,L(T(y,w),z,u))
    ]]></literal>
    <justification jstring="[hyper(6695,a,8292,a)].">
      <j1 rule="hyper" parents="6695 8292"/>
    </justification>
  </clause>

  <clause id="8294">
    <literal><![CDATA[
      K(x,L(T(y,y \ z),u,w)) = K(x,L(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(25(a,2),8293(a,1,2))].">
      <j1 rule="para" parents="25 8293"/>
    </justification>
  </clause>

  <clause id="8295">
    <literal><![CDATA[
      K(x,L(T(y,y * z),u,w)) = K(x,L(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(9(a,1),8294(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="9 8294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8296">
    <literal><![CDATA[
      K(x,L(L(y,z,y * K(z,y)),u,w)) = K(x,L(T(y * K(z,y),z),u,w))
    ]]></literal>
    <justification jstring="[para(4324(a,1),8295(a,1,2,1))].">
      <j1 rule="para" parents="4324 8295"/>
    </justification>
  </clause>

  <clause id="8297">
    <literal><![CDATA[
      L(x \ 1,x,K(x,y) * z) = L(x \ 1,x,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,7334,a(flip),b,6567,a),flip(a)].">
      <j1 rule="hyper" parents="63 7334 6567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8299">
    <literal><![CDATA[
      L(x \ 1,x,y * K(x,z)) = L(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[para(6887(a,1),8297(a,1,3))].">
      <j1 rule="para" parents="6887 8297"/>
    </justification>
  </clause>

  <clause id="8302">
    <literal><![CDATA[
      x * K(x,(x \ y) / y) = L(x,x,(x \ y) / y)
    ]]></literal>
    <justification jstring="[hyper(5457,a,6713,a)].">
      <j1 rule="hyper" parents="5457 6713"/>
    </justification>
  </clause>

  <clause id="8303">
    <literal><![CDATA[
      L(x,x,(x \ y) / y) = x * K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(5061(a,1),8302(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5061 8302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8304">
    <literal><![CDATA[
      L(x,x,(x \ y) / y) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(333,a,4222,a,b,8303,a),flip(a)].">
      <j1 rule="hyper" parents="333 4222 8303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8306">
    <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(29(a,1),6721(a,2,1))].">
      <j1 rule="para" parents="29 6721"/>
    </justification>
  </clause>

  <clause id="8308">
    <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(6424(a,1),6969(a,1,1))].">
      <j1 rule="para" parents="6424 6969"/>
    </justification>
  </clause>

  <clause id="8309">
    <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(121,a,7093,a(flip),b,5634,a(flip))].">
      <j1 rule="hyper" parents="121 7093 5634"/>
    </justification>
  </clause>

  <clause id="8310">
    <literal><![CDATA[
      K(x,R(T(y \ z,z * u),y,u)) = K(x,T((y * u) \ (z * u),y))
    ]]></literal>
    <justification jstring="[para(27(a,2),7224(a,1,2))].">
      <j1 rule="para" parents="27 7224"/>
    </justification>
  </clause>

  <clause id="8311">
    <literal><![CDATA[
      K(x,y) * (K(x * y,z) * x) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * y,z) * T(x,y) = u
    ]]></literal>
    <justification jstring="[para(6405(a,2),7245(a,1))].">
      <j1 rule="para" parents="6405 7245"/>
    </justification>
  </clause>

  <clause id="8312">
    <literal><![CDATA[
      K(R(x,y,z),u * K(x,w)) = K(R(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(333,a,4952,a(flip),b,7401,a),flip(a)].">
      <j1 rule="hyper" parents="333 4952 7401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8313">
    <literal><![CDATA[
      K(R(x,y,z),u * K(w,x)) = K(R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(5995(a,1),8312(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5995 8312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8314">
    <literal><![CDATA[
      x / (x / R(K(y,z),u,w)) = (R(K(y,z),u,w) \ x) \ x
    ]]></literal>
    <justification jstring="[hyper(197,a,7614,a(flip),b,3674,a(flip))].">
      <j1 rule="hyper" parents="197 7614 3674"/>
    </justification>
  </clause>

  <clause id="8315">
    <literal><![CDATA[
      R(x,y \ z,T(y,y \ z)) = R(x,z / y,y)
    ]]></literal>
    <justification jstring="[hyper(35,a,532,a,b,7681,a)].">
      <j1 rule="hyper" parents="35 532 7681"/>
    </justification>
  </clause>

  <clause id="8316">
    <literal><![CDATA[
      K((x * (y / z)) \ u,y) = K((x * (z \ y)) \ u,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,6283,a(flip),b,7684,a),flip(a)].">
      <j1 rule="hyper" parents="63 6283 7684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8317">
    <literal><![CDATA[
      K((x * (y / x)) \ z,y) = K(y \ z,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),8316(a,2,1,1))].">
      <j1 rule="para" parents="10 8316"/>
    </justification>
  </clause>

  <clause id="8318">
    <literal><![CDATA[
      K(x \ (x * y),x) = K(K(z \ x,z) * y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,6310,a(flip),b,8317,a),flip(a)].">
      <j1 rule="hyper" parents="63 6310 8317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8319">
    <literal><![CDATA[
      K(K(x \ y,x) * z,y) = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(4614,a,8318,a),flip(a)].">
      <j1 rule="hyper" parents="4614 8318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8321">
    <literal><![CDATA[
      K(K(x \ y,x) * z,y) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) = u
    ]]></literal>
    <justification jstring="[para(8318(a,1),4614(a,1))].">
      <j1 rule="para" parents="8318 4614"/>
    </justification>
  </clause>

  <clause id="8324">
    <literal><![CDATA[
      (K(x \ y,x) * z) * K(z,y) = T(K(x \ y,x) * z,y)
    ]]></literal>
    <justification jstring="[hyper(126,a,8319,a(flip),b,4215,a(flip))].">
      <j1 rule="hyper" parents="126 8319 4215"/>
    </justification>
  </clause>

  <clause id="8325">
    <literal><![CDATA[
      K(K(x,y) * z,x * y) = K(z,x * y)
    ]]></literal>
    <justification jstring="[para(4374(a,1),8319(a,1,1,1))].">
      <j1 rule="para" parents="4374 8319"/>
    </justification>
  </clause>

  <clause id="8326">
    <literal><![CDATA[
      K(T(x,y) * z,y * x) = K(x * z,y * x)
    ]]></literal>
    <justification jstring="[para(4557(a,1),8325(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4557 8325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8327">
    <literal><![CDATA[
      K(K(x,y) * z,x * y) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,x * y) = u
    ]]></literal>
    <justification jstring="[para(4374(a,1),8321(a,1,1,1))].">
      <j1 rule="para" parents="4374 8321"/>
    </justification>
  </clause>

  <clause id="8328">
    <literal><![CDATA[
      K(((x \ y) \ y) \ z,y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ z,y) = u
    ]]></literal>
    <justification jstring="[para(4703(a,2),8321(a,1,1))].">
      <j1 rule="para" parents="4703 8321"/>
    </justification>
  </clause>

  <clause id="8329">
    <literal><![CDATA[
      K((x \ y) * z,y) != u
    ]]></literal>
    <literal><![CDATA[
      K((y / x) * z,y) = u
    ]]></literal>
    <justification jstring="[para(5049(a,1),8321(a,1,1))].">
      <j1 rule="para" parents="5049 8321"/>
    </justification>
  </clause>

  <clause id="8330">
    <literal><![CDATA[
      T(K(x \ y,x) * z,y) = K(x \ y,x) * T(z,y)
    ]]></literal>
    <justification jstring="[hyper(6089,a,8324,a),flip(a)].">
      <j1 rule="hyper" parents="6089 8324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8331">
    <literal><![CDATA[
      T(K(x \ (y * x),x) * z,y * x) = K(y,x) * T(z,y * x)
    ]]></literal>
    <justification jstring="[para(4374(a,1),8330(a,2,1))].">
      <j1 rule="para" parents="4374 8330"/>
    </justification>
  </clause>

  <clause id="8332">
    <literal><![CDATA[
      T(K(x,y) * z,x * y) = K(x,y) * T(z,x * y)
    ]]></literal>
    <justification jstring="[para(4374(a,1),8331(a,1,1,1))].">
      <j1 rule="para" parents="4374 8331"/>
    </justification>
  </clause>

  <clause id="8333">
    <literal><![CDATA[
      T(x * K(y,z),z * y) = T(x,z * y) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(34,a,5356,a(flip),b,8332,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="34 5356 8332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8334">
    <literal><![CDATA[
      (x * (y * z)) * u != (y * z) * T(x * K(z,y),y * z)
    ]]></literal>
    <literal><![CDATA[
      L(K(z,y),T(x,y * z),y * z) = u
    ]]></literal>
    <justification jstring="[para(8333(a,2),873(a,2,2))].">
      <j1 rule="para" parents="8333 873"/>
    </justification>
  </clause>

  <clause id="8335">
    <literal><![CDATA[
      K(x * R(y,z,u),y) * K(y,x) = y \ R(y,x,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(5127,a,7690,a),flip(a)].">
      <j1 rule="hyper" parents="5127 7690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8336">
    <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(63,a,8200,a,b,8335,a)].">
      <j1 rule="hyper" parents="63 8200 8335"/>
    </justification>
  </clause>

  <clause id="8337">
    <literal><![CDATA[
      (x / R(y,y \ x,y)) * y = T(y,x) * T(y \ x,y)
    ]]></literal>
    <justification jstring="[para(3681(a,1),7727(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3681 7727"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8339">
    <literal><![CDATA[
      x / R(y,y \ x,y) = K(y,x) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(35,a,6565,a,b,8337,a),flip(a)].">
      <j1 rule="hyper" parents="35 6565 8337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8340">
    <literal><![CDATA[
      x / R(y,y \ x,y) = (y * K(x,y)) \ x
    ]]></literal>
    <justification jstring="[hyper(333,a,4833,a,b,8339,a),flip(a)].">
      <j1 rule="hyper" parents="333 4833 8339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8342">
    <literal><![CDATA[
      x / ((y \ x) \ T(x,y)) = (y * K(x,y)) \ x
    ]]></literal>
    <justification jstring="[para(3746(a,1),8340(a,1,2))].">
      <j1 rule="para" parents="3746 8340"/>
    </justification>
  </clause>

  <clause id="8343">
    <literal><![CDATA[
      ((x * K(y,x)) \ y) \ y = (x \ y) \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(192,a,8342,a)].">
      <j1 rule="hyper" parents="192 8342"/>
    </justification>
  </clause>

  <clause id="8344">
    <literal><![CDATA[
      (x \ (y * K(x,y))) \ y = (x \ y) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(4902(a,1),8343(a,1,1))].">
      <j1 rule="para" parents="4902 8343"/>
    </justification>
  </clause>

  <clause id="8345">
    <literal><![CDATA[
      (x \ ((x * y) / x)) \ y = (x \ y) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(4238(a,2),8344(a,1,1,2))].">
      <j1 rule="para" parents="4238 8344"/>
    </justification>
  </clause>

  <clause id="8346">
    <literal><![CDATA[
      K(x,((y \ z) * u) \ (z * u)) = R(K(x,T(y,z * u)),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,7631,a(flip),b,7896,a),flip(a)].">
      <j1 rule="hyper" parents="63 7631 7896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8347">
    <literal><![CDATA[
      L(K(x,T(T(y,z),u * z)),z,u) = K((u * z) / (u * (x \ z)),y)
    ]]></literal>
    <justification jstring="[hyper(333,a,5280,a,b,7901,a),flip(a)].">
      <j1 rule="hyper" parents="333 5280 7901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8348">
    <literal><![CDATA[
      L(T(K(x,T(y,z * u)),u),u,z) = (z * (K(x,y) * u)) / (z * u)
    ]]></literal>
    <justification jstring="[para(6394(a,1),7901(a,1,1))].">
      <j1 rule="para" parents="6394 7901"/>
    </justification>
  </clause>

  <clause id="8349">
    <literal><![CDATA[
      K(x,y) * K(L(x,z,u) * y,x) = L(x,y,L(x,z,u)) \ x
    ]]></literal>
    <justification jstring="[para(7543(a,1),8049(a,1,2))].">
      <j1 rule="para" parents="7543 8049"/>
    </justification>
  </clause>

  <clause id="8350">
    <literal><![CDATA[
      K(L(x,y,z) * u,x) * K(x,u) = L(x,u,L(x,y,z)) \ x
    ]]></literal>
    <justification jstring="[hyper(2006,a,8349,a)].">
      <j1 rule="hyper" parents="2006 8349"/>
    </justification>
  </clause>

  <clause id="8351">
    <literal><![CDATA[
      T(x * R(x \ (x * y),z,u),x) = R(y * a(x,y,x),z,u) * x
    ]]></literal>
    <justification jstring="[hyper(333,a,1591,a,b,8253,a)].">
      <j1 rule="hyper" parents="333 1591 8253"/>
    </justification>
  </clause>

  <clause id="8352">
    <literal><![CDATA[
      K(x,T((y / (x * z)) \ 1,u)) = K(x,T((y / z) \ x,u))
    ]]></literal>
    <justification jstring="[hyper(3568,a,8287,a),flip(a)].">
      <j1 rule="hyper" parents="3568 8287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8354">
    <literal><![CDATA[
      K(x,T((y / z) \ x,y)) = K(x,y \ (x * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,6735,a(flip),b,8352,a),flip(a)].">
      <j1 rule="hyper" parents="63 6735 8352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8355">
    <literal><![CDATA[
      K(x,y \ (x * (z \ y))) = K(x,T(z \ x,y))
    ]]></literal>
    <justification jstring="[para(76(a,1),8354(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="76 8354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8356">
    <literal><![CDATA[
      K(x,(y \ (z * (u \ y))) \ K(z,T(u \ z,y))) = K(x,z \ ((y \ (z * (u \ y))) \ z))
    ]]></literal>
    <justification jstring="[para(8355(a,1),6739(a,1,2,2))].">
      <j1 rule="para" parents="8355 6739"/>
    </justification>
  </clause>

  <clause id="8357">
    <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(2891(a,1),8288(a,2,1,1))].">
      <j1 rule="para" parents="2891 8288"/>
    </justification>
  </clause>

  <clause id="8358">
    <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(63,a,6993,a(flip),b,8306,a)].">
      <j1 rule="hyper" parents="63 6993 8306"/>
    </justification>
  </clause>

  <clause id="8359">
    <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(23(a,1),8358(a,1,2))].">
      <j1 rule="para" parents="23 8358"/>
    </justification>
  </clause>

  <clause id="8360">
    <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(63,a,7745,a(flip),b,8359,a)].">
      <j1 rule="hyper" parents="63 7745 8359"/>
    </justification>
  </clause>

  <clause id="8361">
    <literal><![CDATA[
      K(L(R(x,y,z),u,x),w) = K(R(x,y,z),w)
    ]]></literal>
    <justification jstring="[hyper(7064,a,8360,a),flip(a)].">
      <j1 rule="hyper" parents="7064 8360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8363">
    <literal><![CDATA[
      K(R(L(x,y,x),z,u),w) = K(R(x,z,u),w)
    ]]></literal>
    <justification jstring="[para(29(a,2),8361(a,1,1))].">
      <j1 rule="para" parents="29 8361"/>
    </justification>
  </clause>

  <clause id="8364">
    <literal><![CDATA[
      K(R(x,x \ a(x,y,x),z),u) = K(L(x,y,x),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,8241,a(flip),b,8363,a),flip(a)].">
      <j1 rule="hyper" parents="63 8241 8363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8365">
    <literal><![CDATA[
      K(R(x,x \ a(x,y,x),z),u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(333,a,6303,a(flip),b,8364,a),flip(a)].">
      <j1 rule="hyper" parents="333 6303 8364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8368">
    <literal><![CDATA[
      R(K(x,y),a(x,z,x),u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,5560,a(flip),b,8365,a)].">
      <j1 rule="hyper" parents="63 5560 8365"/>
    </justification>
  </clause>

  <clause id="8369">
    <literal><![CDATA[
      (K(x,y) * a(x,z,x)) * u = K(x,y) * (a(x,z,x) * u)
    ]]></literal>
    <justification jstring="[hyper(125,a,8368,a(flip),b,20,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="125 8368 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8370">
    <literal><![CDATA[
      K(x,x * y) * (a(x,y,x) * z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(8244(a,1),8369(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8244 8369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8371">
    <literal><![CDATA[
      K(x,y) * (a(x,y,x) \ z) = K(x,x * y) * z
    ]]></literal>
    <justification jstring="[hyper(343,a,8370,a),flip(a)].">
      <j1 rule="hyper" parents="343 8370"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8372">
    <literal><![CDATA[
      K(x,y) * (K(y,y * x) * z) = a(y,x,y) \ z
    ]]></literal>
    <justification jstring="[hyper(4577,a,8371,a)].">
      <j1 rule="hyper" parents="4577 8371"/>
    </justification>
  </clause>

  <clause id="8373">
    <literal><![CDATA[
      K(x,y) * (K(y,x * y) * z) = a(y,x,y) \ z
    ]]></literal>
    <justification jstring="[para(4636(a,2),8372(a,1,2,1))].">
      <j1 rule="para" parents="4636 8372"/>
    </justification>
  </clause>

  <clause id="8374">
    <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(7958(a,1),8348(a,1,1,1))].">
      <j1 rule="para" parents="7958 8348"/>
    </justification>
  </clause>

  <clause id="8375">
    <literal><![CDATA[
      R(x * a(y,x,y),z,u) * y = T(y * R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(9(a,1),8351(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 8351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8376">
    <literal><![CDATA[
      ((K(x,y) / z) * (z * K(y,x))) \ (K(x,y) / z) = 1 / (z * K(y,x))
    ]]></literal>
    <justification jstring="[para(5994(a,1),6029(a,2,2))].">
      <j1 rule="para" parents="5994 6029"/>
    </justification>
  </clause>

  <clause id="8377">
    <literal><![CDATA[
      L(x \ 1,x,y * K(x,z)) = L(x \ 1,T(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(6068,a,4448,a)].">
      <j1 rule="hyper" parents="6068 4448"/>
    </justification>
  </clause>

  <clause id="8378">
    <literal><![CDATA[
      L(x \ 1,T(x,y),z) = L(x \ 1,x,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,8299,a(flip),b,8377,a),flip(a)].">
      <j1 rule="hyper" parents="63 8299 8377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8381">
    <literal><![CDATA[
      T(x * L(x \ 1,x,y),z) = T(x,z) * ((y * T(x,z)) \ y)
    ]]></literal>
    <justification jstring="[para(8378(a,1),1968(a,1,1,2))].">
      <j1 rule="para" parents="8378 1968"/>
    </justification>
  </clause>

  <clause id="8382">
    <literal><![CDATA[
      L(x \ 1,x,y) * L(L(x \ 1,T(x,z),y) \ 1,u,w) = L((x \ 1) * L((x \ 1) \ 1,u,w),T(x,z),y)
    ]]></literal>
    <justification jstring="[para(8378(a,1),4030(a,1,1))].">
      <j1 rule="para" parents="8378 4030"/>
    </justification>
  </clause>

  <clause id="8385">
    <literal><![CDATA[
      L(K(x,T(y,z)),u,L(y,w,v5)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(2942,a,6226,a)].">
      <j1 rule="hyper" parents="2942 6226"/>
    </justification>
  </clause>

  <clause id="8386">
    <literal><![CDATA[
      L(K(x,T(y,z)),u,y) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(371(a,1),8385(a,1,3))].">
      <j1 rule="para" parents="371 8385"/>
    </justification>
  </clause>

  <clause id="8387">
    <literal><![CDATA[
      K((x \ 1) * y,T(x \ 1,z)) = K(x \ y,T(x \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,7300,a(flip),b,8386,a)].">
      <j1 rule="hyper" parents="63 7300 8386"/>
    </justification>
  </clause>

  <clause id="8388">
    <literal><![CDATA[
      K((x \ y) \ z,T(x,u)) = K(y \ (x * z),T(x,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,6282,a(flip),b,8386,a),flip(a)].">
      <j1 rule="hyper" parents="63 6282 8386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8389">
    <literal><![CDATA[
      K(x \ (y * z),T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(z / (y \ x),y) = u
    ]]></literal>
    <justification jstring="[para(8388(a,1),7062(a,1))].">
      <j1 rule="para" parents="8388 7062"/>
    </justification>
  </clause>

  <clause id="8390">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,T((x \ y) \ 1,u)) = K((x \ y) \ z,T(y \ x,u))
    ]]></literal>
    <justification jstring="[hyper(333,a,7966,a(flip),b,8387,a),flip(a)].">
      <j1 rule="hyper" parents="333 7966 8387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8391">
    <literal><![CDATA[
      T((x \ y) * (y \ x),z) = (x \ y) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(4917,a,6239,a),flip(a)].">
      <j1 rule="hyper" parents="4917 6239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8392">
    <literal><![CDATA[
      K(x,(y \ z) * (z \ y)) = 1
    ]]></literal>
    <justification jstring="[hyper(122,a,8391,a,b,4224,a),flip(a)].">
      <j1 rule="hyper" parents="122 8391 4224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8395">
    <literal><![CDATA[
      K(x,y * ((z * y) \ z)) = 1
    ]]></literal>
    <justification jstring="[para(9(a,1),8392(a,1,2,1))].">
      <j1 rule="para" parents="9 8392"/>
    </justification>
  </clause>

  <clause id="8396">
    <literal><![CDATA[
      K(x,(y \ (y / z)) * z) = 1
    ]]></literal>
    <justification jstring="[para(79(a,1),8392(a,1,2,2))].">
      <j1 rule="para" parents="79 8392"/>
    </justification>
  </clause>

  <clause id="8397">
    <literal><![CDATA[
      T(x,y * ((z * y) \ z)) = x
    ]]></literal>
    <justification jstring="[hyper(56,a,8395,a)].">
      <j1 rule="hyper" parents="56 8395"/>
    </justification>
  </clause>

  <clause id="8398">
    <literal><![CDATA[
      x / (y * ((z * y) \ z)) = (y * ((z * y) \ z)) \ x
    ]]></literal>
    <justification jstring="[hyper(6748,a,8397,a),flip(a)].">
      <j1 rule="hyper" parents="6748 8397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8399">
    <literal><![CDATA[
      T(x * ((y * x) \ y),z) = x * ((y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(54,a,8397,a)].">
      <j1 rule="hyper" parents="54 8397"/>
    </justification>
  </clause>

  <clause id="8400">
    <literal><![CDATA[
      T(x * L(x \ 1,x,y),z) = x * ((y * x) \ y)
    ]]></literal>
    <justification jstring="[para(227(a,2),8399(a,1,1,2))].">
      <j1 rule="para" parents="227 8399"/>
    </justification>
  </clause>

  <clause id="8401">
    <literal><![CDATA[
      T(x,y) * ((z * T(x,y)) \ z) = x * ((z * x) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,8381,a(flip),b,8400,a)].">
      <j1 rule="hyper" parents="63 8381 8400"/>
    </justification>
  </clause>

  <clause id="8402">
    <literal><![CDATA[
      T(x,y) * ((x * y) \ y) = x * ((y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,4908,a(flip),b,8400,a)].">
      <j1 rule="hyper" parents="63 4908 8400"/>
    </justification>
  </clause>

  <clause id="8405">
    <literal><![CDATA[
      (x * ((y * x) \ y)) \ (y \ (x * y)) = 1 / ((x * y) \ y)
    ]]></literal>
    <justification jstring="[para(8402(a,1),1621(a,1,1))].">
      <j1 rule="para" parents="8402 1621"/>
    </justification>
  </clause>

  <clause id="8407">
    <literal><![CDATA[
      (x * ((y * x) \ y)) \ T(x,z) = 1 / ((y * T(x,z)) \ y)
    ]]></literal>
    <justification jstring="[para(8401(a,1),1626(a,1,1))].">
      <j1 rule="para" parents="8401 1626"/>
    </justification>
  </clause>

  <clause id="8408">
    <literal><![CDATA[
      (x * ((y * x) \ y)) \ T(x,y) = 1 / ((x * y) \ y)
    ]]></literal>
    <justification jstring="[para(22(a,2),8405(a,1,2))].">
      <j1 rule="para" parents="22 8405"/>
    </justification>
  </clause>

  <clause id="8409">
    <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(4197(a,1),6537(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4197 6537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8410">
    <literal><![CDATA[
      K(x,(T(y,z) / u) / (y / u)) * (y / u) = T(y,K(x,z)) / u
    ]]></literal>
    <justification jstring="[para(6841(a,1),6811(a,1,1))].">
      <j1 rule="para" parents="6841 6811"/>
    </justification>
  </clause>

  <clause id="8411">
    <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(8410(a,1),109(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="8410 109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8412">
    <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(8410(a,1),4578(a,1,2))].">
      <j1 rule="para" parents="8410 4578"/>
    </justification>
  </clause>

  <clause id="8413">
    <literal><![CDATA[
      T(x / y,K(((x / y) \ (1 / y)) \ 1,z)) = T(x,K(z,y \ x)) / y
    ]]></literal>
    <justification jstring="[para(5819(a,1),6875(a,2,1))].">
      <j1 rule="para" parents="5819 6875"/>
    </justification>
  </clause>

  <clause id="8414">
    <literal><![CDATA[
      T(x,T((y \ z) / z,T(y,u))) = T(x,(((y \ 1) \ 1) \ z) / z)
    ]]></literal>
    <justification jstring="[hyper(63,a,6948,a(flip),b,7018,a)].">
      <j1 rule="hyper" parents="63 6948 7018"/>
    </justification>
  </clause>

  <clause id="8415">
    <literal><![CDATA[
      T(x,T((y \ z) / z,T(y,u))) = T(x,((y \ 1) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(333,a,3757,a(flip),b,8414,a),flip(a)].">
      <j1 rule="hyper" parents="333 3757 8414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8417">
    <literal><![CDATA[
      T(x,T((y \ z) / z,T(y,u))) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(333,a,3173,a(flip),b,8415,a),flip(a)].">
      <j1 rule="hyper" parents="333 3173 8415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8418">
    <literal><![CDATA[
      K(L(x \ y,x,z),T(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K((z * y) / (z * x),x) = u
    ]]></literal>
    <justification jstring="[para(6383(a,1),7210(a,1))].">
      <j1 rule="para" parents="6383 7210"/>
    </justification>
  </clause>

  <clause id="8420">
    <literal><![CDATA[
      K(T(x,y) / y,z) = K(x / T(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(34,a,6967,a(flip),b,7247,a)].">
      <j1 rule="hyper" parents="34 6967 7247"/>
    </justification>
  </clause>

  <clause id="8421">
    <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(333,a,6614,a(flip),b,7338,a),flip(a)].">
      <j1 rule="hyper" parents="333 6614 7338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8422">
    <literal><![CDATA[
      K(x * y,y) * K(x,K(y,z)) = T(y,T(x,z)) \ R(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,7613,a(flip),b,8421,a)].">
      <j1 rule="hyper" parents="63 7613 8421"/>
    </justification>
  </clause>

  <clause id="8423">
    <literal><![CDATA[
      T(x,T(y,z)) \ R(x,y,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(y * x,T(x,z)) = u
    ]]></literal>
    <justification jstring="[para(8422(a,1),7310(a,1))].">
      <j1 rule="para" parents="8422 7310"/>
    </justification>
  </clause>

  <clause id="8424">
    <literal><![CDATA[
      K(x,T(y,z)) * a(y,x,y) = K(x * y,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(8423,a,8229,a),flip(a)].">
      <j1 rule="hyper" parents="8423 8229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8425">
    <literal><![CDATA[
      K(x / y,z) * a(z,y \ x,z) = K((y \ x) * z,T(z,y))
    ]]></literal>
    <justification jstring="[para(6922(a,1),8424(a,1,1))].">
      <j1 rule="para" parents="6922 8424"/>
    </justification>
  </clause>

  <clause id="8426">
    <literal><![CDATA[
      K(x * y,T(y,z)) \ (K(x,T(y,z)) * y) = L(y,x,y)
    ]]></literal>
    <justification jstring="[para(8424(a,1),8273(a,1,1))].">
      <j1 rule="para" parents="8424 8273"/>
    </justification>
  </clause>

  <clause id="8427">
    <literal><![CDATA[
      K(x * y,T(y,z)) \ (y * K(x,T(y,z))) = L(y,x,y)
    ]]></literal>
    <justification jstring="[para(2736(a,1),8426(a,1,2))].">
      <j1 rule="para" parents="2736 8426"/>
    </justification>
  </clause>

  <clause id="8428">
    <literal><![CDATA[
      T(x,T(y * x,z)) * K(y,T(x,z)) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(6449,a,8427,a)].">
      <j1 rule="hyper" parents="6449 8427"/>
    </justification>
  </clause>

  <clause id="8429">
    <literal><![CDATA[
      T(x,T(x * y,z)) * K(y,T(x,z)) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(4120(a,1),8428(a,1,1))].">
      <j1 rule="para" parents="4120 8428"/>
    </justification>
  </clause>

  <clause id="8430">
    <literal><![CDATA[
      T(x * K(y,x),K(x,z) * u) = T(x,u) * K(y,T(x,u))
    ]]></literal>
    <justification jstring="[para(7354(a,1),7364(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7354 7364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8431">
    <literal><![CDATA[
      T(x * K(y,x),K(x,z) * u) = T(x * K(y,x),u)
    ]]></literal>
    <justification jstring="[hyper(333,a,4649,a(flip),b,8430,a),flip(a)].">
      <j1 rule="hyper" parents="333 4649 8430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8433">
    <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(63,a,5582,a(flip),b,8431,a),flip(a)].">
      <j1 rule="hyper" parents="63 5582 8431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8434">
    <literal><![CDATA[
      K(x,K(y,z)) * ((K(x,y) * z) \ u) = (z * K(x,y)) \ u
    ]]></literal>
    <justification jstring="[para(6019(a,1),7520(a,2,1))].">
      <j1 rule="para" parents="6019 7520"/>
    </justification>
  </clause>

  <clause id="8435">
    <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(333,a,3664,a(flip),b,7659,a),flip(a)].">
      <j1 rule="hyper" parents="333 3664 7659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8436">
    <literal><![CDATA[
      T(T(x,y) * L(x \ y,z,u),x) = T(x * L(x \ y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(333,a,3663,a(flip),b,7660,a),flip(a)].">
      <j1 rule="hyper" parents="333 3663 7660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8437">
    <literal><![CDATA[
      T(x * L(x \ (x * y),z,u),x * y) = T(T(x,x * y) * L(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(9(a,1),8436(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 8436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8438">
    <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(6788(a,1),7786(a,1,1,1))].">
      <j1 rule="para" parents="6788 7786"/>
    </justification>
  </clause>

  <clause id="8439">
    <literal><![CDATA[
      K(T(x,T(y,z)) \ K(y,u),w) = T(K(x \ K(y,u),w),T(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,5967,a(flip),b,7797,a),flip(a)].">
      <j1 rule="hyper" parents="63 5967 7797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8440">
    <literal><![CDATA[
      T(K((x / y) \ K(y,z),u),T(y,x)) = K(x \ T(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,8015,a(flip),b,8439,a),flip(a)].">
      <j1 rule="hyper" parents="63 8015 8439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8441">
    <literal><![CDATA[
      T(K(x \ T(y,z),u),T(y,x)) = K((x / y) \ K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(40,a,6891,a,b,8440,a)].">
      <j1 rule="hyper" parents="40 6891 8440"/>
    </justification>
  </clause>

  <clause id="8446">
    <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(2012(a,2),7835(a,2,2))].">
      <j1 rule="para" parents="2012 7835"/>
    </justification>
  </clause>

  <clause id="8447">
    <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(5995(a,1),7835(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5995 7835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8448">
    <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(2008(a,1),7837(a,2,2))].">
      <j1 rule="para" parents="2008 7837"/>
    </justification>
  </clause>

  <clause id="8449">
    <literal><![CDATA[
      K(x,T(y,L(x,z,u) * w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(7904,a,7736,a),flip(a)].">
      <j1 rule="hyper" parents="7904 7736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8450">
    <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(7909(a,1),5871(a,1,2))].">
      <j1 rule="para" parents="7909 5871"/>
    </justification>
  </clause>

  <clause id="8451">
    <literal><![CDATA[
      K(x,y / ((T(z,u) \ u) / w)) = K(x,y / ((z \ T(u,z)) / w))
    ]]></literal>
    <justification jstring="[hyper(63,a,7922,a(flip),b,7930,a),flip(a)].">
      <j1 rule="hyper" parents="63 7922 7930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8452">
    <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(4490(a,1),7979(a,1,1))].">
      <j1 rule="para" parents="4490 7979"/>
    </justification>
  </clause>

  <clause id="8453">
    <literal><![CDATA[
      (x \ y) / ((x \ 1) \ (y / x)) = ((y / x) / (x \ 1)) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(113(a,1),7989(a,1,2)),flip(a)].">
      <j1 rule="para" parents="113 7989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8454">
    <literal><![CDATA[
      ((x \ y) / (x \ 1)) \ T(x \ y,x) = ((y / x) / (x \ 1)) \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,7988,a,b,8453,a)].">
      <j1 rule="hyper" parents="63 7988 8453"/>
    </justification>
  </clause>

  <clause id="8455">
    <literal><![CDATA[
      K((((x * y) \ x) \ 1) * z,y) = K(z / ((x * y) \ x),y)
    ]]></literal>
    <justification jstring="[para(9(a,1),8008(a,1,2))].">
      <j1 rule="para" parents="9 8008"/>
    </justification>
  </clause>

  <clause id="8456">
    <literal><![CDATA[
      K(x * (((y * z) \ y) \ 1),z) = K(x / ((y * z) \ y),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,8195,a(flip),b,8455,a)].">
      <j1 rule="hyper" parents="63 8195 8455"/>
    </justification>
  </clause>

  <clause id="8457">
    <literal><![CDATA[
      K(x * (((y * z) \ y) \ 1),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(((y * z) \ y) \ x,z) = u
    ]]></literal>
    <justification jstring="[para(8456(a,2),6989(a,1))].">
      <j1 rule="para" parents="8456 6989"/>
    </justification>
  </clause>

  <clause id="8458">
    <literal><![CDATA[
      (K(x,y) * L(K(x,z) \ 1,u,w)) * v5 = K(x,y) * (L(K(z,x),u,w) * v5)
    ]]></literal>
    <justification jstring="[para(4367(a,2),8086(a,1,1,2,1))].">
      <j1 rule="para" parents="4367 8086"/>
    </justification>
  </clause>

  <clause id="8459">
    <literal><![CDATA[
      K(x,(y * (z / y)) / ((z / y) * x)) = K(x,z / ((y \ z) * x))
    ]]></literal>
    <justification jstring="[hyper(333,a,8183,a(flip),b,8184,a),flip(a)].">
      <j1 rule="hyper" parents="333 8183 8184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8460">
    <literal><![CDATA[
      K(x,R(x \ y,x,z / y)) = K(x,z / ((y \ z) * x))
    ]]></literal>
    <justification jstring="[hyper(63,a,7931,a,b,8459,a)].">
      <j1 rule="hyper" parents="63 7931 8459"/>
    </justification>
  </clause>

  <clause id="8461">
    <literal><![CDATA[
      K(x,R(x \ (y / z),x,y / (y / z))) = K(x,y / (z * x))
    ]]></literal>
    <justification jstring="[para(79(a,1),8460(a,2,2,2,1))].">
      <j1 rule="para" parents="79 8460"/>
    </justification>
  </clause>

  <clause id="8462">
    <literal><![CDATA[
      (T(x,L(K(y,z),u,w)) * K(v5,z)) * (K(z,v5) * L(K(y,z),u,w)) = x * ((x * L(K(y,z),u,w)) / x)
    ]]></literal>
    <justification jstring="[hyper(333,a,3311,a(flip),b,8199,a),flip(a)].">
      <j1 rule="hyper" parents="333 3311 8199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8463">
    <literal><![CDATA[
      L(a(x,y,x),K(x,x * y),z) = K(x,y) * K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,8159,a(flip),b,8264,a),flip(a)].">
      <j1 rule="hyper" parents="333 8159 8264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8465">
    <literal><![CDATA[
      L(a(x,y,x),K(x,x * y),z) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,8211,a(flip),b,8463,a),flip(a)].">
      <j1 rule="hyper" parents="333 8211 8463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8466">
    <literal><![CDATA[
      (x / (K(y,y * z) * a(y,z,y))) * K(y,y * z) = x / a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(197,a,8465,a(flip),b,102,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="197 8465 102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8467">
    <literal><![CDATA[
      ((K(x,y) / z) * (z * K(y,x))) * (1 / (z * K(y,x))) = K(x,y) / z
    ]]></literal>
    <justification jstring="[hyper(142,a,8376,a)].">
      <j1 rule="hyper" parents="142 8376"/>
    </justification>
  </clause>

  <clause id="8468">
    <literal><![CDATA[
      T(x / y,K(((x / y) \ (1 / y)) \ 1,z)) = T(x / y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(333,a,7546,a(flip),b,8413,a),flip(a)].">
      <j1 rule="hyper" parents="333 7546 8413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8469">
    <literal><![CDATA[
      T(x / y,K(z,((x / y) \ (1 / y)) \ 1)) = T(x / y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(6868,a,8468,a)].">
      <j1 rule="hyper" parents="6868 8468"/>
    </justification>
  </clause>

  <clause id="8470">
    <literal><![CDATA[
      T(x / y,K(z,(1 / y) \ (x / y))) = T(x / y,K(x,z))
    ]]></literal>
    <justification jstring="[para(5766(a,1),8469(a,1,2))].">
      <j1 rule="para" parents="5766 8469"/>
    </justification>
  </clause>

  <clause id="8471">
    <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(123,a,6255,a(flip),b,8447,a)].">
      <j1 rule="hyper" parents="123 6255 8447"/>
    </justification>
  </clause>

  <clause id="8472">
    <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(5997,a,8448,a)].">
      <j1 rule="hyper" parents="5997 8448"/>
    </justification>
  </clause>

  <clause id="8473">
    <literal><![CDATA[
      (x \ y) / (T(x,x \ y) \ 1) = (y / x) / (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(7986,a,8454,a)].">
      <j1 rule="hyper" parents="7986 8454"/>
    </justification>
  </clause>

  <clause id="8474">
    <literal><![CDATA[
      K(x,y \ z) * ((z \ y) * u) = (z \ y) * (K(x,y \ z) * u)
    ]]></literal>
    <justification jstring="[hyper(5796,a,7978,a),flip(a)].">
      <j1 rule="hyper" parents="5796 7978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8475">
    <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(5903(a,2),5962(a,1))].">
      <j1 rule="para" parents="5903 5962"/>
    </justification>
  </clause>

  <clause id="8476">
    <literal><![CDATA[
      K(x \ (T(y,z) \ u),y) != w
    ]]></literal>
    <literal><![CDATA[
      K((T(y,z) * x) \ u,y) = w
    ]]></literal>
    <justification jstring="[para(6266(a,1),8475(a,1))].">
      <j1 rule="para" parents="6266 8475"/>
    </justification>
  </clause>

  <clause id="8477">
    <literal><![CDATA[
      (x * (y * T(x,z))) \ ((x * y) * T(x,z)) = a(x,y * K(x,z),x)
    ]]></literal>
    <justification jstring="[para(6144(a,1),6065(a,1,2))].">
      <j1 rule="para" parents="6144 6065"/>
    </justification>
  </clause>

  <clause id="8478">
    <literal><![CDATA[
      a(x,y * K(x,z),x) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,T(x,z)) = u
    ]]></literal>
    <justification jstring="[para(8477(a,1),752(a,1))].">
      <j1 rule="para" parents="8477 752"/>
    </justification>
  </clause>

  <clause id="8479">
    <literal><![CDATA[
      x \ R(x,y * K(x,z),x) = K(x,y) * K(y * T(x,z),x)
    ]]></literal>
    <justification jstring="[para(7414(a,1),6070(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7414 6070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8481">
    <literal><![CDATA[
      x \ R(x,y * K(x,z),x) = K(x,y) * K(y * x,x)
    ]]></literal>
    <justification jstring="[para(7400(a,1),8479(a,2,2))].">
      <j1 rule="para" parents="7400 8479"/>
    </justification>
  </clause>

  <clause id="8482">
    <literal><![CDATA[
      x \ R(x,y * K(x,z),x) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,4923,a(flip),b,8481,a),flip(a)].">
      <j1 rule="hyper" parents="333 4923 8481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8484">
    <literal><![CDATA[
      a(x,y * K(x,z),x) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(8237,a,8482,a)].">
      <j1 rule="hyper" parents="8237 8482"/>
    </justification>
  </clause>

  <clause id="8485">
    <literal><![CDATA[
      a(x,y,T(x,z)) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(8478,a,8484,a)].">
      <j1 rule="hyper" parents="8478 8484"/>
    </justification>
  </clause>

  <clause id="8486">
    <literal><![CDATA[
      a(x,y * K(x,z),x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,8210,a(flip),b,8484,a),flip(a)].">
      <j1 rule="hyper" parents="333 8210 8484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8487">
    <literal><![CDATA[
      a(x,y,T(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = u
    ]]></literal>
    <justification jstring="[para(8485(a,2),8237(a,1))].">
      <j1 rule="para" parents="8485 8237"/>
    </justification>
  </clause>

  <clause id="8488">
    <literal><![CDATA[
      a(x,y \ T(z,x),x) = a(x,y \ z,x)
    ]]></literal>
    <justification jstring="[para(6244(a,1),8486(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6244 8486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8489">
    <literal><![CDATA[
      (x * K(y,z)) / (z \ 1) = x / (z \ K(z,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,6553,a(flip),b,6093,a),flip(a)].">
      <j1 rule="hyper" parents="63 6553 6093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8491">
    <literal><![CDATA[
      T(x,y) / (y \ 1) = x / (y \ K(y,x))
    ]]></literal>
    <justification jstring="[para(4222(a,2),8489(a,1,1))].">
      <j1 rule="para" parents="4222 8489"/>
    </justification>
  </clause>

  <clause id="8492">
    <literal><![CDATA[
      (T(x,y) / (y \ 1)) \ x = y \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(192,a,8491,a(flip))].">
      <j1 rule="hyper" parents="192 8491"/>
    </justification>
  </clause>

  <clause id="8493">
    <literal><![CDATA[
      x \ (x / (y \ K(y,x))) = (x / (y \ 1)) / x
    ]]></literal>
    <justification jstring="[hyper(121,a,8491,a(flip),b,3095,a(flip))].">
      <j1 rule="hyper" parents="121 8491 3095"/>
    </justification>
  </clause>

  <clause id="8496">
    <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(6140(a,1),6158(a,1))].">
      <j1 rule="para" parents="6140 6158"/>
    </justification>
  </clause>

  <clause id="8497">
    <literal><![CDATA[
      R(x,K(y \ 1,z),y) = ((x * u) * K(u \ 1,w)) / (K(u \ 1,w) * u)
    ]]></literal>
    <justification jstring="[para(1386(a,2),6175(a,2,2))].">
      <j1 rule="para" parents="1386 6175"/>
    </justification>
  </clause>

  <clause id="8498">
    <literal><![CDATA[
      K(x,y) * T(y,K(z,y) * (x * y)) = L(y,K(z,y) * x,y)
    ]]></literal>
    <justification jstring="[para(7382(a,1),6600(a,1,1))].">
      <j1 rule="para" parents="7382 6600"/>
    </justification>
  </clause>

  <clause id="8499">
    <literal><![CDATA[
      L(x,K(y,x) * z,x) = K(z,x) * T(x,z * x)
    ]]></literal>
    <justification jstring="[para(7349(a,1),8498(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7349 8498"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8501">
    <literal><![CDATA[
      L(x,K(y,x) * z,x) = L(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,4521,a(flip),b,8499,a),flip(a)].">
      <j1 rule="hyper" parents="333 4521 8499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8503">
    <literal><![CDATA[
      L(x,T(x,y) \ z,x) = L(x,x \ z,x)
    ]]></literal>
    <justification jstring="[para(4555(a,1),8501(a,1,2))].">
      <j1 rule="para" parents="4555 8501"/>
    </justification>
  </clause>

  <clause id="8504">
    <literal><![CDATA[
      L(x,y / T(x,z),x) = L(x,x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,7884,a,b,8503,a)].">
      <j1 rule="hyper" parents="63 7884 8503"/>
    </justification>
  </clause>

  <clause id="8506">
    <literal><![CDATA[
      T((x * K(y,z)) / (x / T(z,y)),x * K(y,z)) = L(z,z \ x,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5693,a,b,8504,a)].">
      <j1 rule="hyper" parents="63 5693 8504"/>
    </justification>
  </clause>

  <clause id="8508">
    <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(3033(a,2),6992(a,1,1))].">
      <j1 rule="para" parents="3033 6992"/>
    </justification>
  </clause>

  <clause id="8509">
    <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(333,a,6761,a,b,7003,a)].">
      <j1 rule="hyper" parents="333 6761 7003"/>
    </justification>
  </clause>

  <clause id="8510">
    <literal><![CDATA[
      L(x,y,x) \ (T(x * y,x) \ z) = ((y * x) / y) \ ((x * y) \ z)
    ]]></literal>
    <justification jstring="[para(3370(a,1),7019(a,1,2,1))].">
      <j1 rule="para" parents="3370 7019"/>
    </justification>
  </clause>

  <clause id="8511">
    <literal><![CDATA[
      K(L(x / (y \ 1),y \ 1,y) \ 1,z) = K(T(y * x,y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,7297,a(flip),b,7708,a),flip(a)].">
      <j1 rule="hyper" parents="333 7297 7708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8512">
    <literal><![CDATA[
      L(((x / y) / x) \ 1,(x / y) / x,x) = x / (y \ T(x,y \ 1))
    ]]></literal>
    <justification jstring="[para(3091(a,1),7941(a,2,2))].">
      <j1 rule="para" parents="3091 7941"/>
    </justification>
  </clause>

  <clause id="8513">
    <literal><![CDATA[
      x / (y \ T(x,y \ 1)) = (T(x,y \ 1) / y) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,3098,a(flip),b,8512,a),flip(a)].">
      <j1 rule="hyper" parents="63 3098 8512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8514">
    <literal><![CDATA[
      (T(x,(y \ 1) \ 1) / (y \ 1)) \ x = x / ((y \ 1) \ T(x,y))
    ]]></literal>
    <justification jstring="[para(2983(a,1),8513(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2983 8513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8515">
    <literal><![CDATA[
      x / ((y \ 1) \ T(x,y)) = (T(x,y) / (y \ 1)) \ x
    ]]></literal>
    <justification jstring="[para(2983(a,1),8514(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="2983 8514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8516">
    <literal><![CDATA[
      ((T(x,y) / (y \ 1)) \ x) \ x = (y \ 1) \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(192,a,8515,a)].">
      <j1 rule="hyper" parents="192 8515"/>
    </justification>
  </clause>

  <clause id="8518">
    <literal><![CDATA[
      (x \ K(x,y)) \ y = (x \ 1) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(8492(a,1),8516(a,1,1))].">
      <j1 rule="para" parents="8492 8516"/>
    </justification>
  </clause>

  <clause id="8519">
    <literal><![CDATA[
      (x \ K(x,y)) \ y = (x \ ((x \ 1) \ y)) * x
    ]]></literal>
    <justification jstring="[hyper(333,a,1713,a,b,8518,a),flip(a)].">
      <j1 rule="hyper" parents="333 1713 8518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8520">
    <literal><![CDATA[
      (x \ K(x,y)) \ y = y * (((x \ 1) \ y) / y)
    ]]></literal>
    <justification jstring="[hyper(333,a,3111,a(flip),b,8518,a),flip(a)].">
      <j1 rule="hyper" parents="333 3111 8518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8521">
    <literal><![CDATA[
      x \ ((y \ K(y,x)) \ x) = ((y \ 1) \ x) / x
    ]]></literal>
    <justification jstring="[hyper(121,a,8518,a,b,3111,a(flip))].">
      <j1 rule="hyper" parents="121 8518 3111"/>
    </justification>
  </clause>

  <clause id="8524">
    <literal><![CDATA[
      K(x,L(L(y,z,y * K(z,y)),u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(4239(a,1),8296(a,2,2,1))].">
      <j1 rule="para" parents="4239 8296"/>
    </justification>
  </clause>

  <clause id="8525">
    <literal><![CDATA[
      K(x,L(L(y,z,y),u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(4436(a,1),8524(a,1,2,1))].">
      <j1 rule="para" parents="4436 8524"/>
    </justification>
  </clause>

  <clause id="8526">
    <literal><![CDATA[
      (x * (K(y \ x,y) * z)) / (x * z) = L(K(y \ x,y),z,x)
    ]]></literal>
    <justification jstring="[para(6896(a,1),8374(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6896 8374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8527">
    <literal><![CDATA[
      L(K(x \ y,x),z,y) * (y * z) = y * (K(x \ y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(140,a,8526,a)].">
      <j1 rule="hyper" parents="140 8526"/>
    </justification>
  </clause>

  <clause id="8529">
    <literal><![CDATA[
      L(K(x,y),z,y * x) * ((y * x) * z) = (y * x) * (K(y \ (y * x),y) * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),8527(a,1,1,1,1))].">
      <j1 rule="para" parents="9 8527"/>
    </justification>
  </clause>

  <clause id="8539">
    <literal><![CDATA[
      (x * K(y \ 1,z)) * y = (x * y) * K(y \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(141,a,8497,a)].">
      <j1 rule="hyper" parents="141 8497"/>
    </justification>
  </clause>

  <clause id="8541">
    <literal><![CDATA[
      (x * K(y \ 1,z)) \ ((x * y) * K(y \ 1,z)) = y
    ]]></literal>
    <justification jstring="[hyper(129,a,8539,a)].">
      <j1 rule="hyper" parents="129 8539"/>
    </justification>
  </clause>

  <clause id="8542">
    <literal><![CDATA[
      (x * K(y \ 1,z)) / y = (x / y) * K(y \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(123,a,152,a(flip),b,8539,a)].">
      <j1 rule="hyper" parents="123 152 8539"/>
    </justification>
  </clause>

  <clause id="8543">
    <literal><![CDATA[
      R(T(x,y * K(x \ 1,z)),y,K(x \ 1,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(8541(a,1),1044(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8541 1044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8544">
    <literal><![CDATA[
      (T(x,y \ 1) / y) * K(y \ 1,x) = x / y
    ]]></literal>
    <justification jstring="[para(4207(a,1),8542(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4207 8542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8545">
    <literal><![CDATA[
      x \ y != (z * K(u \ 1,u)) / u
    ]]></literal>
    <literal><![CDATA[
      x * (z / T(u,u \ 1)) = y
    ]]></literal>
    <justification jstring="[para(8542(a,2),5467(a,2))].">
      <j1 rule="para" parents="8542 5467"/>
    </justification>
  </clause>

  <clause id="8546">
    <literal><![CDATA[
      (T(x,y \ 1) / y) \ (x / y) = K(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(129,a,8544,a)].">
      <j1 rule="hyper" parents="129 8544"/>
    </justification>
  </clause>

  <clause id="8547">
    <literal><![CDATA[
      K(x \ 1,(1 / x) \ (y / x)) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3492,a,b,8546,a)].">
      <j1 rule="hyper" parents="63 3492 8546"/>
    </justification>
  </clause>

  <clause id="8548">
    <literal><![CDATA[
      K(x \ 1,(1 / x) \ y) = K(x \ 1,y * x)
    ]]></literal>
    <justification jstring="[para(11(a,1),8547(a,1,2,2))].">
      <j1 rule="para" parents="11 8547"/>
    </justification>
  </clause>

  <clause id="8549">
    <literal><![CDATA[
      K(x \ 1,(x \ 1) \ y) = K(x \ 1,y * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,4792,a(flip),b,8548,a)].">
      <j1 rule="hyper" parents="63 4792 8548"/>
    </justification>
  </clause>

  <clause id="8550">
    <literal><![CDATA[
      K(x \ 1,y * x) = K(x \ 1,x * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,6258,a(flip),b,8549,a),flip(a)].">
      <j1 rule="hyper" parents="63 6258 8549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8551">
    <literal><![CDATA[
      (x \ 1) * (y / (x \ 1)) = y * K(x \ 1,y * x)
    ]]></literal>
    <justification jstring="[hyper(126,a,8549,a(flip),b,4460,a),flip(a)].">
      <j1 rule="hyper" parents="126 8549 4460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8552">
    <literal><![CDATA[
      T(x \ 1,y * x) = T(x \ 1,x * y)
    ]]></literal>
    <justification jstring="[hyper(124,a,8550,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 8550 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8553">
    <literal><![CDATA[
      ((x * y) \ y) * (x * y) = y * K(x \ 1,y * x)
    ]]></literal>
    <justification jstring="[para(8550(a,2),4977(a,2,2))].">
      <j1 rule="para" parents="8550 4977"/>
    </justification>
  </clause>

  <clause id="8554">
    <literal><![CDATA[
      T(x \ 1,y * x) = ((x \ 1) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(333,a,3935,a(flip),b,8552,a),flip(a)].">
      <j1 rule="hyper" parents="333 3935 8552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8555">
    <literal><![CDATA[
      T((x / y) \ 1,y * (x / y)) = T((x / y) \ 1,x)
    ]]></literal>
    <justification jstring="[para(12(a,1),8552(a,2,2))].">
      <j1 rule="para" parents="12 8552"/>
    </justification>
  </clause>

  <clause id="8556">
    <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(8552(a,1),1965(a,1,2,1,1))].">
      <j1 rule="para" parents="8552 1965"/>
    </justification>
  </clause>

  <clause id="8557">
    <literal><![CDATA[
      T(x \ 1,y * x) * L(T(x \ 1,x * y) \ 1,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      T((x \ 1) * L((x \ 1) \ 1,z,u),x * y) = w
    ]]></literal>
    <justification jstring="[para(8552(a,2),1971(a,1,1))].">
      <j1 rule="para" parents="8552 1971"/>
    </justification>
  </clause>

  <clause id="8558">
    <literal><![CDATA[
      T((x \ y) \ 1,y) = (((x \ y) \ 1) \ x) \ x
    ]]></literal>
    <justification jstring="[para(10(a,1),8554(a,1,2))].">
      <j1 rule="para" parents="10 8554"/>
    </justification>
  </clause>

  <clause id="8559">
    <literal><![CDATA[
      K(T(1 / x,y * x),z) = K(((x \ 1) \ y) \ y,z)
    ]]></literal>
    <justification jstring="[para(8554(a,1),3351(a,2,1))].">
      <j1 rule="para" parents="8554 3351"/>
    </justification>
  </clause>

  <clause id="8560">
    <literal><![CDATA[
      (1 / x) * (y / (1 / x)) = y * K(x \ 1,y * x)
    ]]></literal>
    <justification jstring="[hyper(5179,a,8551,a)].">
      <j1 rule="hyper" parents="5179 8551"/>
    </justification>
  </clause>

  <clause id="8561">
    <literal><![CDATA[
      T(x,y * (((z \ 1) * K(u \ 1,(1 / z) * u)) * w)) = T(x,y * (((u \ 1) * ((1 / z) / (u \ 1))) * w))
    ]]></literal>
    <justification jstring="[para(8551(a,2),5593(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="8551 5593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8562">
    <literal><![CDATA[
      x * K((y \ 1) \ 1,x * (y \ 1)) = y * (x / y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3939,a(flip),b,8553,a),flip(a)].">
      <j1 rule="hyper" parents="63 3939 8553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8563">
    <literal><![CDATA[
      K(((x \ 1) \ y) \ y,z) = K(1 / x,T(z,y * x))
    ]]></literal>
    <justification jstring="[hyper(6695,a,8559,a),flip(a)].">
      <j1 rule="hyper" parents="6695 8559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8564">
    <literal><![CDATA[
      (1 / (x \ y)) * (z / (1 / (x \ y))) = z * K(y \ x,z * (x \ y))
    ]]></literal>
    <justification jstring="[para(5852(a,1),8560(a,2,2))].">
      <j1 rule="para" parents="5852 8560"/>
    </justification>
  </clause>

  <clause id="8565">
    <literal><![CDATA[
      x * K(y,x * (y \ 1)) = y * (x / y)
    ]]></literal>
    <justification jstring="[para(3334(a,1),8562(a,1,2))].">
      <j1 rule="para" parents="3334 8562"/>
    </justification>
  </clause>

  <clause id="8566">
    <literal><![CDATA[
      K(x,y * (x \ 1)) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(34,a,4461,a,b,8565,a),flip(a)].">
      <j1 rule="hyper" parents="34 4461 8565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8567">
    <literal><![CDATA[
      (x / (y \ 1)) * K(y,x) = y * ((x / (y \ 1)) / y)
    ]]></literal>
    <justification jstring="[para(12(a,1),8565(a,1,2,2))].">
      <j1 rule="para" parents="12 8565"/>
    </justification>
  </clause>

  <clause id="8568">
    <literal><![CDATA[
      K(x,y * (1 / x)) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,4785,a,b,8566,a)].">
      <j1 rule="hyper" parents="63 4785 8566"/>
    </justification>
  </clause>

  <clause id="8570">
    <literal><![CDATA[
      K(x * (1 / y),y) = 1 / K(y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(197,a,8568,a(flip),b,4367,a),flip(a)].">
      <j1 rule="hyper" parents="197 8568 4367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8571">
    <literal><![CDATA[
      K(x * (1 / y),y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,4371,a(flip),b,8570,a),flip(a)].">
      <j1 rule="hyper" parents="333 4371 8570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8572">
    <literal><![CDATA[
      K((1 / x) * y,x) = K(y * (1 / x),x)
    ]]></literal>
    <justification jstring="[hyper(333,a,4866,a,b,8571,a)].">
      <j1 rule="hyper" parents="333 4866 8571"/>
    </justification>
  </clause>

  <clause id="8573">
    <literal><![CDATA[
      K(x * (1 / y),y) = K(x / y,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,4375,a,b,8571,a),flip(a)].">
      <j1 rule="hyper" parents="333 4375 8571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8574">
    <literal><![CDATA[
      K(x * (y \ 1),y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,4757,a(flip),b,8571,a)].">
      <j1 rule="hyper" parents="63 4757 8571"/>
    </justification>
  </clause>

  <clause id="8575">
    <literal><![CDATA[
      K(x \ y,x) * (y * (1 / x)) = T(y * (1 / x),x)
    ]]></literal>
    <justification jstring="[hyper(125,a,8571,a(flip),b,4261,a(flip))].">
      <j1 rule="hyper" parents="125 8571 4261"/>
    </justification>
  </clause>

  <clause id="8576">
    <literal><![CDATA[
      K((x \ 1) \ y,x \ 1) = K(y * x,x \ 1)
    ]]></literal>
    <justification jstring="[para(76(a,1),8571(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="76 8571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8577">
    <literal><![CDATA[
      (x * (1 / y)) * (x / (x * (1 / y))) = x * K(y \ x,y)
    ]]></literal>
    <justification jstring="[para(8571(a,1),5198(a,2,2))].">
      <j1 rule="para" parents="8571 5198"/>
    </justification>
  </clause>

  <clause id="8578">
    <literal><![CDATA[
      K(x / (1 / y),1 / y) = K(x * y,1 / y)
    ]]></literal>
    <justification jstring="[hyper(63,a,4759,a(flip),b,8573,a),flip(a)].">
      <j1 rule="hyper" parents="63 4759 8573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8579">
    <literal><![CDATA[
      T(K(x / (y / z),y / z),y) = K(x * (1 / (y / z)),z \ y)
    ]]></literal>
    <justification jstring="[para(8573(a,1),5773(a,1,1))].">
      <j1 rule="para" parents="8573 5773"/>
    </justification>
  </clause>

  <clause id="8580">
    <literal><![CDATA[
      K((1 / (1 / x)) * y,1 / x) = K(y * x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(333,a,4759,a(flip),b,8572,a),flip(a)].">
      <j1 rule="hyper" parents="333 4759 8572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8581">
    <literal><![CDATA[
      K((((x * y) \ x) \ 1) \ z,((x * y) \ x) \ 1) = K(z * ((x * y) \ x),y)
    ]]></literal>
    <justification jstring="[hyper(333,a,5774,a(flip),b,8576,a),flip(a)].">
      <j1 rule="hyper" parents="333 5774 8576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8582">
    <literal><![CDATA[
      K(x * y,y \ 1) = K(y * x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,4867,a(flip),b,8576,a),flip(a)].">
      <j1 rule="hyper" parents="63 4867 8576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8583">
    <literal><![CDATA[
      K(x,y / (K(z * u,u \ 1) \ z)) = K(x,y / ((u \ 1) * (z / (1 / u))))
    ]]></literal>
    <justification jstring="[para(8576(a,1),5326(a,1,2,2,1))].">
      <j1 rule="para" parents="8576 5326"/>
    </justification>
  </clause>

  <clause id="8584">
    <literal><![CDATA[
      ((1 / x) \ y) * (1 / x) = y * K(y * x,1 / x)
    ]]></literal>
    <justification jstring="[para(8578(a,1),4464(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8578 4464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8585">
    <literal><![CDATA[
      K(1 / x,T(y,z * x)) = T(K(x \ 1,y),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5907,a(flip),b,8563,a),flip(a)].">
      <j1 rule="hyper" parents="63 5907 8563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8586">
    <literal><![CDATA[
      K(1 / x,T(y,z * x)) = T(K(1 / x,y),z)
    ]]></literal>
    <justification jstring="[para(3333(a,2),8585(a,2,1))].">
      <j1 rule="para" parents="3333 8585"/>
    </justification>
  </clause>

  <clause id="8587">
    <literal><![CDATA[
      K(1 / x,T(y,z * x)) = K(1 / x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(333,a,6365,a,b,8586,a),flip(a)].">
      <j1 rule="hyper" parents="333 6365 8586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8588">
    <literal><![CDATA[
      K(1 / x,T(y,z * x)) = K(1 / T(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(333,a,5287,a,b,8586,a),flip(a)].">
      <j1 rule="hyper" parents="333 5287 8586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8589">
    <literal><![CDATA[
      K(1 / L(x,y,x),z) = K(1 / x,T(T(z,y),y))
    ]]></literal>
    <justification jstring="[hyper(63,a,7693,a(flip),b,8587,a)].">
      <j1 rule="hyper" parents="63 7693 8587"/>
    </justification>
  </clause>

  <clause id="8590">
    <literal><![CDATA[
      K(1 / T(x,y / x),z) = K(1 / x,T(z,y))
    ]]></literal>
    <justification jstring="[para(12(a,1),8588(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 8588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8591">
    <literal><![CDATA[
      K(1 / (x / (x / y)),z) = K(1 / y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,7129,a(flip),b,8590,a)].">
      <j1 rule="hyper" parents="63 7129 8590"/>
    </justification>
  </clause>

  <clause id="8592">
    <literal><![CDATA[
      K(1 / (x \ y),T(z,y)) = K(1 / (y / x),z)
    ]]></literal>
    <justification jstring="[para(76(a,1),8591(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="76 8591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8593">
    <literal><![CDATA[
      K(1 / (x / y),T(z,x)) = K(1 / (y \ x),z)
    ]]></literal>
    <justification jstring="[hyper(7064,a,8592,a),flip(a)].">
      <j1 rule="hyper" parents="7064 8592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8594">
    <literal><![CDATA[
      K(1 / L(x,y,x),z) = K(1 / x,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,6900,a(flip),b,8589,a),flip(a)].">
      <j1 rule="hyper" parents="333 6900 8589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8596">
    <literal><![CDATA[
      x / (T(y,x) \ 1) = y * ((x / (y \ 1)) / y)
    ]]></literal>
    <justification jstring="[hyper(63,a,6170,a(flip),b,8567,a)].">
      <j1 rule="hyper" parents="63 6170 8567"/>
    </justification>
  </clause>

  <clause id="8597">
    <literal><![CDATA[
      x / (y \ K(x,y)) = y * ((x / (y \ 1)) / y)
    ]]></literal>
    <justification jstring="[para(4226(a,1),8596(a,1,2))].">
      <j1 rule="para" parents="4226 8596"/>
    </justification>
  </clause>

  <clause id="8598">
    <literal><![CDATA[
      x \ (y / (x \ K(y,x))) = (y / (x \ 1)) / x
    ]]></literal>
    <justification jstring="[hyper(121,a,8597,a,b,xx)].">
      <j1 rule="hyper" parents="121 8597"/>
    </justification>
  </clause>

  <clause id="8599">
    <literal><![CDATA[
      K(x * y,1 / y) = K(y * x,1 / y)
    ]]></literal>
    <justification jstring="[hyper(63,a,4767,a(flip),b,8580,a),flip(a)].">
      <j1 rule="hyper" parents="63 4767 8580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8600">
    <literal><![CDATA[
      K((x \ y) * x,1 / x) = K(y,1 / x)
    ]]></literal>
    <justification jstring="[para(10(a,1),8599(a,2,1))].">
      <j1 rule="para" parents="10 8599"/>
    </justification>
  </clause>

  <clause id="8601">
    <literal><![CDATA[
      ((1 / (x \ y)) \ z) * (1 / (x \ y)) = z * K(z * (x \ y),y \ x)
    ]]></literal>
    <justification jstring="[para(5768(a,1),8584(a,2,2))].">
      <j1 rule="para" parents="5768 8584"/>
    </justification>
  </clause>

  <clause id="8602">
    <literal><![CDATA[
      T(x,y * K(x \ 1,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,8123,a(flip),b,8543,a)].">
      <j1 rule="hyper" parents="63 8123 8543"/>
    </justification>
  </clause>

  <clause id="8604">
    <literal><![CDATA[
      K(x,y * K(x \ 1,z)) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(121,a,8602,a(flip),b,4222,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="121 8602 4222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8606">
    <literal><![CDATA[
      T(x,K(x \ 1,y) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[para(6390(a,1),8602(a,1,2))].">
      <j1 rule="para" parents="6390 8602"/>
    </justification>
  </clause>

  <clause id="8607">
    <literal><![CDATA[
      T(x,K(1 / x,y) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[para(3333(a,2),8606(a,1,2,1))].">
      <j1 rule="para" parents="3333 8606"/>
    </justification>
  </clause>

  <clause id="8609">
    <literal><![CDATA[
      T(x,K(y,1 / x) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[para(4558(a,1),8607(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4558 8607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8610">
    <literal><![CDATA[
      K(K(x,1 / y) * z,y) = y / T(y,z)
    ]]></literal>
    <justification jstring="[hyper(197,a,8609,a(flip),b,4233,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="197 8609 4233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8611">
    <literal><![CDATA[
      K(x,y * K(x \ 1,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,4215,a,b,8604,a),flip(a)].">
      <j1 rule="hyper" parents="333 4215 8604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8612">
    <literal><![CDATA[
      K(x,y * K(z,x \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(5995(a,1),8611(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5995 8611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8613">
    <literal><![CDATA[
      K(x,T(y,x \ 1) \ z) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(7339(a,1),8611(a,1,2))].">
      <j1 rule="para" parents="7339 8611"/>
    </justification>
  </clause>

  <clause id="8614">
    <literal><![CDATA[
      K(x \ y,z * K(u,y \ x)) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(5766(a,1),8612(a,1,2,2))].">
      <j1 rule="para" parents="5766 8612"/>
    </justification>
  </clause>

  <clause id="8615">
    <literal><![CDATA[
      K(K(x,1 / y) * z,y) = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,4212,a,b,8610,a),flip(a)].">
      <j1 rule="hyper" parents="333 4212 8610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8616">
    <literal><![CDATA[
      K(K(x,y \ 1) * z,y) = K(z,y)
    ]]></literal>
    <justification jstring="[para(4615(a,1),8615(a,1,1,1))].">
      <j1 rule="para" parents="4615 8615"/>
    </justification>
  </clause>

  <clause id="8617">
    <literal><![CDATA[
      K(T(x,1 / y) / z,y) = K(x / z,y)
    ]]></literal>
    <justification jstring="[para(5220(a,1),8615(a,1,1))].">
      <j1 rule="para" parents="5220 8615"/>
    </justification>
  </clause>

  <clause id="8618">
    <literal><![CDATA[
      K(K(x \ 1,y) \ z,x) = K(z,x)
    ]]></literal>
    <justification jstring="[para(4567(a,2),8616(a,1,1))].">
      <j1 rule="para" parents="4567 8616"/>
    </justification>
  </clause>

  <clause id="8619">
    <literal><![CDATA[
      K(K(x,x \ y) * z,x / y) = K(z,x / y)
    ]]></literal>
    <justification jstring="[para(4667(a,1),8616(a,1,1,1))].">
      <j1 rule="para" parents="4667 8616"/>
    </justification>
  </clause>

  <clause id="8620">
    <literal><![CDATA[
      K(x \ T(y,z \ 1),z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(4963(a,1),8616(a,1,1))].">
      <j1 rule="para" parents="4963 8616"/>
    </justification>
  </clause>

  <clause id="8621">
    <literal><![CDATA[
      K(x * K(y,z \ 1),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(6888(a,1),8616(a,1,1))].">
      <j1 rule="para" parents="6888 8616"/>
    </justification>
  </clause>

  <clause id="8622">
    <literal><![CDATA[
      (K(x \ 1,y) \ z) * K(z,x) = T(K(x \ 1,y) \ z,x)
    ]]></literal>
    <justification jstring="[hyper(126,a,8618,a(flip),b,4215,a(flip))].">
      <j1 rule="hyper" parents="126 8618 4215"/>
    </justification>
  </clause>

  <clause id="8623">
    <literal><![CDATA[
      K(x * K(y,z \ u),u \ z) = K(x,u \ z)
    ]]></literal>
    <justification jstring="[para(5766(a,1),8621(a,1,1,2))].">
      <j1 rule="para" parents="5766 8621"/>
    </justification>
  </clause>

  <clause id="8624">
    <literal><![CDATA[
      K(x / T(y,z \ 1),z) = K(x / y,z)
    ]]></literal>
    <justification jstring="[para(5975(a,1),8621(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5975 8621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8625">
    <literal><![CDATA[
      K(T(x / (1 / (1 / y)),1 / z) / (1 / y),z) = K((x / y) / (y \ 1),z)
    ]]></literal>
    <justification jstring="[para(2163(a,1),8617(a,2,1))].">
      <j1 rule="para" parents="2163 8617"/>
    </justification>
  </clause>

  <clause id="8626">
    <literal><![CDATA[
      K(x \ y,(y \ x) * z) = K(x \ y,z * (y \ x))
    ]]></literal>
    <justification jstring="[para(88(a,1),8614(a,1,2)),flip(a)].">
      <j1 rule="para" parents="88 8614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8627">
    <literal><![CDATA[
      K(x \ y,z * (x / y)) = K(x \ y,z * (y \ x))
    ]]></literal>
    <justification jstring="[para(5523(a,1),8614(a,1,2))].">
      <j1 rule="para" parents="5523 8614"/>
    </justification>
  </clause>

  <clause id="8628">
    <literal><![CDATA[
      K((x / y) \ z,y / x) = K((y \ x) \ z,y / x)
    ]]></literal>
    <justification jstring="[para(4981(a,1),8619(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4981 8619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8629">
    <literal><![CDATA[
      K(x * (y / z),y \ z) = K(x * (z \ y),y \ z)
    ]]></literal>
    <justification jstring="[para(5523(a,1),8623(a,1,1))].">
      <j1 rule="para" parents="5523 8623"/>
    </justification>
  </clause>

  <clause id="8630">
    <literal><![CDATA[
      K(x / y,z * (x \ y)) * K(x,K(y,z * (x \ y))) = K(y \ x,(x \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(333,a,7629,a,b,8626,a)].">
      <j1 rule="hyper" parents="333 7629 8626"/>
    </justification>
  </clause>

  <clause id="8631">
    <literal><![CDATA[
      K(x \ (x * (y / x)),(y \ (y / (y / x))) * z) = K(x \ (x * (y / x)),z * ((x * (y / x)) \ x))
    ]]></literal>
    <justification jstring="[para(4508(a,1),8626(a,1,2,1))].">
      <j1 rule="para" parents="4508 8626"/>
    </justification>
  </clause>

  <clause id="8632">
    <literal><![CDATA[
      K((x * (y / x)) \ x,(x \ (x * (y / x))) * z) = K(y \ (y / (y / x)),z * (x \ (x * (y / x))))
    ]]></literal>
    <justification jstring="[para(4508(a,1),8626(a,2,1))].">
      <j1 rule="para" parents="4508 8626"/>
    </justification>
  </clause>

  <clause id="8633">
    <literal><![CDATA[
      T(K(x \ y,z * (y \ x)),x) = K((x / y) \ 1,z * (x / y))
    ]]></literal>
    <justification jstring="[para(8627(a,1),6987(a,1,1))].">
      <j1 rule="para" parents="8627 6987"/>
    </justification>
  </clause>

  <clause id="8634">
    <literal><![CDATA[
      (x * (1 / y)) * (x / (x * (1 / y))) = (y \ x) * y
    ]]></literal>
    <justification jstring="[hyper(333,a,317,a(flip),b,8577,a),flip(a)].">
      <j1 rule="hyper" parents="333 317 8577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8635">
    <literal><![CDATA[
      (K(x,y \ 1) * z) * K(z,y) = T(K(y \ 1,x) \ z,y)
    ]]></literal>
    <justification jstring="[para(4567(a,1),8622(a,1,1))].">
      <j1 rule="para" parents="4567 8622"/>
    </justification>
  </clause>

  <clause id="8636">
    <literal><![CDATA[
      T(K(x \ 1,y) \ z,x) = K(y,x \ 1) * T(z,x)
    ]]></literal>
    <justification jstring="[hyper(6089,a,8635,a),flip(a)].">
      <j1 rule="hyper" parents="6089 8635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8637">
    <literal><![CDATA[
      T(K(x,y \ 1) * z,y) = K(x,y \ 1) * T(z,y)
    ]]></literal>
    <justification jstring="[para(4567(a,1),8636(a,1,1))].">
      <j1 rule="para" parents="4567 8636"/>
    </justification>
  </clause>

  <clause id="8639">
    <literal><![CDATA[
      T(K(x,y \ 1) * T(z,y),K(x,y \ 1)) = T(z * K(x,y \ 1),y)
    ]]></literal>
    <justification jstring="[para(8637(a,1),6104(a,1,1))].">
      <j1 rule="para" parents="8637 6104"/>
    </justification>
  </clause>

  <clause id="8640">
    <literal><![CDATA[
      K(x * (1 / (y / z)),z \ y) = K(x / (y / z),z \ y)
    ]]></literal>
    <justification jstring="[hyper(5954,a,8579,a),flip(a)].">
      <j1 rule="hyper" parents="5954 8579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8641">
    <literal><![CDATA[
      x / (K(y / (z / u),u \ z) * x) = K(u \ z,y * (1 / (z / u)))
    ]]></literal>
    <justification jstring="[para(8640(a,1),4569(a,1,2,1))].">
      <j1 rule="para" parents="8640 4569"/>
    </justification>
  </clause>

  <clause id="8642">
    <literal><![CDATA[
      K((x / y) \ 1,z * (x / y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z * (y \ x)) = u
    ]]></literal>
    <justification jstring="[para(8633(a,1),7066(a,1))].">
      <j1 rule="para" parents="8633 7066"/>
    </justification>
  </clause>

  <clause id="8643">
    <literal><![CDATA[
      (1 / (x \ y)) * (z / (1 / (x \ y))) = z * K(y \ x,z * (y / x))
    ]]></literal>
    <justification jstring="[para(8627(a,2),8564(a,2,2))].">
      <j1 rule="para" parents="8627 8564"/>
    </justification>
  </clause>

  <clause id="8644">
    <literal><![CDATA[
      ((1 / (x \ y)) \ z) * (1 / (x \ y)) = z * K(z * (y / x),y \ x)
    ]]></literal>
    <justification jstring="[para(8629(a,2),8601(a,2,2))].">
      <j1 rule="para" parents="8629 8601"/>
    </justification>
  </clause>

  <clause id="8645">
    <literal><![CDATA[
      T(x * K(y,z \ 1),z) = T(x,z) * K(y,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(6097,a,8639,a),flip(a)].">
      <j1 rule="hyper" parents="6097 8639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8647">
    <literal><![CDATA[
      K(x \ y,z * (1 / (y / x))) = K(x \ y,z / (y / x))
    ]]></literal>
    <justification jstring="[hyper(4579,a,8641,a),flip(a)].">
      <j1 rule="hyper" parents="4579 8641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8648">
    <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(4593(a,1),8508(a,2,2))].">
      <j1 rule="para" parents="4593 8508"/>
    </justification>
  </clause>

  <clause id="8649">
    <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(8508(a,1),7144(a,2,2))].">
      <j1 rule="para" parents="8508 7144"/>
    </justification>
  </clause>

  <clause id="8650">
    <literal><![CDATA[
      a((x \ y) * K(x,y / x),y / (y / x),z) = a(x \ y,x,z)
    ]]></literal>
    <justification jstring="[para(79(a,1),5945(a,1,1,2,1))].">
      <j1 rule="para" parents="79 5945"/>
    </justification>
  </clause>

  <clause id="8652">
    <literal><![CDATA[
      a(x / y,x / (x / y),z) = a(y \ x,y,z)
    ]]></literal>
    <justification jstring="[para(4246(a,1),8650(a,1,1))].">
      <j1 rule="para" parents="4246 8650"/>
    </justification>
  </clause>

  <clause id="8653">
    <literal><![CDATA[
      a(((x * y) / x) / T(x,y),((x * y) / x) / (((x * y) / x) / T(x,y)),z) = a(x \ y,T(x,y),z)
    ]]></literal>
    <justification jstring="[para(3384(a,1),8652(a,2,1))].">
      <j1 rule="para" parents="3384 8652"/>
    </justification>
  </clause>

  <clause id="8654">
    <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(5984(a,1),6082(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5984 6082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8655">
    <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(8654(a,2),544(a,1))].">
      <j1 rule="para" parents="8654 544"/>
    </justification>
  </clause>

  <clause id="8656">
    <literal><![CDATA[
      R(x,K(y,z),T(u,K(y,w))) = R(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(8655,a,7521,a)].">
      <j1 rule="hyper" parents="8655 7521"/>
    </justification>
  </clause>

  <clause id="8657">
    <literal><![CDATA[
      R(R(x,y * z,K(z,u)),y,z) = R(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(8655,a,31,a),flip(a)].">
      <j1 rule="hyper" parents="8655 31"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8658">
    <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(8656(a,2),4594(a,1,1))].">
      <j1 rule="para" parents="8656 4594"/>
    </justification>
  </clause>

  <clause id="8659">
    <literal><![CDATA[
      R(x,y,T(x,z)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(6142(a,1),8657(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6142 8657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8660">
    <literal><![CDATA[
      R(T(x,y),z,T(x,u)) = R(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[para(6148(a,1),8657(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6148 8657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8663">
    <literal><![CDATA[
      R(x,y,x * K(z,x)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,4560,a,b,8659,a)].">
      <j1 rule="hyper" parents="63 4560 8659"/>
    </justification>
  </clause>

  <clause id="8664">
    <literal><![CDATA[
      R(x / y,z,x / y) = R(x / y,z,y \ x)
    ]]></literal>
    <justification jstring="[para(113(a,1),8659(a,1,3)),flip(a)].">
      <j1 rule="para" parents="113 8659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8665">
    <literal><![CDATA[
      R(x,y,(x \ z) \ z) = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(112(a,1),8659(a,1,3))].">
      <j1 rule="para" parents="112 8659"/>
    </justification>
  </clause>

  <clause id="8667">
    <literal><![CDATA[
      R(x \ y,z,y / x) = R(x \ y,z,x \ y)
    ]]></literal>
    <justification jstring="[para(4292(a,1),8663(a,1,3))].">
      <j1 rule="para" parents="4292 8663"/>
    </justification>
  </clause>

  <clause id="8668">
    <literal><![CDATA[
      R(T(x,y),x \ y,T(x,z)) = (x \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(333,a,3721,a(flip),b,8660,a),flip(a)].">
      <j1 rule="hyper" parents="333 3721 8660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8671">
    <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(8660(a,1),1525(a,1,1))].">
      <j1 rule="para" parents="8660 1525"/>
    </justification>
  </clause>

  <clause id="8672">
    <literal><![CDATA[
      R(T(x / y,K(y,x)),z,x / y) = R(x / y,z,y \ x)
    ]]></literal>
    <justification jstring="[para(5477(a,2),8664(a,1,1))].">
      <j1 rule="para" parents="5477 8664"/>
    </justification>
  </clause>

  <clause id="8673">
    <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(5304(a,1),8671(a,1,2,1))].">
      <j1 rule="para" parents="5304 8671"/>
    </justification>
  </clause>

  <clause id="8674">
    <literal><![CDATA[
      (x \ 1) \ ((x \ y) / T(y,x \ 1)) = x * (((x \ y) / y) * K(x \ 1,y))
    ]]></literal>
    <justification jstring="[hyper(333,a,8121,a(flip),b,6177,a),flip(a)].">
      <j1 rule="hyper" parents="333 8121 6177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8675">
    <literal><![CDATA[
      T(x,y) / ((1 / z) \ x) = (1 / z) * K((((z \ 1) \ x) \ 1) \ (z \ 1),y)
    ]]></literal>
    <justification jstring="[para(5011(a,1),6254(a,2,2))].">
      <j1 rule="para" parents="5011 6254"/>
    </justification>
  </clause>

  <clause id="8676">
    <literal><![CDATA[
      ((x \ 1) \ y) * K(x \ 1,x * y) = (x \ K(x * y,x \ 1)) \ y
    ]]></literal>
    <justification jstring="[para(4867(a,1),6259(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4867 6259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8677">
    <literal><![CDATA[
      (x \ K(x * y,x \ 1)) \ y = y / (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(6155,a,8676,a),flip(a)].">
      <j1 rule="hyper" parents="6155 8676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8678">
    <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(5635(a,1),8677(a,1,1,2,2))].">
      <j1 rule="para" parents="5635 8677"/>
    </justification>
  </clause>

  <clause id="8679">
    <literal><![CDATA[
      T(x,T(y,z / T(x,y))) * (z / T(x,y)) = z * K(x,z / T(x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,7109,a(flip),b,6265,a)].">
      <j1 rule="hyper" parents="63 7109 6265"/>
    </justification>
  </clause>

  <clause id="8680">
    <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(6365(a,2),6412(a,1,2,1))].">
      <j1 rule="para" parents="6365 6412"/>
    </justification>
  </clause>

  <clause id="8681">
    <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(1167(a,1),6541(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1167 6541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8682">
    <literal><![CDATA[
      T(x,y) * (((x * y) / x) / T(x,y)) = ((x \ T(y,x)) \ y) * (x \ y)
    ]]></literal>
    <justification jstring="[para(3352(a,1),6687(a,1,2,1))].">
      <j1 rule="para" parents="3352 6687"/>
    </justification>
  </clause>

  <clause id="8683">
    <literal><![CDATA[
      ((x \ T(y,x)) \ y) * (x \ y) = T(x,y) * (y / x)
    ]]></literal>
    <justification jstring="[para(864(a,1),8682(a,1,2)),flip(a)].">
      <j1 rule="para" parents="864 8682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8684">
    <literal><![CDATA[
      (T(x,y) * (y / x)) * K(x \ y,(x \ T(y,x)) \ y) = (x \ y) * ((x \ T(y,x)) \ y)
    ]]></literal>
    <justification jstring="[hyper(125,a,8683,a(flip),b,189,a)].">
      <j1 rule="hyper" parents="125 8683 189"/>
    </justification>
  </clause>

  <clause id="8685">
    <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(333,a,7701,a,b,7106,a),flip(a)].">
      <j1 rule="hyper" parents="333 7701 7106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8686">
    <literal><![CDATA[
      K(x,K((1 / y) / z,(z * y) / u)) = (T(z * y,K(x,u)) / y) / z
    ]]></literal>
    <justification jstring="[hyper(7193,a,7194,a)].">
      <j1 rule="hyper" parents="7193 7194"/>
    </justification>
  </clause>

  <clause id="8687">
    <literal><![CDATA[
      K(x,K((1 / y) / z,(z * y) / u)) = K(x,K(u,(1 / y) / z))
    ]]></literal>
    <justification jstring="[hyper(333,a,7192,a(flip),b,8686,a),flip(a)].">
      <j1 rule="hyper" parents="333 7192 8686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8688">
    <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(555(a,2),8687(a,1,2,2))].">
      <j1 rule="para" parents="555 8687"/>
    </justification>
  </clause>

  <clause id="8689">
    <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(333,a,8446,a(flip),b,7552,a),flip(a)].">
      <j1 rule="hyper" parents="333 8446 7552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8690">
    <literal><![CDATA[
      T(T(x,y) * (x \ (x \ z)),T(x,y)) = T(x \ ((z / x) * T(x,y)),x)
    ]]></literal>
    <justification jstring="[para(113(a,1),7588(a,1,1,2))].">
      <j1 rule="para" parents="113 7588"/>
    </justification>
  </clause>

  <clause id="8691">
    <literal><![CDATA[
      T(x \ (T(x,y) * (x \ z)),T(x,y)) = T(x \ ((z / x) * T(x,y)),x)
    ]]></literal>
    <justification jstring="[para(1053(a,2),8690(a,1,1))].">
      <j1 rule="para" parents="1053 8690"/>
    </justification>
  </clause>

  <clause id="8692">
    <literal><![CDATA[
      T(x \ (x \ (T(x,y) * z)),T(x,y)) = T(x \ ((z / x) * T(x,y)),x)
    ]]></literal>
    <justification jstring="[para(1053(a,2),8691(a,1,1,2))].">
      <j1 rule="para" parents="1053 8691"/>
    </justification>
  </clause>

  <clause id="8693">
    <literal><![CDATA[
      T(x \ (x \ (T(x,y) * z)),T(x,y)) = x \ (T(z / x,x) * T(x,y))
    ]]></literal>
    <justification jstring="[hyper(333,a,6674,a(flip),b,8692,a),flip(a)].">
      <j1 rule="hyper" parents="333 6674 8692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8694">
    <literal><![CDATA[
      T(x \ (x \ (T(x,y) * z)),T(x,y)) = x \ ((x \ z) * T(x,y))
    ]]></literal>
    <justification jstring="[para(113(a,1),8693(a,2,2,1))].">
      <j1 rule="para" parents="113 8693"/>
    </justification>
  </clause>

  <clause id="8695">
    <literal><![CDATA[
      T(x \ (x / y),z) * T(x,y \ 1) = K(z,y \ 1) \ (x / y)
    ]]></literal>
    <justification jstring="[para(79(a,1),7697(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="79 7697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8696">
    <literal><![CDATA[
      (x * T(y,L(z,y,x))) \ (x * (y * (z * K(y,z)))) = L(z,y,x)
    ]]></literal>
    <justification jstring="[para(4329(a,1),7803(a,1,1,2))].">
      <j1 rule="para" parents="4329 7803"/>
    </justification>
  </clause>

  <clause id="8697">
    <literal><![CDATA[
      (x * T(y,L(z,y,x))) \ (x * (T(y,z) * z)) = L(z,y,x)
    ]]></literal>
    <justification jstring="[para(4311(a,1),8696(a,1,2,2))].">
      <j1 rule="para" parents="4311 8696"/>
    </justification>
  </clause>

  <clause id="8698">
    <literal><![CDATA[
      K(x,T((y \ z) / z,u)) = K(x,T(y \ 1,u))
    ]]></literal>
    <justification jstring="[hyper(333,a,7855,a(flip),b,7857,a),flip(a)].">
      <j1 rule="hyper" parents="333 7855 7857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8700">
    <literal><![CDATA[
      K(x,T((y / z) \ 1,u)) = K(x,T(z / y,u))
    ]]></literal>
    <justification jstring="[para(79(a,1),8698(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="79 8698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8701">
    <literal><![CDATA[
      T(x,T((y / z) \ 1,u)) = T(x,T(z / y,u))
    ]]></literal>
    <justification jstring="[hyper(124,a,8700,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 8700 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8702">
    <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(6046(a,1),8701(a,2,2,1))].">
      <j1 rule="para" parents="6046 8701"/>
    </justification>
  </clause>

  <clause id="8703">
    <literal><![CDATA[
      K(T(x,y),((T(x,y) \ 1) * y) \ z) = K(x,z / ((x \ 1) * T(y,x)))
    ]]></literal>
    <justification jstring="[para(3613(a,1),8043(a,1,1))].">
      <j1 rule="para" parents="3613 8043"/>
    </justification>
  </clause>

  <clause id="8704">
    <literal><![CDATA[
      K(T(x,y),((T(x,y) \ 1) * y) \ z) = K(x,z / ((x \ 1) * y))
    ]]></literal>
    <justification jstring="[hyper(333,a,7921,a(flip),b,8703,a),flip(a)].">
      <j1 rule="hyper" parents="333 7921 8703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8705">
    <literal><![CDATA[
      T(x,y * x) * ((T(x,x * y) * K(z,x)) \ u) = K(x,z) * u
    ]]></literal>
    <justification jstring="[para(2716(a,1),8197(a,1,1,1))].">
      <j1 rule="para" parents="2716 8197"/>
    </justification>
  </clause>

  <clause id="8706">
    <literal><![CDATA[
      T(x,y * x) * (L(x,y,x) \ z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(4733(a,1),8705(a,1,2,1))].">
      <j1 rule="para" parents="4733 8705"/>
    </justification>
  </clause>

  <clause id="8707">
    <literal><![CDATA[
      T(x,x * y) * (L(x,y,x) \ z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(3678(a,1),8706(a,1,1))].">
      <j1 rule="para" parents="3678 8706"/>
    </justification>
  </clause>

  <clause id="8708">
    <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(1451(a,1),8254(a,1,2,2))].">
      <j1 rule="para" parents="1451 8254"/>
    </justification>
  </clause>

  <clause id="8709">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,T(y \ x,u)) = K((x \ y) \ z,T(y \ x,u))
    ]]></literal>
    <justification jstring="[hyper(7967,a,8390,a)].">
      <j1 rule="hyper" parents="7967 8390"/>
    </justification>
  </clause>

  <clause id="8710">
    <literal><![CDATA[
      T(T(x,x * y) * R(y,z,u),x) = T(x * R(y,z,u),x * y)
    ]]></literal>
    <justification jstring="[para(9(a,1),8435(a,1,1,2,1))].">
      <j1 rule="para" parents="9 8435"/>
    </justification>
  </clause>

  <clause id="8711">
    <literal><![CDATA[
      T(T(x,x * y) * L(y,z,u),x) = T(x * L(y,z,u),x * y)
    ]]></literal>
    <justification jstring="[para(9(a,1),8437(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 8437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8713">
    <literal><![CDATA[
      K((((x * y) \ x) \ 1) \ z,y) = K(z * ((x * y) \ x),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,5774,a(flip),b,8581,a)].">
      <j1 rule="hyper" parents="63 5774 8581"/>
    </justification>
  </clause>

  <clause id="8715">
    <literal><![CDATA[
      K((x / y) / (y \ 1),1 / y) = K((y \ x) / (y \ 1),1 / y)
    ]]></literal>
    <justification jstring="[para(2846(a,1),8625(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2846 8625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8716">
    <literal><![CDATA[
      K((x / y) / (y \ 1),1 / y) = K((y \ x) / (1 / y),1 / y)
    ]]></literal>
    <justification jstring="[hyper(333,a,4765,a,b,8715,a),flip(a)].">
      <j1 rule="hyper" parents="333 4765 8715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8717">
    <literal><![CDATA[
      K((x / y) / (1 / y),1 / y) = K((y \ x) / (1 / y),1 / y)
    ]]></literal>
    <justification jstring="[hyper(63,a,4765,a,b,8716,a)].">
      <j1 rule="hyper" parents="63 4765 8716"/>
    </justification>
  </clause>

  <clause id="8718">
    <literal><![CDATA[
      (x / y) / ((x / y) / (1 / y)) = (1 / y) * K((y \ x) / (1 / y),1 / y)
    ]]></literal>
    <justification jstring="[para(8717(a,1),4221(a,2,2))].">
      <j1 rule="para" parents="8717 4221"/>
    </justification>
  </clause>

  <clause id="8719">
    <literal><![CDATA[
      (x \ 1) \ ((x \ y) / T(y,x \ 1)) = x * ((x \ y) / T(y,x \ 1))
    ]]></literal>
    <justification jstring="[para(5450(a,1),8674(a,2,2))].">
      <j1 rule="para" parents="5450 8674"/>
    </justification>
  </clause>

  <clause id="8720">
    <literal><![CDATA[
      (x \ 1) \ ((x \ y) / T(y,x \ 1)) = x * (y \ (x \ y))
    ]]></literal>
    <justification jstring="[para(3592(a,1),8719(a,2,2))].">
      <j1 rule="para" parents="3592 8719"/>
    </justification>
  </clause>

  <clause id="8721">
    <literal><![CDATA[
      (x \ 1) \ (y \ (x \ y)) = x * (y \ (x \ y))
    ]]></literal>
    <justification jstring="[para(3592(a,1),8720(a,1,2))].">
      <j1 rule="para" parents="3592 8720"/>
    </justification>
  </clause>

  <clause id="8722">
    <literal><![CDATA[
      ((1 / (x \ 1)) \ (x \ 1)) * (x * (y \ (x \ y))) = (1 / (x \ 1)) \ (y \ (x \ y))
    ]]></literal>
    <justification jstring="[para(8721(a,1),1469(a,1,2))].">
      <j1 rule="para" parents="8721 1469"/>
    </justification>
  </clause>

  <clause id="8723">
    <literal><![CDATA[
      T(x,y) / ((1 / z) \ x) = K(((((z \ 1) \ x) \ 1) * z) \ 1,y) / z
    ]]></literal>
    <justification jstring="[hyper(333,a,7699,a(flip),b,8675,a),flip(a)].">
      <j1 rule="hyper" parents="333 7699 8675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8724">
    <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(63,a,6648,a,b,8681,a)].">
      <j1 rule="hyper" parents="63 6648 8681"/>
    </justification>
  </clause>

  <clause id="8725">
    <literal><![CDATA[
      K(x / y,z) * K(K(y \ x,z) * x,x) = K(x / T(y,x),z)
    ]]></literal>
    <justification jstring="[para(3878(a,1),8685(a,2,1))].">
      <j1 rule="para" parents="3878 8685"/>
    </justification>
  </clause>

  <clause id="8726">
    <literal><![CDATA[
      T(x * K(x / y,z),x) = x * K(x / T(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(126,a,8725,a(flip),b,7106,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="126 8725 7106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8727">
    <literal><![CDATA[
      T(x * K(x / y,z),x) = x * K(T(x,y) / y,z)
    ]]></literal>
    <justification jstring="[para(3625(a,2),8726(a,2,2,1))].">
      <j1 rule="para" parents="3625 8726"/>
    </justification>
  </clause>

  <clause id="8728">
    <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(111(a,1),8708(a,1,2)),flip(a)].">
      <j1 rule="para" parents="111 8708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8729">
    <literal><![CDATA[
      (x / y) / ((x / y) / (1 / y)) = (1 / y) * K((y \ x) * y,1 / y)
    ]]></literal>
    <justification jstring="[para(8578(a,1),8718(a,2,2))].">
      <j1 rule="para" parents="8578 8718"/>
    </justification>
  </clause>

  <clause id="8730">
    <literal><![CDATA[
      (x / y) / ((x / y) / (1 / y)) = (1 / y) * K(x,1 / y)
    ]]></literal>
    <justification jstring="[para(8600(a,1),8729(a,2,2))].">
      <j1 rule="para" parents="8600 8729"/>
    </justification>
  </clause>

  <clause id="8731">
    <literal><![CDATA[
      (x / y) / ((x / y) / (1 / y)) = K(x,1 / y) / y
    ]]></literal>
    <justification jstring="[hyper(333,a,4885,a(flip),b,8730,a),flip(a)].">
      <j1 rule="hyper" parents="333 4885 8730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8732">
    <literal><![CDATA[
      x / ((y / (x \ y)) / (1 / (x \ y))) = K(y,1 / (x \ y)) / (x \ y)
    ]]></literal>
    <justification jstring="[para(76(a,1),8731(a,1,1))].">
      <j1 rule="para" parents="76 8731"/>
    </justification>
  </clause>

  <clause id="8733">
    <literal><![CDATA[
      K(x,1 / (y \ x)) / (y \ x) = y / (y / (1 / (y \ x)))
    ]]></literal>
    <justification jstring="[para(76(a,1),8732(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="76 8732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8735">
    <literal><![CDATA[
      K(x,y / x) / (y \ x) = y / (y / (1 / (y \ x)))
    ]]></literal>
    <justification jstring="[para(4724(a,1),8733(a,1,1))].">
      <j1 rule="para" parents="4724 8733"/>
    </justification>
  </clause>

  <clause id="8736">
    <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(8735(a,2),2231(a,1,2))].">
      <j1 rule="para" parents="8735 2231"/>
    </justification>
  </clause>

  <clause id="8737">
    <literal><![CDATA[
      (x / y) \ (L(y,z,u) * (y \ x)) = x \ ((L(y,z,u) * (y \ x)) * y)
    ]]></literal>
    <justification jstring="[hyper(6649,a,8724,a)].">
      <j1 rule="hyper" parents="6649 8724"/>
    </justification>
  </clause>

  <clause id="8740">
    <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(63,a,6534,a(flip),b,7480,a)].">
      <j1 rule="hyper" parents="63 6534 7480"/>
    </justification>
  </clause>

  <clause id="8742">
    <literal><![CDATA[
      R(x,T(y,T(x,z)),R(x,u,w)) = R(x,y,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,5582,a(flip),b,8740,a),flip(a)].">
      <j1 rule="hyper" parents="63 5582 8740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8743">
    <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(6917(a,1),8742(a,1,2))].">
      <j1 rule="para" parents="6917 8742"/>
    </justification>
  </clause>

  <clause id="8744">
    <literal><![CDATA[
      T((T(x,y) \ R(T(z,y),u,w)) * K(y,x \ R(z,u,w)),y) = T(x,y) \ R(T(z,y),u,w)
    ]]></literal>
    <justification jstring="[para(7411(a,1),7596(a,1,1,2))].">
      <j1 rule="para" parents="7411 7596"/>
    </justification>
  </clause>

  <clause id="8745">
    <literal><![CDATA[
      K(x,T((y * R(x,z,u)) / w,w)) = K(x,(w / R(x,z,u)) \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,7945,a(flip),b,7752,a)].">
      <j1 rule="hyper" parents="63 7945 7752"/>
    </justification>
  </clause>

  <clause id="8747">
    <literal><![CDATA[
      K(x,(y / R(x,z,u)) \ w) = K(x,y \ (w * R(x,z,u)))
    ]]></literal>
    <justification jstring="[para(113(a,1),8745(a,1,2)),flip(a)].">
      <j1 rule="para" parents="113 8745"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8748">
    <literal><![CDATA[
      K(x,(R(x,y,z) \ u) \ w) = K(x,u \ (w * R(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,7470,a(flip),b,8747,a)].">
      <j1 rule="hyper" parents="63 7470 8747"/>
    </justification>
  </clause>

  <clause id="8749">
    <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(6836,a,7821,a)].">
      <j1 rule="hyper" parents="6836 7821"/>
    </justification>
  </clause>

  <clause id="8750">
    <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(7104(a,1),8278(a,1,1))].">
      <j1 rule="para" parents="7104 8278"/>
    </justification>
  </clause>

  <clause id="8751">
    <literal><![CDATA[
      R(K(x,(T(y,z) / u) / (y / u)),y / u,u) = T(y,K(x,z)) / y
    ]]></literal>
    <justification jstring="[hyper(333,a,156,a(flip),b,8411,a),flip(a)].">
      <j1 rule="hyper" parents="333 156 8411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8752">
    <literal><![CDATA[
      R(K(x,(T(y,z) / u) / (y / u)),y / u,u) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(333,a,4261,a,b,8751,a),flip(a)].">
      <j1 rule="hyper" parents="333 4261 8751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8754">
    <literal><![CDATA[
      R(K(x,(T(y,z) / u) / (y / u)),y / u,u) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(333,a,6785,a,b,8752,a),flip(a)].">
      <j1 rule="hyper" parents="333 6785 8752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8755">
    <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(7450(a,1),8433(a,1,1,2))].">
      <j1 rule="para" parents="7450 8433"/>
    </justification>
  </clause>

  <clause id="8756">
    <literal><![CDATA[
      R(x,K(x,y) * z,R(x,u,w)) = R(x,z,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,5582,a(flip),b,8755,a),flip(a)].">
      <j1 rule="hyper" parents="63 5582 8755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8758">
    <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(8756(a,1),5714(a,2,2,2,1,1))].">
      <j1 rule="para" parents="8756 5714"/>
    </justification>
  </clause>

  <clause id="8759">
    <literal><![CDATA[
      L(K(x,y),z,y * x) * ((y * x) * z) = (y * x) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),8529(a,2,2,1,1))].">
      <j1 rule="para" parents="9 8529"/>
    </justification>
  </clause>

  <clause id="8760">
    <literal><![CDATA[
      ((x * y) * (K(y,x) * z)) / (z * T(x * y,z)) = L(K(y,x),z,x * y)
    ]]></literal>
    <justification jstring="[hyper(123,a,8759,a(flip),b,235,a)].">
      <j1 rule="hyper" parents="123 8759 235"/>
    </justification>
  </clause>

  <clause id="8761">
    <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(8759(a,1),268(a,1,1)),flip(b)].">
      <j1 rule="para" parents="8759 268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8763">
    <literal><![CDATA[
      R(x,K(y,z),u * K(z,y)) * u = (x * K(y,z)) * (K(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(6846(a,1),8658(a,1,1,3))].">
      <j1 rule="para" parents="6846 8658"/>
    </justification>
  </clause>

  <clause id="8764">
    <literal><![CDATA[
      R(x,K(y,z),u * K(z,y)) * u = (x * K(y,z)) * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(4567(a,1),8763(a,2,2))].">
      <j1 rule="para" parents="4567 8763"/>
    </justification>
  </clause>

  <clause id="8765">
    <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(8749(a,1),6836(a,1))].">
      <j1 rule="para" parents="8749 6836"/>
    </justification>
  </clause>

  <clause id="8766">
    <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(6889(a,1),8750(a,1,1,2,1))].">
      <j1 rule="para" parents="6889 8750"/>
    </justification>
  </clause>

  <clause id="8767">
    <literal><![CDATA[
      a(x,y * K(z,u),K(u,z)) = L(K(z,u),y,x) * K(u,z)
    ]]></literal>
    <justification jstring="[hyper(6038,a,7844,a)].">
      <j1 rule="hyper" parents="6038 7844"/>
    </justification>
  </clause>

  <clause id="8768">
    <literal><![CDATA[
      a(x,y * K(z,u),K(u,z)) = K(u,z) * L(K(z,u),y,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,2008,a(flip),b,8767,a),flip(a)].">
      <j1 rule="hyper" parents="333 2008 8767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8769">
    <literal><![CDATA[
      K(x,y) * L(K(y,x),z * K(x,y),u) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(5995(a,1),8768(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5995 8768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8770">
    <literal><![CDATA[
      T(x,a(y,z,K(x,u))) = x
    ]]></literal>
    <justification jstring="[para(8769(a,1),7362(a,1,2))].">
      <j1 rule="para" parents="8769 7362"/>
    </justification>
  </clause>

  <clause id="8771">
    <literal><![CDATA[
      K(x,y) * a(z,u,K(y,w)) = a(z,u,K(y,w)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(8770(a,1),6390(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8770 6390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8772">
    <literal><![CDATA[
      T(T(T(x,y \ x) / y,x),x / z) = K(y \ x,z \ x) * (x / y)
    ]]></literal>
    <justification jstring="[para(7584(a,1),6723(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7584 6723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8773">
    <literal><![CDATA[
      T(T(T(x,y \ x) / y,x),x / z) = T(x / y,T(z \ x,y))
    ]]></literal>
    <justification jstring="[hyper(333,a,6511,a(flip),b,8772,a),flip(a)].">
      <j1 rule="hyper" parents="333 6511 8772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8774">
    <literal><![CDATA[
      T(x / y,T(z \ x,y)) = T(x / y,x / z)
    ]]></literal>
    <justification jstring="[para(3367(a,1),8773(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3367 8773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8775">
    <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(6901(a,1),6939(a,1,2,2,1))].">
      <j1 rule="para" parents="6901 6939"/>
    </justification>
  </clause>

  <clause id="8777">
    <literal><![CDATA[
      x \ (((y * T(x,K(z,u))) / y) * w) = x * (T(T(x,K(z,u)),y) \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,7228,a(flip),b,7231,a),flip(a)].">
      <j1 rule="hyper" parents="63 7228 7231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8778">
    <literal><![CDATA[
      x \ (T((y * x) / y,K(z,u)) * w) = x * (T(T(x,K(z,u)),y) \ w)
    ]]></literal>
    <justification jstring="[para(476(a,1),8777(a,1,2,1))].">
      <j1 rule="para" parents="476 8777"/>
    </justification>
  </clause>

  <clause id="8779">
    <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(63,a,6994,a(flip),b,8778,a)].">
      <j1 rule="hyper" parents="63 6994 8778"/>
    </justification>
  </clause>

  <clause id="8780">
    <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(6365(a,2),8779(a,1,2,1,2))].">
      <j1 rule="para" parents="6365 8779"/>
    </justification>
  </clause>

  <clause id="8781">
    <literal><![CDATA[
      T(x * K(x * K(y,z),u),K(y,z)) = K(y,z) \ T(x / K(z,y),T(u,K(z,y)))
    ]]></literal>
    <justification jstring="[para(5994(a,1),7249(a,1,1,2,1))].">
      <j1 rule="para" parents="5994 7249"/>
    </justification>
  </clause>

  <clause id="8782">
    <literal><![CDATA[
      T(T(x,K(y,z \ u)),(z \ u) \ y) = T(x,y / (((z \ 1) \ 1) \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,3189,a(flip),b,7576,a)].">
      <j1 rule="hyper" parents="63 3189 7576"/>
    </justification>
  </clause>

  <clause id="8783">
    <literal><![CDATA[
      T(x,y / (((z \ 1) \ 1) \ u)) = T(x,y / (z \ u))
    ]]></literal>
    <justification jstring="[hyper(7578,a,8782,a),flip(a)].">
      <j1 rule="hyper" parents="7578 8782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8784">
    <literal><![CDATA[
      K(x,R(x,y,z) \ (R(x,y,z) * (R(T(x,u),y,z) * w))) = K(x,R(x,y,z) * w)
    ]]></literal>
    <justification jstring="[para(27(a,2),7600(a,1,2,2,2,1))].">
      <j1 rule="para" parents="27 7600"/>
    </justification>
  </clause>

  <clause id="8785">
    <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(333,a,6521,a(flip),b,7689,a),flip(a)].">
      <j1 rule="hyper" parents="333 6521 7689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8787">
    <literal><![CDATA[
      K(x,(T(y * z,z \ 1) / u) * w) = K(x,((((y * z) \ y) \ y) / u) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,7510,a(flip),b,7799,a)].">
      <j1 rule="hyper" parents="63 7510 7799"/>
    </justification>
  </clause>

  <clause id="8788">
    <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(252(a,1),7809(a,2,1))].">
      <j1 rule="para" parents="252 7809"/>
    </justification>
  </clause>

  <clause id="8789">
    <literal><![CDATA[
      (R(x,y,R(x,z,u)) * w) * x = (x * w) * R(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,7756,a(flip),b,8788,a),flip(a)].">
      <j1 rule="hyper" parents="63 7756 8788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8790">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,T(y \ x,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(z * ((x \ y) \ 1),T(y \ x,u)) = w
    ]]></literal>
    <justification jstring="[para(7968(a,1),7967(a,1))].">
      <j1 rule="para" parents="7968 7967"/>
    </justification>
  </clause>

  <clause id="8791">
    <literal><![CDATA[
      L(T((1 / x) \ y,z),1 / x,L(x,x,x)) = T(1 \ (L(x,x,x) * y),z)
    ]]></literal>
    <justification jstring="[para(8233(a,1),8235(a,1,2))].">
      <j1 rule="para" parents="8233 8235"/>
    </justification>
  </clause>

  <clause id="8792">
    <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(8279(a,1),8203(a,1))].">
      <j1 rule="para" parents="8279 8203"/>
    </justification>
  </clause>

  <clause id="8793">
    <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(1587(a,1),8336(a,1,2))].">
      <j1 rule="para" parents="1587 8336"/>
    </justification>
  </clause>

  <clause id="8794">
    <literal><![CDATA[
      x * a(x,y,R(x,z,u)) = R(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(753,a,8793,a)].">
      <j1 rule="hyper" parents="753 8793"/>
    </justification>
  </clause>

  <clause id="8795">
    <literal><![CDATA[
      x \ R(x,y,R(x,z,u)) = a(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(752,a,8793,a),flip(a)].">
      <j1 rule="hyper" parents="752 8793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8796">
    <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(8793(a,1),752(a,1))].">
      <j1 rule="para" parents="8793 752"/>
    </justification>
  </clause>

  <clause id="8797">
    <literal><![CDATA[
      K(x * R(y,z,u),y) * K(y,x) = a(y,x,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,8335,a,b,8795,a)].">
      <j1 rule="hyper" parents="63 8335 8795"/>
    </justification>
  </clause>

  <clause id="8798">
    <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(8795(a,1),7808(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8795 7808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8799">
    <literal><![CDATA[
      T(x,y) \ R(T(x,y),T(z,x),R(T(x,y),u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(T(x,y),z,R(T(x,y),u,w)) = v5
    ]]></literal>
    <justification jstring="[para(8743(a,2),8796(a,1,2))].">
      <j1 rule="para" parents="8743 8796"/>
    </justification>
  </clause>

  <clause id="8800">
    <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(7461(a,1),8797(a,1,1))].">
      <j1 rule="para" parents="7461 8797"/>
    </justification>
  </clause>

  <clause id="8801">
    <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(4689,a,8798,a)].">
      <j1 rule="hyper" parents="4689 8798"/>
    </justification>
  </clause>

  <clause id="8802">
    <literal><![CDATA[
      ((x \ y) \ y) \ R((x \ y) \ y,z,R(x,u,w)) = a(x,z,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,1048,a(flip),b,8801,a)].">
      <j1 rule="hyper" parents="63 1048 8801"/>
    </justification>
  </clause>

  <clause id="8803">
    <literal><![CDATA[
      (x \ (x \ 1)) * (x * (y \ (x \ y))) = (1 / (x \ 1)) \ (y \ (x \ y))
    ]]></literal>
    <justification jstring="[para(76(a,1),8722(a,1,1,1))].">
      <j1 rule="para" parents="76 8722"/>
    </justification>
  </clause>

  <clause id="8806">
    <literal><![CDATA[
      (1 / (x \ 1)) \ (y \ (x \ y)) = (x * x) \ (x * (y \ (x \ y)))
    ]]></literal>
    <justification jstring="[hyper(735,a,8803,a),flip(a)].">
      <j1 rule="hyper" parents="735 8803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8808">
    <literal><![CDATA[
      L(x \ (y \ (x \ y)),x,x) = (1 / (x \ 1)) \ (y \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(333,a,99,a,b,8806,a)].">
      <j1 rule="hyper" parents="333 99 8806"/>
    </justification>
  </clause>

  <clause id="8810">
    <literal><![CDATA[
      L(x \ (y \ (x \ y)),x,x) = x \ (y \ (x \ y))
    ]]></literal>
    <justification jstring="[para(76(a,1),8808(a,2,1))].">
      <j1 rule="para" parents="76 8808"/>
    </justification>
  </clause>

  <clause id="8812">
    <literal><![CDATA[
      T(x * K(x * K(y,z),u),K(z,y)) = K(y,z) \ T(x / K(z,y),T(u,K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(6868,a,8781,a)].">
      <j1 rule="hyper" parents="6868 8781"/>
    </justification>
  </clause>

  <clause id="8813">
    <literal><![CDATA[
      K(x,R(T(x,y),z,u) * w) = K(x,R(x,z,u) * w)
    ]]></literal>
    <justification jstring="[para(9(a,1),8784(a,1,2))].">
      <j1 rule="para" parents="9 8784"/>
    </justification>
  </clause>

  <clause id="8815">
    <literal><![CDATA[
      T(x * K(x * K(y,z),u),K(z,y)) = K(y,z) \ T(x * K(y,z),T(u,K(z,y)))
    ]]></literal>
    <justification jstring="[para(5994(a,1),8812(a,2,2,1))].">
      <j1 rule="para" parents="5994 8812"/>
    </justification>
  </clause>

  <clause id="8816">
    <literal><![CDATA[
      L(K((x / y) \ x,z),x \ (x / (1 / (1 / y))),u) = K(1 / (x \ (x / y)),z)
    ]]></literal>
    <justification jstring="[para(5856(a,1),6133(a,1,1))].">
      <j1 rule="para" parents="5856 6133"/>
    </justification>
  </clause>

  <clause id="8817">
    <literal><![CDATA[
      L(K(x,y),z \ (z / (1 / (1 / x))),u) = K(1 / (z \ (z / x)),y)
    ]]></literal>
    <justification jstring="[para(79(a,1),8816(a,1,1,1))].">
      <j1 rule="para" parents="79 8816"/>
    </justification>
  </clause>

  <clause id="8819">
    <literal><![CDATA[
      L(K(x,y),1 / (1 / (z \ (z / x))),u) = K(1 / (z \ (z / x)),y)
    ]]></literal>
    <justification jstring="[para(2899(a,2),8817(a,1,2))].">
      <j1 rule="para" parents="2899 8817"/>
    </justification>
  </clause>

  <clause id="8820">
    <literal><![CDATA[
      L(K(x,y),z \ (z / x),u) = K(1 / (z \ (z / x)),y)
    ]]></literal>
    <justification jstring="[hyper(2629,a,8819,a)].">
      <j1 rule="hyper" parents="2629 8819"/>
    </justification>
  </clause>

  <clause id="8821">
    <literal><![CDATA[
      L(K(x,y),z \ (z / x),u) = K((z / x) \ z,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,5856,a(flip),b,8820,a),flip(a)].">
      <j1 rule="hyper" parents="333 5856 8820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8822">
    <literal><![CDATA[
      L(K(x,y),z \ (z / x),u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,706,a(flip),b,8821,a),flip(a)].">
      <j1 rule="hyper" parents="333 706 8821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8824">
    <literal><![CDATA[
      (x / y) \ (x * (K(y,z) * (x \ (x / y)))) = T(K(y,z),x \ (x / y))
    ]]></literal>
    <justification jstring="[para(8822(a,1),838(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8822 838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8825">
    <literal><![CDATA[
      (x / y) \ (x * (K(y,z) * (x \ (x / y)))) = T(K(y,z),1 / y)
    ]]></literal>
    <justification jstring="[hyper(333,a,5828,a(flip),b,8824,a),flip(a)].">
      <j1 rule="hyper" parents="333 5828 8824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8827">
    <literal><![CDATA[
      (x / y) \ (x * (K(y,z) * (x \ (x / y)))) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,1381,a(flip),b,8825,a),flip(a)].">
      <j1 rule="hyper" parents="333 1381 8825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8828">
    <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(6370(a,1),6973(a,2,1,2))].">
      <j1 rule="para" parents="6370 6973"/>
    </justification>
  </clause>

  <clause id="8829">
    <literal><![CDATA[
      R(x,y / T(x,z),T(x,z)) = ((y * K(x,y / T(x,z))) * x) / y
    ]]></literal>
    <justification jstring="[para(8679(a,1),7254(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="8679 7254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8830">
    <literal><![CDATA[
      ((x * K(y,x / T(y,z))) * y) / x = R(y,x / T(y,z),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,8659,a(flip),b,8829,a),flip(a)].">
      <j1 rule="hyper" parents="63 8659 8829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8832">
    <literal><![CDATA[
      R(x,y / T(x,z),x) = ((y * K(x,y / x)) * x) / y
    ]]></literal>
    <justification jstring="[para(7421(a,1),8830(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7421 8830"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8833">
    <literal><![CDATA[
      R(x,y / T(x,z),x) = ((x * (y / x)) * x) / y
    ]]></literal>
    <justification jstring="[para(318(a,1),8832(a,2,1,1))].">
      <j1 rule="para" parents="318 8832"/>
    </justification>
  </clause>

  <clause id="8835">
    <literal><![CDATA[
      R(x,y / T(x,z),x) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y / x,x) = u
    ]]></literal>
    <justification jstring="[para(8833(a,2),799(a,1))].">
      <j1 rule="para" parents="8833 799"/>
    </justification>
  </clause>

  <clause id="8836">
    <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(27(a,2),7785(a,1,1,2))].">
      <j1 rule="para" parents="27 7785"/>
    </justification>
  </clause>

  <clause id="8837">
    <literal><![CDATA[
      (x / T(y,x)) * L(z,K(x,y),y \ x) = (x / y) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(5082,a,7792,a),flip(a)].">
      <j1 rule="hyper" parents="5082 7792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8838">
    <literal><![CDATA[
      (x \ y) * (a(x,x \ y,x) * z) = (y / T(x,y)) * L(z,K(y,x),x \ y)
    ]]></literal>
    <justification jstring="[hyper(333,a,8285,a,b,8837,a)].">
      <j1 rule="hyper" parents="333 8285 8837"/>
    </justification>
  </clause>

  <clause id="8839">
    <literal><![CDATA[
      ((x \ y) * a(x,x \ y,x)) \ ((y / T(x,y)) * L(z,K(y,x),x \ y)) = L(z,a(x,x \ y,x),x \ y)
    ]]></literal>
    <justification jstring="[hyper(121,a,8838,a(flip),b,97,a)].">
      <j1 rule="hyper" parents="121 8838 97"/>
    </justification>
  </clause>

  <clause id="8840">
    <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(8079(a,1),7846(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="8079 7846"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8841">
    <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(2005(a,1),8840(a,1,2,2))].">
      <j1 rule="para" parents="2005 8840"/>
    </justification>
  </clause>

  <clause id="8842">
    <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(8841(a,1),5485(a,1,1))].">
      <j1 rule="para" parents="8841 5485"/>
    </justification>
  </clause>

  <clause id="8843">
    <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(6101(a,1),8842(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6101 8842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8844">
    <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(6788(a,2),7900(a,1,2,1))].">
      <j1 rule="para" parents="6788 7900"/>
    </justification>
  </clause>

  <clause id="8845">
    <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(4565(a,1),8050(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4565 8050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8846">
    <literal><![CDATA[
      L(x * K(y,z),K(z,y),x * K(y,z)) = T(K(y,z) * x,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,3676,a(flip),b,8845,a),flip(a)].">
      <j1 rule="hyper" parents="333 3676 8845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8847">
    <literal><![CDATA[
      K((x \ y) \ z,T(y \ x,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(z * ((x \ y) \ 1),T(y \ x,u)) = w
    ]]></literal>
    <justification jstring="[para(8709(a,1),8790(a,1))].">
      <j1 rule="para" parents="8709 8790"/>
    </justification>
  </clause>

  <clause id="8848">
    <literal><![CDATA[
      K(x * ((y \ z) \ 1),T(z \ y,z)) = K((y \ z) \ x,y / z)
    ]]></literal>
    <justification jstring="[hyper(8847,a,6923,a)].">
      <j1 rule="hyper" parents="8847 6923"/>
    </justification>
  </clause>

  <clause id="8849">
    <literal><![CDATA[
      K(x * ((y \ z) \ 1),y / z) = K((y \ z) \ x,y / z)
    ]]></literal>
    <justification jstring="[hyper(7076,a,8848,a)].">
      <j1 rule="hyper" parents="7076 8848"/>
    </justification>
  </clause>

  <clause id="8850">
    <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(6386(a,1),8800(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6386 8800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8851">
    <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(333,a,8797,a(flip),b,8850,a),flip(a)].">
      <j1 rule="hyper" parents="333 8797 8850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8853">
    <literal><![CDATA[
      a(x,T(y,x),R(x,z,u)) = a(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[para(534(a,1),8851(a,1,2,2))].">
      <j1 rule="para" parents="534 8851"/>
    </justification>
  </clause>

  <clause id="8854">
    <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(6840(a,1),8836(a,1,2))].">
      <j1 rule="para" parents="6840 8836"/>
    </justification>
  </clause>

  <clause id="8855">
    <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(7814(a,1),8844(a,1,2))].">
      <j1 rule="para" parents="7814 8844"/>
    </justification>
  </clause>

  <clause id="8856">
    <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(2739(a,1),8854(a,1,2))].">
      <j1 rule="para" parents="2739 8854"/>
    </justification>
  </clause>

  <clause id="8858">
    <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(8856(a,1),5582(a,1,1,2))].">
      <j1 rule="para" parents="8856 5582"/>
    </justification>
  </clause>

  <clause id="8859">
    <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(4649(a,1),8858(a,1,1))].">
      <j1 rule="para" parents="4649 8858"/>
    </justification>
  </clause>

  <clause id="8860">
    <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(63,a,5683,a(flip),b,8859,a),flip(a)].">
      <j1 rule="hyper" parents="63 5683 8859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8861">
    <literal><![CDATA[
      (x * (y \ z)) * (u * (((x * (y \ z)) \ z) / u)) = (x * (u * ((x \ y) / u))) * (y \ z)
    ]]></literal>
    <justification jstring="[para(4127(a,1),4143(a,2,1))].">
      <j1 rule="para" parents="4127 4143"/>
    </justification>
  </clause>

  <clause id="8862">
    <literal><![CDATA[
      ((K(x,y) * z) * (z \ x)) / T(x,y) = a(K(x,y),z,z \ x)
    ]]></literal>
    <justification jstring="[para(7915(a,1),4351(a,1,2))].">
      <j1 rule="para" parents="7915 4351"/>
    </justification>
  </clause>

  <clause id="8864">
    <literal><![CDATA[
      R(K(R(x,y,z),u),R(x,y,z),y * z) = ((T(x,u) * y) * z) / ((x * y) * z)
    ]]></literal>
    <justification jstring="[para(107(a,1),5085(a,1,1)),flip(a)].">
      <j1 rule="para" parents="107 5085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8865">
    <literal><![CDATA[
      ((T(x,y) * z) * u) / ((x * z) * u) = K(R(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(3568,a,8864,a),flip(a)].">
      <j1 rule="hyper" parents="3568 8864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8867">
    <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(5455(a,1),5489(a,2,1))].">
      <j1 rule="para" parents="5455 5489"/>
    </justification>
  </clause>

  <clause id="8868">
    <literal><![CDATA[
      R(R(x,y,T(z,u)),y * T(z,u),K(u,z)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,20,a,b,8867,a),flip(a)].">
      <j1 rule="hyper" parents="333 20 8867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8870">
    <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(234(a,1),8868(a,1,2))].">
      <j1 rule="para" parents="234 8868"/>
    </justification>
  </clause>

  <clause id="8871">
    <literal><![CDATA[
      R(R(x,y / z,z),y,K(z \ y,z)) = R(x,z \ y,z)
    ]]></literal>
    <justification jstring="[para(8315(a,1),8870(a,1,1))].">
      <j1 rule="para" parents="8315 8870"/>
    </justification>
  </clause>

  <clause id="8872">
    <literal><![CDATA[
      x \ K((x * ((1 / y) / x)) \ 1,z) = (y \ T(y * K(x \ 1,x),z)) / x
    ]]></literal>
    <justification jstring="[hyper(63,a,4495,a,b,5596,a)].">
      <j1 rule="hyper" parents="63 4495 5596"/>
    </justification>
  </clause>

  <clause id="8873">
    <literal><![CDATA[
      x \ K((x * ((y \ 1) / x)) \ 1,z) = (y \ T(y * K(x \ 1,x),z)) / x
    ]]></literal>
    <justification jstring="[para(5194(a,1),8872(a,1,2))].">
      <j1 rule="para" parents="5194 8872"/>
    </justification>
  </clause>

  <clause id="8874">
    <literal><![CDATA[
      x \ K((x * ((y \ 1) / x)) \ 1,z) = ((y \ T(y,z)) * K(x \ 1,x)) / x
    ]]></literal>
    <justification jstring="[para(4156(a,1),8873(a,2,1))].">
      <j1 rule="para" parents="4156 8873"/>
    </justification>
  </clause>

  <clause id="8875">
    <literal><![CDATA[
      x \ K((x * ((y \ 1) / x)) \ 1,z) = (K(y,z) * K(x \ 1,x)) / x
    ]]></literal>
    <justification jstring="[para(4215(a,2),8874(a,2,1,1))].">
      <j1 rule="para" parents="4215 8874"/>
    </justification>
  </clause>

  <clause id="8876">
    <literal><![CDATA[
      K((x * ((y \ 1) / x)) \ 1,z) = x * (K(y,z) / T(x,x \ 1))
    ]]></literal>
    <justification jstring="[hyper(8545,a,8875,a),flip(a)].">
      <j1 rule="hyper" parents="8545 8875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8877">
    <literal><![CDATA[
      K((x * ((y \ 1) / x)) \ 1,z) = x * (K(y,z) / ((x \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(112(a,1),8876(a,2,2,2))].">
      <j1 rule="para" parents="112 8876"/>
    </justification>
  </clause>

  <clause id="8878">
    <literal><![CDATA[
      T(x,K(y,x \ z)) / (z * T(z \ x,y)) = (x * (x / (z * T(z \ x,y)))) / x
    ]]></literal>
    <justification jstring="[para(7164(a,1),5963(a,1,1))].">
      <j1 rule="para" parents="7164 5963"/>
    </justification>
  </clause>

  <clause id="8879">
    <literal><![CDATA[
      T(x,K(y,z)) / (z * T(z \ x,y)) = (x * (x / (z * T(z \ x,y)))) / x
    ]]></literal>
    <justification jstring="[para(7041(a,1),8878(a,1,1))].">
      <j1 rule="para" parents="7041 8878"/>
    </justification>
  </clause>

  <clause id="8880">
    <literal><![CDATA[
      T(x,K(y,z)) / (z * T(z \ x,y)) = (x * K(y,(z / x) \ 1)) / x
    ]]></literal>
    <justification jstring="[para(4966(a,1),8879(a,2,1,2))].">
      <j1 rule="para" parents="4966 8879"/>
    </justification>
  </clause>

  <clause id="8881">
    <literal><![CDATA[
      T(x,K(y,z)) / (z * T(z \ x,y)) = K(y,T((z / x) \ 1,x))
    ]]></literal>
    <justification jstring="[hyper(333,a,6884,a(flip),b,8880,a),flip(a)].">
      <j1 rule="hyper" parents="333 6884 8880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8882">
    <literal><![CDATA[
      T(x,K(y,z)) / (z * T(z \ x,y)) = K(y,(x \ z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(333,a,6492,a(flip),b,8881,a),flip(a)].">
      <j1 rule="hyper" parents="333 6492 8881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8883">
    <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(333,a,4105,a,b,5986,a)].">
      <j1 rule="hyper" parents="333 4105 5986"/>
    </justification>
  </clause>

  <clause id="8884">
    <literal><![CDATA[
      T(T(x,((y \ 1) * z) \ u),K(((y \ 1) * z) \ u,w)) = T(x,T(((1 / y) * z) \ u,w))
    ]]></literal>
    <justification jstring="[para(3178(a,1),6204(a,1,1))].">
      <j1 rule="para" parents="3178 6204"/>
    </justification>
  </clause>

  <clause id="8885">
    <literal><![CDATA[
      K(x,y) * (z * T(L(K(y,x),u,w),z)) = L(K(y,x),u,w) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(7729(a,1),6263(a,1,2,2))].">
      <j1 rule="para" parents="7729 6263"/>
    </justification>
  </clause>

  <clause id="8886">
    <literal><![CDATA[
      L(K(x,y),z,u) * (K(y,x) * w) = K(y,x) * (L(K(x,y),z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(595,a,8885,a),flip(a)].">
      <j1 rule="hyper" parents="595 8885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8887">
    <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(3022(a,1),6717(a,1,1))].">
      <j1 rule="para" parents="3022 6717"/>
    </justification>
  </clause>

  <clause id="8888">
    <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(200(a,1),7292(a,1,1))].">
      <j1 rule="para" parents="200 7292"/>
    </justification>
  </clause>

  <clause id="8890">
    <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(5994(a,1),8888(a,1,2))].">
      <j1 rule="para" parents="5994 8888"/>
    </justification>
  </clause>

  <clause id="8891">
    <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(5718(a,1),8890(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5718 8890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8892">
    <literal><![CDATA[
      K(R(x,y,z),u) * (x \ R(x,y,z)) = x \ R(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,7,a(flip),b,8891,a),flip(a)].">
      <j1 rule="hyper" parents="333 7 8891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8893">
    <literal><![CDATA[
      K(x,R(y,z,u)) * (y \ R(T(y,x),z,u)) = y \ R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(4577,a,8892,a)].">
      <j1 rule="hyper" parents="4577 8892"/>
    </justification>
  </clause>

  <clause id="8894">
    <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(7817(a,1),8893(a,1,1))].">
      <j1 rule="para" parents="7817 8893"/>
    </justification>
  </clause>

  <clause id="8895">
    <literal><![CDATA[
      K(T(x,y) * z,T(T(x,u),w)) = K(x * z,T(T(x,u),w))
    ]]></literal>
    <justification jstring="[hyper(333,a,4812,a(flip),b,7505,a),flip(a)].">
      <j1 rule="hyper" parents="333 4812 7505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8896">
    <literal><![CDATA[
      K(((x \ y) \ y) * z,T(T(x,u),w)) = K(x * z,T(T(x,u),w))
    ]]></literal>
    <justification jstring="[para(112(a,1),8895(a,1,1,1))].">
      <j1 rule="para" parents="112 8895"/>
    </justification>
  </clause>

  <clause id="8897">
    <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(63,a,7535,a(flip),b,8157,a),flip(a)].">
      <j1 rule="hyper" parents="63 7535 8157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8899">
    <literal><![CDATA[
      K(x,R(y * K(z,x),u,w)) = K(x,R(y,K(z,x) * u,w))
    ]]></literal>
    <justification jstring="[para(20(a,2),8897(a,1,2))].">
      <j1 rule="para" parents="20 8897"/>
    </justification>
  </clause>

  <clause id="8900">
    <literal><![CDATA[
      K(x,R(y,K(z,x) * u,w)) = K(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,8188,a(flip),b,8899,a),flip(a)].">
      <j1 rule="hyper" parents="63 8188 8899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8902">
    <literal><![CDATA[
      K(x,R(y,K(x,z) * u,w)) = K(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[para(4558(a,1),8900(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4558 8900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8903">
    <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(613(a,1),8902(a,1,2)),flip(a)].">
      <j1 rule="para" parents="613 8902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8904">
    <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(6336(a,1),8175(a,2,2))].">
      <j1 rule="para" parents="6336 8175"/>
    </justification>
  </clause>

  <clause id="8905">
    <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(333,a,7341,a(flip),b,8904,a),flip(a)].">
      <j1 rule="hyper" parents="333 7341 8904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8907">
    <literal><![CDATA[
      a(x,y,x) \ (x * L(x \ a(x,y,x),z,u)) = L(x,y,x) \ L(L(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(8239(a,1),8240(a,2,2,1))].">
      <j1 rule="para" parents="8239 8240"/>
    </justification>
  </clause>

  <clause id="8908">
    <literal><![CDATA[
      a(x,y,x) \ (x * L(x \ a(x,y,x),z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x \ L(x,z,u),y,x) = w
    ]]></literal>
    <justification jstring="[para(8907(a,2),4034(a,1))].">
      <j1 rule="para" parents="8907 4034"/>
    </justification>
  </clause>

  <clause id="8909">
    <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(8369(a,1),8283(a,1,2,2))].">
      <j1 rule="para" parents="8369 8283"/>
    </justification>
  </clause>

  <clause id="8910">
    <literal><![CDATA[
      (T(x,y) / z) / K(((1 / z) / (x / z)) \ 1,y) = T(x / z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(333,a,8470,a(flip),b,8452,a),flip(a)].">
      <j1 rule="hyper" parents="333 8470 8452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8911">
    <literal><![CDATA[
      (T(x,y) / z) / K(((z \ 1) / (x / z)) \ 1,y) = T(x / z,K(x,y))
    ]]></literal>
    <justification jstring="[para(5010(a,1),8910(a,1,2))].">
      <j1 rule="para" parents="5010 8910"/>
    </justification>
  </clause>

  <clause id="8912">
    <literal><![CDATA[
      (T(x,y) / z) * K(y,((z \ 1) / (x / z)) \ 1) = T(x / z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(5999,a,8911,a)].">
      <j1 rule="hyper" parents="5999 8911"/>
    </justification>
  </clause>

  <clause id="8913">
    <literal><![CDATA[
      (T(x,y) / z) * K(y,(x / z) / (z \ 1)) = T(x / z,K(x,y))
    ]]></literal>
    <justification jstring="[para(5055(a,1),8912(a,1,2))].">
      <j1 rule="para" parents="5055 8912"/>
    </justification>
  </clause>

  <clause id="8914">
    <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(6365(a,2),8913(a,1,1,1))].">
      <j1 rule="para" parents="6365 8913"/>
    </justification>
  </clause>

  <clause id="8915">
    <literal><![CDATA[
      (T(x,y) * (y / x)) * K(x \ y,x) = (x \ y) * ((x \ T(y,x)) \ y)
    ]]></literal>
    <justification jstring="[para(8035(a,1),8684(a,1,2))].">
      <j1 rule="para" parents="8035 8684"/>
    </justification>
  </clause>

  <clause id="8916">
    <literal><![CDATA[
      (x \ y) * ((x \ T(y,x)) \ y) = (y / x) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,6485,a(flip),b,8915,a),flip(a)].">
      <j1 rule="hyper" parents="63 6485 8915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8918">
    <literal><![CDATA[
      (x \ y) * ((x \ T(y,x)) \ y) = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(333,a,861,a(flip),b,8916,a),flip(a)].">
      <j1 rule="hyper" parents="333 861 8916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8919">
    <literal><![CDATA[
      (x * (y * ((x \ (z / u)) / y))) * ((z / u) \ z) = (x * u) * (y * (((x * ((z / u) \ z)) \ z) / y))
    ]]></literal>
    <justification jstring="[para(79(a,1),8861(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="79 8861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8920">
    <literal><![CDATA[
      (x / y) \ T(x * K(y,z),(x / y) \ 1) = T(x * (y / x),z)
    ]]></literal>
    <justification jstring="[para(3113(a,1),8883(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3113 8883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8921">
    <literal><![CDATA[
      K(x * K(y,z),(x / y) \ 1) = T(x * (y / x),z) / T(y,z)
    ]]></literal>
    <justification jstring="[para(8920(a,1),6047(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8920 6047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8922">
    <literal><![CDATA[
      K((x / y) \ 1,x * K(y,z)) = T(y,z) / T(x * (y / x),z)
    ]]></literal>
    <justification jstring="[para(8920(a,1),6048(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8920 6048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8923">
    <literal><![CDATA[
      K(x * K(y,z),(x / y) \ 1) = K(x,x \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(333,a,4632,a(flip),b,8921,a),flip(a)].">
      <j1 rule="hyper" parents="333 4632 8921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8924">
    <literal><![CDATA[
      K(K(x,y) * z,z \ x) = K(z,z \ T(x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,7554,a(flip),b,8923,a)].">
      <j1 rule="hyper" parents="63 7554 8923"/>
    </justification>
  </clause>

  <clause id="8925">
    <literal><![CDATA[
      K((x / y) \ 1,x * K(y,z)) = T(x * (y / x),z) \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,6672,a(flip),b,8922,a),flip(a)].">
      <j1 rule="hyper" parents="333 6672 8922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8926">
    <literal><![CDATA[
      K((x / y) \ 1,x * K(y,z)) = K(x \ T(y,z),x)
    ]]></literal>
    <justification jstring="[hyper(333,a,4676,a(flip),b,8925,a),flip(a)].">
      <j1 rule="hyper" parents="333 4676 8925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8927">
    <literal><![CDATA[
      K(x \ y,K(y,z) * x) = K(x \ T(y,z),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,7555,a(flip),b,8926,a)].">
      <j1 rule="hyper" parents="63 7555 8926"/>
    </justification>
  </clause>

  <clause id="8928">
    <literal><![CDATA[
      T(x,T(((1 / y) * z) \ u,w)) = T(x,T(((y \ 1) * z) \ u,w))
    ]]></literal>
    <justification jstring="[hyper(7056,a,8884,a),flip(a)].">
      <j1 rule="hyper" parents="7056 8884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8929">
    <literal><![CDATA[
      ((x \ y) \ R(x \ y,z,x \ y)) * (y / x) = R(y / x,z,x \ y)
    ]]></literal>
    <justification jstring="[para(4292(a,1),8887(a,2,1))].">
      <j1 rule="para" parents="4292 8887"/>
    </justification>
  </clause>

  <clause id="8930">
    <literal><![CDATA[
      a(x \ y,z,x \ y) * (y / x) = R(y / x,z,x \ y)
    ]]></literal>
    <justification jstring="[para(8210(a,1),8929(a,1,1))].">
      <j1 rule="para" parents="8210 8929"/>
    </justification>
  </clause>

  <clause id="8931">
    <literal><![CDATA[
      R(T(x / y,K(y,x)),z,x / y) = a(y \ x,z,y \ x) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(333,a,8672,a,b,8930,a)].">
      <j1 rule="hyper" parents="333 8672 8930"/>
    </justification>
  </clause>

  <clause id="8932">
    <literal><![CDATA[
      a(x / y,z,x / y) = a(y \ x,z,y \ x)
    ]]></literal>
    <justification jstring="[hyper(35,a,8271,a(flip),b,8931,a(flip))].">
      <j1 rule="hyper" parents="35 8271 8931"/>
    </justification>
  </clause>

  <clause id="8933">
    <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(4241(a,1),8909(a,1,2))].">
      <j1 rule="para" parents="4241 8909"/>
    </justification>
  </clause>

  <clause id="8934">
    <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(5071,a,5115,a),flip(a)].">
      <j1 rule="hyper" parents="5071 5115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8936">
    <literal><![CDATA[
      K((x / R(1 / y,y,z)) \ 1,z / (y * z)) = K(z / (x * (y * z)),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(333,a,4965,a(flip),b,8934,a),flip(a)].">
      <j1 rule="hyper" parents="333 4965 8934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8937">
    <literal><![CDATA[
      K((x / R(1 / y,y,z)) \ 1,y \ 1) = K(z / (x * (y * z)),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(5071,a,8936,a)].">
      <j1 rule="hyper" parents="5071 8936"/>
    </justification>
  </clause>

  <clause id="8938">
    <literal><![CDATA[
      K(R(1 / x,x,y) / z,x \ 1) = K(y / (z * (x * y)),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(5090,a,8937,a)].">
      <j1 rule="hyper" parents="5090 8937"/>
    </justification>
  </clause>

  <clause id="8940">
    <literal><![CDATA[
      K(x \ R(1 / y,y,z),y \ 1) = K(z / (x * (y * z)),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,6486,a(flip),b,8938,a)].">
      <j1 rule="hyper" parents="63 6486 8938"/>
    </justification>
  </clause>

  <clause id="8941">
    <literal><![CDATA[
      K(x \ R(y \ 1,y,z),y \ 1) = K(z / (x * (y * z)),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,5007,a(flip),b,8940,a)].">
      <j1 rule="hyper" parents="63 5007 8940"/>
    </justification>
  </clause>

  <clause id="8942">
    <literal><![CDATA[
      K(x / (y * (z * x)),z \ 1) = K(y \ (x / (z * x)),z \ 1)
    ]]></literal>
    <justification jstring="[para(230(a,1),8940(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="230 8940"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8943">
    <literal><![CDATA[
      K(x / (y * ((z \ 1) * x)),(z \ 1) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ (x / ((z \ 1) * x)),z) = u
    ]]></literal>
    <justification jstring="[para(8942(a,2),5841(a,1))].">
      <j1 rule="para" parents="8942 5841"/>
    </justification>
  </clause>

  <clause id="8944">
    <literal><![CDATA[
      L(T(x,y),x \ (z * K(u,x)),x) = T(L(x,x \ z,x),y)
    ]]></literal>
    <justification jstring="[para(8506(a,1),5491(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8506 5491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8945">
    <literal><![CDATA[
      L(T(x,y),x \ (K(z,x) * u),x) = T(L(x,x \ u,x),y)
    ]]></literal>
    <justification jstring="[para(6357(a,1),8944(a,1,2,2))].">
      <j1 rule="para" parents="6357 8944"/>
    </justification>
  </clause>

  <clause id="8947">
    <literal><![CDATA[
      L(T(x,y),x \ (K(z,x) * u),x) = L(T(x,y),x \ u,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,25,a,b,8945,a),flip(a)].">
      <j1 rule="hyper" parents="333 25 8945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8948">
    <literal><![CDATA[
      L(T(x,y),x \ T(z,x),x) = L(T(x,y),x \ z,x)
    ]]></literal>
    <justification jstring="[para(2065(a,2),8947(a,1,2,2))].">
      <j1 rule="para" parents="2065 8947"/>
    </justification>
  </clause>

  <clause id="8949">
    <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(8948(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8948 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8950">
    <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(333,a,29,a(flip),b,8949,a),flip(a)].">
      <j1 rule="hyper" parents="333 29 8949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8954">
    <literal><![CDATA[
      (x * y) \ (R(T(z * K(x,z),u),x,y) \ ((x * z) * y)) = K(u,(x * y) \ ((x * z) * y))
    ]]></literal>
    <justification jstring="[para(27(a,2),6658(a,1,2,1))].">
      <j1 rule="para" parents="27 6658"/>
    </justification>
  </clause>

  <clause id="8955">
    <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(3407(a,1),7111(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3407 7111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8956">
    <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(3407(a,1),8955(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3407 8955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8958">
    <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(8956(a,1),675(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="8956 675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8960">
    <literal><![CDATA[
      K((x / y) \ z,R((x / y) \ 1,x / y,y)) = K(((x / y) \ 1) * z,y / x)
    ]]></literal>
    <justification jstring="[hyper(5849,a,8177,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="5849 8177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8961">
    <literal><![CDATA[
      K((x / y) \ z,T(y / x,x / y)) = K(((x / y) \ 1) * z,y / x)
    ]]></literal>
    <justification jstring="[para(690(a,1),8960(a,1,2))].">
      <j1 rule="para" parents="690 8960"/>
    </justification>
  </clause>

  <clause id="8962">
    <literal><![CDATA[
      K(((x / y) \ 1) * z,y / x) = K((x / y) \ z,y / x)
    ]]></literal>
    <justification jstring="[hyper(5849,a,8961,a),flip(a)].">
      <j1 rule="hyper" parents="5849 8961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8963">
    <literal><![CDATA[
      K(((x / y) \ 1) * z,y / x) = K((y \ x) \ z,y / x)
    ]]></literal>
    <justification jstring="[hyper(333,a,8628,a(flip),b,8962,a),flip(a)].">
      <j1 rule="hyper" parents="333 8628 8962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8964">
    <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(5791(a,1),8649(a,1,2))].">
      <j1 rule="para" parents="5791 8649"/>
    </justification>
  </clause>

  <clause id="8965">
    <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(63,a,7817,a(flip),b,8964,a)].">
      <j1 rule="hyper" parents="63 7817 8964"/>
    </justification>
  </clause>

  <clause id="8966">
    <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(5307(a,1),8673(a,1,2))].">
      <j1 rule="para" parents="5307 8673"/>
    </justification>
  </clause>

  <clause id="8967">
    <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(333,a,7497,a(flip),b,8966,a),flip(a)].">
      <j1 rule="hyper" parents="333 7497 8966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8969">
    <literal><![CDATA[
      a(T(x,y),T(z,x),R(T(x,y),u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(T(x,y),z,R(T(x,y),u,w)) = v5
    ]]></literal>
    <justification jstring="[para(8795(a,1),8799(a,1))].">
      <j1 rule="para" parents="8795 8799"/>
    </justification>
  </clause>

  <clause id="8970">
    <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(8969,a,5549,a)].">
      <j1 rule="hyper" parents="8969 5549"/>
    </justification>
  </clause>

  <clause id="8971">
    <literal><![CDATA[
      a(x,y,R(T(x,y),z,u)) = a(R(x,z,u),y,x)
    ]]></literal>
    <justification jstring="[hyper(5163,a,8970,a)].">
      <j1 rule="hyper" parents="5163 8970"/>
    </justification>
  </clause>

  <clause id="8972">
    <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(6365(a,2),8894(a,1,2,2,1))].">
      <j1 rule="para" parents="6365 8894"/>
    </justification>
  </clause>

  <clause id="8973">
    <literal><![CDATA[
      (x * y) * K(z,(x * y) \ ((x * u) * y)) != w
    ]]></literal>
    <literal><![CDATA[
      R(T(u * K(x,u),z),x,y) \ ((x * u) * y) = w
    ]]></literal>
    <justification jstring="[para(8954(a,1),273(a,1,2)),flip(b)].">
      <j1 rule="para" parents="8954 273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8974">
    <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(4567(a,1),8972(a,1,2))].">
      <j1 rule="para" parents="4567 8972"/>
    </justification>
  </clause>

  <clause id="8975">
    <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(8974(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="8974 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8976">
    <literal><![CDATA[
      K(x,T(y / ((K(x,z) * u) * w),v5)) = K(x,T(y / (u * w),v5))
    ]]></literal>
    <justification jstring="[hyper(333,a,7855,a(flip),b,8155,a),flip(a)].">
      <j1 rule="hyper" parents="333 7855 8155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8977">
    <literal><![CDATA[
      K(x,T(y / ((z * T(x,u)) * w),v5)) = K(x,T(y / ((z * x) * w),v5))
    ]]></literal>
    <justification jstring="[para(7717(a,1),8976(a,1,2,1,2,1))].">
      <j1 rule="para" parents="7717 8976"/>
    </justification>
  </clause>

  <clause id="8978">
    <literal><![CDATA[
      (x \ y) * K((x \ 1) \ (x \ y),y \ z) = x \ T(y,((x \ 1) \ (x \ y)) \ z)
    ]]></literal>
    <justification jstring="[para(10(a,1),8450(a,1,2,2,1))].">
      <j1 rule="para" parents="10 8450"/>
    </justification>
  </clause>

  <clause id="8979">
    <literal><![CDATA[
      x \ T(y,((x \ 1) \ (x \ y)) \ z) = x \ T(y,y \ z)
    ]]></literal>
    <justification jstring="[hyper(6270,a,8978,a),flip(a)].">
      <j1 rule="hyper" parents="6270 8978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8981">
    <literal><![CDATA[
      T((x / (1 / (x \ y))) / x,1 / (y / x)) = (((x / (1 / (x \ y))) / x) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,8133,a(flip),b,8736,a)].">
      <j1 rule="hyper" parents="63 8133 8736"/>
    </justification>
  </clause>

  <clause id="8982">
    <literal><![CDATA[
      T((x / (1 / (x \ y))) / x,1 / (y / x)) = (1 / ((x / ((x \ y) \ 1)) / x)) \ 1
    ]]></literal>
    <justification jstring="[para(2909(a,2),8981(a,2,1))].">
      <j1 rule="para" parents="2909 8981"/>
    </justification>
  </clause>

  <clause id="8983">
    <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(8982(a,2),593(a,1))].">
      <j1 rule="para" parents="8982 593"/>
    </justification>
  </clause>

  <clause id="8984">
    <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(1535(a,2),5410(a,2,2,1))].">
      <j1 rule="para" parents="1535 5410"/>
    </justification>
  </clause>

  <clause id="8985">
    <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(6788(a,1),5498(a,1,2,2))].">
      <j1 rule="para" parents="6788 5498"/>
    </justification>
  </clause>

  <clause id="8986">
    <literal><![CDATA[
      K(x \ T(y,z),x) * (K(y,z) * (x * (x \ y))) = L(x \ y,x,K(y,z)) * (K(y,z) * x)
    ]]></literal>
    <justification jstring="[para(8927(a,1),6291(a,1,1))].">
      <j1 rule="para" parents="8927 6291"/>
    </justification>
  </clause>

  <clause id="8987">
    <literal><![CDATA[
      L(x \ y,x,K(y,z)) * (K(y,z) * x) = K(x \ T(y,z),x) * (K(y,z) * y)
    ]]></literal>
    <justification jstring="[para(10(a,1),8986(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 8986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8989">
    <literal><![CDATA[
      L(x \ y,x,K(y,z)) * (K(y,z) * x) = K(x \ T(y,z),x) * T(y,z)
    ]]></literal>
    <justification jstring="[para(4274(a,2),8987(a,2,2))].">
      <j1 rule="para" parents="4274 8987"/>
    </justification>
  </clause>

  <clause id="8990">
    <literal><![CDATA[
      L(x \ y,x,K(y,z)) * (K(y,z) * x) = (x \ T(y,z)) * x
    ]]></literal>
    <justification jstring="[hyper(333,a,4184,a(flip),b,8989,a),flip(a)].">
      <j1 rule="hyper" parents="333 4184 8989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8991">
    <literal><![CDATA[
      L(x \ y,x,K(y,z)) * (K(y,z) * x) = T((x \ y) * x,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,4105,a,b,8990,a),flip(a)].">
      <j1 rule="hyper" parents="333 4105 8990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8992">
    <literal><![CDATA[
      L(x \ y,x,K(y,z)) * (K(y,z) * x) != u
    ]]></literal>
    <literal><![CDATA[
      T((x \ y) * x,z) = u
    ]]></literal>
    <justification jstring="[para(8990(a,2),4116(a,1))].">
      <j1 rule="para" parents="8990 4116"/>
    </justification>
  </clause>

  <clause id="8993">
    <literal><![CDATA[
      L(x \ L(y,z,u),x,K(L(y,z,u),y \ w)) * (K(L(y,z,u),w / y) * x) = T((x \ L(y,z,u)) * x,w / y)
    ]]></literal>
    <justification jstring="[para(5271(a,1),8991(a,1,1,3))].">
      <j1 rule="para" parents="5271 8991"/>
    </justification>
  </clause>

  <clause id="8994">
    <literal><![CDATA[
      L(K(x * y,x) * K(x,K(z * y,x * y)),y,z) = (z * (T(x * y,x) / T(x,y))) / (z * y)
    ]]></literal>
    <justification jstring="[para(6788(a,1),7512(a,1,1,2))].">
      <j1 rule="para" parents="6788 7512"/>
    </justification>
  </clause>

  <clause id="8995">
    <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(66(a,1),8984(a,2,2,1,1,2))].">
      <j1 rule="para" parents="66 8984"/>
    </justification>
  </clause>

  <clause id="8996">
    <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(25(a,2),8995(a,2,2))].">
      <j1 rule="para" parents="25 8995"/>
    </justification>
  </clause>

  <clause id="8998">
    <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(333,a,701,a(flip),b,8996,a),flip(a)].">
      <j1 rule="hyper" parents="333 701 8996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8999">
    <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(333,a,1343,a(flip),b,8998,a),flip(a)].">
      <j1 rule="hyper" parents="333 1343 8998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9000">
    <literal><![CDATA[
      (x \ L(x,y,z)) * K(L(x,y,z),u) = x \ L(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(3334(a,1),8999(a,1,2))].">
      <j1 rule="para" parents="3334 8999"/>
    </justification>
  </clause>

  <clause id="9001">
    <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(6361(a,1),8985(a,2,1))].">
      <j1 rule="para" parents="6361 8985"/>
    </justification>
  </clause>

  <clause id="9002">
    <literal><![CDATA[
      (x \ T(x * y,x)) \ (y * K(x,K(z,x * y))) = K(x,T(x * y,z))
    ]]></literal>
    <justification jstring="[hyper(333,a,7831,a(flip),b,9001,a),flip(a)].">
      <j1 rule="hyper" parents="333 7831 9001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9004">
    <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(5569(a,2),9002(a,1,1))].">
      <j1 rule="para" parents="5569 9002"/>
    </justification>
  </clause>

  <clause id="9005">
    <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(7418(a,1),9004(a,1,2,2))].">
      <j1 rule="para" parents="7418 9004"/>
    </justification>
  </clause>

  <clause id="9006">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) \ K(x,z) = K(y,T(y * K(x,z),x))
    ]]></literal>
    <justification jstring="[hyper(348,a,9005,a)].">
      <j1 rule="hyper" parents="348 9005"/>
    </justification>
  </clause>

  <clause id="9007">
    <literal><![CDATA[
      K(T(x / y,x) \ x,z) * K(z,y) = K(x,T(x * K(z,y),z))
    ]]></literal>
    <justification jstring="[hyper(4580,a,9006,a)].">
      <j1 rule="hyper" parents="4580 9006"/>
    </justification>
  </clause>

  <clause id="9008">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) * K(z,x) = K(y,T(y * K(z,x),z))
    ]]></literal>
    <justification jstring="[para(7702(a,1),9007(a,1,1))].">
      <j1 rule="para" parents="7702 9007"/>
    </justification>
  </clause>

  <clause id="9009">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) * K(z,x) = K(y,y * K(z,x))
    ]]></literal>
    <justification jstring="[hyper(333,a,7435,a(flip),b,9008,a),flip(a)].">
      <j1 rule="hyper" parents="333 7435 9008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9010">
    <literal><![CDATA[
      K(x * K(y,z),x) = K(x,x * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,5619,a(flip),b,9009,a)].">
      <j1 rule="hyper" parents="63 5619 9009"/>
    </justification>
  </clause>

  <clause id="9011">
    <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(9010(a,1),5098(a,1,1,1,2))].">
      <j1 rule="para" parents="9010 5098"/>
    </justification>
  </clause>

  <clause id="9012">
    <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(4222(a,2),9011(a,1,1,1))].">
      <j1 rule="para" parents="4222 9011"/>
    </justification>
  </clause>

  <clause id="9013">
    <literal><![CDATA[
      R(T(x,K(y,z)),K(z,y),x) = T(x,x * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(5306,a,9012,a),flip(a)].">
      <j1 rule="hyper" parents="5306 9012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9014">
    <literal><![CDATA[
      T(x,x * K(y,z)) \ T(K(z,y) * x,x) = K(z,T(y,x))
    ]]></literal>
    <justification jstring="[para(9013(a,1),8967(a,1,1))].">
      <j1 rule="para" parents="9013 8967"/>
    </justification>
  </clause>

  <clause id="9015">
    <literal><![CDATA[
      L(K(x * y,x) * K(x,K(z * y,y)),y,z) = (z * (T(x * y,x) / T(x,y))) / (z * y)
    ]]></literal>
    <justification jstring="[para(7024(a,1),8994(a,1,1,2))].">
      <j1 rule="para" parents="7024 8994"/>
    </justification>
  </clause>

  <clause id="9016">
    <literal><![CDATA[
      L(K(x * y,x) * K(x,K(y * z,y)),y,z) = (z * (T(x * y,x) / T(x,y))) / (z * y)
    ]]></literal>
    <justification jstring="[para(4543(a,1),9015(a,1,1,2,2))].">
      <j1 rule="para" parents="4543 9015"/>
    </justification>
  </clause>

  <clause id="9017">
    <literal><![CDATA[
      L(K(x * y,x) * K(x,K(y,y * z)),y,z) = (z * (T(x * y,x) / T(x,y))) / (z * y)
    ]]></literal>
    <justification jstring="[para(6800(a,1),9016(a,1,1,2))].">
      <j1 rule="para" parents="6800 9016"/>
    </justification>
  </clause>

  <clause id="9018">
    <literal><![CDATA[
      (x * (T(y * z,y) / T(y,z))) / (x * z) = L(K(y * z,y) * K(y,K(z,x)),z,x)
    ]]></literal>
    <justification jstring="[para(6874(a,1),9017(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6874 9017"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9019">
    <literal><![CDATA[
      L(K(x * y,x) * K(x,K(y,z)),y,z) = (z * (x \ T(x * y,x))) / (z * y)
    ]]></literal>
    <justification jstring="[para(7481(a,1),9018(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7481 9018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9020">
    <literal><![CDATA[
      (x * (y \ T(y * z,y))) / (x * z) = L(K(y * z,T(y,x)),z,x)
    ]]></literal>
    <justification jstring="[para(7092(a,1),9019(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7092 9019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9021">
    <literal><![CDATA[
      L(K(x * y,T(x,z)),y,z) = K((z * y) / (z * (x \ 1)),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,5279,a(flip),b,9020,a),flip(a)].">
      <j1 rule="hyper" parents="63 5279 9020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9022">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * L(u * (z / u),y,x)) = L(K(u,u \ L(z,y,x)),L(z,y,x),x * y)
    ]]></literal>
    <justification jstring="[para(2545(a,2),4669(a,1,2,2))].">
      <j1 rule="para" parents="2545 4669"/>
    </justification>
  </clause>

  <clause id="9023">
    <literal><![CDATA[
      R(x,y,K(y,z)) * (R(y,u,w) * K(y,z)) = (x * R(x \ (x * y),u,w)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(6122(a,1),6125(a,1,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="6122 6125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9024">
    <literal><![CDATA[
      R(x,y,K(y,z)) * (R(y,u,w) * K(y,z)) = (x * R(y,u,w)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),9023(a,2,1,2,1))].">
      <j1 rule="para" parents="9 9023"/>
    </justification>
  </clause>

  <clause id="9025">
    <literal><![CDATA[
      (x * R(y,z,u)) * K(y,w) = x * (R(y,z,u) * K(y,w))
    ]]></literal>
    <justification jstring="[para(6122(a,1),9024(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6122 9024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9026">
    <literal><![CDATA[
      L(K(x,y),R(x,z,u),w) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(501,a,9025,a)].">
      <j1 rule="hyper" parents="501 9025"/>
    </justification>
  </clause>

  <clause id="9028">
    <literal><![CDATA[
      a(x,R(y,z,u),K(y,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(120,a,9025,a(flip),b,84,a),flip(a)].">
      <j1 rule="hyper" parents="120 9025 84"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9030">
    <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(5452(a,1),6655(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5452 6655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9031">
    <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(333,a,6210,a(flip),b,9030,a),flip(a)].">
      <j1 rule="hyper" parents="333 6210 9030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9032">
    <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(6634(a,1),9031(a,2,1))].">
      <j1 rule="para" parents="6634 9031"/>
    </justification>
  </clause>

  <clause id="9033">
    <literal><![CDATA[
      T(x,T(y / T(y / z,u),w)) = T(x,T(T(z \ y,u) \ y,w))
    ]]></literal>
    <justification jstring="[para(9032(a,1),7242(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9032 7242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9034">
    <literal><![CDATA[
      T(T(x,y) * L(x \ (z / (x \ 1)),u,w),K(x,y)) = (L(z,u,w) / (x \ 1)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(5605(a,1),7728(a,1,1))].">
      <j1 rule="para" parents="5605 7728"/>
    </justification>
  </clause>

  <clause id="9035">
    <literal><![CDATA[
      x * (L(x \ (y / (x \ 1)),z,u) * K(x,w)) = (L(y,z,u) / (x \ 1)) * K(x,w)
    ]]></literal>
    <justification jstring="[hyper(6236,a,9034,a)].">
      <j1 rule="hyper" parents="6236 9034"/>
    </justification>
  </clause>

  <clause id="9036">
    <literal><![CDATA[
      L((x / (y \ 1)) / y,z,u) * T(y,w) = (L(x,z,u) / (y \ 1)) * K(y,w)
    ]]></literal>
    <justification jstring="[hyper(8496,a,9035,a)].">
      <j1 rule="hyper" parents="8496 9035"/>
    </justification>
  </clause>

  <clause id="9037">
    <literal><![CDATA[
      L((x / (y \ 1)) / y,z,u) * T(y,w) = L(x,z,u) / (T(y,w) \ 1)
    ]]></literal>
    <justification jstring="[hyper(333,a,6170,a(flip),b,9036,a),flip(a)].">
      <j1 rule="hyper" parents="333 6170 9036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9038">
    <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(4241(a,1),7748(a,1,1))].">
      <j1 rule="para" parents="4241 7748"/>
    </justification>
  </clause>

  <clause id="9039">
    <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(752,a,9038,a),flip(a)].">
      <j1 rule="hyper" parents="752 9038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9040">
    <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(9038(a,1),752(a,1))].">
      <j1 rule="para" parents="9038 752"/>
    </justification>
  </clause>

  <clause id="9041">
    <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(4518(a,1),9039(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4518 9039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9042">
    <literal><![CDATA[
      K(x,y) \ T((K(x,K(y,z)) * u) * K(x,y),w) = T(K(x,T(y,z)) * u,w) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,6847,a(flip),b,8089,a),flip(a)].">
      <j1 rule="hyper" parents="63 6847 8089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9043">
    <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(4567(a,1),8160(a,1,1,1))].">
      <j1 rule="para" parents="4567 8160"/>
    </justification>
  </clause>

  <clause id="9044">
    <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(8877(a,2),8196(a,2,2,2))].">
      <j1 rule="para" parents="8877 8196"/>
    </justification>
  </clause>

  <clause id="9045">
    <literal><![CDATA[
      K(x \ (x * (y / x)),z * ((x * (y / x)) \ x)) = K(y / x,(y \ (y / (y / x))) * z)
    ]]></literal>
    <justification jstring="[hyper(4614,a,8631,a),flip(a)].">
      <j1 rule="hyper" parents="4614 8631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9047">
    <literal><![CDATA[
      K(x \ (x * (y / x)),z * ((x * (y / x)) \ x)) = K(y / x,(y \ ((y / x) \ y)) * z)
    ]]></literal>
    <justification jstring="[hyper(333,a,7509,a(flip),b,9045,a),flip(a)].">
      <j1 rule="hyper" parents="333 7509 9045"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9048">
    <literal><![CDATA[
      K(x \ (x * (y / x)),z * ((x * (y / x)) \ x)) = K(y / x,(y \ x) * z)
    ]]></literal>
    <justification jstring="[para(79(a,1),9047(a,2,2,1,2))].">
      <j1 rule="para" parents="79 9047"/>
    </justification>
  </clause>

  <clause id="9049">
    <literal><![CDATA[
      K(x / y,z * ((y * (x / y)) \ y)) = K(x / y,(x \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(4614,a,9048,a)].">
      <j1 rule="hyper" parents="4614 9048"/>
    </justification>
  </clause>

  <clause id="9051">
    <literal><![CDATA[
      K(x \ (x / (x / y)),z * (y \ (y * (x / y)))) = K((y * (x / y)) \ y,(x / y) * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),8632(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 8632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9052">
    <literal><![CDATA[
      K(x \ (x / (x / y)),z * (y \ (y * (x / y)))) = K((x / y) \ 1,(x / y) * z)
    ]]></literal>
    <justification jstring="[hyper(333,a,5861,a(flip),b,9051,a),flip(a)].">
      <j1 rule="hyper" parents="333 5861 9051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9055">
    <literal><![CDATA[
      K(x \ (x / (x / y)),z * (y \ (y * (x / y)))) = K(y / x,(x / y) * z)
    ]]></literal>
    <justification jstring="[hyper(333,a,4965,a(flip),b,9052,a),flip(a)].">
      <j1 rule="hyper" parents="333 4965 9052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9056">
    <literal><![CDATA[
      a(x / y,((y * x) / y) / (((y * x) / y) / T(y,x)),z) = a(y \ x,T(y,x),z)
    ]]></literal>
    <justification jstring="[para(864(a,1),8653(a,1,1))].">
      <j1 rule="para" parents="864 8653"/>
    </justification>
  </clause>

  <clause id="9057">
    <literal><![CDATA[
      a(x / y,((y * x) / y) / (x / y),z) = a(y \ x,T(y,x),z)
    ]]></literal>
    <justification jstring="[para(864(a,1),9056(a,1,2,2))].">
      <j1 rule="para" parents="864 9056"/>
    </justification>
  </clause>

  <clause id="9058">
    <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(8309(a,1),8678(a,1,1))].">
      <j1 rule="para" parents="8309 8678"/>
    </justification>
  </clause>

  <clause id="9059">
    <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(5635(a,1),9058(a,2,2))].">
      <j1 rule="para" parents="5635 9058"/>
    </justification>
  </clause>

  <clause id="9060">
    <literal><![CDATA[
      R(T(K(x,y),z),u,w) \ z = z / R(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(7500(a,1),9059(a,1,1,1))].">
      <j1 rule="para" parents="7500 9059"/>
    </justification>
  </clause>

  <clause id="9061">
    <literal><![CDATA[
      x / (x / R(K(y,z),u,w)) = R(T(K(y,z),x),u,w)
    ]]></literal>
    <justification jstring="[hyper(198,a,9060,a)].">
      <j1 rule="hyper" parents="198 9060"/>
    </justification>
  </clause>

  <clause id="9063">
    <literal><![CDATA[
      (R(K(x,y),z,u) \ w) \ w = R(T(K(x,y),w),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,8314,a(flip),b,9061,a)].">
      <j1 rule="hyper" parents="63 8314 9061"/>
    </justification>
  </clause>

  <clause id="9064">
    <literal><![CDATA[
      ((K(x,y) * z) * u) \ (z * u) = R(T(K(y,x),z * u),z,u)
    ]]></literal>
    <justification jstring="[para(5638(a,1),9063(a,1,1))].">
      <j1 rule="para" parents="5638 9063"/>
    </justification>
  </clause>

  <clause id="9065">
    <literal><![CDATA[
      ((K(x,y) * z) * u) \ (z * u) = R(K(y,T(x,z * u)),z,u)
    ]]></literal>
    <justification jstring="[para(6365(a,2),9064(a,2,1))].">
      <j1 rule="para" parents="6365 9064"/>
    </justification>
  </clause>

  <clause id="9066">
    <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(7236(a,1),9065(a,2,1))].">
      <j1 rule="para" parents="7236 9065"/>
    </justification>
  </clause>

  <clause id="9067">
    <literal><![CDATA[
      (x * (y * ((x \ (z / u)) / y))) * ((z / u) \ z) = (x * u) * (y * (((x * u) \ z) / y))
    ]]></literal>
    <justification jstring="[para(79(a,1),8919(a,2,2,2,1,1,2))].">
      <j1 rule="para" parents="79 8919"/>
    </justification>
  </clause>

  <clause id="9068">
    <literal><![CDATA[
      (x * (y * ((x \ (z / u)) / y))) * u = (x * u) * (y * (((x * u) \ z) / y))
    ]]></literal>
    <justification jstring="[hyper(596,a,9067,a)].">
      <j1 rule="hyper" parents="596 9067"/>
    </justification>
  </clause>

  <clause id="9069">
    <literal><![CDATA[
      ((x * y) * (z * (((x * y) \ u) / z))) / u = K(z,u / ((x * z) * y))
    ]]></literal>
    <justification jstring="[para(9068(a,1),5723(a,1,1))].">
      <j1 rule="para" parents="9068 5723"/>
    </justification>
  </clause>

  <clause id="9070">
    <literal><![CDATA[
      K(x,y / ((z * u) * x)) = K(x,y / ((z * x) * u))
    ]]></literal>
    <justification jstring="[hyper(5545,a,9069,a)].">
      <j1 rule="hyper" parents="5545 9069"/>
    </justification>
  </clause>

  <clause id="9071">
    <literal><![CDATA[
      K(x,y / ((z * y) * x)) = K(x,1 / (z * x))
    ]]></literal>
    <justification jstring="[hyper(333,a,5064,a(flip),b,9070,a),flip(a)].">
      <j1 rule="hyper" parents="333 5064 9070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9072">
    <literal><![CDATA[
      K(x,y / ((z * x) * u)) = K(x,y / (x * (z * u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,7920,a(flip),b,9070,a),flip(a)].">
      <j1 rule="hyper" parents="63 7920 9070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9073">
    <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(111(a,1),9070(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="111 9070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9074">
    <literal><![CDATA[
      K(x,y / ((z * y) * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,1 / (z * x)) = u
    ]]></literal>
    <justification jstring="[para(9070(a,2),5105(a,1))].">
      <j1 rule="para" parents="9070 5105"/>
    </justification>
  </clause>

  <clause id="9075">
    <literal><![CDATA[
      K(x,1 / ((y / z) * x)) = K(x,z / (y * x))
    ]]></literal>
    <justification jstring="[para(12(a,1),9071(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="12 9071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9076">
    <literal><![CDATA[
      K(x,y / ((x * z) * u)) = K(x,y / (x * (z * u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,8145,a(flip),b,9072,a)].">
      <j1 rule="hyper" parents="63 8145 9072"/>
    </justification>
  </clause>

  <clause id="9077">
    <literal><![CDATA[
      x * K(x,y / (x * (z * u))) = T(x,y / ((x * z) * u))
    ]]></literal>
    <justification jstring="[hyper(126,a,9076,a(flip),b,4215,a(flip))].">
      <j1 rule="hyper" parents="126 9076 4215"/>
    </justification>
  </clause>

  <clause id="9078">
    <literal><![CDATA[
      (x \ 1) / (x \ K(x,y / (x * (z * u)))) = K(y / ((x * z) * u),x)
    ]]></literal>
    <justification jstring="[para(9076(a,1),4688(a,1,2,2))].">
      <j1 rule="para" parents="9076 4688"/>
    </justification>
  </clause>

  <clause id="9079">
    <literal><![CDATA[
      K(x / ((y * z) * u),y) = K(x / (y * (z * u)),y)
    ]]></literal>
    <justification jstring="[hyper(4730,a,9078,a),flip(a)].">
      <j1 rule="hyper" parents="4730 9078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9080">
    <literal><![CDATA[
      K(x / (y * (z * x)),y) = K(z \ (y \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(7685,a,9079,a),flip(a)].">
      <j1 rule="hyper" parents="7685 9079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9081">
    <literal><![CDATA[
      K(x / ((y * x) * z),z) = K(y \ (z \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,7791,a,b,9080,a)].">
      <j1 rule="hyper" parents="63 7791 9080"/>
    </justification>
  </clause>

  <clause id="9082">
    <literal><![CDATA[
      K((x \ y) / (z * y),z) = K(x \ (z \ 1),z)
    ]]></literal>
    <justification jstring="[para(10(a,1),9080(a,1,1,2,2))].">
      <j1 rule="para" parents="10 9080"/>
    </justification>
  </clause>

  <clause id="9083">
    <literal><![CDATA[
      K((x / y) \ (z \ 1),z) = K(y / (x * z),z)
    ]]></literal>
    <justification jstring="[para(12(a,1),9081(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12 9081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9084">
    <literal><![CDATA[
      K(((x \ y) * x) / (z * (y / (y / x))),z) = K((x / y) \ (z \ 1),z)
    ]]></literal>
    <justification jstring="[para(5255(a,1),9082(a,1,1,1))].">
      <j1 rule="para" parents="5255 9082"/>
    </justification>
  </clause>

  <clause id="9085">
    <literal><![CDATA[
      K(((x \ y) * x) / (z * (y / (y / x))),z) = K(y / (x * z),z)
    ]]></literal>
    <justification jstring="[hyper(333,a,9083,a(flip),b,9084,a),flip(a)].">
      <j1 rule="hyper" parents="333 9083 9084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9086">
    <literal><![CDATA[
      K(R(x \ (y / z),x,y / (y / z)),x) = K(y / (z * x),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,5089,a,b,9085,a)].">
      <j1 rule="hyper" parents="63 5089 9085"/>
    </justification>
  </clause>

  <clause id="9087">
    <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(333,a,6370,a(flip),b,9073,a),flip(a)].">
      <j1 rule="hyper" parents="333 6370 9073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9088">
    <literal><![CDATA[
      L(K(x,x \ L(y,z,u)),L(y,z,u),u * z) = (u * (z * y)) \ (u * (z * (x * (y / x))))
    ]]></literal>
    <justification jstring="[para(97(a,1),9022(a,1,2)),flip(a)].">
      <j1 rule="para" parents="97 9022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9089">
    <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(2296(a,1),9043(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2296 9043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9090">
    <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(6015(a,1),9089(a,2,1))].">
      <j1 rule="para" parents="6015 9089"/>
    </justification>
  </clause>

  <clause id="9091">
    <literal><![CDATA[
      K(x,y * K(((z \ 1) \ 1) \ K(u,x),(z \ 1) \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,7416,a(flip),b,9044,a),flip(a)].">
      <j1 rule="hyper" parents="333 7416 9044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9093">
    <literal><![CDATA[
      K(x,y * K(z \ K(u,x),z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(2966(a,1),9091(a,1,2,2))].">
      <j1 rule="para" parents="2966 9091"/>
    </justification>
  </clause>

  <clause id="9095">
    <literal><![CDATA[
      K(x,y * (K(z,x) / u)) = K(x,y * (u \ K(z,x)))
    ]]></literal>
    <justification jstring="[para(6011(a,1),9093(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6011 9093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9096">
    <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(3865(a,1),9066(a,1,1))].">
      <j1 rule="para" parents="3865 9066"/>
    </justification>
  </clause>

  <clause id="9097">
    <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(6887(a,1),9096(a,1,1,2))].">
      <j1 rule="para" parents="6887 9096"/>
    </justification>
  </clause>

  <clause id="9098">
    <literal><![CDATA[
      R(K(x,L(y,z,L(y,u,w))),L(y,u,w),z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(7735,a,9097,a),flip(a)].">
      <j1 rule="hyper" parents="7735 9097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9099">
    <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(4330(a,1),4452(a,1,1,1,1))].">
      <j1 rule="para" parents="4330 4452"/>
    </justification>
  </clause>

  <clause id="9100">
    <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(5591(a,1),9099(a,1,1))].">
      <j1 rule="para" parents="5591 9099"/>
    </justification>
  </clause>

  <clause id="9101">
    <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(333,a,4467,a(flip),b,9100,a),flip(a)].">
      <j1 rule="hyper" parents="333 4467 9100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9102">
    <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(30(a,1),9101(a,1,1,2))].">
      <j1 rule="para" parents="30 9101"/>
    </justification>
  </clause>

  <clause id="9103">
    <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(63,a,6950,a(flip),b,9102,a)].">
      <j1 rule="hyper" parents="63 6950 9102"/>
    </justification>
  </clause>

  <clause id="9104">
    <literal><![CDATA[
      T(x * L(L(y,x,y),z,u),y) = T(x,y) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,7278,a(flip),b,9103,a)].">
      <j1 rule="hyper" parents="63 7278 9103"/>
    </justification>
  </clause>

  <clause id="9105">
    <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(9104(a,1),4839(a,1,2,2))].">
      <j1 rule="para" parents="9104 4839"/>
    </justification>
  </clause>

  <clause id="9106">
    <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(6474(a,1),9105(a,1,1))].">
      <j1 rule="para" parents="6474 9105"/>
    </justification>
  </clause>

  <clause id="9107">
    <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(4242(a,1),6245(a,2,2))].">
      <j1 rule="para" parents="4242 6245"/>
    </justification>
  </clause>

  <clause id="9108">
    <literal><![CDATA[
      L(K((x \ 1) \ (x \ y),z),x \ y,T(x,x \ y)) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,6045,a(flip),b,9107,a),flip(a)].">
      <j1 rule="hyper" parents="333 6045 9107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9110">
    <literal><![CDATA[
      L(K((x \ 1) \ (x \ y),z),y / x,x) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5102,a(flip),b,9108,a)].">
      <j1 rule="hyper" parents="63 5102 9108"/>
    </justification>
  </clause>

  <clause id="9111">
    <literal><![CDATA[
      K(x / ((y \ 1) * z),y * K(y \ z,y)) = K((y \ L(z,y \ 1,y)) \ x,y)
    ]]></literal>
    <justification jstring="[para(5537(a,1),7556(a,1,2))].">
      <j1 rule="para" parents="5537 7556"/>
    </justification>
  </clause>

  <clause id="9112">
    <literal><![CDATA[
      K(T(x / ((y \ 1) * z),y \ z),y) = K((y \ L(z,y \ 1,y)) \ x,y)
    ]]></literal>
    <justification jstring="[hyper(7008,a,9111,a)].">
      <j1 rule="hyper" parents="7008 9111"/>
    </justification>
  </clause>

  <clause id="9113">
    <literal><![CDATA[
      K(T(x / ((y \ 1) * z),y \ z),y) = K(((y \ 1) * z) \ x,y)
    ]]></literal>
    <justification jstring="[para(439(a,1),9112(a,2,1,1))].">
      <j1 rule="para" parents="439 9112"/>
    </justification>
  </clause>

  <clause id="9114">
    <literal><![CDATA[
      K(T(x / ((y \ 1) * z),z),y) = K(((y \ 1) * z) \ x,y)
    ]]></literal>
    <justification jstring="[hyper(7201,a,9113,a)].">
      <j1 rule="hyper" parents="7201 9113"/>
    </justification>
  </clause>

  <clause id="9115">
    <literal><![CDATA[
      K(((T(x,y) \ 1) * y) \ z,T(x,y)) = K(z / ((T(x,y) \ 1) * y),x)
    ]]></literal>
    <justification jstring="[hyper(7063,a,9114,a),flip(a)].">
      <j1 rule="hyper" parents="7063 9114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9116">
    <literal><![CDATA[
      K(((T(x,y) \ 1) * y) \ z,T(x,y)) = K(z / ((x \ 1) * y),x)
    ]]></literal>
    <justification jstring="[hyper(333,a,8143,a(flip),b,9115,a),flip(a)].">
      <j1 rule="hyper" parents="333 8143 9115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9118">
    <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(1637(a,2),8255(a,1,2,2))].">
      <j1 rule="para" parents="1637 8255"/>
    </justification>
  </clause>

  <clause id="9119">
    <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(97(a,1),9118(a,1,2)),flip(a)].">
      <j1 rule="para" parents="97 9118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9120">
    <literal><![CDATA[
      (x * y) \ (T(x,y) * R(T(x,y) \ (x * y),z,u)) = ((y * x) \ x) * R(((y * x) \ x) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(5041(a,1),5047(a,2,2,1,1))].">
      <j1 rule="para" parents="5041 5047"/>
    </justification>
  </clause>

  <clause id="9121">
    <literal><![CDATA[
      (x * y) \ (T(x,y) * R(T(x,y) \ (x * y),z,u)) = (y * x) \ (x * R(x \ (y * x),z,u))
    ]]></literal>
    <justification jstring="[hyper(333,a,1538,a(flip),b,9120,a),flip(a)].">
      <j1 rule="hyper" parents="333 1538 9120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9122">
    <literal><![CDATA[
      (x * y) \ (T(x,y) * R(T(x,y) \ (x * y),z,u)) = (y * x) \ (x * R(T(y,x),z,u))
    ]]></literal>
    <justification jstring="[para(22(a,2),9121(a,2,2,2,1))].">
      <j1 rule="para" parents="22 9121"/>
    </justification>
  </clause>

  <clause id="9123">
    <literal><![CDATA[
      (x * y) \ (T(x,y) * R(T(x,y) \ (x * y),z,u)) = (y * x) \ (R(y,z,u) * x)
    ]]></literal>
    <justification jstring="[para(252(a,1),9122(a,2,2))].">
      <j1 rule="para" parents="252 9122"/>
    </justification>
  </clause>

  <clause id="9124">
    <literal><![CDATA[
      (x * y) \ (T(x,y) * R(T(y,x),z,u)) = (y * x) \ (R(y,z,u) * x)
    ]]></literal>
    <justification jstring="[para(3620(a,1),9123(a,1,2,2,1))].">
      <j1 rule="para" parents="3620 9123"/>
    </justification>
  </clause>

  <clause id="9125">
    <literal><![CDATA[
      (x * y) \ (R(y,z,u) * T(x,y)) = (y * x) \ (R(y,z,u) * x)
    ]]></literal>
    <justification jstring="[para(3638(a,1),9124(a,1,2))].">
      <j1 rule="para" parents="3638 9124"/>
    </justification>
  </clause>

  <clause id="9126">
    <literal><![CDATA[
      ((x * y) * z) \ (R(z,x,y) * T(x * y,z)) = (z * (x * y)) \ ((z * x) * y)
    ]]></literal>
    <justification jstring="[para(107(a,1),9125(a,2,2))].">
      <j1 rule="para" parents="107 9125"/>
    </justification>
  </clause>

  <clause id="9127">
    <literal><![CDATA[
      (x * y) \ (R(y,y,x) * T(x,y)) = (y * x) \ (y \ ((y * y) * x))
    ]]></literal>
    <justification jstring="[para(1511(a,2),9125(a,2,2))].">
      <j1 rule="para" parents="1511 9125"/>
    </justification>
  </clause>

  <clause id="9128">
    <literal><![CDATA[
      a(x,y,z) = ((y * z) * x) \ (R(x,y,z) * T(y * z,x))
    ]]></literal>
    <justification jstring="[hyper(333,a,14,a,b,9126,a)].">
      <j1 rule="hyper" parents="333 14 9126"/>
    </justification>
  </clause>

  <clause id="9129">
    <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(63,a,8156,a(flip),b,5691,a),flip(a)].">
      <j1 rule="hyper" parents="63 8156 5691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9131">
    <literal><![CDATA[
      K((x * ((y * x) \ y)) \ ((1 / ((y * x) \ y)) \ z),1 / ((y * x) \ y)) = K(x \ z,y \ (y * x))
    ]]></literal>
    <justification jstring="[hyper(333,a,5768,a(flip),b,6558,a),flip(a)].">
      <j1 rule="hyper" parents="333 5768 6558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9132">
    <literal><![CDATA[
      K((x * ((y * x) \ y)) \ ((1 / ((y * x) \ y)) \ z),1 / ((y * x) \ y)) = K(x \ z,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),9131(a,2,2))].">
      <j1 rule="para" parents="9 9131"/>
    </justification>
  </clause>

  <clause id="9133">
    <literal><![CDATA[
      K((x * ((y * x) \ y)) \ ((1 / ((y * x) \ y)) \ z),y \ (y * x)) = K(x \ z,x)
    ]]></literal>
    <justification jstring="[hyper(5953,a,9132,a)].">
      <j1 rule="hyper" parents="5953 9132"/>
    </justification>
  </clause>

  <clause id="9134">
    <literal><![CDATA[
      K((x * ((y * x) \ y)) \ ((1 / ((y * x) \ y)) \ z),x) = K(x \ z,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),9133(a,1,2))].">
      <j1 rule="para" parents="9 9133"/>
    </justification>
  </clause>

  <clause id="9135">
    <literal><![CDATA[
      K(((x * y) \ x) \ (y \ ((1 / ((x * y) \ x)) \ z)),y) = K(y \ z,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,6307,a(flip),b,9134,a)].">
      <j1 rule="hyper" parents="63 6307 9134"/>
    </justification>
  </clause>

  <clause id="9136">
    <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(5767(a,1),6619(a,2,1))].">
      <j1 rule="para" parents="5767 6619"/>
    </justification>
  </clause>

  <clause id="9137">
    <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(79(a,1),9136(a,2,1,2))].">
      <j1 rule="para" parents="79 9136"/>
    </justification>
  </clause>

  <clause id="9139">
    <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(333,a,6632,a,b,9137,a),flip(a)].">
      <j1 rule="hyper" parents="333 6632 9137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9140">
    <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(333,a,6636,a(flip),b,9139,a),flip(a)].">
      <j1 rule="hyper" parents="333 6636 9139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9141">
    <literal><![CDATA[
      x / (T(y,z) \ R(x,y \ 1,y)) = T((x * (1 / y)) \ x,z)
    ]]></literal>
    <justification jstring="[para(9140(a,1),6657(a,1,2))].">
      <j1 rule="para" parents="9140 6657"/>
    </justification>
  </clause>

  <clause id="9148">
    <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(1264(a,1),8556(a,2,1))].">
      <j1 rule="para" parents="1264 8556"/>
    </justification>
  </clause>

  <clause id="9149">
    <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(4273(a,1),5262(a,1,2))].">
      <j1 rule="para" parents="4273 5262"/>
    </justification>
  </clause>

  <clause id="9150">
    <literal><![CDATA[
      (L(x \ 1,y,z) \ (x \ 1)) \ (L(x \ 1,y,z) \ K(x \ 1,x)) = T(x,x \ (L(x \ 1,y,z) \ 1))
    ]]></literal>
    <justification jstring="[para(1880(a,1),5610(a,1,2))].">
      <j1 rule="para" parents="1880 5610"/>
    </justification>
  </clause>

  <clause id="9151">
    <literal><![CDATA[
      (L(x \ 1,y,z) \ (x \ 1)) \ (L(1 / x,y,z) \ 1) = T(x,x \ (L(x \ 1,y,z) \ 1))
    ]]></literal>
    <justification jstring="[para(2859(a,1),9150(a,1,2))].">
      <j1 rule="para" parents="2859 9150"/>
    </justification>
  </clause>

  <clause id="9152">
    <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(246(a,1),7538(a,1,1)),flip(a)].">
      <j1 rule="para" parents="246 7538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9153">
    <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(199(a,1),7894(a,1,1,1))].">
      <j1 rule="para" parents="199 7894"/>
    </justification>
  </clause>

  <clause id="9154">
    <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(199(a,1),9153(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="199 9153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9155">
    <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(199(a,1),9154(a,2,2,3,1))].">
      <j1 rule="para" parents="199 9154"/>
    </justification>
  </clause>

  <clause id="9156">
    <literal><![CDATA[
      (x \ 1) * (R(K(y,x),x \ K(x,z),u) * u) = (K(y,x) * (x \ 1)) * u
    ]]></literal>
    <justification jstring="[para(5343(a,1),8078(a,2,1,1))].">
      <j1 rule="para" parents="5343 8078"/>
    </justification>
  </clause>

  <clause id="9157">
    <literal><![CDATA[
      (x \ 1) * (R(K(y,x),x \ K(x,z),u) * u) = (T(x,y) \ 1) * u
    ]]></literal>
    <justification jstring="[para(4555(a,1),9156(a,2,1))].">
      <j1 rule="para" parents="4555 9156"/>
    </justification>
  </clause>

  <clause id="9159">
    <literal><![CDATA[
      (x \ 1) * (R(K(y,x),x \ 1,z) * z) = (T(x,y) \ 1) * z
    ]]></literal>
    <justification jstring="[para(171(a,1),9157(a,1,2,1,2,2))].">
      <j1 rule="para" parents="171 9157"/>
    </justification>
  </clause>

  <clause id="9160">
    <literal><![CDATA[
      (x \ 1) * (K(y,x) * z) = (T(x,y) \ 1) * z
    ]]></literal>
    <justification jstring="[para(4895(a,1),9159(a,1,2,1))].">
      <j1 rule="para" parents="4895 9159"/>
    </justification>
  </clause>

  <clause id="9161">
    <literal><![CDATA[
      (T(x,y) \ 1) \ ((x \ 1) * z) = K(y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(631,a,9160,a)].">
      <j1 rule="hyper" parents="631 9160"/>
    </justification>
  </clause>

  <clause id="9162">
    <literal><![CDATA[
      (T(x,y) \ 1) * (x * y) = (x \ 1) * (y * x)
    ]]></literal>
    <justification jstring="[para(4201(a,1),9160(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4201 9160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9164">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ 1) * z) = L(z,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(9160(a,1),5345(a,1,2))].">
      <j1 rule="para" parents="9160 5345"/>
    </justification>
  </clause>

  <clause id="9165">
    <literal><![CDATA[
      L(x,T(y,z) \ 1,y) = L(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,4078,a(flip),b,9164,a)].">
      <j1 rule="hyper" parents="63 4078 9164"/>
    </justification>
  </clause>

  <clause id="9167">
    <literal><![CDATA[
      L(x,((y \ z) \ z) \ 1,(y \ z) \ z) = L(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,4163,a(flip),b,9165,a)].">
      <j1 rule="hyper" parents="63 4163 9165"/>
    </justification>
  </clause>

  <clause id="9169">
    <literal><![CDATA[
      L((x \ 1) * L((x \ 1) \ 1,y,z),T(x,u),w) = L(x \ 1,x,w) * L(L(x \ 1,x,w) \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(8378(a,1),8382(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="8378 8382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9170">
    <literal><![CDATA[
      L((x \ 1) * L((x \ 1) \ 1,y,z),T(x,u),w) = L((x \ 1) * L((x \ 1) \ 1,y,z),x,w)
    ]]></literal>
    <justification jstring="[hyper(333,a,4030,a(flip),b,9169,a),flip(a)].">
      <j1 rule="hyper" parents="333 4030 9169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9172">
    <literal><![CDATA[
      L((x \ 1) * L((x \ 1) \ 1,y,z),T(x,u),w) = L(x \ L(x,y,z),x,w)
    ]]></literal>
    <justification jstring="[para(1264(a,1),9170(a,2,1))].">
      <j1 rule="para" parents="1264 9170"/>
    </justification>
  </clause>

  <clause id="9173">
    <literal><![CDATA[
      L(x \ L(x,y,z),T(x,u),w) = L(x \ L(x,y,z),x,w)
    ]]></literal>
    <justification jstring="[para(1264(a,1),9172(a,1,1))].">
      <j1 rule="para" parents="1264 9172"/>
    </justification>
  </clause>

  <clause id="9174">
    <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(333,a,5108,a(flip),b,4810,a),flip(a)].">
      <j1 rule="hyper" parents="333 5108 4810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9175">
    <literal><![CDATA[
      ((x * y) * K(T(z,(1 / y) \ x),x * y)) / y = x * K(z,(x \ (1 / y)) \ 1)
    ]]></literal>
    <justification jstring="[para(4238(a,1),9174(a,1,1))].">
      <j1 rule="para" parents="4238 9174"/>
    </justification>
  </clause>

  <clause id="9176">
    <literal><![CDATA[
      ((x * y) * K(z,x * y)) / y = x * K(z,(x \ (1 / y)) \ 1)
    ]]></literal>
    <justification jstring="[para(6437(a,1),9175(a,1,1,2))].">
      <j1 rule="para" parents="6437 9175"/>
    </justification>
  </clause>

  <clause id="9177">
    <literal><![CDATA[
      ((x * y) * K(z,x * y)) / y = x * K(z,(1 / y) \ x)
    ]]></literal>
    <justification jstring="[para(5766(a,1),9176(a,2,2))].">
      <j1 rule="para" parents="5766 9176"/>
    </justification>
  </clause>

  <clause id="9178">
    <literal><![CDATA[
      ((x * y) * K(z,x * y)) / y = x * K(z,(y \ 1) \ x)
    ]]></literal>
    <justification jstring="[para(4792(a,1),9177(a,2,2))].">
      <j1 rule="para" parents="4792 9177"/>
    </justification>
  </clause>

  <clause id="9179">
    <literal><![CDATA[
      (x * K(y,(z \ 1) \ x)) * z = (x * z) * K(y,x * z)
    ]]></literal>
    <justification jstring="[hyper(140,a,9178,a)].">
      <j1 rule="hyper" parents="140 9178"/>
    </justification>
  </clause>

  <clause id="9180">
    <literal><![CDATA[
      (x \ y) * K(z,(x \ 1) \ (x \ y)) = x \ (y * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(35,a,5109,a(flip),b,9179,a),flip(a)].">
      <j1 rule="hyper" parents="35 5109 9179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9181">
    <literal><![CDATA[
      (x \ y) \ (x \ (y * K(z,y))) = K(z,(x \ 1) \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(129,a,9180,a)].">
      <j1 rule="hyper" parents="129 9180"/>
    </justification>
  </clause>

  <clause id="9182">
    <literal><![CDATA[
      (x \ K(y,z)) \ (x \ K(y,T(z,u))) = K(u,(x \ 1) \ (x \ K(y,z)))
    ]]></literal>
    <justification jstring="[para(6842(a,1),9181(a,1,2,2))].">
      <j1 rule="para" parents="6842 9181"/>
    </justification>
  </clause>

  <clause id="9184">
    <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(6763(a,1),8051(a,2,1))].">
      <j1 rule="para" parents="6763 8051"/>
    </justification>
  </clause>

  <clause id="9185">
    <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(63,a,8802,a(flip),b,8758,a)].">
      <j1 rule="hyper" parents="63 8802 8758"/>
    </justification>
  </clause>

  <clause id="9186">
    <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(9040,a,9185,a)].">
      <j1 rule="hyper" parents="9040 9185"/>
    </justification>
  </clause>

  <clause id="9189">
    <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(8789(a,1),9186(a,2,2,2))].">
      <j1 rule="para" parents="8789 9186"/>
    </justification>
  </clause>

  <clause id="9190">
    <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(10(a,1),9189(a,2,2,2,1))].">
      <j1 rule="para" parents="10 9189"/>
    </justification>
  </clause>

  <clause id="9191">
    <literal><![CDATA[
      a(T(x,y),z,R(x,u,w)) = x \ R(x,z,R(x,u,w))
    ]]></literal>
    <justification jstring="[para(9(a,1),9190(a,2,2))].">
      <j1 rule="para" parents="9 9190"/>
    </justification>
  </clause>

  <clause id="9193">
    <literal><![CDATA[
      a(T(x,y),z,R(x,u,w)) = a(x,z,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(333,a,8795,a(flip),b,9191,a),flip(a)].">
      <j1 rule="hyper" parents="333 8795 9191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9194">
    <literal><![CDATA[
      a(x,T(x,y) \ z,R(x,u,w)) = a(x,x \ z,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,9041,a(flip),b,9193,a),flip(a)].">
      <j1 rule="hyper" parents="63 9041 9193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9197">
    <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(333,a,7337,a(flip),b,9184,a),flip(a)].">
      <j1 rule="hyper" parents="333 7337 9184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9198">
    <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(7387(a,1),5272(a,1,3))].">
      <j1 rule="para" parents="7387 5272"/>
    </justification>
  </clause>

  <clause id="9200">
    <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(7760(a,1),8176(a,1,1))].">
      <j1 rule="para" parents="7760 8176"/>
    </justification>
  </clause>

  <clause id="9201">
    <literal><![CDATA[
      T(x * K(y,z),L(L(T(y,x),u,w),K(y,z),x)) = L(T(y,x),u,w) \ (L(y,u,w) * (x * K(y,z)))
    ]]></literal>
    <justification jstring="[para(5437(a,1),8192(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5437 8192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9202">
    <literal><![CDATA[
      T(x * K(y,z),L(L(T(y,x),u,w),K(y,z),x)) = K(x,L(y,u,w)) * (x * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(333,a,4702,a(flip),b,9201,a),flip(a)].">
      <j1 rule="hyper" parents="333 4702 9201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9204">
    <literal><![CDATA[
      T(x * K(y,z),L(L(T(y,x),u,w),K(y,z),x)) = T(x,L(y,u,w)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,4273,a(flip),b,9202,a),flip(a)].">
      <j1 rule="hyper" parents="333 4273 9202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9205">
    <literal><![CDATA[
      T(x * K(y,z),L(T(y,x),u,w)) = T(x,L(y,u,w)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(5437(a,1),9204(a,1,2))].">
      <j1 rule="para" parents="5437 9204"/>
    </justification>
  </clause>

  <clause id="9206">
    <literal><![CDATA[
      T(x * K(y,z),L(y,u,w)) = T(x,L(y,u,w)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,7377,a(flip),b,9205,a)].">
      <j1 rule="hyper" parents="63 7377 9205"/>
    </justification>
  </clause>

  <clause id="9208">
    <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(8557,a,9148,a)].">
      <j1 rule="hyper" parents="8557 9148"/>
    </justification>
  </clause>

  <clause id="9209">
    <literal><![CDATA[
      T(x \ L(x,y,z),u * x) = T(x \ L(x,y,z),x * u)
    ]]></literal>
    <justification jstring="[para(1264(a,1),9208(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1264 9208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9210">
    <literal><![CDATA[
      L(x \ L(y,z,u),x,K(L(y,z,u),y \ w)) * (K(L(y,z,u),y \ w) * x) = T((x \ L(y,z,u)) * x,w / y)
    ]]></literal>
    <justification jstring="[para(5271(a,1),8993(a,1,2,1))].">
      <j1 rule="para" parents="5271 8993"/>
    </justification>
  </clause>

  <clause id="9211">
    <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(6336(a,1),9200(a,1,2))].">
      <j1 rule="para" parents="6336 9200"/>
    </justification>
  </clause>

  <clause id="9213">
    <literal><![CDATA[
      T((x \ L(y,z,u)) * x,w / y) = T((x \ L(y,z,u)) * x,y \ w)
    ]]></literal>
    <justification jstring="[hyper(8992,a,9210,a),flip(a)].">
      <j1 rule="hyper" parents="8992 9210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9214">
    <literal><![CDATA[
      T((x \ L(y,y \ z,y)) * x,y \ T(z,y)) = T((x \ y) * x,z)
    ]]></literal>
    <justification jstring="[hyper(5621,a,9213,a),flip(a)].">
      <j1 rule="hyper" parents="5621 9213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9215">
    <literal><![CDATA[
      L(T((x \ y) * x,y \ T(z,y)),y \ z,y) = T((x \ y) * x,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,2552,a,b,9214,a)].">
      <j1 rule="hyper" parents="63 2552 9214"/>
    </justification>
  </clause>

  <clause id="9216">
    <literal><![CDATA[
      L(T((x \ y) * x,y \ z),y \ z,y) = T((x \ y) * x,z)
    ]]></literal>
    <justification jstring="[para(7636(a,1),9215(a,1,1))].">
      <j1 rule="para" parents="7636 9215"/>
    </justification>
  </clause>

  <clause id="9217">
    <literal><![CDATA[
      x * T((y \ z) * y,x) = z * (((y \ z) * y) * (z \ x))
    ]]></literal>
    <justification jstring="[hyper(126,a,9216,a(flip),b,754,a(flip))].">
      <j1 rule="hyper" parents="126 9216 754"/>
    </justification>
  </clause>

  <clause id="9218">
    <literal><![CDATA[
      x * (((y \ x) * y) * (x \ z)) = ((y \ x) * y) * z
    ]]></literal>
    <justification jstring="[hyper(300,a,9217,a),flip(a)].">
      <j1 rule="hyper" parents="300 9217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9219">
    <literal><![CDATA[
      (((x * (y * x)) / x) / y) * (z / (((x * (y * x)) / x) / y)) = z * K(L(x,T(y,x),x),T(x,y * x) \ z)
    ]]></literal>
    <justification jstring="[para(3822(a,1),7800(a,2,2,1))].">
      <j1 rule="para" parents="3822 7800"/>
    </justification>
  </clause>

  <clause id="9220">
    <literal><![CDATA[
      (((x * (y * x)) / x) / y) * (z / (((x * (y * x)) / x) / y)) = z * K(L(x,T(y,x),x),T(x,x * y) \ z)
    ]]></literal>
    <justification jstring="[para(3678(a,1),9219(a,2,2,2,1))].">
      <j1 rule="para" parents="3678 9219"/>
    </justification>
  </clause>

  <clause id="9221">
    <literal><![CDATA[
      (((x * (y * x)) / x) / y) * (z / (((x * (y * x)) / x) / y)) = z * K(x,T(x,x * y) \ z)
    ]]></literal>
    <justification jstring="[para(6303(a,1),9220(a,2,2))].">
      <j1 rule="para" parents="6303 9220"/>
    </justification>
  </clause>

  <clause id="9223">
    <literal><![CDATA[
      (((x * (y * x)) / x) / y) * (z / (((x * (y * x)) / x) / y)) = z * K(x,x \ z)
    ]]></literal>
    <justification jstring="[para(7410(a,1),9221(a,2,2))].">
      <j1 rule="para" parents="7410 9221"/>
    </justification>
  </clause>

  <clause id="9224">
    <literal><![CDATA[
      (((x * (y * x)) / x) / y) * (z / (((x * (y * x)) / x) / y)) = x * (z / x)
    ]]></literal>
    <justification jstring="[hyper(333,a,4461,a(flip),b,9223,a),flip(a)].">
      <j1 rule="hyper" parents="333 4461 9223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9226">
    <literal><![CDATA[
      L(x,T(y,x),x) * (z / (((x * (y * x)) / x) / y)) = x * (z / x)
    ]]></literal>
    <justification jstring="[para(3822(a,1),9224(a,1,1))].">
      <j1 rule="para" parents="3822 9224"/>
    </justification>
  </clause>

  <clause id="9227">
    <literal><![CDATA[
      L(x,T(y,x),x) * (z / L(x,T(y,x),x)) = x * (z / x)
    ]]></literal>
    <justification jstring="[para(3822(a,1),9226(a,1,2,2))].">
      <j1 rule="para" parents="3822 9226"/>
    </justification>
  </clause>

  <clause id="9228">
    <literal><![CDATA[
      L(x,y,x) * (z / L(x,T(y,x),x)) = x * (z / x)
    ]]></literal>
    <justification jstring="[para(3823(a,1),9227(a,1,1))].">
      <j1 rule="para" parents="3823 9227"/>
    </justification>
  </clause>

  <clause id="9229">
    <literal><![CDATA[
      L(x,y,x) * (z / L(x,y,x)) = x * (z / x)
    ]]></literal>
    <justification jstring="[para(3823(a,1),9228(a,1,2,2))].">
      <j1 rule="para" parents="3823 9228"/>
    </justification>
  </clause>

  <clause id="9230">
    <literal><![CDATA[
      L(x,y,x) * ((z * x) / L(x,y,x)) = x * z
    ]]></literal>
    <justification jstring="[para(11(a,1),9229(a,2,2))].">
      <j1 rule="para" parents="11 9229"/>
    </justification>
  </clause>

  <clause id="9231">
    <literal><![CDATA[
      L(x,y,x) * (z * a(x,y,x)) = x * z
    ]]></literal>
    <justification jstring="[para(8270(a,1),9230(a,1,2))].">
      <j1 rule="para" parents="8270 9230"/>
    </justification>
  </clause>

  <clause id="9232">
    <literal><![CDATA[
      L(x,y,x) \ (x * z) = z * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(129,a,9231,a)].">
      <j1 rule="hyper" parents="129 9231"/>
    </justification>
  </clause>

  <clause id="9233">
    <literal><![CDATA[
      (x \ y) * a(x,z,x) = L(x,z,x) \ y
    ]]></literal>
    <justification jstring="[hyper(121,a,10,a(flip),b,9231,a),flip(a)].">
      <j1 rule="hyper" parents="121 10 9231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9234">
    <literal><![CDATA[
      x * (L(x,y,x) \ z) = z * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1258,a(flip),b,9232,a)].">
      <j1 rule="hyper" parents="63 1258 9232"/>
    </justification>
  </clause>

  <clause id="9235">
    <literal><![CDATA[
      (L(x,x \ y,x) \ y) \ ((y / T(x,y)) * L(z,K(y,x),x \ y)) = L(z,a(x,x \ y,x),x \ y)
    ]]></literal>
    <justification jstring="[para(9233(a,1),8839(a,1,1))].">
      <j1 rule="para" parents="9233 8839"/>
    </justification>
  </clause>

  <clause id="9236">
    <literal><![CDATA[
      L(x,y,x) * (x \ z) = z / a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(603,a,9234,a),flip(a)].">
      <j1 rule="hyper" parents="603 9234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9237">
    <literal><![CDATA[
      T(x,y) * (L(T(x,y),z,x) \ u) = u * a(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,7344,a,b,9234,a)].">
      <j1 rule="hyper" parents="63 7344 9234"/>
    </justification>
  </clause>

  <clause id="9238">
    <literal><![CDATA[
      K(x,y) * (z * a(x,u,x)) = T(x,y) * (L(x,u,x) \ z)
    ]]></literal>
    <justification jstring="[hyper(126,a,9234,a(flip),b,4295,a)].">
      <j1 rule="hyper" parents="126 9234 4295"/>
    </justification>
  </clause>

  <clause id="9239">
    <literal><![CDATA[
      x * a(y,y \ x,y) = y * (T(x,y) / y)
    ]]></literal>
    <justification jstring="[para(3881(a,1),9234(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3881 9234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9240">
    <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(6588(a,1),9234(a,1,2,1))].">
      <j1 rule="para" parents="6588 9234"/>
    </justification>
  </clause>

  <clause id="9241">
    <literal><![CDATA[
      x * a(y,y \ x,y) = T(y * (x / y),y)
    ]]></literal>
    <justification jstring="[hyper(333,a,4083,a,b,9239,a),flip(a)].">
      <j1 rule="hyper" parents="333 4083 9239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9242">
    <literal><![CDATA[
      x \ (y * (T(x,y) / y)) = a(y,y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(129,a,9239,a)].">
      <j1 rule="hyper" parents="129 9239"/>
    </justification>
  </clause>

  <clause id="9243">
    <literal><![CDATA[
      x \ (y * (T(x,y) / y)) != z
    ]]></literal>
    <literal><![CDATA[
      a(y,y \ x,y) = z
    ]]></literal>
    <justification jstring="[para(9239(a,1),342(a,1,2))].">
      <j1 rule="para" parents="9239 342"/>
    </justification>
  </clause>

  <clause id="9244">
    <literal><![CDATA[
      L(x,y,z) \ (u * (L(T(x,u),y,z) / u)) = a(u,u \ L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(25(a,2),9242(a,1,2,2,1))].">
      <j1 rule="para" parents="25 9242"/>
    </justification>
  </clause>

  <clause id="9245">
    <literal><![CDATA[
      K(x,x * y) * (z * a(x,y,x)) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(333,a,8707,a(flip),b,9238,a),flip(a)].">
      <j1 rule="hyper" parents="333 8707 9238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9246">
    <literal><![CDATA[
      a(x,y,x) * z = z * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(34,a,8370,a,b,9245,a)].">
      <j1 rule="hyper" parents="34 8370 9245"/>
    </justification>
  </clause>

  <clause id="9247">
    <literal><![CDATA[
      (a(x,y,x) \ z) * a(x,y,x) = z
    ]]></literal>
    <justification jstring="[hyper(34,a,8371,a(flip),b,9245,a),flip(a)].">
      <j1 rule="hyper" parents="34 8371 9245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9248">
    <literal><![CDATA[
      a(x,y,x) \ (z * a(x,y,x)) = z
    ]]></literal>
    <justification jstring="[hyper(34,a,8371,a,b,9245,a(flip))].">
      <j1 rule="hyper" parents="34 8371 9245"/>
    </justification>
  </clause>

  <clause id="9249">
    <literal><![CDATA[
      (a(x,y,x) \ z) \ z = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(416,a,9246,a)].">
      <j1 rule="hyper" parents="416 9246"/>
    </justification>
  </clause>

  <clause id="9250">
    <literal><![CDATA[
      x / a(y,z,y) = a(y,z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(362,a,9246,a)].">
      <j1 rule="hyper" parents="362 9246"/>
    </justification>
  </clause>

  <clause id="9251">
    <literal><![CDATA[
      a(x,x \ y,x) * y = x * (T(y,x) / x)
    ]]></literal>
    <justification jstring="[hyper(333,a,9239,a(flip),b,9246,a),flip(a)].">
      <j1 rule="hyper" parents="333 9239 9246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9252">
    <literal><![CDATA[
      T(x,a(y,z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(257,a,9246,a)].">
      <j1 rule="hyper" parents="257 9246"/>
    </justification>
  </clause>

  <clause id="9253">
    <literal><![CDATA[
      T(a(x,y,x),z) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(253,a,9246,a,b,xx)].">
      <j1 rule="hyper" parents="253 9246"/>
    </justification>
  </clause>

  <clause id="9254">
    <literal><![CDATA[
      x * (a(y,z,y) * u) = x * (u * a(y,z,y))
    ]]></literal>
    <justification jstring="[hyper(126,a,9246,a,b,9,a)].">
      <j1 rule="hyper" parents="126 9246 9"/>
    </justification>
  </clause>

  <clause id="9255">
    <literal><![CDATA[
      a(x,x,x) \ (1 / x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(121,a,8234,a(flip),b,9246,a)].">
      <j1 rule="hyper" parents="121 8234 9246"/>
    </justification>
  </clause>

  <clause id="9256">
    <literal><![CDATA[
      (x * y) * a(y,x,y) = T(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,8248,a(flip),b,9246,a),flip(a)].">
      <j1 rule="hyper" parents="63 8248 9246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9257">
    <literal><![CDATA[
      (a(x,y,x) * z) \ u = (z * a(x,y,x)) \ u
    ]]></literal>
    <justification jstring="[hyper(61,a,9246,a)].">
      <j1 rule="hyper" parents="61 9246"/>
    </justification>
  </clause>

  <clause id="9258">
    <literal><![CDATA[
      a(x,y,x) * K(z,a(x,y,x)) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,6316,a,b,9246,a)].">
      <j1 rule="hyper" parents="35 6316 9246"/>
    </justification>
  </clause>

  <clause id="9259">
    <literal><![CDATA[
      a(x,y,x) * z != z * u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = u
    ]]></literal>
    <justification jstring="[para(9246(a,2),43(a,1))].">
      <j1 rule="para" parents="9246 43"/>
    </justification>
  </clause>

  <clause id="9261">
    <literal><![CDATA[
      (a(x,y,x) \ z) * a(x,y,x) != u
    ]]></literal>
    <literal><![CDATA[
      z = u
    ]]></literal>
    <justification jstring="[para(9246(a,1),274(a,1))].">
      <j1 rule="para" parents="9246 274"/>
    </justification>
  </clause>

  <clause id="9262">
    <literal><![CDATA[
      (x * y) \ ((x * a(z,u,z)) * y) = R(T(a(z,u,z),x * y),x,y)
    ]]></literal>
    <justification jstring="[para(9246(a,1),674(a,1,2,1))].">
      <j1 rule="para" parents="9246 674"/>
    </justification>
  </clause>

  <clause id="9263">
    <literal><![CDATA[
      (x * (y * a(z,u,z))) \ (x * (y * (w * a(z,u,z)))) != v5
    ]]></literal>
    <literal><![CDATA[
      L(L(w,a(z,u,z),y),y * a(z,u,z),x) = v5
    ]]></literal>
    <justification jstring="[para(9246(a,1),877(a,1,2,2,2))].">
      <j1 rule="para" parents="9246 877"/>
    </justification>
  </clause>

  <clause id="9266">
    <literal><![CDATA[
      x / a(y,z,y) != u
    ]]></literal>
    <literal><![CDATA[
      a(y,z,y) \ x = u
    ]]></literal>
    <justification jstring="[para(9252(a,1),423(a,1))].">
      <j1 rule="para" parents="9252 423"/>
    </justification>
  </clause>

  <clause id="9267">
    <literal><![CDATA[
      T(x,y \ R(y,z,y)) = x
    ]]></literal>
    <justification jstring="[para(8208(a,1),9252(a,1,2))].">
      <j1 rule="para" parents="8208 9252"/>
    </justification>
  </clause>

  <clause id="9268">
    <literal><![CDATA[
      (x * (y \ R(y,z,y))) / x = y \ R(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(197,a,9267,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="197 9267 22"/>
    </justification>
  </clause>

  <clause id="9270">
    <literal><![CDATA[
      T(a(x,y,x),z) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,8210,a,b,9253,a),flip(a)].">
      <j1 rule="hyper" parents="333 8210 9253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9271">
    <literal><![CDATA[
      x * a(y,z,y) != u
    ]]></literal>
    <literal><![CDATA[
      a(y,z,y) * x = u
    ]]></literal>
    <justification jstring="[para(9253(a,1),300(a,1,2))].">
      <j1 rule="para" parents="9253 300"/>
    </justification>
  </clause>

  <clause id="9272">
    <literal><![CDATA[
      x * (a(x,y,x) \ z) = L(x,y,x) * z
    ]]></literal>
    <justification jstring="[hyper(126,a,9247,a(flip),b,9232,a),flip(a)].">
      <j1 rule="hyper" parents="126 9247 9232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9273">
    <literal><![CDATA[
      L(x,y,x) * (x \ z) = a(x,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(63,a,9236,a,b,9250,a)].">
      <j1 rule="hyper" parents="63 9236 9250"/>
    </justification>
  </clause>

  <clause id="9274">
    <literal><![CDATA[
      (x / (K(y,y * z) * a(y,z,y))) * K(y,y * z) = a(y,z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,8466,a,b,9250,a)].">
      <j1 rule="hyper" parents="63 8466 9250"/>
    </justification>
  </clause>

  <clause id="9275">
    <literal><![CDATA[
      T(a(x / y,z,x / y),u) = (x / y) \ R(x / y,z,y \ x)
    ]]></literal>
    <justification jstring="[para(8664(a,1),9270(a,2,2))].">
      <j1 rule="para" parents="8664 9270"/>
    </justification>
  </clause>

  <clause id="9276">
    <literal><![CDATA[
      (x * y) \ T(y * x,y) != z
    ]]></literal>
    <literal><![CDATA[
      a(y,x,y) = z
    ]]></literal>
    <justification jstring="[para(9256(a,1),342(a,1,2))].">
      <j1 rule="para" parents="9256 342"/>
    </justification>
  </clause>

  <clause id="9277">
    <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(9256(a,1),967(a,1,1,2))].">
      <j1 rule="para" parents="9256 967"/>
    </justification>
  </clause>

  <clause id="9278">
    <literal><![CDATA[
      a(x,y,x) \ y = x \ ((x * (y * x)) / x)
    ]]></literal>
    <justification jstring="[hyper(121,a,3722,a,b,9272,a),flip(a)].">
      <j1 rule="hyper" parents="121 3722 9272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9279">
    <literal><![CDATA[
      a(x,x \ y,x) \ y = (x \ y) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(34,a,782,a,b,9272,a),flip(a)].">
      <j1 rule="hyper" parents="34 782 9272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9280">
    <literal><![CDATA[
      a(x,y,x) \ (x * z) = L(x,y,x) * z
    ]]></literal>
    <justification jstring="[hyper(34,a,1252,a(flip),b,9272,a),flip(a)].">
      <j1 rule="hyper" parents="34 1252 9272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9281">
    <literal><![CDATA[
      a(x,y,x) * (L(x,y,x) * z) = x * z
    ]]></literal>
    <justification jstring="[hyper(126,a,155,a(flip),b,9273,a(flip))].">
      <j1 rule="hyper" parents="126 155 9273"/>
    </justification>
  </clause>

  <clause id="9282">
    <literal><![CDATA[
      (x / y) \ (a(y,z,y) \ x) = L(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(121,a,9273,a(flip),b,6716,a(flip))].">
      <j1 rule="hyper" parents="121 9273 6716"/>
    </justification>
  </clause>

  <clause id="9283">
    <literal><![CDATA[
      a(x,y,x) \ x != z
    ]]></literal>
    <literal><![CDATA[
      L(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(9273(a,1),209(a,1))].">
      <j1 rule="para" parents="9273 209"/>
    </justification>
  </clause>

  <clause id="9284">
    <literal><![CDATA[
      (x * (y * a(z,u,z))) / (x * y) = L(a(z,u,z),y,x)
    ]]></literal>
    <justification jstring="[para(9258(a,1),4429(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9258 4429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9285">
    <literal><![CDATA[
      L(x,y,x) * (x \ z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) \ z = u
    ]]></literal>
    <justification jstring="[para(9236(a,2),9266(a,1))].">
      <j1 rule="para" parents="9236 9266"/>
    </justification>
  </clause>

  <clause id="9286">
    <literal><![CDATA[
      (x * ((a(y,z,y) * u) * w)) \ ((x * (u * a(y,z,y))) * w) = a(x,a(y,z,y) * u,w)
    ]]></literal>
    <justification jstring="[para(9254(a,1),14(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="9254 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9287">
    <literal><![CDATA[
      (T(x * y,x) / x) / y = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[para(5524(a,1),9268(a,1,1))].">
      <j1 rule="para" parents="5524 9268"/>
    </justification>
  </clause>

  <clause id="9288">
    <literal><![CDATA[
      (x \ R(x,y \ 1,x)) / (T(x * (y \ 1),x) / x) = y
    ]]></literal>
    <justification jstring="[hyper(123,a,9287,a(flip),b,6253,a(flip))].">
      <j1 rule="hyper" parents="123 9287 6253"/>
    </justification>
  </clause>

  <clause id="9289">
    <literal><![CDATA[
      R(x,x \ 1,y \ R(y,x \ 1,y)) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,5525,a,b,9288,a)].">
      <j1 rule="hyper" parents="63 5525 9288"/>
    </justification>
  </clause>

  <clause id="9291">
    <literal><![CDATA[
      R(x,x \ 1,a(y,x \ 1,y)) = x
    ]]></literal>
    <justification jstring="[para(8210(a,1),9289(a,1,3))].">
      <j1 rule="para" parents="8210 9289"/>
    </justification>
  </clause>

  <clause id="9292">
    <literal><![CDATA[
      (x \ 1) * a(y,x \ 1,y) = x \ a(y,x \ 1,y)
    ]]></literal>
    <justification jstring="[para(9291(a,1),430(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9291 430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9293">
    <literal><![CDATA[
      x * (T(y * (x \ 1),y) / y) = a(y,x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(126,a,8225,a,b,9292,a(flip))].">
      <j1 rule="hyper" parents="126 8225 9292"/>
    </justification>
  </clause>

  <clause id="9294">
    <literal><![CDATA[
      T(x \ a(y,x \ 1,y),y) = y \ T(y * (x \ 1),y)
    ]]></literal>
    <justification jstring="[para(9292(a,1),8252(a,1,1))].">
      <j1 rule="para" parents="9292 8252"/>
    </justification>
  </clause>

  <clause id="9295">
    <literal><![CDATA[
      K(x \ (y * z),z) * K(z,z \ T(z * ((y \ x) \ 1),z)) = a(z,(y \ x) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,8017,a,b,9293,a)].">
      <j1 rule="hyper" parents="63 8017 9293"/>
    </justification>
  </clause>

  <clause id="9296">
    <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(9294(a,1),1795(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9294 1795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9297">
    <literal><![CDATA[
      a(T(x,y),z,T(x,y)) = a(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(34,a,9237,a(flip),b,9240,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="34 9237 9240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9299">
    <literal><![CDATA[
      ((x * y) * a(y,z,y)) \ ((y * x) * y) = L(T(y,x),z,T(y,x))
    ]]></literal>
    <justification jstring="[para(9297(a,1),8275(a,1,1,2))].">
      <j1 rule="para" parents="9297 8275"/>
    </justification>
  </clause>

  <clause id="9300">
    <literal><![CDATA[
      K(T(x,y * z) * z,T(x,y * z)) = a(x,z,x) * K(z,T(x,y))
    ]]></literal>
    <justification jstring="[para(9297(a,1),8257(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9297 8257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9303">
    <literal><![CDATA[
      (x * y) \ ((x * a(z,u,z)) * y) = R(a(z,u,z),x,y)
    ]]></literal>
    <justification jstring="[para(9253(a,1),9262(a,2,1))].">
      <j1 rule="para" parents="9253 9262"/>
    </justification>
  </clause>

  <clause id="9305">
    <literal><![CDATA[
      (x * y) \ ((T(z * x,z) / z) * y) = R(a(z,x,z),x,y)
    ]]></literal>
    <justification jstring="[para(8225(a,2),9303(a,1,2,1))].">
      <j1 rule="para" parents="8225 9303"/>
    </justification>
  </clause>

  <clause id="9306">
    <literal><![CDATA[
      L(a(x,T(y,z),x),T(y,z),z) = R(a(x,y,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,8728,a,b,9305,a)].">
      <j1 rule="hyper" parents="63 8728 9305"/>
    </justification>
  </clause>

  <clause id="9307">
    <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(4239(a,1),9306(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4239 9306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9309">
    <literal><![CDATA[
      L(x,y,z) \ L(u * (T(x,u) / u),y,z) = a(u,u \ L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(2545(a,2),9244(a,1,2))].">
      <j1 rule="para" parents="2545 9244"/>
    </justification>
  </clause>

  <clause id="9310">
    <literal><![CDATA[
      (x / K(y,z)) * K(y,y * z) = a(y,z,y) \ x
    ]]></literal>
    <justification jstring="[para(8244(a,1),9274(a,1,1,2))].">
      <j1 rule="para" parents="8244 9274"/>
    </justification>
  </clause>

  <clause id="9311">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,z * y) = a(z,y,z) \ x
    ]]></literal>
    <justification jstring="[para(5994(a,1),9310(a,1,1))].">
      <j1 rule="para" parents="5994 9310"/>
    </justification>
  </clause>

  <clause id="9312">
    <literal><![CDATA[
      (x / R(y,z,y)) * y = a(y,z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,7998,a(flip),b,9311,a)].">
      <j1 rule="hyper" parents="63 7998 9311"/>
    </justification>
  </clause>

  <clause id="9313">
    <literal><![CDATA[
      (x / R(y,z,y)) * y = x / a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,9250,a,b,9312,a),flip(a)].">
      <j1 rule="hyper" parents="333 9250 9312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9314">
    <literal><![CDATA[
      (x * a(y,z,y)) / R(y,z,y) = x / y
    ]]></literal>
    <justification jstring="[hyper(123,a,9248,a(flip),b,9312,a),flip(a)].">
      <j1 rule="hyper" parents="123 9248 9312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9315">
    <literal><![CDATA[
      a(x,y,x) \ (z / x) = z / R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1577,a(flip),b,9312,a),flip(a)].">
      <j1 rule="hyper" parents="63 1577 9312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9316">
    <literal><![CDATA[
      (x / R(y,z,y)) * a(y,z,y) = x / y
    ]]></literal>
    <justification jstring="[hyper(125,a,1577,a(flip),b,9313,a(flip))].">
      <j1 rule="hyper" parents="125 1577 9313"/>
    </justification>
  </clause>

  <clause id="9317">
    <literal><![CDATA[
      (x / R(y,z,y)) * y != u
    ]]></literal>
    <literal><![CDATA[
      a(y,z,y) \ x = u
    ]]></literal>
    <justification jstring="[para(9313(a,2),9266(a,1))].">
      <j1 rule="para" parents="9313 9266"/>
    </justification>
  </clause>

  <clause id="9318">
    <literal><![CDATA[
      (x / y) * R(y,z,y) = x * a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(140,a,9314,a)].">
      <j1 rule="hyper" parents="140 9314"/>
    </justification>
  </clause>

  <clause id="9319">
    <literal><![CDATA[
      (x * y) * a(y,z,y) = x * R(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(125,a,11,a(flip),b,9314,a),flip(a)].">
      <j1 rule="hyper" parents="125 11 9314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9320">
    <literal><![CDATA[
      R(x,y,x) * (x \ z) = z * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,6595,a,b,9318,a)].">
      <j1 rule="hyper" parents="63 6595 9318"/>
    </justification>
  </clause>

  <clause id="9321">
    <literal><![CDATA[
      (x / y) * ((y \ z) \ T(z,y)) = x * a(y,y \ z,y)
    ]]></literal>
    <justification jstring="[para(3746(a,1),9318(a,1,2))].">
      <j1 rule="para" parents="3746 9318"/>
    </justification>
  </clause>

  <clause id="9322">
    <literal><![CDATA[
      a(x,y,x) * (z * x) = z * R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(9271,a,9319,a)].">
      <j1 rule="hyper" parents="9271 9319"/>
    </justification>
  </clause>

  <clause id="9323">
    <literal><![CDATA[
      (x * y) \ (x * R(y,z,y)) = a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(129,a,9319,a)].">
      <j1 rule="hyper" parents="129 9319"/>
    </justification>
  </clause>

  <clause id="9324">
    <literal><![CDATA[
      (x * R(y,z,y)) / (x * y) = a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(123,a,9319,a(flip),b,9246,a)].">
      <j1 rule="hyper" parents="123 9319 9246"/>
    </justification>
  </clause>

  <clause id="9325">
    <literal><![CDATA[
      (x * (y * R(z,u,z))) / (x * (y * z)) = L(a(z,u,z),y * z,x)
    ]]></literal>
    <justification jstring="[para(9319(a,1),9284(a,1,1,2))].">
      <j1 rule="para" parents="9319 9284"/>
    </justification>
  </clause>

  <clause id="9326">
    <literal><![CDATA[
      (x * R(y,z,y)) \ ((y * x) * y) = L(T(y,x),z,T(y,x))
    ]]></literal>
    <justification jstring="[para(9319(a,1),9299(a,1,1))].">
      <j1 rule="para" parents="9319 9299"/>
    </justification>
  </clause>

  <clause id="9327">
    <literal><![CDATA[
      (x * y) \ (R(x,z,x) * y) = a(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(649,a,9320,a)].">
      <j1 rule="hyper" parents="649 9320"/>
    </justification>
  </clause>

  <clause id="9328">
    <literal><![CDATA[
      (x * y) * a(x,z,x) = R(x,z,x) * y
    ]]></literal>
    <justification jstring="[hyper(575,a,9320,a),flip(a)].">
      <j1 rule="hyper" parents="575 9320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9329">
    <literal><![CDATA[
      R(x,y,x) * (x \ z) = a(x,y,x) * z
    ]]></literal>
    <justification jstring="[hyper(333,a,9246,a,b,9320,a),flip(a)].">
      <j1 rule="hyper" parents="333 9246 9320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9330">
    <literal><![CDATA[
      x * (y * a(x,z,x)) = R(x,z,x) * y
    ]]></literal>
    <justification jstring="[hyper(126,a,9320,a(flip),b,1510,a)].">
      <j1 rule="hyper" parents="126 9320 1510"/>
    </justification>
  </clause>

  <clause id="9332">
    <literal><![CDATA[
      (x * R(x \ y,z,x \ y)) / y = a(x \ y,z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(123,a,9322,a(flip),b,154,a(flip))].">
      <j1 rule="hyper" parents="123 9322 154"/>
    </justification>
  </clause>

  <clause id="9333">
    <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(97(a,1),9324(a,1,2))].">
      <j1 rule="para" parents="97 9324"/>
    </justification>
  </clause>

  <clause id="9334">
    <literal><![CDATA[
      a(x,y,x) * (x * z) = R(x,y,x) * z
    ]]></literal>
    <justification jstring="[hyper(9271,a,9328,a)].">
      <j1 rule="hyper" parents="9271 9328"/>
    </justification>
  </clause>

  <clause id="9335">
    <literal><![CDATA[
      x * (a(x,y,x) * z) = R(x,y,x) * z
    ]]></literal>
    <justification jstring="[hyper(126,a,9329,a(flip),b,1510,a)].">
      <j1 rule="hyper" parents="126 9329 1510"/>
    </justification>
  </clause>

  <clause id="9336">
    <literal><![CDATA[
      (x * y) \ (R(x,z,x) * y) != u
    ]]></literal>
    <literal><![CDATA[
      L(a(x,z,x),y,x) = u
    ]]></literal>
    <justification jstring="[para(9330(a,1),504(a,1,2))].">
      <j1 rule="para" parents="9330 504"/>
    </justification>
  </clause>

  <clause id="9337">
    <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(9330(a,1),8238(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9330 8238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9338">
    <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(9334(a,1),544(a,1,1,1))].">
      <j1 rule="para" parents="9334 544"/>
    </justification>
  </clause>

  <clause id="9339">
    <literal><![CDATA[
      a(x,y,x) \ (x \ z) = R(x,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(629,a,9335,a),flip(a)].">
      <j1 rule="hyper" parents="629 9335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9340">
    <literal><![CDATA[
      a(x,y,x) * (R(x,y,x) \ z) = x \ z
    ]]></literal>
    <justification jstring="[hyper(121,a,10,a(flip),b,9335,a),flip(a)].">
      <j1 rule="hyper" parents="121 10 9335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9341">
    <literal><![CDATA[
      x * (y \ L(y,z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      a(y,z,y) \ x = u
    ]]></literal>
    <justification jstring="[para(8000(a,1),9317(a,1))].">
      <j1 rule="para" parents="8000 9317"/>
    </justification>
  </clause>

  <clause id="9342">
    <literal><![CDATA[
      L(a(x,y,x),z,x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(9336,a,9327,a)].">
      <j1 rule="hyper" parents="9336 9327"/>
    </justification>
  </clause>

  <clause id="9343">
    <literal><![CDATA[
      L(a(x,y,x),z,x) = (u * x) \ (u * R(x,y,x))
    ]]></literal>
    <justification jstring="[hyper(333,a,9323,a,b,9342,a),flip(a)].">
      <j1 rule="hyper" parents="333 9323 9342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9344">
    <literal><![CDATA[
      L(a(x \ y,z,x \ y),u,x \ y) = y \ (x * R(x \ y,z,x \ y))
    ]]></literal>
    <justification jstring="[hyper(333,a,158,a(flip),b,9343,a),flip(a)].">
      <j1 rule="hyper" parents="333 158 9343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9347">
    <literal><![CDATA[
      L(T(x,a(y,z,y)),a(y,z,y),y) = x
    ]]></literal>
    <justification jstring="[hyper(333,a,9,a(flip),b,9337,a),flip(a)].">
      <j1 rule="hyper" parents="333 9 9337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9349">
    <literal><![CDATA[
      L(x,a(y,z,y),y) = x
    ]]></literal>
    <justification jstring="[para(9252(a,1),9347(a,1,1))].">
      <j1 rule="para" parents="9252 9347"/>
    </justification>
  </clause>

  <clause id="9351">
    <literal><![CDATA[
      L(x,a(y,z,y),T(y,u)) = x
    ]]></literal>
    <justification jstring="[para(9297(a,1),9349(a,1,2))].">
      <j1 rule="para" parents="9297 9349"/>
    </justification>
  </clause>

  <clause id="9352">
    <literal><![CDATA[
      (T(x,y) * a(x,z,x)) * u = T(x,y) * (a(x,z,x) * u)
    ]]></literal>
    <justification jstring="[hyper(1170,a,9351,a),flip(a)].">
      <j1 rule="hyper" parents="1170 9351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9353">
    <literal><![CDATA[
      T(x,y) * (a(x,z,x) * u) = R(T(x,y),z,x) * u
    ]]></literal>
    <justification jstring="[para(8221(a,1),9352(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8221 9352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9354">
    <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(9353(a,1),8933(a,1,2))].">
      <j1 rule="para" parents="9353 8933"/>
    </justification>
  </clause>

  <clause id="9359">
    <literal><![CDATA[
      L(a((x \ y) \ y,z,(x \ y) \ y),u,(x \ y) \ y) = y \ (R(x,z,(x \ y) \ y) * (x \ y))
    ]]></literal>
    <justification jstring="[para(676(a,1),9344(a,2,2))].">
      <j1 rule="para" parents="676 9344"/>
    </justification>
  </clause>

  <clause id="9360">
    <literal><![CDATA[
      L(x,y \ R(T(y,z),u,y),y) = x
    ]]></literal>
    <justification jstring="[hyper(344,a,9354,a)].">
      <j1 rule="hyper" parents="344 9354"/>
    </justification>
  </clause>

  <clause id="9362">
    <literal><![CDATA[
      L(x,K(y,z) * a(y,u,y),y) = x
    ]]></literal>
    <justification jstring="[para(8230(a,1),9360(a,1,2))].">
      <j1 rule="para" parents="8230 9360"/>
    </justification>
  </clause>

  <clause id="9363">
    <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(4239(a,1),9307(a,2,2))].">
      <j1 rule="para" parents="4239 9307"/>
    </justification>
  </clause>

  <clause id="9364">
    <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(3613(a,1),9277(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3613 9277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9365">
    <literal><![CDATA[
      K(x \ (y * z),z) * K(z,(y \ x) \ 1) = a(z,(y \ x) \ 1,z)
    ]]></literal>
    <justification jstring="[para(7412(a,1),9295(a,1,2))].">
      <j1 rule="para" parents="7412 9295"/>
    </justification>
  </clause>

  <clause id="9366">
    <literal><![CDATA[
      K(x \ (y * z),z) * K(z,x \ y) = a(z,(y \ x) \ 1,z)
    ]]></literal>
    <justification jstring="[para(5766(a,1),9365(a,1,2))].">
      <j1 rule="para" parents="5766 9365"/>
    </justification>
  </clause>

  <clause id="9368">
    <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(462(a,1),9333(a,1,1))].">
      <j1 rule="para" parents="462 9333"/>
    </justification>
  </clause>

  <clause id="9369">
    <literal><![CDATA[
      L(a((x \ y) \ y,z,(x \ y) \ y),u,(x \ y) \ y) = y \ (R(x,z,x) * (x \ y))
    ]]></literal>
    <justification jstring="[para(8665(a,1),9359(a,2,2,1))].">
      <j1 rule="para" parents="8665 9359"/>
    </justification>
  </clause>

  <clause id="9371">
    <literal><![CDATA[
      L(a((x \ y) \ y,z,(x \ y) \ y),u,(x \ y) \ y) = y \ (y * a(x,z,x))
    ]]></literal>
    <justification jstring="[para(9320(a,1),9369(a,2,2))].">
      <j1 rule="para" parents="9320 9369"/>
    </justification>
  </clause>

  <clause id="9372">
    <literal><![CDATA[
      a((x \ y) \ y,z,(x \ y) \ y) = a(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(377,a,9371,a),flip(a)].">
      <j1 rule="hyper" parents="377 9371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9373">
    <literal><![CDATA[
      (x / T(y,x)) \ ((x / T(y,x)) * L(z,K(x,y),y \ x)) = L(z,a(y,y \ x,y),y \ x)
    ]]></literal>
    <justification jstring="[para(3880(a,1),9235(a,1,1))].">
      <j1 rule="para" parents="3880 9235"/>
    </justification>
  </clause>

  <clause id="9374">
    <literal><![CDATA[
      L(x,a(y,y \ z,y),y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,K(z,y),y \ z) = u
    ]]></literal>
    <justification jstring="[para(9373(a,1),342(a,1))].">
      <j1 rule="para" parents="9373 342"/>
    </justification>
  </clause>

  <clause id="9393">
    <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(97(a,1),1699(a,1,2,1,2,1))].">
      <j1 rule="para" parents="97 1699"/>
    </justification>
  </clause>

  <clause id="9394">
    <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(63,a,1696,a(flip),b,9393,a),flip(a)].">
      <j1 rule="hyper" parents="63 1696 9393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9395">
    <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(1697(a,1),9394(a,2,2))].">
      <j1 rule="para" parents="1697 9394"/>
    </justification>
  </clause>

  <clause id="9396">
    <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(501,a,9395,a),flip(a)].">
      <j1 rule="hyper" parents="501 9395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9397">
    <literal><![CDATA[
      L(x * ((y * (x \ 1)) / y),z,u) = y \ T(y,L(x,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,3071,a(flip),b,9396,a),flip(a)].">
      <j1 rule="hyper" parents="63 3071 9396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9398">
    <literal><![CDATA[
      L(x \ T(x,y \ 1),z,u) = x \ T(x,L(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(3071(a,1),9397(a,1,1))].">
      <j1 rule="para" parents="3071 9397"/>
    </justification>
  </clause>

  <clause id="9399">
    <literal><![CDATA[
      L(x \ T(x,y \ 1),z,u) = K(x,L(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(333,a,4215,a,b,9398,a),flip(a)].">
      <j1 rule="hyper" parents="333 4215 9398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9400">
    <literal><![CDATA[
      L(K(x,y \ 1),z,u) = K(x,L(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(4215(a,2),9399(a,1,1))].">
      <j1 rule="para" parents="4215 9399"/>
    </justification>
  </clause>

  <clause id="9401">
    <literal><![CDATA[
      K(x,L(K(y,z),u,w) \ 1) = L(K(x,K(z,y)),u,w)
    ]]></literal>
    <justification jstring="[para(4367(a,1),9400(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4367 9400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9402">
    <literal><![CDATA[
      K(x,L(y \ 1,z,u) \ 1) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(4621(a,1),9400(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4621 9400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9403">
    <literal><![CDATA[
      K(x,L(T(y \ 1,z),u,w) \ 1) = L(T(K(x,y),z),u,w)
    ]]></literal>
    <justification jstring="[para(4937(a,1),9400(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4937 9400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9404">
    <literal><![CDATA[
      K(x,L(y \ z,u,w) \ 1) = L(K(x,z \ y),u,w)
    ]]></literal>
    <justification jstring="[para(5766(a,1),9400(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5766 9400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9405">
    <literal><![CDATA[
      (x * L(K(y,z),u,w)) \ x = L(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,6003,a(flip),b,9402,a)].">
      <j1 rule="hyper" parents="63 6003 9402"/>
    </justification>
  </clause>

  <clause id="9406">
    <literal><![CDATA[
      x / L(K(y,z),u,w) = x * L(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(197,a,9402,a(flip),b,6003,a(flip))].">
      <j1 rule="hyper" parents="197 9402 6003"/>
    </justification>
  </clause>

  <clause id="9408">
    <literal><![CDATA[
      L(K(x,y),z,u) \ w = L(K(y,x),z,u) * w
    ]]></literal>
    <justification jstring="[para(9402(a,1),5376(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9402 5376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9409">
    <literal><![CDATA[
      T(x,y * L(K(x,z),u,w)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(9402(a,1),7367(a,1,2,2))].">
      <j1 rule="para" parents="9402 7367"/>
    </justification>
  </clause>

  <clause id="9410">
    <literal><![CDATA[
      K(x * L(K(y,z),u,w),y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(9402(a,1),7395(a,1,1,2))].">
      <j1 rule="para" parents="9402 7395"/>
    </justification>
  </clause>

  <clause id="9411">
    <literal><![CDATA[
      K(x,y * L(K(x,z),u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(9402(a,1),7414(a,1,2,2))].">
      <j1 rule="para" parents="9402 7414"/>
    </justification>
  </clause>

  <clause id="9412">
    <literal><![CDATA[
      K(x \ L(K(y,z),u,w),y) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(9402(a,1),7611(a,1,1,2))].">
      <j1 rule="para" parents="9402 7611"/>
    </justification>
  </clause>

  <clause id="9413">
    <literal><![CDATA[
      T(x,y * K(L(x,z,u),w)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(6298(a,1),9409(a,1,2,2))].">
      <j1 rule="para" parents="6298 9409"/>
    </justification>
  </clause>

  <clause id="9414">
    <literal><![CDATA[
      K(x * (y * K(z,u)),z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(97(a,1),9410(a,1,1))].">
      <j1 rule="para" parents="97 9410"/>
    </justification>
  </clause>

  <clause id="9415">
    <literal><![CDATA[
      K(x * K(L(y,z,u),w),y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(6298(a,1),9410(a,1,1,2))].">
      <j1 rule="para" parents="6298 9410"/>
    </justification>
  </clause>

  <clause id="9416">
    <literal><![CDATA[
      K(x,y * (z * K(x,u))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(97(a,1),9411(a,1,2))].">
      <j1 rule="para" parents="97 9411"/>
    </justification>
  </clause>

  <clause id="9417">
    <literal><![CDATA[
      T(x,L(x,y,z) * (z * y)) = T(x,z * (y * x))
    ]]></literal>
    <justification jstring="[para(493(a,1),9413(a,1,2))].">
      <j1 rule="para" parents="493 9413"/>
    </justification>
  </clause>

  <clause id="9419">
    <literal><![CDATA[
      K(L(x,y,z) * u,x) = K(u * L(x,y,z),x)
    ]]></literal>
    <justification jstring="[para(88(a,1),9415(a,1,1))].">
      <j1 rule="para" parents="88 9415"/>
    </justification>
  </clause>

  <clause id="9420">
    <literal><![CDATA[
      K((L(x,y,z) \ u) * L(x,y,z),x) = K(u,x)
    ]]></literal>
    <justification jstring="[para(316(a,1),9415(a,1,1)),flip(a)].">
      <j1 rule="para" parents="316 9415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9421">
    <literal><![CDATA[
      K(K(L(x,y,z),u) * w,x) = K(w,x)
    ]]></literal>
    <justification jstring="[para(6390(a,1),9415(a,1,1))].">
      <j1 rule="para" parents="6390 9415"/>
    </justification>
  </clause>

  <clause id="9422">
    <literal><![CDATA[
      K(x \ L(T(x,y),z,u),x) = K(x \ L(x,z,u),x)
    ]]></literal>
    <justification jstring="[para(9000(a,1),9415(a,1,1))].">
      <j1 rule="para" parents="9000 9415"/>
    </justification>
  </clause>

  <clause id="9423">
    <literal><![CDATA[
      K(x,T(y,K(L(x,z,u),w) * v5)) = K(x * K(v5,x),y)
    ]]></literal>
    <justification jstring="[para(9421(a,1),6935(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9421 6935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9424">
    <literal><![CDATA[
      K(x * (y / T(z,u)),u) = K(x * (y / z),u)
    ]]></literal>
    <justification jstring="[para(5450(a,1),9414(a,1,1,2))].">
      <j1 rule="para" parents="5450 9414"/>
    </justification>
  </clause>

  <clause id="9425">
    <literal><![CDATA[
      K(x * (y * K(z,u)),u) = K(x * y,u)
    ]]></literal>
    <justification jstring="[para(5995(a,1),9414(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5995 9414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9426">
    <literal><![CDATA[
      K(x * (y \ T(z,u)),u) = K(x * (y \ z),u)
    ]]></literal>
    <justification jstring="[para(6244(a,1),9414(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6244 9414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9427">
    <literal><![CDATA[
      K(x * (K(y,z) * u),y) = K(x * u,y)
    ]]></literal>
    <justification jstring="[para(6390(a,1),9414(a,1,1,2))].">
      <j1 rule="para" parents="6390 9414"/>
    </justification>
  </clause>

  <clause id="9428">
    <literal><![CDATA[
      K(x * (y / R(z,u,z)),z) = K(x * (y / T(z,u)),z)
    ]]></literal>
    <justification jstring="[para(7995(a,1),9414(a,1,1,2))].">
      <j1 rule="para" parents="7995 9414"/>
    </justification>
  </clause>

  <clause id="9429">
    <literal><![CDATA[
      K(x,y * (z / T(u,x))) = K(x,y * (z / u))
    ]]></literal>
    <justification jstring="[para(5450(a,1),9416(a,1,2,2))].">
      <j1 rule="para" parents="5450 9416"/>
    </justification>
  </clause>

  <clause id="9430">
    <literal><![CDATA[
      K(x,y * (z * K(u,x))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(5995(a,1),9416(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5995 9416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9431">
    <literal><![CDATA[
      K(x,y * (K(x,z) * u)) = K(x,y * u)
    ]]></literal>
    <justification jstring="[para(6390(a,1),9416(a,1,2,2))].">
      <j1 rule="para" parents="6390 9416"/>
    </justification>
  </clause>

  <clause id="9432">
    <literal><![CDATA[
      K(x,y * (T(z,x) \ u)) = K(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[para(7339(a,1),9416(a,1,2,2))].">
      <j1 rule="para" parents="7339 9416"/>
    </justification>
  </clause>

  <clause id="9433">
    <literal><![CDATA[
      K(x,y * (z * L(K(x,u),w,v5))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(9402(a,1),9416(a,1,2,2,2))].">
      <j1 rule="para" parents="9402 9416"/>
    </justification>
  </clause>

  <clause id="9434">
    <literal><![CDATA[
      K(x * (T(y,z) * u),y) = K(x * (y * u),y)
    ]]></literal>
    <justification jstring="[para(4273(a,1),9427(a,1,1,2))].">
      <j1 rule="para" parents="4273 9427"/>
    </justification>
  </clause>

  <clause id="9435">
    <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(9427(a,1),4946(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="9427 4946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9436">
    <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(9427(a,1),4950(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="9427 4950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9437">
    <literal><![CDATA[
      K(x / y,z * (y * (x / y))) = K(x / y,z * x)
    ]]></literal>
    <justification jstring="[para(318(a,1),9430(a,1,2,2))].">
      <j1 rule="para" parents="318 9430"/>
    </justification>
  </clause>

  <clause id="9438">
    <literal><![CDATA[
      K(x,y * (z * L(K(u,x),w,v5))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(5372(a,1),9430(a,1,2,2,2))].">
      <j1 rule="para" parents="5372 9430"/>
    </justification>
  </clause>

  <clause id="9439">
    <literal><![CDATA[
      K(x,T(y * (z * K(u,x)),w)) = T(K(x,y * z),w)
    ]]></literal>
    <justification jstring="[para(9430(a,1),6365(a,2,1))].">
      <j1 rule="para" parents="9430 6365"/>
    </justification>
  </clause>

  <clause id="9440">
    <literal><![CDATA[
      T(x,y * (K(x,z) * u)) = T(x,y * u)
    ]]></literal>
    <justification jstring="[hyper(124,a,9431,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 9431 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9441">
    <literal><![CDATA[
      K(x,y * (z * (K(u,x) * w))) = K(x,y * (z * w))
    ]]></literal>
    <justification jstring="[para(5354(a,1),9431(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5354 9431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9442">
    <literal><![CDATA[
      K(x,y * ((K(x,z) * u) \ w)) = K(x,y * ((u * K(x,z)) \ w))
    ]]></literal>
    <justification jstring="[para(8434(a,1),9431(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8434 9431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9443">
    <literal><![CDATA[
      K(L(x,y,z),u \ L(K(x,w),v5,v6)) = L(x * K(u \ 1,x),y,z) \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(9412(a,1),4948(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9412 4948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9444">
    <literal><![CDATA[
      (((x \ y) \ y) * L(K(z,u),w,v5)) \ T(x,x \ y) = L(K(u,z),w,v5)
    ]]></literal>
    <justification jstring="[hyper(693,a,9405,a)].">
      <j1 rule="hyper" parents="693 9405"/>
    </justification>
  </clause>

  <clause id="9445">
    <literal><![CDATA[
      1 / L(K(x,y),z,u) = L(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(217,a,9405,a)].">
      <j1 rule="hyper" parents="217 9405"/>
    </justification>
  </clause>

  <clause id="9446">
    <literal><![CDATA[
      x / L(L(K(y,z),u,w),K(z,v5),v6) = x * L(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(197,a,8162,a,b,9405,a)].">
      <j1 rule="hyper" parents="197 8162 9405"/>
    </justification>
  </clause>

  <clause id="9447">
    <literal><![CDATA[
      (x * (y * K(z,u))) * L(K(u,z),y,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(39,a,18,a(flip),b,9405,a),flip(a)].">
      <j1 rule="hyper" parents="39 18 9405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9448">
    <literal><![CDATA[
      L(K(x,y),z,u) \ 1 = L(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(7(a,1),9405(a,1,1))].">
      <j1 rule="para" parents="7 9405"/>
    </justification>
  </clause>

  <clause id="9449">
    <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(9405(a,1),301(a,1,2)),flip(b)].">
      <j1 rule="para" parents="9405 301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9450">
    <literal><![CDATA[
      (x * (y * K(z,u))) \ (x * y) = L(K(u,z),y,x)
    ]]></literal>
    <justification jstring="[para(97(a,1),9405(a,1,1))].">
      <j1 rule="para" parents="97 9405"/>
    </justification>
  </clause>

  <clause id="9451">
    <literal><![CDATA[
      (x * ((x \ y) * K(z,u))) \ y = L(K(u,z),x \ y,x)
    ]]></literal>
    <justification jstring="[para(463(a,1),9405(a,1,1))].">
      <j1 rule="para" parents="463 9405"/>
    </justification>
  </clause>

  <clause id="9452">
    <literal><![CDATA[
      L(K(x,y),z,u) \ 1 != w
    ]]></literal>
    <literal><![CDATA[
      L(K(y,x),z,u) = w
    ]]></literal>
    <justification jstring="[para(9445(a,1),345(a,1,1))].">
      <j1 rule="para" parents="9445 345"/>
    </justification>
  </clause>

  <clause id="9453">
    <literal><![CDATA[
      K(x,L(y,z / y,u)) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,6299,a,b,9448,a)].">
      <j1 rule="hyper" parents="63 6299 9448"/>
    </justification>
  </clause>

  <clause id="9454">
    <literal><![CDATA[
      1 / L(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(y,x),z,u) = w
    ]]></literal>
    <justification jstring="[para(9448(a,1),301(a,1,2)),flip(b)].">
      <j1 rule="para" parents="9448 301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9455">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) = K(L(K(x,y),u,w),z)
    ]]></literal>
    <justification jstring="[para(9448(a,1),6781(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9448 6781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9456">
    <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(63,a,6913,a(flip),b,9453,a),flip(a)].">
      <j1 rule="hyper" parents="63 6913 9453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9457">
    <literal><![CDATA[
      L(K(x,y),z * y,u) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(11(a,1),9453(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11 9453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9458">
    <literal><![CDATA[
      L(K(x,y \ z),z,u) = K(x,L(y \ z,y,u))
    ]]></literal>
    <justification jstring="[para(76(a,1),9453(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="76 9453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9460">
    <literal><![CDATA[
      K(x,T(L(y,z / y,u),w)) = T(L(K(x,y),z,u),w)
    ]]></literal>
    <justification jstring="[para(9453(a,1),6365(a,2,1))].">
      <j1 rule="para" parents="9453 6365"/>
    </justification>
  </clause>

  <clause id="9462">
    <literal><![CDATA[
      L(K(x,T(y,z)),u,K(y,w)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(6569(a,1),9453(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6569 9453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9463">
    <literal><![CDATA[
      L(K(x,y),z,K(u,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(6597(a,1),9453(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6597 9453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9464">
    <literal><![CDATA[
      K(L(x,y,K(z,u)),u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(7827,a,9463,a)].">
      <j1 rule="hyper" parents="7827 9463"/>
    </justification>
  </clause>

  <clause id="9465">
    <literal><![CDATA[
      K((K(x,y) * z) \ u,y) = K(z \ (K(y,x) * u),y)
    ]]></literal>
    <justification jstring="[para(4581(a,1),9464(a,1,1))].">
      <j1 rule="para" parents="4581 9464"/>
    </justification>
  </clause>

  <clause id="9466">
    <literal><![CDATA[
      K(x,L(y,z,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6363,a,9457,a),flip(a)].">
      <j1 rule="hyper" parents="6363 9457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9467">
    <literal><![CDATA[
      L(L(K(x,y),z * y,u),y,w) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(5764,a,9457,a)].">
      <j1 rule="hyper" parents="5764 9457"/>
    </justification>
  </clause>

  <clause id="9469">
    <literal><![CDATA[
      K(x \ 1,L(y,z,x)) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,8120,a(flip),b,9457,a),flip(a)].">
      <j1 rule="hyper" parents="63 8120 9457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9470">
    <literal><![CDATA[
      K(x,L(y,z,x \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,8117,a(flip),b,9457,a),flip(a)].">
      <j1 rule="hyper" parents="63 8117 9457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9471">
    <literal><![CDATA[
      K(x,L(y,z,K(u,x))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,6605,a(flip),b,9457,a),flip(a)].">
      <j1 rule="hyper" parents="63 6605 9457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9472">
    <literal><![CDATA[
      K(x,L(y,z,K(x,u))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,6576,a(flip),b,9457,a),flip(a)].">
      <j1 rule="hyper" parents="63 6576 9457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9473">
    <literal><![CDATA[
      K(x,L(y,z,T(y,u))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,6266,a(flip),b,9457,a),flip(a)].">
      <j1 rule="hyper" parents="63 6266 9457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9474">
    <literal><![CDATA[
      K(x,L(y,z,T(x,u))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,6264,a(flip),b,9457,a),flip(a)].">
      <j1 rule="hyper" parents="63 6264 9457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9475">
    <literal><![CDATA[
      K(x,L(y,z,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,6213,a(flip),b,9457,a),flip(a)].">
      <j1 rule="hyper" parents="63 6213 9457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9476">
    <literal><![CDATA[
      K(x,L(y,y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(9457(a,1),509(a,1))].">
      <j1 rule="para" parents="9457 509"/>
    </justification>
  </clause>

  <clause id="9477">
    <literal><![CDATA[
      K(x,L(L(y,z,x),u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(30(a,1),9466(a,1,2))].">
      <j1 rule="para" parents="30 9466"/>
    </justification>
  </clause>

  <clause id="9478">
    <literal><![CDATA[
      K(x,(x * y) \ z) = K(x,y \ (x \ z))
    ]]></literal>
    <justification jstring="[para(311(a,1),9466(a,1,2))].">
      <j1 rule="para" parents="311 9466"/>
    </justification>
  </clause>

  <clause id="9479">
    <literal><![CDATA[
      K(x,(x \ 1) \ y) = K(x,x * y)
    ]]></literal>
    <justification jstring="[para(514(a,1),9466(a,1,2)),flip(a)].">
      <j1 rule="para" parents="514 9466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9480">
    <literal><![CDATA[
      K(x,(x \ y) \ z) = K(x,y \ (x * z))
    ]]></literal>
    <justification jstring="[para(515(a,1),9466(a,1,2)),flip(a)].">
      <j1 rule="para" parents="515 9466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9481">
    <literal><![CDATA[
      K(x,(y * (x / y)) \ (x * z)) = K(x,K(y \ x,y) * z)
    ]]></literal>
    <justification jstring="[para(5395(a,1),9466(a,1,2))].">
      <j1 rule="para" parents="5395 9466"/>
    </justification>
  </clause>

  <clause id="9482">
    <literal><![CDATA[
      K(L(x,y,z),L(u,w,x)) = L(K(x,u),y * x,z)
    ]]></literal>
    <justification jstring="[para(9466(a,1),6298(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9466 6298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9483">
    <literal><![CDATA[
      T(x,L(y,z,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(124,a,9475,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 9475 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9484">
    <literal><![CDATA[
      T(x,L(y,z,y)) = x * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(126,a,9475,a(flip),b,4215,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="126 9475 4215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9487">
    <literal><![CDATA[
      T(x,L(T(y,z),u,y)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(6588(a,1),9483(a,1,2))].">
      <j1 rule="para" parents="6588 9483"/>
    </justification>
  </clause>

  <clause id="9488">
    <literal><![CDATA[
      K(R(x,x \ 1,y),L(z,u,x \ 1)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5561,a,b,9470,a)].">
      <j1 rule="hyper" parents="63 5561 9470"/>
    </justification>
  </clause>

  <clause id="9489">
    <literal><![CDATA[
      K(x,((x \ 1) * y) \ z) = K(x,y \ ((x \ 1) \ z))
    ]]></literal>
    <justification jstring="[para(311(a,1),9470(a,1,2))].">
      <j1 rule="para" parents="311 9470"/>
    </justification>
  </clause>

  <clause id="9490">
    <literal><![CDATA[
      K(x,(K(y,x) * z) \ u) = K(x,z \ (K(x,y) * u))
    ]]></literal>
    <justification jstring="[para(4581(a,1),9471(a,1,2))].">
      <j1 rule="para" parents="4581 9471"/>
    </justification>
  </clause>

  <clause id="9491">
    <literal><![CDATA[
      K(x,L(L(y,z,K(x,u)),w,v5)) = K(x,L(y,w,v5))
    ]]></literal>
    <justification jstring="[para(30(a,1),9472(a,1,2))].">
      <j1 rule="para" parents="30 9472"/>
    </justification>
  </clause>

  <clause id="9492">
    <literal><![CDATA[
      K(x,K(y,L(z,u,K(x,w)))) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[para(9472(a,1),6785(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9472 6785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9493">
    <literal><![CDATA[
      K(x,T(L(y,z,T(x,u)),w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[para(25(a,1),9474(a,1,2))].">
      <j1 rule="para" parents="25 9474"/>
    </justification>
  </clause>

  <clause id="9494">
    <literal><![CDATA[
      K(x,(T(x,y) * z) \ u) = K(x,z \ (T(x,y) \ u))
    ]]></literal>
    <justification jstring="[para(311(a,1),9474(a,1,2))].">
      <j1 rule="para" parents="311 9474"/>
    </justification>
  </clause>

  <clause id="9495">
    <literal><![CDATA[
      T(x,L(y,z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = u
    ]]></literal>
    <justification jstring="[para(9484(a,2),4285(a,1))].">
      <j1 rule="para" parents="9484 4285"/>
    </justification>
  </clause>

  <clause id="9496">
    <literal><![CDATA[
      T(x,T(y / z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(3781(a,1),9495(a,1,2))].">
      <j1 rule="para" parents="3781 9495"/>
    </justification>
  </clause>

  <clause id="9497">
    <literal><![CDATA[
      K(x,T(y / (x * z),z)) = K(x,z \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(63,a,6533,a,b,9478,a)].">
      <j1 rule="hyper" parents="63 6533 9478"/>
    </justification>
  </clause>

  <clause id="9498">
    <literal><![CDATA[
      K(x,(x \ y) \ (x \ z)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(10(a,1),9478(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 9478"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9499">
    <literal><![CDATA[
      K(x,((x \ 1) * y) \ (x \ z)) = K(x,L(y,x \ 1,x) \ z)
    ]]></literal>
    <justification jstring="[para(275(a,1),9478(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="275 9478"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9500">
    <literal><![CDATA[
      (x * ((y / z) / x)) * z = y * K(x,z \ (x \ y))
    ]]></literal>
    <justification jstring="[para(9478(a,1),5765(a,2,2))].">
      <j1 rule="para" parents="9478 5765"/>
    </justification>
  </clause>

  <clause id="9502">
    <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(9480(a,1),7565(a,1,2,2))].">
      <j1 rule="para" parents="9480 7565"/>
    </justification>
  </clause>

  <clause id="9503">
    <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(9480(a,1),7621(a,1,1,2))].">
      <j1 rule="para" parents="9480 7621"/>
    </justification>
  </clause>

  <clause id="9504">
    <literal><![CDATA[
      (K(x,y) * z) * K(u,T(x,w)) = K(x,y) * (z * K(u,T(x,w)))
    ]]></literal>
    <justification jstring="[hyper(126,a,9462,a(flip),b,3220,a(flip))].">
      <j1 rule="hyper" parents="126 9462 3220"/>
    </justification>
  </clause>

  <clause id="9505">
    <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(5451(a,1),9496(a,1,2,1))].">
      <j1 rule="para" parents="5451 9496"/>
    </justification>
  </clause>

  <clause id="9506">
    <literal><![CDATA[
      L(K(x,y),z,u) * (L(K(y,x),z,u) * w) = w
    ]]></literal>
    <justification jstring="[hyper(344,a,9408,a)].">
      <j1 rule="hyper" parents="344 9408"/>
    </justification>
  </clause>

  <clause id="9508">
    <literal><![CDATA[
      K(x * (((y \ 1) \ z) / z),y) = K(x * (z \ ((y \ 1) \ z)),y)
    ]]></literal>
    <justification jstring="[para(3598(a,1),9424(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3598 9424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9509">
    <literal><![CDATA[
      K(x * (y / (z * y)),z \ 1) = K(x * ((z * y) \ y),z \ 1)
    ]]></literal>
    <justification jstring="[para(3765(a,1),9424(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3765 9424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9511">
    <literal><![CDATA[
      L(K(x,y \ z),z,u) = K(x,(u * y) \ (u * z))
    ]]></literal>
    <justification jstring="[para(99(a,1),9458(a,2,2))].">
      <j1 rule="para" parents="99 9458"/>
    </justification>
  </clause>

  <clause id="9512">
    <literal><![CDATA[
      L(K(x,y \ (z \ u)),z \ u,z) = K(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[para(311(a,1),9458(a,2,2))].">
      <j1 rule="para" parents="311 9458"/>
    </justification>
  </clause>

  <clause id="9513">
    <literal><![CDATA[
      L(K(x,(y \ z) \ u),u,y) = K(x,z \ (y * u))
    ]]></literal>
    <justification jstring="[para(515(a,1),9458(a,2,2))].">
      <j1 rule="para" parents="515 9458"/>
    </justification>
  </clause>

  <clause id="9514">
    <literal><![CDATA[
      K(T(x,y * z),u / ((y * T(x,y * z)) * z)) = K(x,(y * z) \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,9087,a,b,9497,a)].">
      <j1 rule="hyper" parents="63 9087 9497"/>
    </justification>
  </clause>

  <clause id="9515">
    <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(9506(a,1),342(a,1,2))].">
      <j1 rule="para" parents="9506 342"/>
    </justification>
  </clause>

  <clause id="9516">
    <literal><![CDATA[
      K(x,y * (z * (u * K(w,x)))) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(97(a,1),9438(a,1,2,2))].">
      <j1 rule="para" parents="97 9438"/>
    </justification>
  </clause>

  <clause id="9517">
    <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(123,a,9447,a(flip),b,6892,a),flip(a)].">
      <j1 rule="hyper" parents="123 9447 6892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9519">
    <literal><![CDATA[
      L(K(x,y),z,L(y,u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(7735,a,9450,a),flip(a)].">
      <j1 rule="hyper" parents="7735 9450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9520">
    <literal><![CDATA[
      L(K(x,y),z,y \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,8118,a(flip),b,9450,a),flip(a)].">
      <j1 rule="hyper" parents="63 8118 9450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9521">
    <literal><![CDATA[
      (x * (y \ T(y * z,y))) \ (x * z) = L(K(y,y * z),z,x)
    ]]></literal>
    <justification jstring="[para(5479(a,2),9450(a,1,1,2))].">
      <j1 rule="para" parents="5479 9450"/>
    </justification>
  </clause>

  <clause id="9522">
    <literal><![CDATA[
      (x * (K(y,z) * u)) \ (x * u) = L(K(z,T(y,u)),u,x)
    ]]></literal>
    <justification jstring="[para(6357(a,1),9450(a,1,1,2))].">
      <j1 rule="para" parents="6357 9450"/>
    </justification>
  </clause>

  <clause id="9523">
    <literal><![CDATA[
      K(L(x,y,z \ 1),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(7827,a,9520,a)].">
      <j1 rule="hyper" parents="7827 9520"/>
    </justification>
  </clause>

  <clause id="9526">
    <literal><![CDATA[
      K(((x \ 1) * y) \ (z * (x \ 1)),x) = K(y \ T(z,x \ 1),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,6285,a(flip),b,9520,a)].">
      <j1 rule="hyper" parents="63 6285 9520"/>
    </justification>
  </clause>

  <clause id="9527">
    <literal><![CDATA[
      K(((x \ 1) * y) \ z,T(x,y)) = K(((x \ 1) \ z) / y,x)
    ]]></literal>
    <justification jstring="[hyper(7200,a,9523,a)].">
      <j1 rule="hyper" parents="7200 9523"/>
    </justification>
  </clause>

  <clause id="9528">
    <literal><![CDATA[
      K(L(x,y,L(z,u,w)),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(7827,a,9519,a)].">
      <j1 rule="hyper" parents="7827 9519"/>
    </justification>
  </clause>

  <clause id="9529">
    <literal><![CDATA[
      K(x,L(y,z,L(y,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,9457,a(flip),b,9519,a)].">
      <j1 rule="hyper" parents="63 9457 9519"/>
    </justification>
  </clause>

  <clause id="9530">
    <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(3718(a,1),9528(a,1,1))].">
      <j1 rule="para" parents="3718 9528"/>
    </justification>
  </clause>

  <clause id="9531">
    <literal><![CDATA[
      R(K(x,y),L(y,z,u),w) = K(x,y)
    ]]></literal>
    <justification jstring="[para(9529(a,1),9098(a,1,1))].">
      <j1 rule="para" parents="9529 9098"/>
    </justification>
  </clause>

  <clause id="9532">
    <literal><![CDATA[
      K((L(x,y,z) * u) / w,x) = K(L(x,y,z) / (w / u),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,5564,a(flip),b,9531,a)].">
      <j1 rule="hyper" parents="63 5564 9531"/>
    </justification>
  </clause>

  <clause id="9534">
    <literal><![CDATA[
      K(x,L(y,z / y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x,y),z,u) = w
    ]]></literal>
    <justification jstring="[para(6299(a,2),9452(a,1))].">
      <j1 rule="para" parents="6299 9452"/>
    </justification>
  </clause>

  <clause id="9535">
    <literal><![CDATA[
      L(K(x,L(y,z,u)),y,w) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(9457(a,1),9467(a,1,1))].">
      <j1 rule="para" parents="9457 9467"/>
    </justification>
  </clause>

  <clause id="9536">
    <literal><![CDATA[
      K((x \ y) \ z,L(z,u,w)) = K(y \ (x * z),L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,6282,a(flip),b,9535,a),flip(a)].">
      <j1 rule="hyper" parents="63 6282 9535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9537">
    <literal><![CDATA[
      a(x,y,K(z,L(y,u,w))) = 1
    ]]></literal>
    <justification jstring="[hyper(53,a,9535,a)].">
      <j1 rule="hyper" parents="53 9535"/>
    </justification>
  </clause>

  <clause id="9538">
    <literal><![CDATA[
      K(L(x,y,z),L(u,w,x)) = K(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(333,a,6298,a(flip),b,9482,a),flip(a)].">
      <j1 rule="hyper" parents="333 6298 9482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9539">
    <literal><![CDATA[
      L(K(x,y),z * x,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(L(x,z,u),y) = w
    ]]></literal>
    <justification jstring="[para(9482(a,1),9476(a,1))].">
      <j1 rule="para" parents="9482 9476"/>
    </justification>
  </clause>

  <clause id="9540">
    <literal><![CDATA[
      K(L(x,y,z),(x \ u) \ w) = K(L(x,y,z),u \ (x * w))
    ]]></literal>
    <justification jstring="[para(515(a,1),9538(a,1,2)),flip(a)].">
      <j1 rule="para" parents="515 9538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9541">
    <literal><![CDATA[
      K(x,(y * z) \ (y * x)) = K(x,z \ x)
    ]]></literal>
    <justification jstring="[hyper(6136,a,9511,a),flip(a)].">
      <j1 rule="hyper" parents="6136 9511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9542">
    <literal><![CDATA[
      L(K(x,x \ y),y,z) = K(x,z \ (x \ (z * y)))
    ]]></literal>
    <justification jstring="[hyper(333,a,7874,a(flip),b,9511,a),flip(a)].">
      <j1 rule="hyper" parents="333 7874 9511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9543">
    <literal><![CDATA[
      K(x,L(y \ z,y,u)) = K(x,(u * y) \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,9458,a(flip),b,9511,a)].">
      <j1 rule="hyper" parents="63 9458 9511"/>
    </justification>
  </clause>

  <clause id="9544">
    <literal><![CDATA[
      K(x,(y * (z \ u)) \ (y * u)) = L(K(x,T(z,u)),u,y)
    ]]></literal>
    <justification jstring="[para(6367(a,1),9511(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6367 9511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9545">
    <literal><![CDATA[
      K(x,(y \ z) \ x) = K(x,z \ (y * x))
    ]]></literal>
    <justification jstring="[para(10(a,1),9541(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 9541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9546">
    <literal><![CDATA[
      K(x \ y,(x * z) \ y) = K(x \ y,z \ (x \ y))
    ]]></literal>
    <justification jstring="[para(10(a,1),9541(a,1,2,2))].">
      <j1 rule="para" parents="10 9541"/>
    </justification>
  </clause>

  <clause id="9547">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ x) = K(x,u \ (K(z,y) * x))
    ]]></literal>
    <justification jstring="[para(4558(a,1),9541(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4558 9541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9548">
    <literal><![CDATA[
      K(x,L(y,z,u) \ (y * x)) = K(x,(x / L(y,z,u)) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,5675,a(flip),b,9545,a),flip(a)].">
      <j1 rule="hyper" parents="63 5675 9545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9549">
    <literal><![CDATA[
      K(x,((y * K(z,y)) \ u) \ x) = K(x,u \ (y * (K(z,y) * x)))
    ]]></literal>
    <justification jstring="[para(3542(a,1),9545(a,2,2,2))].">
      <j1 rule="para" parents="3542 9545"/>
    </justification>
  </clause>

  <clause id="9550">
    <literal><![CDATA[
      K(x,(y \ z) \ R(x,u,w)) = K(x,z \ (y * R(x,u,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,9026,a(flip),b,9513,a)].">
      <j1 rule="hyper" parents="63 9026 9513"/>
    </justification>
  </clause>

  <clause id="9551">
    <literal><![CDATA[
      K(L(x,y,z),(z \ u) \ (x * y)) = K(x,u \ (z * (x * y)))
    ]]></literal>
    <justification jstring="[hyper(63,a,7779,a(flip),b,9513,a)].">
      <j1 rule="hyper" parents="63 7779 9513"/>
    </justification>
  </clause>

  <clause id="9552">
    <literal><![CDATA[
      K((x \ y) \ z,u \ (x * z)) = K(y \ (x * z),(x \ u) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,6282,a(flip),b,9513,a),flip(a)].">
      <j1 rule="hyper" parents="63 6282 9513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9553">
    <literal><![CDATA[
      (x * y) * K(z,u \ (x * y)) = x * (y * K(z,(x \ u) \ y))
    ]]></literal>
    <justification jstring="[hyper(126,a,9513,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="126 9513 18"/>
    </justification>
  </clause>

  <clause id="9554">
    <literal><![CDATA[
      L(T(K(x,(y \ z) \ u),w),u,y) = T(K(x,z \ (y * u)),w)
    ]]></literal>
    <justification jstring="[para(9513(a,1),25(a,2,1))].">
      <j1 rule="para" parents="9513 25"/>
    </justification>
  </clause>

  <clause id="9555">
    <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(9513(a,1),3549(a,1))].">
      <j1 rule="para" parents="9513 3549"/>
    </justification>
  </clause>

  <clause id="9556">
    <literal><![CDATA[
      K(x,y \ (z * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(z \ y) \ x) = u
    ]]></literal>
    <justification jstring="[para(9513(a,1),6136(a,1))].">
      <j1 rule="para" parents="9513 6136"/>
    </justification>
  </clause>

  <clause id="9558">
    <literal><![CDATA[
      K(x,(y * (z / u)) \ (y * z)) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x,u),z,y) = w
    ]]></literal>
    <justification jstring="[para(101(a,1),9534(a,1,2))].">
      <j1 rule="para" parents="101 9534"/>
    </justification>
  </clause>

  <clause id="9559">
    <literal><![CDATA[
      L(K(x,x \ y),y,x \ z) = K(x,z \ ((x \ z) * y))
    ]]></literal>
    <justification jstring="[hyper(333,a,9498,a(flip),b,9542,a),flip(a)].">
      <j1 rule="hyper" parents="333 9498 9542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9561">
    <literal><![CDATA[
      K(x,L(y \ z,y,u / y)) = K(x,u \ ((u / y) * z))
    ]]></literal>
    <justification jstring="[para(12(a,1),9543(a,2,2,1))].">
      <j1 rule="para" parents="12 9543"/>
    </justification>
  </clause>

  <clause id="9562">
    <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(5744(a,1),9543(a,2,2,1))].">
      <j1 rule="para" parents="5744 9543"/>
    </justification>
  </clause>

  <clause id="9563">
    <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(5899(a,1),9543(a,2,2,1))].">
      <j1 rule="para" parents="5899 9543"/>
    </justification>
  </clause>

  <clause id="9564">
    <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(9162(a,1),9543(a,2,2,2))].">
      <j1 rule="para" parents="9162 9543"/>
    </justification>
  </clause>

  <clause id="9565">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) = K(x,L(K(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(9448(a,1),9401(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9448 9401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9567">
    <literal><![CDATA[
      L(K(x,y \ z),z,z \ 1) = K(x,((1 / z) * y) \ 1)
    ]]></literal>
    <justification jstring="[para(2655(a,1),9404(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2655 9404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9568">
    <literal><![CDATA[
      L(K(x,y \ z),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(u * y) \ (u * z)) = w
    ]]></literal>
    <justification jstring="[para(9404(a,1),5951(a,1))].">
      <j1 rule="para" parents="9404 5951"/>
    </justification>
  </clause>

  <clause id="9569">
    <literal><![CDATA[
      K(x \ L(T(x,y),z,u),x) = 1
    ]]></literal>
    <justification jstring="[hyper(333,a,2518,a(flip),b,9422,a),flip(a)].">
      <j1 rule="hyper" parents="333 2518 9422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9571">
    <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(9569(a,1),9211(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9569 9211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9572">
    <literal><![CDATA[
      K(x,T(y * (z * K(u,x)),w)) = K(x,T(y * z,w))
    ]]></literal>
    <justification jstring="[hyper(333,a,6365,a,b,9439,a),flip(a)].">
      <j1 rule="hyper" parents="333 6365 9439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9573">
    <literal><![CDATA[
      K(x \ (K(y,z) * u),y) = K(x \ u,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,7610,a(flip),b,9465,a),flip(a)].">
      <j1 rule="hyper" parents="63 7610 9465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9575">
    <literal><![CDATA[
      K(x \ (y * z),z) = K(x \ (z * y),z)
    ]]></literal>
    <justification jstring="[para(4201(a,1),9573(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4201 9573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9576">
    <literal><![CDATA[
      K(x \ (K(y,z) * u),z) = K(x \ u,z)
    ]]></literal>
    <justification jstring="[para(4558(a,1),9573(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4558 9573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9577">
    <literal><![CDATA[
      K(x \ (y / z),z \ y) = K(x \ (z \ y),z \ y)
    ]]></literal>
    <justification jstring="[para(4407(a,1),9573(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4407 9573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9578">
    <literal><![CDATA[
      K(x \ (T(y,z) \ u),y) = K(x \ (y \ u),y)
    ]]></literal>
    <justification jstring="[para(4518(a,1),9573(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4518 9573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9579">
    <literal><![CDATA[
      K(x \ (K(y,z) * u),T(y,w)) = K(x \ u,T(y,w))
    ]]></literal>
    <justification jstring="[para(6901(a,1),9573(a,1,1,2,1))].">
      <j1 rule="para" parents="6901 9573"/>
    </justification>
  </clause>

  <clause id="9580">
    <literal><![CDATA[
      K(x \ (y * K(z,u)),z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(6887(a,1),9573(a,1,1,2))].">
      <j1 rule="para" parents="6887 9573"/>
    </justification>
  </clause>

  <clause id="9582">
    <literal><![CDATA[
      K(x \ (y / (z * y)),z \ 1) = K(x \ ((z * y) \ y),z \ 1)
    ]]></literal>
    <justification jstring="[para(5068(a,1),9576(a,1,1,2))].">
      <j1 rule="para" parents="5068 9576"/>
    </justification>
  </clause>

  <clause id="9583">
    <literal><![CDATA[
      K(x \ (y * K(z,u)),T(z,w)) = K(x \ y,T(z,w))
    ]]></literal>
    <justification jstring="[para(6901(a,1),9580(a,1,1,2,2))].">
      <j1 rule="para" parents="6901 9580"/>
    </justification>
  </clause>

  <clause id="9584">
    <literal><![CDATA[
      K(x \ (y * (z * u)),u) = K(x \ (y * (u * z)),u)
    ]]></literal>
    <justification jstring="[para(7301(a,1),9580(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7301 9580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9585">
    <literal><![CDATA[
      K((T(x,y) * z) \ u,x) = K(z \ (x \ u),x)
    ]]></literal>
    <justification jstring="[hyper(8476,a,9578,a)].">
      <j1 rule="hyper" parents="8476 9578"/>
    </justification>
  </clause>

  <clause id="9587">
    <literal><![CDATA[
      K((T(x,y) * z) \ u,K(x,w)) = K(w,K(z \ (x \ u),x))
    ]]></literal>
    <justification jstring="[para(9585(a,1),6788(a,2,2))].">
      <j1 rule="para" parents="9585 6788"/>
    </justification>
  </clause>

  <clause id="9588">
    <literal><![CDATA[
      K(x,y \ (K(x,z) * u)) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[hyper(7653,a,9490,a),flip(a)].">
      <j1 rule="hyper" parents="7653 9490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9589">
    <literal><![CDATA[
      K(x,y \ (K(x,z) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ u) = w
    ]]></literal>
    <justification jstring="[para(9490(a,1),7653(a,1))].">
      <j1 rule="para" parents="9490 7653"/>
    </justification>
  </clause>

  <clause id="9591">
    <literal><![CDATA[
      K(x,y \ T(x,z)) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[para(4274(a,2),9588(a,1,2,2))].">
      <j1 rule="para" parents="4274 9588"/>
    </justification>
  </clause>

  <clause id="9592">
    <literal><![CDATA[
      K(x,y \ (z * x)) = K(x,y \ (x * z))
    ]]></literal>
    <justification jstring="[para(4201(a,1),9588(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4201 9588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9593">
    <literal><![CDATA[
      K(x,y \ ((x \ z) * x)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(4208(a,1),9588(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4208 9588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9594">
    <literal><![CDATA[
      K(x,y \ (T(x,z) \ u)) = K(x,y \ (x \ u))
    ]]></literal>
    <justification jstring="[para(4518(a,1),9588(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4518 9588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9595">
    <literal><![CDATA[
      K(x,y \ (z \ T(u,x))) = K(x,y \ (z \ u))
    ]]></literal>
    <justification jstring="[para(4840(a,1),9588(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4840 9588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9596">
    <literal><![CDATA[
      K(x,T(y \ (K(x,z) * u),w)) = T(K(x,y \ u),w)
    ]]></literal>
    <justification jstring="[para(9588(a,1),6365(a,2,1))].">
      <j1 rule="para" parents="9588 6365"/>
    </justification>
  </clause>

  <clause id="9597">
    <literal><![CDATA[
      K(x,y \ (z * K(u,x))) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(6943(a,1),9588(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6943 9588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9598">
    <literal><![CDATA[
      T(x,y \ T(x,z)) = T(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(124,a,9591,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 9591 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9599">
    <literal><![CDATA[
      T(x,T(x,y) / z) = T(x,z \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,5896,a,b,9598,a)].">
      <j1 rule="hyper" parents="63 5896 9598"/>
    </justification>
  </clause>

  <clause id="9600">
    <literal><![CDATA[
      T(x,T(y \ x,z)) = T(x,T(y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,6509,a(flip),b,9598,a)].">
      <j1 rule="hyper" parents="63 6509 9598"/>
    </justification>
  </clause>

  <clause id="9601">
    <literal><![CDATA[
      T(K(x \ T(y,z),u),T(y,x \ y)) = T(K(x \ T(y,z),u),y)
    ]]></literal>
    <justification jstring="[para(9598(a,1),6196(a,1,2))].">
      <j1 rule="para" parents="9598 6196"/>
    </justification>
  </clause>

  <clause id="9603">
    <literal><![CDATA[
      K(x,(x \ y) \ z) = K(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[hyper(333,a,9480,a,b,9592,a)].">
      <j1 rule="hyper" parents="333 9480 9592"/>
    </justification>
  </clause>

  <clause id="9604">
    <literal><![CDATA[
      K(x,T((y / z) \ x,y)) = K(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[hyper(333,a,8354,a,b,9592,a)].">
      <j1 rule="hyper" parents="333 8354 9592"/>
    </justification>
  </clause>

  <clause id="9605">
    <literal><![CDATA[
      K(x,y \ ((z \ y) * x)) = K(x,T(z \ x,y))
    ]]></literal>
    <justification jstring="[hyper(333,a,8355,a(flip),b,9592,a),flip(a)].">
      <j1 rule="hyper" parents="333 8355 9592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9606">
    <literal><![CDATA[
      T(x,y \ (z * x)) = T(x,y \ (x * z))
    ]]></literal>
    <justification jstring="[hyper(124,a,9592,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 9592 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9607">
    <literal><![CDATA[
      T(x,y \ ((x \ z) * x)) = x * K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(126,a,9593,a(flip),b,4215,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="126 9593 4215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9608">
    <literal><![CDATA[
      K(x,y \ (z * L(K(u,x),w,v5))) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(5372(a,1),9597(a,1,2,2,2))].">
      <j1 rule="para" parents="5372 9597"/>
    </justification>
  </clause>

  <clause id="9609">
    <literal><![CDATA[
      K(x,y \ (z * (u / x))) = K(x,y \ (z * (x \ u)))
    ]]></literal>
    <justification jstring="[para(6011(a,1),9597(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6011 9597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9610">
    <literal><![CDATA[
      T(x,T(y,z) \ T(x,u)) = T(x,T(y \ x,z))
    ]]></literal>
    <justification jstring="[hyper(333,a,9598,a,b,9600,a)].">
      <j1 rule="hyper" parents="333 9598 9600"/>
    </justification>
  </clause>

  <clause id="9611">
    <literal><![CDATA[
      K(x,(x * y) \ (z * x)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(9(a,1),9603(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 9603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9612">
    <literal><![CDATA[
      K(x,y \ (((x \ y) * z) * x)) = K(x,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),9603(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9 9603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9613">
    <literal><![CDATA[
      L(x,y,z) \ L(T(x,u \ (x * w)),y,z) = K(L(x,y,z),u \ (w * x))
    ]]></literal>
    <justification jstring="[para(9606(a,1),4283(a,1,2,1))].">
      <j1 rule="para" parents="9606 4283"/>
    </justification>
  </clause>

  <clause id="9614">
    <literal><![CDATA[
      K(x,y \ ((T(z,x) / u) \ z)) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(79(a,1),9595(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="79 9595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9615">
    <literal><![CDATA[
      T(K(x,y \ (z * x)),y) = K(x,(y / z) \ x)
    ]]></literal>
    <justification jstring="[para(9604(a,1),6896(a,1,1))].">
      <j1 rule="para" parents="9604 6896"/>
    </justification>
  </clause>

  <clause id="9616">
    <literal><![CDATA[
      K(x,T(y \ x,x * z)) = K(x,z \ (y \ (x * z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,9611,a(flip),b,9605,a),flip(a)].">
      <j1 rule="hyper" parents="63 9611 9605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9617">
    <literal><![CDATA[
      T(x,(y \ 1) \ (x \ z)) = x * K(x,(y \ x) \ z)
    ]]></literal>
    <justification jstring="[hyper(7798,a,9607,a)].">
      <j1 rule="hyper" parents="7798 9607"/>
    </justification>
  </clause>

  <clause id="9618">
    <literal><![CDATA[
      T(x,T(y,z) \ T(x,u)) = x / K(y \ x,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(333,a,6425,a,b,9610,a),flip(a)].">
      <j1 rule="hyper" parents="333 6425 9610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9619">
    <literal><![CDATA[
      K(x,((T(y,x) / z) \ 1) \ z) = z \ ((T(y,x) / z) \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,6269,a(flip),b,9614,a),flip(a)].">
      <j1 rule="hyper" parents="63 6269 9614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9620">
    <literal><![CDATA[
      K(x,T(y \ (z * x),T(y,z))) = K(x,(y / z) \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,8194,a,b,9615,a)].">
      <j1 rule="hyper" parents="63 8194 9615"/>
    </justification>
  </clause>

  <clause id="9621">
    <literal><![CDATA[
      K(x,(y * x) / z) = K(x,(z / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,6906,a(flip),b,9615,a)].">
      <j1 rule="hyper" parents="63 6906 9615"/>
    </justification>
  </clause>

  <clause id="9622">
    <literal><![CDATA[
      K(x,y / (x \ z)) = K(x,(z / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(7537,a,9621,a)].">
      <j1 rule="hyper" parents="7537 9621"/>
    </justification>
  </clause>

  <clause id="9623">
    <literal><![CDATA[
      T(x,(y * x) / z) = T(x,(z / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(124,a,9621,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 9621 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9624">
    <literal><![CDATA[
      K(x,y / (z / x)) = K(x,(z / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,6327,a(flip),b,9621,a)].">
      <j1 rule="hyper" parents="63 6327 9621"/>
    </justification>
  </clause>

  <clause id="9625">
    <literal><![CDATA[
      K(x,(y / z) \ x) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / (x \ y)) = u
    ]]></literal>
    <justification jstring="[para(9621(a,1),7537(a,1))].">
      <j1 rule="para" parents="9621 7537"/>
    </justification>
  </clause>

  <clause id="9626">
    <literal><![CDATA[
      K(x,T(y \ (x * z),z)) = K(x,z / (x \ y))
    ]]></literal>
    <justification jstring="[hyper(333,a,7248,a,b,9622,a)].">
      <j1 rule="hyper" parents="333 7248 9622"/>
    </justification>
  </clause>

  <clause id="9627">
    <literal><![CDATA[
      K(x,(x * y) / z) = K(x,y / (x \ z))
    ]]></literal>
    <justification jstring="[hyper(333,a,5661,a,b,9622,a)].">
      <j1 rule="hyper" parents="333 5661 9622"/>
    </justification>
  </clause>

  <clause id="9628">
    <literal><![CDATA[
      K(x,((x * y) / z) \ x) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(9(a,1),9622(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 9622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9629">
    <literal><![CDATA[
      R(K(x,(y / (z / u)) \ x),z / u,u) = K(x,z / ((x \ y) * u))
    ]]></literal>
    <justification jstring="[para(9622(a,1),5646(a,1,1))].">
      <j1 rule="para" parents="9622 5646"/>
    </justification>
  </clause>

  <clause id="9630">
    <literal><![CDATA[
      K(x,(x \ y) / (x \ z)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(10(a,1),9627(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 9627"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9631">
    <literal><![CDATA[
      K(x,y / (x \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(z / y) \ x) = u
    ]]></literal>
    <justification jstring="[para(9627(a,1),5663(a,1))].">
      <j1 rule="para" parents="9627 5663"/>
    </justification>
  </clause>

  <clause id="9633">
    <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(8339(a,1),9628(a,1,2,1))].">
      <j1 rule="para" parents="8339 9628"/>
    </justification>
  </clause>

  <clause id="9634">
    <literal><![CDATA[
      K(x,(x \ y) / (z / x)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(7465,a,9630,a)].">
      <j1 rule="hyper" parents="7465 9630"/>
    </justification>
  </clause>

  <clause id="9636">
    <literal><![CDATA[
      K(x,(x \ y) / z) = K(x,y / (z * x))
    ]]></literal>
    <justification jstring="[para(11(a,1),9634(a,1,2,2))].">
      <j1 rule="para" parents="11 9634"/>
    </justification>
  </clause>

  <clause id="9637">
    <literal><![CDATA[
      K(x,(x * y) / (z * x)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(9(a,1),9636(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 9636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9638">
    <literal><![CDATA[
      (x * K(y,z / (u * y))) \ x = K((y \ z) / u,y)
    ]]></literal>
    <justification jstring="[para(9636(a,1),5990(a,1,1,2))].">
      <j1 rule="para" parents="9636 5990"/>
    </justification>
  </clause>

  <clause id="9639">
    <literal><![CDATA[
      K(x,T(y \ (x * z),z)) * u != u * w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z / (x \ y),u)) = w
    ]]></literal>
    <justification jstring="[para(9626(a,2),6496(a,1,1))].">
      <j1 rule="para" parents="9626 6496"/>
    </justification>
  </clause>

  <clause id="9640">
    <literal><![CDATA[
      K(x,y \ T(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ x) = u
    ]]></literal>
    <justification jstring="[para(4274(a,2),9589(a,1,2,2))].">
      <j1 rule="para" parents="4274 9589"/>
    </justification>
  </clause>

  <clause id="9641">
    <literal><![CDATA[
      K(x,y \ (x * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (z * x)) = u
    ]]></literal>
    <justification jstring="[para(4201(a,1),9589(a,1,2,2))].">
      <j1 rule="para" parents="4201 9589"/>
    </justification>
  </clause>

  <clause id="9642">
    <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(7741(a,1),9589(a,1,2,2))].">
      <j1 rule="para" parents="7741 9589"/>
    </justification>
  </clause>

  <clause id="9643">
    <literal><![CDATA[
      K(x,y \ (z * (u * K(w,x)))) = K(x,y \ (z * u))
    ]]></literal>
    <justification jstring="[para(97(a,1),9608(a,1,2,2))].">
      <j1 rule="para" parents="97 9608"/>
    </justification>
  </clause>

  <clause id="9644">
    <literal><![CDATA[
      K(x,(y * (z / u)) \ (y * x)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u / (x \ z)) = w
    ]]></literal>
    <justification jstring="[para(9541(a,2),9625(a,1))].">
      <j1 rule="para" parents="9541 9625"/>
    </justification>
  </clause>

  <clause id="9645">
    <literal><![CDATA[
      K(x,(y * x) / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(z / y) \ x) = u
    ]]></literal>
    <justification jstring="[para(7482(a,2),9631(a,1))].">
      <j1 rule="para" parents="7482 9631"/>
    </justification>
  </clause>

  <clause id="9646">
    <literal><![CDATA[
      K(x,(T(x,y) * z) \ u) = K(x,z \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(333,a,9594,a(flip),b,9494,a),flip(a)].">
      <j1 rule="hyper" parents="333 9594 9494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9648">
    <literal><![CDATA[
      K(x,y \ (x \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(x * y) \ z) = u
    ]]></literal>
    <justification jstring="[para(9646(a,1),7651(a,1))].">
      <j1 rule="para" parents="9646 7651"/>
    </justification>
  </clause>

  <clause id="9649">
    <literal><![CDATA[
      (x * y) * K(z,x \ (z \ (x * y))) = x * (z * (y / z))
    ]]></literal>
    <justification jstring="[hyper(63,a,4128,a(flip),b,9500,a),flip(a)].">
      <j1 rule="hyper" parents="63 4128 9500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9650">
    <literal><![CDATA[
      x * K(y,z \ (y \ x)) = z * (y * ((z \ x) / y))
    ]]></literal>
    <justification jstring="[hyper(63,a,4127,a(flip),b,9500,a),flip(a)].">
      <j1 rule="hyper" parents="63 4127 9500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9651">
    <literal><![CDATA[
      K(x \ y,z \ (x \ y)) * (y / x) = T(y / x,T((x * z) \ y,x))
    ]]></literal>
    <justification jstring="[para(9546(a,1),6511(a,1,1))].">
      <j1 rule="para" parents="9546 6511"/>
    </justification>
  </clause>

  <clause id="9652">
    <literal><![CDATA[
      K(x,T(y * x,z)) = K(x,T(x * y,z))
    ]]></literal>
    <justification jstring="[para(4286(a,1),9572(a,1,2,1))].">
      <j1 rule="para" parents="4286 9572"/>
    </justification>
  </clause>

  <clause id="9653">
    <literal><![CDATA[
      K(x,T(y * K(x,z),u)) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[para(4387(a,1),9572(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4387 9572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9654">
    <literal><![CDATA[
      K(x,T(y * (z / T(u,x)),w)) = K(x,T(y * (z / u),w))
    ]]></literal>
    <justification jstring="[para(5975(a,1),9572(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="5975 9572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9655">
    <literal><![CDATA[
      K(x,T(y / (z / x),u)) = K(x,T(y / (x \ z),u))
    ]]></literal>
    <justification jstring="[para(5520(a,1),9653(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5520 9653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9656">
    <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(9577(a,1),4952(a,1,1,1,2))].">
      <j1 rule="para" parents="9577 4952"/>
    </justification>
  </clause>

  <clause id="9657">
    <literal><![CDATA[
      K(x \ y,T(z,y)) = K((K(z,u) * y) / x,z)
    ]]></literal>
    <justification jstring="[hyper(7368,a,9579,a),flip(a)].">
      <j1 rule="hyper" parents="7368 9579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9658">
    <literal><![CDATA[
      K(x \ (y * z),T(z,u)) = K(x \ (z * y),T(z,u))
    ]]></literal>
    <justification jstring="[para(4201(a,1),9579(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4201 9579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9659">
    <literal><![CDATA[
      K((K(x,y) * z) / u,x) = K(z / u,x)
    ]]></literal>
    <justification jstring="[hyper(7062,a,9657,a),flip(a)].">
      <j1 rule="hyper" parents="7062 9657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9660">
    <literal><![CDATA[
      K(x,(K(x,y) * z) / u) = (w * K(z / u,x)) \ w
    ]]></literal>
    <justification jstring="[para(9659(a,1),5990(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9659 5990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9661">
    <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(498(a,1),9584(a,2,1))].">
      <j1 rule="para" parents="498 9584"/>
    </justification>
  </clause>

  <clause id="9662">
    <literal><![CDATA[
      K(x,T(y \ (K(x,z) * u),w)) = K(x,T(y \ u,w))
    ]]></literal>
    <justification jstring="[hyper(333,a,6365,a,b,9596,a),flip(a)].">
      <j1 rule="hyper" parents="333 6365 9596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9663">
    <literal><![CDATA[
      K(x,(y * (z * (u / x))) \ (z * (x \ u))) = K(x,(z * (u / x)) \ (y \ (z * (u / x))))
    ]]></literal>
    <justification jstring="[hyper(63,a,7219,a(flip),b,9609,a),flip(a)].">
      <j1 rule="hyper" parents="63 7219 9609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9664">
    <literal><![CDATA[
      K(x,y \ (z \ (x * y))) = K(x,T(z \ x,y))
    ]]></literal>
    <justification jstring="[hyper(6699,a,9616,a),flip(a)].">
      <j1 rule="hyper" parents="6699 9616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9665">
    <literal><![CDATA[
      K(x,L(K(y,z),u,w) * (v5 \ (x * L(K(z,y),u,w)))) = K(x,T(v5 \ x,L(K(z,y),u,w)))
    ]]></literal>
    <justification jstring="[para(9408(a,1),9664(a,1,2))].">
      <j1 rule="para" parents="9408 9664"/>
    </justification>
  </clause>

  <clause id="9666">
    <literal><![CDATA[
      K(x,(y \ 1) \ (x \ z)) = K(x,(y \ x) \ z)
    ]]></literal>
    <justification jstring="[hyper(4305,a,9617,a)].">
      <j1 rule="hyper" parents="4305 9617"/>
    </justification>
  </clause>

  <clause id="9667">
    <literal><![CDATA[
      K(x,(y \ x) \ (x * z)) = K(x,(y \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(9(a,1),9666(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 9666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9668">
    <literal><![CDATA[
      K(x,(y \ x) \ (z * x)) = K(x,(y \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(9641,a,9667,a)].">
      <j1 rule="hyper" parents="9641 9667"/>
    </justification>
  </clause>

  <clause id="9669">
    <literal><![CDATA[
      K(T(x,y) \ T(z,u),z) = K(x \ z,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(4247,a,9618,a)].">
      <j1 rule="hyper" parents="4247 9618"/>
    </justification>
  </clause>

  <clause id="9671">
    <literal><![CDATA[
      K(x,T(y,z) \ T(x,u)) = 1 / K(y \ x,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(197,a,9669,a(flip),b,4367,a),flip(a)].">
      <j1 rule="hyper" parents="197 9669 4367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9672">
    <literal><![CDATA[
      K((x \ y) / z,x) = K(y / (z * x),x)
    ]]></literal>
    <justification jstring="[hyper(6024,a,9638,a),flip(a)].">
      <j1 rule="hyper" parents="6024 9638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9674">
    <literal><![CDATA[
      K(x,y \ (z * (K(x,u) * w))) = K(x,y \ (z * w))
    ]]></literal>
    <justification jstring="[para(6355(a,1),9643(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="6355 9643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9675">
    <literal><![CDATA[
      K(x,(y * z) \ (x \ y)) = K(x,z \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(34,a,7878,a(flip),b,9650,a),flip(a)].">
      <j1 rule="hyper" parents="34 7878 9650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9677">
    <literal><![CDATA[
      K((x * y) \ (z \ x),z) = (u * K(z,y \ (z \ 1))) \ u
    ]]></literal>
    <justification jstring="[para(9675(a,1),5990(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9675 5990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9678">
    <literal><![CDATA[
      K(x \ (y * (z * K(y,u))),T(y,w)) = K(x \ (z * T(y,u)),T(y,w))
    ]]></literal>
    <justification jstring="[para(5982(a,1),9658(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5982 9658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9679">
    <literal><![CDATA[
      K(x,(K(x,y) * z) / u) = K(x,z / u)
    ]]></literal>
    <justification jstring="[hyper(333,a,5990,a(flip),b,9660,a),flip(a)].">
      <j1 rule="hyper" parents="333 5990 9660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9680">
    <literal><![CDATA[
      K(x,(T(y,x) * z) / u) = K(x,(y * z) / u)
    ]]></literal>
    <justification jstring="[para(4557(a,1),9679(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4557 9679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9681">
    <literal><![CDATA[
      K(x,(y * K(z,x)) / u) = K(x,y / u)
    ]]></literal>
    <justification jstring="[para(6943(a,1),9679(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6943 9679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9682">
    <literal><![CDATA[
      K(x,(y * T(x,z)) / u) = K(x,(y * x) / u)
    ]]></literal>
    <justification jstring="[para(7717(a,1),9679(a,1,2,1))].">
      <j1 rule="para" parents="7717 9679"/>
    </justification>
  </clause>

  <clause id="9683">
    <literal><![CDATA[
      K(x,K(y,(z * K(u,y)) / w)) = K(x,K(y,1 / (z / w)))
    ]]></literal>
    <justification jstring="[para(9681(a,2),7165(a,2,2)),flip(a)].">
      <j1 rule="para" parents="9681 7165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9684">
    <literal><![CDATA[
      K(x,(T(y / (z \ u),x) * K(z \ u,z)) / w) = K(x,(y / (u / z)) / w)
    ]]></literal>
    <justification jstring="[para(6012(a,1),9680(a,2,2,1))].">
      <j1 rule="para" parents="6012 9680"/>
    </justification>
  </clause>

  <clause id="9685">
    <literal><![CDATA[
      K(x,(y * T(x,z)) / u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (x \ u)) = w
    ]]></literal>
    <justification jstring="[para(9682(a,2),7537(a,1))].">
      <j1 rule="para" parents="9682 7537"/>
    </justification>
  </clause>

  <clause id="9686">
    <literal><![CDATA[
      K(x,T(y \ (z * x),u)) = K(x,T(y \ (x * z),u))
    ]]></literal>
    <justification jstring="[para(4201(a,1),9662(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="4201 9662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9687">
    <literal><![CDATA[
      K(x,T(y,z) \ T(x,u)) = K(x,T(y \ x,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,6424,a(flip),b,9671,a),flip(a)].">
      <j1 rule="hyper" parents="119 6424 9671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9688">
    <literal><![CDATA[
      K(x,T(y \ x,z)) = K(x,T(y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(9640,a,9687,a),flip(a)].">
      <j1 rule="hyper" parents="9640 9687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9689">
    <literal><![CDATA[
      K(x,T(y,K(z,z \ x)) \ x) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(7075,a,9688,a),flip(a)].">
      <j1 rule="hyper" parents="7075 9688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9690">
    <literal><![CDATA[
      K(x,(K(y \ x,y) * z) \ x) = K(x,(z * K(y \ x,y)) \ x)
    ]]></literal>
    <justification jstring="[para(6035(a,1),9689(a,1,2,1))].">
      <j1 rule="para" parents="6035 9689"/>
    </justification>
  </clause>

  <clause id="9691">
    <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(498(a,1),9674(a,1,2))].">
      <j1 rule="para" parents="498 9674"/>
    </justification>
  </clause>

  <clause id="9693">
    <literal><![CDATA[
      K(x,T(y \ (z * x),z)) = K(x,(y / z) \ x)
    ]]></literal>
    <justification jstring="[hyper(333,a,7248,a(flip),b,9686,a),flip(a)].">
      <j1 rule="hyper" parents="333 7248 9686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9694">
    <literal><![CDATA[
      K(x,T(y,K(L(x,z,u),w) * v5)) = K(x,T(y,v5))
    ]]></literal>
    <justification jstring="[hyper(333,a,6935,a(flip),b,9423,a),flip(a)].">
      <j1 rule="hyper" parents="333 6935 9423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9695">
    <literal><![CDATA[
      K(x,T(y,L(x,z,u) * (u * z))) = K(x,T(y,u * (z * x)))
    ]]></literal>
    <justification jstring="[para(4202(a,1),9694(a,1,2,2))].">
      <j1 rule="para" parents="4202 9694"/>
    </justification>
  </clause>

  <clause id="9696">
    <literal><![CDATA[
      K(x * (R(y,z,y) \ u),y) = K(x * (u / T(y,z)),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,7431,a(flip),b,9428,a)].">
      <j1 rule="hyper" parents="63 7431 9428"/>
    </justification>
  </clause>

  <clause id="9697">
    <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(9451(a,1),8114(a,1))].">
      <j1 rule="para" parents="9451 8114"/>
    </justification>
  </clause>

  <clause id="9698">
    <literal><![CDATA[
      L(K(x,R(y,z,y) \ (z \ u)),z \ u,z) = K(x,T(y * z,y) \ u)
    ]]></literal>
    <justification jstring="[para(3744(a,1),9512(a,2,2,1))].">
      <j1 rule="para" parents="3744 9512"/>
    </justification>
  </clause>

  <clause id="9699">
    <literal><![CDATA[
      L(K(x,K(y,z) * (u \ w)),u \ w,u) = K(x,(u * K(z,y)) \ w)
    ]]></literal>
    <justification jstring="[para(4567(a,1),9512(a,1,1,2))].">
      <j1 rule="para" parents="4567 9512"/>
    </justification>
  </clause>

  <clause id="9700">
    <literal><![CDATA[
      K(x,(x * y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (x \ z)) = u
    ]]></literal>
    <justification jstring="[para(9512(a,1),6363(a,1))].">
      <j1 rule="para" parents="9512 6363"/>
    </justification>
  </clause>

  <clause id="9701">
    <literal><![CDATA[
      L(K(x,y \ (z \ u)),z \ u,z) = K(x,(z * T(y,x \ 1)) \ u)
    ]]></literal>
    <justification jstring="[para(8613(a,1),9512(a,1,1))].">
      <j1 rule="para" parents="8613 9512"/>
    </justification>
  </clause>

  <clause id="9702">
    <literal><![CDATA[
      L(K(x,y \ (x \ (z \ u))),z \ u,z) = K(x,(z * (x * y)) \ u)
    ]]></literal>
    <justification jstring="[para(9478(a,1),9512(a,1,1))].">
      <j1 rule="para" parents="9478 9512"/>
    </justification>
  </clause>

  <clause id="9703">
    <literal><![CDATA[
      L(K(x,y \ ((z \ u) * x)),z \ u,z) = K(x,(z * (x \ y)) \ u)
    ]]></literal>
    <justification jstring="[para(9603(a,1),9512(a,1,1))].">
      <j1 rule="para" parents="9603 9512"/>
    </justification>
  </clause>

  <clause id="9704">
    <literal><![CDATA[
      K(x,(K(y,z / x) \ z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(x \ z,y) \ (x \ u)) = w
    ]]></literal>
    <justification jstring="[para(4629(a,2),9700(a,1,2,1))].">
      <j1 rule="para" parents="4629 9700"/>
    </justification>
  </clause>

  <clause id="9705">
    <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(63,a,7981,a,b,9522,a)].">
      <j1 rule="hyper" parents="63 7981 9522"/>
    </justification>
  </clause>

  <clause id="9706">
    <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(1261(a,1),9544(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1261 9544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9707">
    <literal><![CDATA[
      L(K(x,y \ z),z,z \ 1) = K(x,((z \ 1) * y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(333,a,4802,a(flip),b,9567,a),flip(a)].">
      <j1 rule="hyper" parents="333 4802 9567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9708">
    <literal><![CDATA[
      K(x * (R(x,y,x) \ z),x) = K(z,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,7443,a(flip),b,9696,a),flip(a)].">
      <j1 rule="hyper" parents="333 7443 9696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9709">
    <literal><![CDATA[
      K(R(x,y,x) * z,x) = K(x * z,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),9708(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 9708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9710">
    <literal><![CDATA[
      K(x * R(y,z,y),y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,7460,a(flip),b,9709,a)].">
      <j1 rule="hyper" parents="63 7460 9709"/>
    </justification>
  </clause>

  <clause id="9711">
    <literal><![CDATA[
      T(x,y * R(x,z,x)) = 1 / (x \ K(x * y,x))
    ]]></literal>
    <justification jstring="[para(9710(a,1),4403(a,2,2,2))].">
      <j1 rule="para" parents="9710 4403"/>
    </justification>
  </clause>

  <clause id="9712">
    <literal><![CDATA[
      T(x,y * R(x,z,x)) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(333,a,4403,a,b,9711,a),flip(a)].">
      <j1 rule="hyper" parents="333 4403 9711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9713">
    <literal><![CDATA[
      T(x,y * R(x,z,x)) = x * K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(333,a,4222,a(flip),b,9712,a),flip(a)].">
      <j1 rule="hyper" parents="333 4222 9712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9714">
    <literal><![CDATA[
      K(x,y * R(x,z,x)) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(4305,a,9713,a)].">
      <j1 rule="hyper" parents="4305 9713"/>
    </justification>
  </clause>

  <clause id="9715">
    <literal><![CDATA[
      K(x,R(x,y,x) * z) = K(x,x * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,7467,a,b,9714,a)].">
      <j1 rule="hyper" parents="63 7467 9714"/>
    </justification>
  </clause>

  <clause id="9716">
    <literal><![CDATA[
      K(R(x,y,x),R(x,z,x) * u) = K(x,x * u)
    ]]></literal>
    <justification jstring="[hyper(6532,a,9715,a)].">
      <j1 rule="hyper" parents="6532 9715"/>
    </justification>
  </clause>

  <clause id="9717">
    <literal><![CDATA[
      (1 / x) \ K(y,((x \ 1) * z) \ 1) = x * K(y,z \ x)
    ]]></literal>
    <justification jstring="[hyper(121,a,9707,a(flip),b,2652,a)].">
      <j1 rule="hyper" parents="121 9707 2652"/>
    </justification>
  </clause>

  <clause id="9718">
    <literal><![CDATA[
      K(x,((y \ 1) * (y / z)) \ 1) = L(K(x,z),y,y \ 1)
    ]]></literal>
    <justification jstring="[para(79(a,1),9707(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="79 9707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9719">
    <literal><![CDATA[
      L(T(K(x,y),z),u,w) \ v5 = L(T(K(y,x),z),u,w) * v5
    ]]></literal>
    <justification jstring="[para(9403(a,1),5380(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9403 5380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9720">
    <literal><![CDATA[
      K(x,L(y,z / T(y,u),w)) = L(K(x,y),z,w)
    ]]></literal>
    <justification jstring="[para(6901(a,1),9456(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6901 9456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9721">
    <literal><![CDATA[
      L(K(x,y),y * z,u) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(191(a,1),9720(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="191 9720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9722">
    <literal><![CDATA[
      K(x,L(y,y \ z,u)) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(281(a,1),9720(a,1,2,2))].">
      <j1 rule="para" parents="281 9720"/>
    </justification>
  </clause>

  <clause id="9723">
    <literal><![CDATA[
      L(K(x,y),z * K(y,u),w) = K(x,L(y,z / y,w))
    ]]></literal>
    <justification jstring="[para(5977(a,1),9720(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5977 9720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9725">
    <literal><![CDATA[
      K(x * y,L(x,y,z)) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(6136,a,9721,a),flip(a)].">
      <j1 rule="hyper" parents="6136 9721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9726">
    <literal><![CDATA[
      (x * (y * z)) * K(u,L(y,z,x)) = x * ((y * z) * K(u,y))
    ]]></literal>
    <justification jstring="[hyper(126,a,9721,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="126 9721 18"/>
    </justification>
  </clause>

  <clause id="9727">
    <literal><![CDATA[
      L(K(x,y / z),y,u) = K(x,L(y / z,z,u))
    ]]></literal>
    <justification jstring="[para(12(a,1),9721(a,1,2))].">
      <j1 rule="para" parents="12 9721"/>
    </justification>
  </clause>

  <clause id="9728">
    <literal><![CDATA[
      L(K(x,y),z * K(y,u),w) = L(K(x,y),z,w)
    ]]></literal>
    <justification jstring="[hyper(333,a,9453,a(flip),b,9723,a),flip(a)].">
      <j1 rule="hyper" parents="333 9453 9723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9729">
    <literal><![CDATA[
      K(x,y) * L(K(y,x),z,u) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(9728(a,1),8769(a,1,2))].">
      <j1 rule="para" parents="9728 8769"/>
    </justification>
  </clause>

  <clause id="9730">
    <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(9728(a,2),9455(a,2,1)),flip(a)].">
      <j1 rule="para" parents="9728 9455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9731">
    <literal><![CDATA[
      K(x,y) * a(z,u,K(y,x)) = L(K(x,y),u,z)
    ]]></literal>
    <justification jstring="[hyper(4577,a,9729,a)].">
      <j1 rule="hyper" parents="4577 9729"/>
    </justification>
  </clause>

  <clause id="9732">
    <literal><![CDATA[
      L(K(x,y),z,u) * K(y,x) = a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(2010,a,9729,a)].">
      <j1 rule="hyper" parents="2010 9729"/>
    </justification>
  </clause>

  <clause id="9733">
    <literal><![CDATA[
      (K(x,y) / z) * (z * K(y,x)) = a(K(x,y) / z,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(756,a,9729,a)].">
      <j1 rule="hyper" parents="756 9729"/>
    </justification>
  </clause>

  <clause id="9734">
    <literal><![CDATA[
      T(x,y) * L(K(y,x),z,u) = x * a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(126,a,9729,a(flip),b,4515,a),flip(a)].">
      <j1 rule="hyper" parents="126 9729 4515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9735">
    <literal><![CDATA[
      K(x,y) * (L(K(y,x),z,u) * w) = a(u,z,K(x,y)) * w
    ]]></literal>
    <justification jstring="[para(9729(a,1),5706(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9729 5706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9736">
    <literal><![CDATA[
      K(x,y) * K(L(y,z,u),x) = a(u,z * y,K(x,y))
    ]]></literal>
    <justification jstring="[para(6298(a,1),9729(a,1,2))].">
      <j1 rule="para" parents="6298 9729"/>
    </justification>
  </clause>

  <clause id="9737">
    <literal><![CDATA[
      (x * K(y,z)) * a(u,w,K(z,y)) = x * L(K(y,z),w,u)
    ]]></literal>
    <justification jstring="[para(9729(a,1),8199(a,1,2))].">
      <j1 rule="para" parents="9729 8199"/>
    </justification>
  </clause>

  <clause id="9738">
    <literal><![CDATA[
      (x * a(y,z,K(u,w))) * K(w,u) = x * L(K(w,u),z,y)
    ]]></literal>
    <justification jstring="[para(9729(a,1),8472(a,1,1,2))].">
      <j1 rule="para" parents="9729 8472"/>
    </justification>
  </clause>

  <clause id="9739">
    <literal><![CDATA[
      K(x,y) * K(y,L(x,z,u)) = a(u,z * x,K(x,y))
    ]]></literal>
    <justification jstring="[para(9457(a,1),9729(a,1,2))].">
      <j1 rule="para" parents="9457 9729"/>
    </justification>
  </clause>

  <clause id="9741">
    <literal><![CDATA[
      x \ y != K(z,u) * L(K(u,z),w,v5)
    ]]></literal>
    <literal><![CDATA[
      x * a(v5,w,K(z,u)) = y
    ]]></literal>
    <justification jstring="[para(9731(a,1),4592(a,2,2))].">
      <j1 rule="para" parents="9731 4592"/>
    </justification>
  </clause>

  <clause id="9742">
    <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(9731(a,1),9441(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="9731 9441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9743">
    <literal><![CDATA[
      (x * y) \ ((x * (y * K(z,u))) * K(u,z)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,7844,a,b,9732,a)].">
      <j1 rule="hyper" parents="63 7844 9732"/>
    </justification>
  </clause>

  <clause id="9744">
    <literal><![CDATA[
      L(K(x,y),z,u) * a(u,z,K(x,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(34,a,9506,a,b,9732,a)].">
      <j1 rule="hyper" parents="34 9506 9732"/>
    </justification>
  </clause>

  <clause id="9745">
    <literal><![CDATA[
      K(x,L(y,z,u)) * K(y,x) = a(u,z * y,K(y,x))
    ]]></literal>
    <justification jstring="[para(9457(a,1),9732(a,1,1))].">
      <j1 rule="para" parents="9457 9732"/>
    </justification>
  </clause>

  <clause id="9746">
    <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(6289(a,1),9744(a,1,1))].">
      <j1 rule="para" parents="6289 9744"/>
    </justification>
  </clause>

  <clause id="9747">
    <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(126,a,9736,a(flip),b,4189,a),flip(a)].">
      <j1 rule="hyper" parents="126 9736 4189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9748">
    <literal><![CDATA[
      K(x,x \ (x * y)) = K(x,K(z \ x,z) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,5575,a(flip),b,9481,a)].">
      <j1 rule="hyper" parents="63 5575 9481"/>
    </justification>
  </clause>

  <clause id="9750">
    <literal><![CDATA[
      K(x,K(y \ x,y) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),9748(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9 9748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9751">
    <literal><![CDATA[
      K(x,y * K(z \ x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(7211,a,9750,a)].">
      <j1 rule="hyper" parents="7211 9750"/>
    </justification>
  </clause>

  <clause id="9752">
    <literal><![CDATA[
      K(x * y,K(y,x) * z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),9750(a,1,2,1,1))].">
      <j1 rule="para" parents="9 9750"/>
    </justification>
  </clause>

  <clause id="9754">
    <literal><![CDATA[
      K(x,K(y,y \ x) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(4558(a,1),9750(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4558 9750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9755">
    <literal><![CDATA[
      K(x,(x / y) * z) = K(x,(y \ x) * z)
    ]]></literal>
    <justification jstring="[para(5049(a,1),9750(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5049 9750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9756">
    <literal><![CDATA[
      K(x,y) * ((y * K(z \ x,z)) * x) = x * (y * K(z \ x,z))
    ]]></literal>
    <justification jstring="[hyper(125,a,9751,a(flip),b,4200,a(flip))].">
      <j1 rule="hyper" parents="125 9751 4200"/>
    </justification>
  </clause>

  <clause id="9757">
    <literal><![CDATA[
      K(x,y \ T(z,((y \ 1) \ (y \ z)) \ x)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(6244(a,1),9751(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6244 9751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9758">
    <literal><![CDATA[
      T(x,K(y,y \ x) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(124,a,9754,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 9754 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9759">
    <literal><![CDATA[
      R(K(x,x \ y),z,T(y,K(x,x \ y) * z)) = (y * (K(x,x \ y) * z)) / (z * T(y,z))
    ]]></literal>
    <justification jstring="[para(9758(a,1),248(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9758 248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9760">
    <literal><![CDATA[
      T((K(x,y) * z) * K(y * x,z),y * x) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(9752(a,1),4239(a,1,1,2))].">
      <j1 rule="para" parents="9752 4239"/>
    </justification>
  </clause>

  <clause id="9761">
    <literal><![CDATA[
      K((L(x,y,z) * u) / w,x) = K((w / u) \ L(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(333,a,5934,a(flip),b,9532,a),flip(a)].">
      <j1 rule="hyper" parents="333 5934 9532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9762">
    <literal><![CDATA[
      K(L(x,y,z),u \ ((1 / x) \ L(K(x,w),v5,v6))) = K(L(x,y,z),(x \ u) \ L(K(x,w),v5,v6))
    ]]></literal>
    <justification jstring="[para(4664(a,2),9540(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4664 9540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9763">
    <literal><![CDATA[
      K(x,(x / L(y,z,u)) * y) = K(x,y * (L(y,z,u) \ x))
    ]]></literal>
    <justification jstring="[para(1258(a,1),9548(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1258 9548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9764">
    <literal><![CDATA[
      K(x,(y * z) \ (y * u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x,z \ u),u,y) = w
    ]]></literal>
    <justification jstring="[para(76(a,1),9558(a,1,2,1,2))].">
      <j1 rule="para" parents="76 9558"/>
    </justification>
  </clause>

  <clause id="9765">
    <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(6367(a,1),9568(a,1,1))].">
      <j1 rule="para" parents="6367 9568"/>
    </justification>
  </clause>

  <clause id="9766">
    <literal><![CDATA[
      K(x,L(y \ z,y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(u * y) \ (u * z)) = w
    ]]></literal>
    <justification jstring="[para(9458(a,1),9568(a,1))].">
      <j1 rule="para" parents="9458 9568"/>
    </justification>
  </clause>

  <clause id="9767">
    <literal><![CDATA[
      K((T(x,y) * z) \ u,K(x,w)) = K(x,K(w,z \ (x \ u)))
    ]]></literal>
    <justification jstring="[hyper(333,a,6788,a(flip),b,9587,a),flip(a)].">
      <j1 rule="hyper" parents="333 6788 9587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9769">
    <literal><![CDATA[
      K((x * y) \ (z \ x),z) = K(y \ (z \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(333,a,5990,a(flip),b,9677,a),flip(a)].">
      <j1 rule="hyper" parents="333 5990 9677"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9770">
    <literal><![CDATA[
      K((x \ y) \ (z \ 1),z) = K(y \ (z \ x),z)
    ]]></literal>
    <justification jstring="[para(10(a,1),9769(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 9769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9772">
    <literal><![CDATA[
      L(K((x \ y) \ (z \ 1),z),z \ 1,u) = K(y \ (z \ x),z)
    ]]></literal>
    <justification jstring="[hyper(5759,a,9770,a)].">
      <j1 rule="hyper" parents="5759 9770"/>
    </justification>
  </clause>

  <clause id="9774">
    <literal><![CDATA[
      K(x,K(y,(z * K(u,y)) / w)) = K(x,K(y,z / w))
    ]]></literal>
    <justification jstring="[hyper(333,a,7165,a(flip),b,9683,a),flip(a)].">
      <j1 rule="hyper" parents="333 7165 9683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9775">
    <literal><![CDATA[
      K(x,K(y,K(z,y) / u)) = K(x,K(y,1 / u))
    ]]></literal>
    <justification jstring="[para(7(a,1),9774(a,1,2,2,1))].">
      <j1 rule="para" parents="7 9774"/>
    </justification>
  </clause>

  <clause id="9776">
    <literal><![CDATA[
      (K(x,y) / z) * K(u,K(y,1 / z)) = T(K(x,y) / z,K(u,y))
    ]]></literal>
    <justification jstring="[para(9775(a,1),6794(a,1,2))].">
      <j1 rule="para" parents="9775 6794"/>
    </justification>
  </clause>

  <clause id="9777">
    <literal><![CDATA[
      L(T(K(x,y),z),z,z \ 1) * u = ((1 / z) * (K(y,x) * z)) \ u
    ]]></literal>
    <justification jstring="[para(2654(a,1),9719(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2654 9719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9778">
    <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(333,a,6781,a,b,9730,a),flip(a)].">
      <j1 rule="hyper" parents="333 6781 9730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9779">
    <literal><![CDATA[
      L(K(x,y),z,u) * (K(y,x) * w) = a(u,z,K(y,x)) * w
    ]]></literal>
    <justification jstring="[hyper(63,a,8886,a,b,9735,a)].">
      <j1 rule="hyper" parents="63 8886 9735"/>
    </justification>
  </clause>

  <clause id="9780">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (L(K(z,u),y,x) * w) = K(z,u) * w
    ]]></literal>
    <justification jstring="[para(9506(a,1),9735(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9506 9735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9781">
    <literal><![CDATA[
      (x * K(y,z)) * u != x * L(K(y,z),w,v5)
    ]]></literal>
    <literal><![CDATA[
      a(v5,w,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(9737(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="9737 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9782">
    <literal><![CDATA[
      (x * T(y,z)) * L(K(z,y),u,w) = (x * y) * a(w,u,K(y,z))
    ]]></literal>
    <justification jstring="[para(5455(a,1),9737(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5455 9737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9783">
    <literal><![CDATA[
      K(x,y \ T(z,z \ x)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(8979(a,1),9757(a,1,2))].">
      <j1 rule="para" parents="8979 9757"/>
    </justification>
  </clause>

  <clause id="9784">
    <literal><![CDATA[
      T(x,y \ T(z,z \ x)) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(124,a,9783,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 9783 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9785">
    <literal><![CDATA[
      K(x,y \ ((z \ x) \ x)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(112(a,1),9783(a,1,2,2))].">
      <j1 rule="para" parents="112 9783"/>
    </justification>
  </clause>

  <clause id="9786">
    <literal><![CDATA[
      T(x,y \ (x / z)) = T(x,y \ (z \ x))
    ]]></literal>
    <justification jstring="[para(332(a,1),9784(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="332 9784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9787">
    <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(5950,a,9785,a),flip(a)].">
      <j1 rule="hyper" parents="5950 9785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9788">
    <literal><![CDATA[
      (K(x,y) * z) * T(y * x,z) = (y * x) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(126,a,9760,a(flip),b,6054,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="126 9760 6054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9789">
    <literal><![CDATA[
      L(K(x,y),z,u) * (K(y,x) * w) = a(u,z,K(x,y)) \ w
    ]]></literal>
    <justification jstring="[hyper(121,a,4558,a(flip),b,9780,a),flip(a)].">
      <j1 rule="hyper" parents="121 4558 9780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9790">
    <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(9788(a,2),8760(a,1,1))].">
      <j1 rule="para" parents="9788 8760"/>
    </justification>
  </clause>

  <clause id="9791">
    <literal><![CDATA[
      a(x,y,K(z,u)) \ w = a(x,y,K(u,z)) * w
    ]]></literal>
    <justification jstring="[hyper(63,a,9779,a(flip),b,9789,a),flip(a)].">
      <j1 rule="hyper" parents="63 9779 9789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9792">
    <literal><![CDATA[
      x / (a(y,z,K(u,w)) * x) = a(y,z,K(w,u))
    ]]></literal>
    <justification jstring="[hyper(197,a,9779,a(flip),b,9789,a(flip))].">
      <j1 rule="hyper" parents="197 9779 9789"/>
    </justification>
  </clause>

  <clause id="9793">
    <literal><![CDATA[
      a(x,y,K(z,u)) \ K(w,u) = K(w,u) * a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(333,a,8771,a,b,9791,a),flip(a)].">
      <j1 rule="hyper" parents="333 8771 9791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9794">
    <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(9791(a,1),142(a,1))].">
      <j1 rule="para" parents="9791 142"/>
    </justification>
  </clause>

  <clause id="9795">
    <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(9793(a,2),43(a,1))].">
      <j1 rule="para" parents="9793 43"/>
    </justification>
  </clause>

  <clause id="9796">
    <literal><![CDATA[
      (x / (K(y,z) * L(K(u,y),w,v5))) * K(y,z) = x * L(K(y,u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,368,a(flip),b,9446,a)].">
      <j1 rule="hyper" parents="63 368 9446"/>
    </justification>
  </clause>

  <clause id="9797">
    <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(9521(a,1),5522(a,1,1,2))].">
      <j1 rule="para" parents="9521 5522"/>
    </justification>
  </clause>

  <clause id="9798">
    <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(498(a,1),9551(a,2,2))].">
      <j1 rule="para" parents="498 9551"/>
    </justification>
  </clause>

  <clause id="9799">
    <literal><![CDATA[
      L(T(K(x,(y \ z) \ u),w),u,y) = K(x,T(z \ (y * u),w))
    ]]></literal>
    <justification jstring="[hyper(333,a,6365,a,b,9554,a),flip(a)].">
      <j1 rule="hyper" parents="333 6365 9554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9801">
    <literal><![CDATA[
      K(x,T(y,z * (u * x))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,8449,a(flip),b,9695,a),flip(a)].">
      <j1 rule="hyper" parents="63 8449 9695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9803">
    <literal><![CDATA[
      K(x,T(y,z * (x * u))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,7498,a(flip),b,9801,a)].">
      <j1 rule="hyper" parents="63 7498 9801"/>
    </justification>
  </clause>

  <clause id="9804">
    <literal><![CDATA[
      K(x,T(y,z * (u / x))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(12(a,1),9801(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="12 9801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9805">
    <literal><![CDATA[
      K(x,T(x * y,z * y)) = K(x,T(x * y,z))
    ]]></literal>
    <justification jstring="[hyper(6714,a,9803,a),flip(a)].">
      <j1 rule="hyper" parents="6714 9803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9806">
    <literal><![CDATA[
      K(x,T(y,z * (x \ u))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(10(a,1),9803(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="10 9803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9807">
    <literal><![CDATA[
      K(x,T(x * y,z * y)) = K(x,T(y * x,z))
    ]]></literal>
    <justification jstring="[hyper(333,a,9652,a,b,9805,a),flip(a)].">
      <j1 rule="hyper" parents="333 9652 9805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9808">
    <literal><![CDATA[
      K(x,T((y * (x \ z)) \ u,y * z)) = K(x,u / (y * (x \ z)))
    ]]></literal>
    <justification jstring="[hyper(7076,a,9806,a),flip(a)].">
      <j1 rule="hyper" parents="7076 9806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9809">
    <literal><![CDATA[
      K(x,T(x \ y,z * y)) = K(x,T(x \ y,z))
    ]]></literal>
    <justification jstring="[hyper(6714,a,9806,a),flip(a)].">
      <j1 rule="hyper" parents="6714 9806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9810">
    <literal><![CDATA[
      (x * y) * R(K(z,z \ y),x,y) = (K(z,T(z \ y,x)) * x) * y
    ]]></literal>
    <justification jstring="[para(9809(a,1),6908(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9809 6908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9811">
    <literal><![CDATA[
      (x * (y * z)) * K(u,L(y,z,x)) = x * (y * (z * K(u,y)))
    ]]></literal>
    <justification jstring="[para(6212(a,1),9726(a,2,2))].">
      <j1 rule="para" parents="6212 9726"/>
    </justification>
  </clause>

  <clause id="9812">
    <literal><![CDATA[
      a(K(x,y) / z,z,K(x,y)) * (1 / (z * K(y,x))) = K(x,y) / z
    ]]></literal>
    <justification jstring="[para(9733(a,1),8467(a,1,1))].">
      <j1 rule="para" parents="9733 8467"/>
    </justification>
  </clause>

  <clause id="9813">
    <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(333,a,4428,a,b,9743,a)].">
      <j1 rule="hyper" parents="333 4428 9743"/>
    </justification>
  </clause>

  <clause id="9814">
    <literal><![CDATA[
      K(x \ (y * (z \ 1)),z) = K(x \ (z \ y),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,6282,a(flip),b,9772,a)].">
      <j1 rule="hyper" parents="63 6282 9772"/>
    </justification>
  </clause>

  <clause id="9815">
    <literal><![CDATA[
      L(K(x,T((y \ z) \ u,w)),u,y) = K(x,T(z \ (y * u),w))
    ]]></literal>
    <justification jstring="[para(6365(a,2),9799(a,1,1))].">
      <j1 rule="para" parents="6365 9799"/>
    </justification>
  </clause>

  <clause id="9816">
    <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(4132(a,2),9811(a,2,2))].">
      <j1 rule="para" parents="4132 9811"/>
    </justification>
  </clause>

  <clause id="9817">
    <literal><![CDATA[
      K(x,T(y \ (z * x),u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T((z \ y) \ x,u)) = w
    ]]></literal>
    <justification jstring="[para(9815(a,1),6136(a,1))].">
      <j1 rule="para" parents="9815 6136"/>
    </justification>
  </clause>

  <clause id="9818">
    <literal><![CDATA[
      K(x,T((y \ z) \ x,y)) = K(x,(z / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(9817,a,9693,a)].">
      <j1 rule="hyper" parents="9817 9693"/>
    </justification>
  </clause>

  <clause id="9819">
    <literal><![CDATA[
      K(x,((y * z) / y) \ x) = K(x,T(z \ x,y))
    ]]></literal>
    <justification jstring="[para(9(a,1),9818(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="9 9818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9820">
    <literal><![CDATA[
      K(x,T(y \ x,y \ z)) = K(x,(z / (z / y)) \ x)
    ]]></literal>
    <justification jstring="[para(3697(a,1),9819(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3697 9819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9821">
    <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(449(a,1),9508(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="449 9508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9822">
    <literal><![CDATA[
      K(((x \ 1) * y) \ (x \ z),x) = K(y \ T(z,x \ 1),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,9814,a(flip),b,9526,a)].">
      <j1 rule="hyper" parents="63 9814 9526"/>
    </justification>
  </clause>

  <clause id="9823">
    <literal><![CDATA[
      K(((x \ 1) * y) \ (x \ z),x) = K(y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,8620,a(flip),b,9822,a),flip(a)].">
      <j1 rule="hyper" parents="333 8620 9822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9824">
    <literal><![CDATA[
      K(((x \ 1) * y) \ z,x) = K(y \ (z * x),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,7432,a(flip),b,9823,a)].">
      <j1 rule="hyper" parents="63 7432 9823"/>
    </justification>
  </clause>

  <clause id="9825">
    <literal><![CDATA[
      K(x \ (y * T(z,x)),T(z,x)) = K(y / ((z \ 1) * x),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,9116,a(flip),b,9824,a),flip(a)].">
      <j1 rule="hyper" parents="63 9116 9824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9826">
    <literal><![CDATA[
      K(L(x,y,y \ 1) \ z,y) = K((x * y) \ (z * y),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,7638,a(flip),b,9824,a)].">
      <j1 rule="hyper" parents="63 7638 9824"/>
    </justification>
  </clause>

  <clause id="9827">
    <literal><![CDATA[
      K(L(x,y,y \ 1) \ z,y) = K(x \ z,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,7484,a(flip),b,9826,a),flip(a)].">
      <j1 rule="hyper" parents="333 7484 9826"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9828">
    <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(9827(a,1),4812(a,1,2,1,2))].">
      <j1 rule="para" parents="9827 4812"/>
    </justification>
  </clause>

  <clause id="9829">
    <literal><![CDATA[
      K((x * T(y,z)) / z,y) = K(x / ((y \ 1) * z),y)
    ]]></literal>
    <justification jstring="[hyper(7072,a,9825,a)].">
      <j1 rule="hyper" parents="7072 9825"/>
    </justification>
  </clause>

  <clause id="9830">
    <literal><![CDATA[
      K(x,(K(y,z) * (y \ u)) \ x) = K(x,u \ (y * (K(z,y) * x)))
    ]]></literal>
    <justification jstring="[para(4833(a,1),9549(a,1,2,1))].">
      <j1 rule="para" parents="4833 9549"/>
    </justification>
  </clause>

  <clause id="9831">
    <literal><![CDATA[
      K((x \ 1) \ y,z \ (x * y)) = K(x * y,(x \ z) \ y)
    ]]></literal>
    <justification jstring="[para(65(a,1),9552(a,2,1))].">
      <j1 rule="para" parents="65 9552"/>
    </justification>
  </clause>

  <clause id="9832">
    <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(1516(a,1),9552(a,2,1))].">
      <j1 rule="para" parents="1516 9552"/>
    </justification>
  </clause>

  <clause id="9833">
    <literal><![CDATA[
      K(x,K(y \ (z * u),u \ (z \ 1))) = K(x,K(z * u,(z \ y) \ u))
    ]]></literal>
    <justification jstring="[para(9831(a,1),7156(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9831 7156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9834">
    <literal><![CDATA[
      K(x,(R(x,y,z) \ u) \ w) = K(x,u \ (R(x,y,z) * w))
    ]]></literal>
    <justification jstring="[hyper(34,a,6150,a,b,9553,a)].">
      <j1 rule="hyper" parents="34 6150 9553"/>
    </justification>
  </clause>

  <clause id="9837">
    <literal><![CDATA[
      K(x,y \ (R(x,z,u) * w)) = K(x,y \ (w * R(x,z,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,8748,a(flip),b,9834,a),flip(a)].">
      <j1 rule="hyper" parents="63 8748 9834"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9839">
    <literal><![CDATA[
      K(x,y \ ((z * u) * R(x,z,u))) = K(x,y \ ((x * z) * u))
    ]]></literal>
    <justification jstring="[para(107(a,1),9837(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="107 9837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9840">
    <literal><![CDATA[
      K(x / (y * (z * x)),z \ 1) = K(y \ ((z * x) \ x),z \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,8942,a,b,9582,a)].">
      <j1 rule="hyper" parents="63 8942 9582"/>
    </justification>
  </clause>

  <clause id="9841">
    <literal><![CDATA[
      T(K(x \ T(y,z),u),T(y,x)) = T(K(x \ T(y,z),u),y)
    ]]></literal>
    <justification jstring="[hyper(7280,a,9601,a)].">
      <j1 rule="hyper" parents="7280 9601"/>
    </justification>
  </clause>

  <clause id="9842">
    <literal><![CDATA[
      K((x / y) \ K(y,z),u) = T(K(x \ T(y,z),u),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,8441,a(flip),b,9841,a)].">
      <j1 rule="hyper" parents="63 8441 9841"/>
    </justification>
  </clause>

  <clause id="9843">
    <literal><![CDATA[
      K(x,(K(y \ x,y) * z) \ x) = K(x,z \ x)
    ]]></literal>
    <justification jstring="[hyper(333,a,5578,a(flip),b,9690,a),flip(a)].">
      <j1 rule="hyper" parents="333 5578 9690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9845">
    <literal><![CDATA[
      K(x,y \ (K(z,z \ x) * x)) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,9547,a(flip),b,9843,a)].">
      <j1 rule="hyper" parents="63 9547 9843"/>
    </justification>
  </clause>

  <clause id="9846">
    <literal><![CDATA[
      K(x,y \ (z * (x / z))) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[para(4297(a,1),9845(a,1,2,2))].">
      <j1 rule="para" parents="4297 9845"/>
    </justification>
  </clause>

  <clause id="9847">
    <literal><![CDATA[
      K(x,y \ ((z \ x) * z)) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[para(76(a,1),9846(a,1,2,2,2))].">
      <j1 rule="para" parents="76 9846"/>
    </justification>
  </clause>

  <clause id="9848">
    <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(9847(a,1),9558(a,1))].">
      <j1 rule="para" parents="9847 9558"/>
    </justification>
  </clause>

  <clause id="9849">
    <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(4567(a,1),9697(a,1,1,2))].">
      <j1 rule="para" parents="4567 9697"/>
    </justification>
  </clause>

  <clause id="9850">
    <literal><![CDATA[
      L(K(x,y \ ((z \ u) * x)),z \ u,z) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z * (x \ y)) \ u) = w
    ]]></literal>
    <justification jstring="[para(9603(a,1),9697(a,1,1))].">
      <j1 rule="para" parents="9603 9697"/>
    </justification>
  </clause>

  <clause id="9851">
    <literal><![CDATA[
      T(K(x,y) / z,K(x,y)) = T(K(x,y),1 / z) / z
    ]]></literal>
    <justification jstring="[hyper(63,a,6780,a(flip),b,9776,a),flip(a)].">
      <j1 rule="hyper" parents="63 6780 9776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9852">
    <literal><![CDATA[
      T(K(x,y) / z,K(x,y)) = K(x,T(y,1 / z)) / z
    ]]></literal>
    <justification jstring="[para(6365(a,2),9851(a,2,1))].">
      <j1 rule="para" parents="6365 9851"/>
    </justification>
  </clause>

  <clause id="9853">
    <literal><![CDATA[
      T(K(x,y) / z,K(x,y)) = K(x,T(y,z)) / z
    ]]></literal>
    <justification jstring="[para(7268(a,1),9852(a,2,1))].">
      <j1 rule="para" parents="7268 9852"/>
    </justification>
  </clause>

  <clause id="9854">
    <literal><![CDATA[
      T(K(x,y) / z,K(x,y)) * K(u,z) = K(x,T(y,z)) / T(z,u)
    ]]></literal>
    <justification jstring="[hyper(125,a,9853,a,b,5445,a)].">
      <j1 rule="hyper" parents="125 9853 5445"/>
    </justification>
  </clause>

  <clause id="9855">
    <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(5369(a,1),9778(a,2,1,1))].">
      <j1 rule="para" parents="5369 9778"/>
    </justification>
  </clause>

  <clause id="9856">
    <literal><![CDATA[
      x * (T(y,z) * L(K(z,y),u,w)) = (x * y) * a(w,u,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,6525,a(flip),b,9782,a)].">
      <j1 rule="hyper" parents="63 6525 9782"/>
    </justification>
  </clause>

  <clause id="9857">
    <literal><![CDATA[
      (x * y) * a(z,u,K(y,w)) = x * (y * a(z,u,K(y,w)))
    ]]></literal>
    <justification jstring="[para(9734(a,1),9856(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9734 9856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9858">
    <literal><![CDATA[
      a(x,y,a(z,u,K(y,w))) = 1
    ]]></literal>
    <justification jstring="[hyper(120,a,9857,a(flip),b,84,a),flip(a)].">
      <j1 rule="hyper" parents="120 9857 84"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9859">
    <literal><![CDATA[
      a(x,T(y,z),a(u,w,K(y,v5))) = 1
    ]]></literal>
    <justification jstring="[para(6901(a,1),9858(a,1,3,3))].">
      <j1 rule="para" parents="6901 9858"/>
    </justification>
  </clause>

  <clause id="9860">
    <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(5222(a,2),9699(a,2,2,1))].">
      <j1 rule="para" parents="5222 9699"/>
    </justification>
  </clause>

  <clause id="9861">
    <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(7705(a,2),9699(a,2,2,1))].">
      <j1 rule="para" parents="7705 9699"/>
    </justification>
  </clause>

  <clause id="9862">
    <literal><![CDATA[
      K(x,(y * T(z,x \ 1)) \ u) = K(x,(y * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(9697,a,9701,a),flip(a)].">
      <j1 rule="hyper" parents="9697 9701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9863">
    <literal><![CDATA[
      K(x,((x \ 1) * y) \ z) = K(x,(y * (x \ 1)) \ z)
    ]]></literal>
    <justification jstring="[para(111(a,1),9862(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="111 9862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9864">
    <literal><![CDATA[
      K(x,(y * (((x \ 1) * z) / (x \ 1))) \ u) = K(x,(y * z) \ u)
    ]]></literal>
    <justification jstring="[para(238(a,1),9862(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="238 9862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9865">
    <literal><![CDATA[
      L(K(x,y \ ((z \ u) * x)),z \ u,z) = K(x,(z * (y / x)) \ u)
    ]]></literal>
    <justification jstring="[hyper(7652,a,9703,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="7652 9703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9866">
    <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(6690,a,9706,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="6690 9706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9867">
    <literal><![CDATA[
      K(x,T(y,L(y,z,u) * w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,8385,a(flip),b,9866,a),flip(a)].">
      <j1 rule="hyper" parents="63 8385 9866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9869">
    <literal><![CDATA[
      K(x,T(y,L(y,z,u) \ w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[para(10(a,1),9867(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 9867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9870">
    <literal><![CDATA[
      K(x,T(y,z * (u * y))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(9417(a,1),9867(a,1,2))].">
      <j1 rule="para" parents="9417 9867"/>
    </justification>
  </clause>

  <clause id="9871">
    <literal><![CDATA[
      K(x,T(y,z \ L(y,u,w))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(7286,a,9869,a)].">
      <j1 rule="hyper" parents="7286 9869"/>
    </justification>
  </clause>

  <clause id="9872">
    <literal><![CDATA[
      T(x,T(y,z \ L(y,u,w))) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(124,a,9871,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 9871 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9873">
    <literal><![CDATA[
      T(x / L(y,z,u),T(y,x)) = T(x / L(y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,7305,a(flip),b,9872,a),flip(a)].">
      <j1 rule="hyper" parents="63 7305 9872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9874">
    <literal><![CDATA[
      K(x,T(y \ z,u * z)) = K(x,T(y \ z,u * y))
    ]]></literal>
    <justification jstring="[para(10(a,1),9870(a,1,2,2,2))].">
      <j1 rule="para" parents="10 9870"/>
    </justification>
  </clause>

  <clause id="9875">
    <literal><![CDATA[
      K(x,T(y,z * (y * u))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(7373(a,1),9870(a,1,2))].">
      <j1 rule="para" parents="7373 9870"/>
    </justification>
  </clause>

  <clause id="9876">
    <literal><![CDATA[
      K(x * y,T(x,z * y)) = K(x * y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(6701,a,9875,a),flip(a)].">
      <j1 rule="hyper" parents="6701 9875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9877">
    <literal><![CDATA[
      K(T(x,y) * z,T(x,u * z)) = K(x * z,T(x,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,7479,a,b,9876,a)].">
      <j1 rule="hyper" parents="63 7479 9876"/>
    </justification>
  </clause>

  <clause id="9878">
    <literal><![CDATA[
      K(x,T(y \ x,z * y)) = K(x,T(y \ x,z))
    ]]></literal>
    <justification jstring="[hyper(6701,a,9874,a),flip(a)].">
      <j1 rule="hyper" parents="6701 9874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9879">
    <literal><![CDATA[
      K(x,T(y \ x,z / y)) = K(x,T(y \ x,z))
    ]]></literal>
    <justification jstring="[para(12(a,1),9878(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 9878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9880">
    <literal><![CDATA[
      K(x,T(y \ x,y \ z)) = K(x,T(y \ x,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,7246,a(flip),b,9879,a)].">
      <j1 rule="hyper" parents="63 7246 9879"/>
    </justification>
  </clause>

  <clause id="9881">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ x) = K(x,T(z \ x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,9820,a(flip),b,9880,a)].">
      <j1 rule="hyper" parents="63 9820 9880"/>
    </justification>
  </clause>

  <clause id="9882">
    <literal><![CDATA[
      K(x,T(y \ x,x * z)) = K(x,((x * z) / y) / z)
    ]]></literal>
    <justification jstring="[hyper(63,a,9628,a(flip),b,9881,a),flip(a)].">
      <j1 rule="hyper" parents="63 9628 9881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9883">
    <literal><![CDATA[
      a(x,y,x) * K(y,T(x,z)) = K(x * y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,9300,a(flip),b,9877,a)].">
      <j1 rule="hyper" parents="63 9300 9877"/>
    </justification>
  </clause>

  <clause id="9884">
    <literal><![CDATA[
      K(x * y,T(x,z)) * K(x,T(y,z)) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(6454,a,9883,a)].">
      <j1 rule="hyper" parents="6454 9883"/>
    </justification>
  </clause>

  <clause id="9886">
    <literal><![CDATA[
      K(x * T(y,z),T(x,u)) * K(x,T(T(y,u),z)) = a(x,T(y,z),x)
    ]]></literal>
    <justification jstring="[para(23(a,1),9884(a,1,2,2))].">
      <j1 rule="para" parents="23 9884"/>
    </justification>
  </clause>

  <clause id="9887">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,T((x \ y) \ 1,x)) * K((x \ y) \ 1,T(z,T(x,y))) = a((x \ y) \ 1,z,(x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(6463(a,1),9884(a,1,1,2))].">
      <j1 rule="para" parents="6463 9884"/>
    </justification>
  </clause>

  <clause id="9888">
    <literal><![CDATA[
      K(((x \ y) \ y) * z,T(T(x,y),u)) * K((x \ y) \ y,T(z,u)) = a((x \ y) \ y,z,(x \ y) \ y)
    ]]></literal>
    <justification jstring="[para(6754(a,1),9884(a,1,1))].">
      <j1 rule="para" parents="6754 9884"/>
    </justification>
  </clause>

  <clause id="9889">
    <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(8700(a,1),9884(a,1,1))].">
      <j1 rule="para" parents="8700 9884"/>
    </justification>
  </clause>

  <clause id="9890">
    <literal><![CDATA[
      K(x,((x * y) / z) / y) = K(x,T(z \ x,y))
    ]]></literal>
    <justification jstring="[hyper(6699,a,9882,a),flip(a)].">
      <j1 rule="hyper" parents="6699 9882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9891">
    <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(63,a,7742,a(flip),b,9890,a)].">
      <j1 rule="hyper" parents="63 7742 9890"/>
    </justification>
  </clause>

  <clause id="9893">
    <literal><![CDATA[
      ((1 / x) * (K(y,z) * x)) \ u = ((1 / x) * (K(z,y) * x)) * u
    ]]></literal>
    <justification jstring="[para(2654(a,1),9777(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2654 9777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9894">
    <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(9893(a,1),5604(a,1,2,2))].">
      <j1 rule="para" parents="9893 5604"/>
    </justification>
  </clause>

  <clause id="9895">
    <literal><![CDATA[
      (x * y) * R(K(z,z \ y),x,y) = (x * K(z,z \ y)) * y
    ]]></literal>
    <justification jstring="[para(6887(a,1),9810(a,2,1))].">
      <j1 rule="para" parents="6887 9810"/>
    </justification>
  </clause>

  <clause id="9896">
    <literal><![CDATA[
      (x * K(y,y \ z)) * z != (x * z) * u
    ]]></literal>
    <literal><![CDATA[
      R(K(y,y \ z),x,z) = u
    ]]></literal>
    <justification jstring="[para(9895(a,1),43(a,1))].">
      <j1 rule="para" parents="9895 43"/>
    </justification>
  </clause>

  <clause id="9897">
    <literal><![CDATA[
      a(K(x,y) / z,z,K(y,x)) * (K(x,y) / z) = 1 / (z * K(y,x))
    ]]></literal>
    <justification jstring="[hyper(9794,a,9812,a)].">
      <j1 rule="hyper" parents="9794 9812"/>
    </justification>
  </clause>

  <clause id="9898">
    <literal><![CDATA[
      L(K(x,y \ ((z \ u) * x)),z \ u,z) = K((x \ 1) \ 1,(z * (y / x)) \ u)
    ]]></literal>
    <justification jstring="[hyper(333,a,3334,a,b,9865,a),flip(a)].">
      <j1 rule="hyper" parents="333 3334 9865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9899">
    <literal><![CDATA[
      L(K(x,(y \ x) \ ((z \ u) * x)),z \ u,z) = K(x,(z * ((((y \ x) / x) * y) * (1 / y))) \ u)
    ]]></literal>
    <justification jstring="[para(2221(a,2),9865(a,2,2,1,2))].">
      <j1 rule="para" parents="2221 9865"/>
    </justification>
  </clause>

  <clause id="9900">
    <literal><![CDATA[
      a(x,T(y,z),x) != u * K(x,T(T(y,w),z))
    ]]></literal>
    <literal><![CDATA[
      K(x * T(y,z),T(x,w)) = u
    ]]></literal>
    <justification jstring="[para(9886(a,1),44(a,1))].">
      <j1 rule="para" parents="9886 44"/>
    </justification>
  </clause>

  <clause id="9906">
    <literal><![CDATA[
      T(x / y,T((y * z) \ x,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x / y,T(z \ (y \ x),y)) = u
    ]]></literal>
    <justification jstring="[para(9651(a,1),6512(a,1))].">
      <j1 rule="para" parents="9651 6512"/>
    </justification>
  </clause>

  <clause id="9907">
    <literal><![CDATA[
      K(x \ ((y * z) * K(y,u)),T(y,w)) = K(x \ (z * T(y,u)),T(y,w))
    ]]></literal>
    <justification jstring="[para(6140(a,2),9678(a,1,1,2))].">
      <j1 rule="para" parents="6140 9678"/>
    </justification>
  </clause>

  <clause id="9908">
    <literal><![CDATA[
      K(x,y * (z * a(u,w,K(x,v5)))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(333,a,9438,a(flip),b,9742,a),flip(a)].">
      <j1 rule="hyper" parents="333 9438 9742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9910">
    <literal><![CDATA[
      K(x,y * (((z * u) / z) * w)) = K(x,y * (u * (K(z,u) * w)))
    ]]></literal>
    <justification jstring="[para(6224(a,2),9908(a,1,2,2))].">
      <j1 rule="para" parents="6224 9908"/>
    </justification>
  </clause>

  <clause id="9911">
    <literal><![CDATA[
      (x / a(y,z,K(u,w))) * K(u,w) = x * L(K(u,w),z,y)
    ]]></literal>
    <justification jstring="[para(9729(a,1),9796(a,1,1,2))].">
      <j1 rule="para" parents="9729 9796"/>
    </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(35,a,9738,a,b,9911,a),flip(a)].">
      <j1 rule="hyper" parents="35 9738 9911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9913">
    <literal><![CDATA[
      (x * a(y,z,K(u,w))) \ x = a(y,z,K(w,u))
    ]]></literal>
    <justification jstring="[hyper(415,a,9912,a)].">
      <j1 rule="hyper" parents="415 9912"/>
    </justification>
  </clause>

  <clause id="9914">
    <literal><![CDATA[
      T(x * y,z) * a(x,y,K(z,x * y)) = x * (y * K(x * y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,4301,a(flip),b,9912,a),flip(a)].">
      <j1 rule="hyper" parents="63 4301 9912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9915">
    <literal><![CDATA[
      (x * a(y,z,K(u,w))) \ x != v5
    ]]></literal>
    <literal><![CDATA[
      a(y,z,K(w,u)) = v5
    ]]></literal>
    <justification jstring="[para(9912(a,1),345(a,1,1))].">
      <j1 rule="para" parents="9912 345"/>
    </justification>
  </clause>

  <clause id="9916">
    <literal><![CDATA[
      (T(x,x \ y) * a(z,u,K(w,v5))) \ ((x \ y) \ y) != v6
    ]]></literal>
    <literal><![CDATA[
      a(z,u,K(v5,w)) = v6
    ]]></literal>
    <justification jstring="[para(325(a,1),9915(a,1))].">
      <j1 rule="para" parents="325 9915"/>
    </justification>
  </clause>

  <clause id="9917">
    <literal><![CDATA[
      K(x \ (y * T(z,u)),T(z,w)) = K(x \ (z * y),T(z,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,9583,a(flip),b,9907,a),flip(a)].">
      <j1 rule="hyper" parents="63 9583 9907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9919">
    <literal><![CDATA[
      K(x \ (y * z),T(y,z)) = K((z * T(y,u)) / x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,7494,a(flip),b,9917,a),flip(a)].">
      <j1 rule="hyper" parents="63 7494 9917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9921">
    <literal><![CDATA[
      K((x * T(y,z)) / u,y) != w
    ]]></literal>
    <literal><![CDATA[
      K(x / (y \ u),y) = w
    ]]></literal>
    <justification jstring="[para(9919(a,1),8389(a,1))].">
      <j1 rule="para" parents="9919 8389"/>
    </justification>
  </clause>

  <clause id="9922">
    <literal><![CDATA[
      K(x / ((y \ 1) * z),y) = K(x / (y \ z),y)
    ]]></literal>
    <justification jstring="[hyper(9921,a,9829,a),flip(a)].">
      <j1 rule="hyper" parents="9921 9829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9923">
    <literal><![CDATA[
      K((x * y) / z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / (x \ z),x) = u
    ]]></literal>
    <justification jstring="[para(111(a,1),9921(a,1,1,1))].">
      <j1 rule="para" parents="111 9921"/>
    </justification>
  </clause>

  <clause id="9924">
    <literal><![CDATA[
      K(x / (y \ T(z,y \ 1)),y) = K(x / (z * (y \ 1)),y)
    ]]></literal>
    <justification jstring="[para(111(a,1),9922(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="111 9922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9925">
    <literal><![CDATA[
      K(x / (y \ T(z,y \ 1)),y) = K((y * x) / z,y)
    ]]></literal>
    <justification jstring="[hyper(9923,a,8624,a)].">
      <j1 rule="hyper" parents="9923 8624"/>
    </justification>
  </clause>

  <clause id="9926">
    <literal><![CDATA[
      K(x / (y \ z),y) = K((z / x) \ y,y)
    ]]></literal>
    <justification jstring="[hyper(9923,a,5922,a)].">
      <j1 rule="hyper" parents="9923 5922"/>
    </justification>
  </clause>

  <clause id="9927">
    <literal><![CDATA[
      K(x / (y \ T(z,y \ 1)),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x / (y \ z),y) = u
    ]]></literal>
    <justification jstring="[para(9925(a,2),9923(a,1))].">
      <j1 rule="para" parents="9925 9923"/>
    </justification>
  </clause>

  <clause id="9928">
    <literal><![CDATA[
      K(x / (y * (z \ 1)),z) = K(x / (z \ y),z)
    ]]></literal>
    <justification jstring="[hyper(9927,a,9924,a),flip(a)].">
      <j1 rule="hyper" parents="9927 9924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9929">
    <literal><![CDATA[
      L(K(x * y,T(x,z)),y,z) = K((z * y) / (x \ z),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,9021,a,b,9928,a)].">
      <j1 rule="hyper" parents="63 9021 9928"/>
    </justification>
  </clause>

  <clause id="9930">
    <literal><![CDATA[
      L(K(x * y,T(x,z)),y,z) = K((z / (z * y)) \ x,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,9926,a(flip),b,9929,a),flip(a)].">
      <j1 rule="hyper" parents="333 9926 9929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9931">
    <literal><![CDATA[
      L(K(x * y,T(y,z)),x,z) = K((z / (z * x)) \ y,y)
    ]]></literal>
    <justification jstring="[para(5207(a,2),9930(a,1,1))].">
      <j1 rule="para" parents="5207 9930"/>
    </justification>
  </clause>

  <clause id="9932">
    <literal><![CDATA[
      (x * y) / (x * (y * K(z,u))) = L(T(K(u,z),x * y),y,x)
    ]]></literal>
    <justification jstring="[para(7536(a,1),9517(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7536 9517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9933">
    <literal><![CDATA[
      (x * y) / (x * (y * K(z,u))) = L(K(u,T(z,x * y)),y,x)
    ]]></literal>
    <justification jstring="[para(6365(a,2),9932(a,2,1))].">
      <j1 rule="para" parents="6365 9932"/>
    </justification>
  </clause>

  <clause id="9935">
    <literal><![CDATA[
      L(K(x,T(x * y,z * y)),y,z) = (z * y) / (z * (x \ T(x * y,x)))
    ]]></literal>
    <justification jstring="[para(5479(a,2),9933(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5479 9933"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9936">
    <literal><![CDATA[
      L(K(x,T(T(y,z),u * z)),z,u) = (u * z) / (u * (K(y,x) * z))
    ]]></literal>
    <justification jstring="[para(6357(a,1),9933(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6357 9933"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9937">
    <literal><![CDATA[
      K((x * y) / (x * (z \ y)),u) = (x * y) / (x * (K(u,z) * y))
    ]]></literal>
    <justification jstring="[hyper(63,a,8347,a(flip),b,9936,a)].">
      <j1 rule="hyper" parents="63 8347 9936"/>
    </justification>
  </clause>

  <clause id="9938">
    <literal><![CDATA[
      K((x * y) / (x * (z \ y)),u) = K(z,(x * y) / (x * (u \ y)))
    ]]></literal>
    <justification jstring="[hyper(5359,a,9937,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="5359 9937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9939">
    <literal><![CDATA[
      K(x,(y * z) / (y * (u \ z))) = (y * (K(x,u) * z)) / (y * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5280,a(flip),b,9938,a),flip(a)].">
      <j1 rule="hyper" parents="63 5280 9938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9940">
    <literal><![CDATA[
      K(x,((y * x) * z) / ((y * x) * (y \ z))) = L(K(x,y),z,y * x)
    ]]></literal>
    <justification jstring="[hyper(8761,a,9939,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="8761 9939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9941">
    <literal><![CDATA[
      K(x,((y * x) * z) / (x * (y * (y \ z)))) = L(K(x,y),z,y * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,9072,a(flip),b,9940,a)].">
      <j1 rule="hyper" parents="63 9072 9940"/>
    </justification>
  </clause>

  <clause id="9942">
    <literal><![CDATA[
      L(K(x,y),z,y * x) = K(x,((y * x) * z) / (x * z))
    ]]></literal>
    <justification jstring="[para(10(a,1),9941(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="10 9941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9943">
    <literal><![CDATA[
      L(K(x,y),z,y * x) = K(x,R(y,x,z))
    ]]></literal>
    <justification jstring="[para(20(a,2),9942(a,2,2))].">
      <j1 rule="para" parents="20 9942"/>
    </justification>
  </clause>

  <clause id="9945">
    <literal><![CDATA[
      K(L(x,y,z),u \ (w * x)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(L(x,y,z),u \ (x * w)) = v5
    ]]></literal>
    <justification jstring="[para(9613(a,1),4472(a,1))].">
      <j1 rule="para" parents="9613 4472"/>
    </justification>
  </clause>

  <clause id="9946">
    <literal><![CDATA[
      K(x,T(y / (x \ z),u)) = K(x,T((z / y) \ x,u))
    ]]></literal>
    <justification jstring="[hyper(9639,a,7294,a)].">
      <j1 rule="hyper" parents="9639 7294"/>
    </justification>
  </clause>

  <clause id="9947">
    <literal><![CDATA[
      K(x,T(y / (x \ z),z)) = K(x,z \ (x * y))
    ]]></literal>
    <justification jstring="[hyper(333,a,8354,a(flip),b,9946,a),flip(a)].">
      <j1 rule="hyper" parents="333 8354 9946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9949">
    <literal><![CDATA[
      K(L(x,y,y \ 1) \ z,T(y,u)) = K(x \ z,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(4984,a,9828,a),flip(a)].">
      <j1 rule="hyper" parents="4984 9828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9950">
    <literal><![CDATA[
      K(((1 / x) * y) \ z,T(x,u)) = K((x \ y) \ z,T(x,u))
    ]]></literal>
    <justification jstring="[para(2655(a,1),9949(a,1,1,1))].">
      <j1 rule="para" parents="2655 9949"/>
    </justification>
  </clause>

  <clause id="9951">
    <literal><![CDATA[
      K(((x \ 1) * y) \ z,T(x,u)) = K((x \ y) \ z,T(x,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,4769,a(flip),b,9950,a)].">
      <j1 rule="hyper" parents="63 4769 9950"/>
    </justification>
  </clause>

  <clause id="9952">
    <literal><![CDATA[
      K(((x \ 1) * y) \ z,T(x,u)) = K(y \ (x * z),T(x,u))
    ]]></literal>
    <justification jstring="[hyper(333,a,8388,a(flip),b,9951,a),flip(a)].">
      <j1 rule="hyper" parents="333 8388 9951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9953">
    <literal><![CDATA[
      K(x \ (y * z),T(y,x)) = K(((y \ 1) \ z) / x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,9527,a(flip),b,9952,a),flip(a)].">
      <j1 rule="hyper" parents="63 9527 9952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9954">
    <literal><![CDATA[
      K(((x \ 1) \ y) / z,x) = K((x * y) / z,x)
    ]]></literal>
    <justification jstring="[hyper(7072,a,9953,a),flip(a)].">
      <j1 rule="hyper" parents="7072 9953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9955">
    <literal><![CDATA[
      K(((x \ 1) \ y) / z,x) = K((z / y) \ x,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,5922,a(flip),b,9954,a),flip(a)].">
      <j1 rule="hyper" parents="333 5922 9954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9956">
    <literal><![CDATA[
      K((x / ((y \ 1) * z)) \ y,y) = K(z / x,y)
    ]]></literal>
    <justification jstring="[para(9(a,1),9955(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 9955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9957">
    <literal><![CDATA[
      K(x / (y * ((z \ 1) * x)),z) = K(y \ z,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),9956(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11 9956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9958">
    <literal><![CDATA[
      K(x / (y * ((z \ 1) * x)),(z \ 1) \ 1) = K(y \ z,z)
    ]]></literal>
    <justification jstring="[hyper(4741,a,9957,a)].">
      <j1 rule="hyper" parents="4741 9957"/>
    </justification>
  </clause>

  <clause id="9959">
    <literal><![CDATA[
      K(x \ (y / ((z \ 1) * y)),z) = K(x \ z,z)
    ]]></literal>
    <justification jstring="[hyper(8943,a,9958,a)].">
      <j1 rule="hyper" parents="8943 9958"/>
    </justification>
  </clause>

  <clause id="9960">
    <literal><![CDATA[
      K(x \ R(y \ 1,y,z),y \ 1) = K(x \ (y \ 1),y \ 1)
    ]]></literal>
    <justification jstring="[para(1940(a,2),9959(a,1,1,2))].">
      <j1 rule="para" parents="1940 9959"/>
    </justification>
  </clause>

  <clause id="9961">
    <literal><![CDATA[
      K(x / (y * (z * x)),z \ 1) = K(y \ (z \ 1),z \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,8941,a(flip),b,9960,a)].">
      <j1 rule="hyper" parents="63 8941 9960"/>
    </justification>
  </clause>

  <clause id="9963">
    <literal><![CDATA[
      K(x \ ((y * z) \ z),y \ 1) = K(x \ (y \ 1),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,9840,a(flip),b,9961,a)].">
      <j1 rule="hyper" parents="63 9840 9961"/>
    </justification>
  </clause>

  <clause id="9965">
    <literal><![CDATA[
      T(x / y,T(z \ (y \ x),y)) = T(x / y,x / (y * z))
    ]]></literal>
    <justification jstring="[hyper(9906,a,8774,a)].">
      <j1 rule="hyper" parents="9906 8774"/>
    </justification>
  </clause>

  <clause id="9966">
    <literal><![CDATA[
      (x * y) / (x * (z \ T(z * y,z))) = L(K(z,T(y * z,x)),y,x)
    ]]></literal>
    <justification jstring="[para(9807(a,1),9935(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9807 9935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9968">
    <literal><![CDATA[
      K(x,T(y / ((z * T(x,z * u)) * u),z * u)) = K(x,(z * u) \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(6695,a,9514,a)].">
      <j1 rule="hyper" parents="6695 9514"/>
    </justification>
  </clause>

  <clause id="9969">
    <literal><![CDATA[
      K((x * (y * z)) \ (x * ((z * u) * y)),y) = K(L(u,y * z,x),y)
    ]]></literal>
    <justification jstring="[hyper(333,a,6306,a(flip),b,9661,a),flip(a)].">
      <j1 rule="hyper" parents="333 6306 9661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9971">
    <literal><![CDATA[
      K((x * y) \ (z \ (x * ((y * u) * z))),z) = K(L(u,z * y,x),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,8112,a(flip),b,9969,a)].">
      <j1 rule="hyper" parents="63 8112 9969"/>
    </justification>
  </clause>

  <clause id="9972">
    <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(6516,a,9747,a)].">
      <j1 rule="hyper" parents="6516 9747"/>
    </justification>
  </clause>

  <clause id="9973">
    <literal><![CDATA[
      x / T(x / y,L(y,z,u)) = y * a(u,z * y,K(y \ x,y))
    ]]></literal>
    <justification jstring="[para(180(a,1),9972(a,1,2,2))].">
      <j1 rule="para" parents="180 9972"/>
    </justification>
  </clause>

  <clause id="9974">
    <literal><![CDATA[
      K(x,(y * (z / x)) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * (x \ z)) \ u) = w
    ]]></literal>
    <justification jstring="[para(9865(a,1),9850(a,1))].">
      <j1 rule="para" parents="9865 9850"/>
    </justification>
  </clause>

  <clause id="9975">
    <literal><![CDATA[
      K(x,(y * (x \ z)) \ (x \ u)) = K(x,(y * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(9974,a,7633,a)].">
      <j1 rule="hyper" parents="9974 7633"/>
    </justification>
  </clause>

  <clause id="9976">
    <literal><![CDATA[
      K(x,(y * (x \ 1)) \ (x \ z)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(8(a,1),9975(a,2,2,1))].">
      <j1 rule="para" parents="8 9975"/>
    </justification>
  </clause>

  <clause id="9977">
    <literal><![CDATA[
      K(x,(y * (x * z)) \ u) = K(x,(y * z) \ (x \ u))
    ]]></literal>
    <justification jstring="[para(9(a,1),9975(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="9 9975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9978">
    <literal><![CDATA[
      K(x,((x \ 1) * y) \ (x \ z)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,9863,a,b,9976,a)].">
      <j1 rule="hyper" parents="63 9863 9976"/>
    </justification>
  </clause>

  <clause id="9979">
    <literal><![CDATA[
      K(x,(y / (x \ 1)) \ z) = K(x,y \ (x \ z))
    ]]></literal>
    <justification jstring="[para(12(a,1),9976(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12 9976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9980">
    <literal><![CDATA[
      K(x,L(y,x \ 1,x) \ z) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,9499,a(flip),b,9978,a)].">
      <j1 rule="hyper" parents="63 9499 9978"/>
    </justification>
  </clause>

  <clause id="9981">
    <literal><![CDATA[
      K(x,T((x \ 1) \ y,z) \ u) = K(x,T(x * y,z) \ u)
    ]]></literal>
    <justification jstring="[para(643(a,1),9980(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="643 9980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9982">
    <literal><![CDATA[
      L(K(x,y \ (x \ (z \ u))),z \ u,z) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z * (y / (x \ 1))) \ u) = w
    ]]></literal>
    <justification jstring="[para(9979(a,1),9697(a,1,1))].">
      <j1 rule="para" parents="9979 9697"/>
    </justification>
  </clause>

  <clause id="9983">
    <literal><![CDATA[
      L(K(x,y \ (x \ (z \ u))),z \ u,z) = K(x,(z * y) \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,9702,a,b,9977,a)].">
      <j1 rule="hyper" parents="63 9702 9977"/>
    </justification>
  </clause>

  <clause id="9984">
    <literal><![CDATA[
      K(x,T(y / ((z * x) * u),z * u)) = K(x,(z * u) \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(63,a,8977,a(flip),b,9968,a)].">
      <j1 rule="hyper" parents="63 8977 9968"/>
    </justification>
  </clause>

  <clause id="9986">
    <literal><![CDATA[
      K(x,((y * x) * z) \ u) = K(x,(y * z) \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,8153,a(flip),b,9984,a)].">
      <j1 rule="hyper" parents="63 8153 9984"/>
    </justification>
  </clause>

  <clause id="9987">
    <literal><![CDATA[
      K(x,((x \ y) * z) \ (x \ u)) = K(x,(y * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,8142,a(flip),b,9986,a),flip(a)].">
      <j1 rule="hyper" parents="63 8142 9986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9992">
    <literal><![CDATA[
      K(x,((x \ y) * z) \ 1) = K(x,(y * z) \ x)
    ]]></literal>
    <justification jstring="[para(66(a,1),9987(a,1,2,2))].">
      <j1 rule="para" parents="66 9987"/>
    </justification>
  </clause>

  <clause id="9993">
    <literal><![CDATA[
      K(L(x,y,z),u * (K(x,w) * v5)) = K(L(x,y,z),u * v5)
    ]]></literal>
    <justification jstring="[hyper(333,a,4946,a(flip),b,9435,a),flip(a)].">
      <j1 rule="hyper" parents="333 4946 9435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9994">
    <literal><![CDATA[
      K(L(x,y,z),K(u,x) * w) = K(L(x,y,z),w)
    ]]></literal>
    <justification jstring="[para(4558(a,1),9993(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4558 9993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9995">
    <literal><![CDATA[
      K(L(x,y,z),L(K(u,x),w,v5) * v6) = K(L(x,y,z),v6)
    ]]></literal>
    <justification jstring="[para(5372(a,1),9994(a,1,2,1))].">
      <j1 rule="para" parents="5372 9994"/>
    </justification>
  </clause>

  <clause id="9996">
    <literal><![CDATA[
      K(x * (K(y,z) * u),R(y,w,v5)) = K(x * u,R(y,w,v5))
    ]]></literal>
    <justification jstring="[hyper(333,a,4950,a(flip),b,9436,a),flip(a)].">
      <j1 rule="hyper" parents="333 4950 9436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9997">
    <literal><![CDATA[
      K(x * y,R(y,z,u)) = K(y * x,R(y,z,u))
    ]]></literal>
    <justification jstring="[para(4342(a,1),9996(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4342 9996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9998">
    <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(333,a,8,a(flip),b,9571,a),flip(a)].">
      <j1 rule="hyper" parents="333 8 9571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10000">
    <literal><![CDATA[
      R(T(x,y),z,x) \ T(x,u) = T(x,y) \ L(T(x,u),z,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,8905,a(flip),b,9998,a),flip(a)].">
      <j1 rule="hyper" parents="63 8905 9998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10001">
    <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(63,a,9547,a(flip),b,9633,a)].">
      <j1 rule="hyper" parents="63 9547 9633"/>
    </justification>
  </clause>

  <clause id="10002">
    <literal><![CDATA[
      R(K(x,y),z,T(y * x,z)) = L(K(x,y),z,y * x)
    ]]></literal>
    <justification jstring="[hyper(544,a,9790,a)].">
      <j1 rule="hyper" parents="544 9790"/>
    </justification>
  </clause>

  <clause id="10003">
    <literal><![CDATA[
      R(K(x,y),z,T(y * x,z)) = K(x,R(y,x,z))
    ]]></literal>
    <justification jstring="[hyper(333,a,9943,a(flip),b,10002,a),flip(a)].">
      <j1 rule="hyper" parents="333 9943 10002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10004">
    <literal><![CDATA[
      K(x,R(y,x,z)) * ((y * x) * z) = (K(x,y) * z) * T(y * x,z)
    ]]></literal>
    <justification jstring="[para(10003(a,1),532(a,1,1))].">
      <j1 rule="para" parents="10003 532"/>
    </justification>
  </clause>

  <clause id="10005">
    <literal><![CDATA[
      (K(x,y) * z) * T(y * x,z) = (y * (K(x,y) * x)) * z
    ]]></literal>
    <justification jstring="[hyper(63,a,5660,a(flip),b,10004,a),flip(a)].">
      <j1 rule="hyper" parents="63 5660 10004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10006">
    <literal><![CDATA[
      (K(x,y) * z) * T(y * x,z) = (x * y) * z
    ]]></literal>
    <justification jstring="[para(4342(a,1),10005(a,2,1))].">
      <j1 rule="para" parents="4342 10005"/>
    </justification>
  </clause>

  <clause id="10007">
    <literal><![CDATA[
      (x * y) * (K(y,x) * z) = (y * x) * z
    ]]></literal>
    <justification jstring="[hyper(63,a,9788,a(flip),b,10006,a)].">
      <j1 rule="hyper" parents="63 9788 10006"/>
    </justification>
  </clause>

  <clause id="10008">
    <literal><![CDATA[
      (x * y) \ ((y * x) * z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(121,a,10006,a(flip),b,9788,a(flip))].">
      <j1 rule="hyper" parents="121 10006 9788"/>
    </justification>
  </clause>

  <clause id="10009">
    <literal><![CDATA[
      L(x,K(y,z),z * y) = x
    ]]></literal>
    <justification jstring="[hyper(874,a,10007,a)].">
      <j1 rule="hyper" parents="874 10007"/>
    </justification>
  </clause>

  <clause id="10010">
    <literal><![CDATA[
      K(x,y) \ ((y * x) \ z) = (x * y) \ z
    ]]></literal>
    <justification jstring="[hyper(629,a,10007,a),flip(a)].">
      <j1 rule="hyper" parents="629 10007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10011">
    <literal><![CDATA[
      x * (K(y \ x,y) * z) = ((y \ x) * y) * z
    ]]></literal>
    <justification jstring="[hyper(582,a,10007,a)].">
      <j1 rule="hyper" parents="582 10007"/>
    </justification>
  </clause>

  <clause id="10013">
    <literal><![CDATA[
      ((x \ y) * x) \ (y * z) = K(x,x \ y) * z
    ]]></literal>
    <justification jstring="[hyper(121,a,153,a(flip),b,10007,a)].">
      <j1 rule="hyper" parents="121 153 10007"/>
    </justification>
  </clause>

  <clause id="10014">
    <literal><![CDATA[
      K(x,y) * ((x * y) \ z) = (y * x) \ z
    ]]></literal>
    <justification jstring="[hyper(121,a,10,a(flip),b,10007,a),flip(a)].">
      <j1 rule="hyper" parents="121 10 10007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10016">
    <literal><![CDATA[
      (x * y) * (1 / T(x,y)) = (y * x) * (1 / x)
    ]]></literal>
    <justification jstring="[para(4507(a,1),10007(a,1,2))].">
      <j1 rule="para" parents="4507 10007"/>
    </justification>
  </clause>

  <clause id="10017">
    <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(10007(a,1),7001(a,1,1,1))].">
      <j1 rule="para" parents="10007 7001"/>
    </justification>
  </clause>

  <clause id="10018">
    <literal><![CDATA[
      (K(x,y) * z) * (K(y,T(x,z)) * u) = (z * K(x,y)) * (K(y,x) * u)
    ]]></literal>
    <justification jstring="[para(6409(a,1),10007(a,1,2))].">
      <j1 rule="para" parents="6409 10007"/>
    </justification>
  </clause>

  <clause id="10019">
    <literal><![CDATA[
      L(x,K(y,z),y * z) = x
    ]]></literal>
    <justification jstring="[hyper(4391,a,10009,a)].">
      <j1 rule="hyper" parents="4391 10009"/>
    </justification>
  </clause>

  <clause id="10022">
    <literal><![CDATA[
      ((x * y) * K(x,y)) * z = (x * y) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(1170,a,10019,a),flip(a)].">
      <j1 rule="hyper" parents="1170 10019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10023">
    <literal><![CDATA[
      L(x,K(y,y \ z),z) = x
    ]]></literal>
    <justification jstring="[para(10(a,1),10019(a,1,3))].">
      <j1 rule="para" parents="10 10019"/>
    </justification>
  </clause>

  <clause id="10024">
    <literal><![CDATA[
      (x * (y / x)) \ (y * z) = K(x \ y,x) * z
    ]]></literal>
    <justification jstring="[hyper(63,a,5395,a(flip),b,10023,a)].">
      <j1 rule="hyper" parents="63 5395 10023"/>
    </justification>
  </clause>

  <clause id="10025">
    <literal><![CDATA[
      K(x,x \ y) * (y \ z) = ((x \ y) * x) \ z
    ]]></literal>
    <justification jstring="[hyper(126,a,158,a(flip),b,10010,a)].">
      <j1 rule="hyper" parents="126 158 10010"/>
    </justification>
  </clause>

  <clause id="10026">
    <literal><![CDATA[
      T(x,y) * ((x * y) \ z) = x * ((y * x) \ z)
    ]]></literal>
    <justification jstring="[hyper(126,a,10010,a(flip),b,4547,a),flip(a)].">
      <j1 rule="hyper" parents="126 10010 4547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10027">
    <literal><![CDATA[
      K(x,y) * ((x * y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      (y * x) \ z = u
    ]]></literal>
    <justification jstring="[para(10010(a,1),273(a,1,2)),flip(b)].">
      <j1 rule="para" parents="10010 273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10028">
    <literal><![CDATA[
      K(x,y) \ K(y * x,z) = (x * y) \ T(y * x,z)
    ]]></literal>
    <justification jstring="[para(4215(a,2),10010(a,1,2))].">
      <j1 rule="para" parents="4215 10010"/>
    </justification>
  </clause>

  <clause id="10029">
    <literal><![CDATA[
      ((x * y) \ z) * L(u,(y * x) \ z,K(y,x)) = K(y,x) * (((y * x) \ z) * u)
    ]]></literal>
    <justification jstring="[para(10010(a,1),4588(a,1,1))].">
      <j1 rule="para" parents="10010 4588"/>
    </justification>
  </clause>

  <clause id="10030">
    <literal><![CDATA[
      T((x * y) \ z,K(y,x)) = ((y * x) \ z) * K(y,x)
    ]]></literal>
    <justification jstring="[para(10010(a,1),6020(a,1,1))].">
      <j1 rule="para" parents="10010 6020"/>
    </justification>
  </clause>

  <clause id="10031">
    <literal><![CDATA[
      ((x * y) / x) \ ((y * x) \ z) = y \ ((x * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(121,a,10014,a(flip),b,4824,a)].">
      <j1 rule="hyper" parents="121 10014 4824"/>
    </justification>
  </clause>

  <clause id="10032">
    <literal><![CDATA[
      T(x,y) * ((x * y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      x * ((y * x) \ z) = u
    ]]></literal>
    <justification jstring="[para(10014(a,1),4698(a,1,2))].">
      <j1 rule="para" parents="10014 4698"/>
    </justification>
  </clause>

  <clause id="10033">
    <literal><![CDATA[
      x / y != K(z,u) * ((z * u) \ w)
    ]]></literal>
    <literal><![CDATA[
      ((u * z) \ w) * y = x
    ]]></literal>
    <justification jstring="[para(10014(a,1),4596(a,2,2))].">
      <j1 rule="para" parents="10014 4596"/>
    </justification>
  </clause>

  <clause id="10034">
    <literal><![CDATA[
      L(K(x \ y,x),z,y) * (y * z) = ((x \ y) * x) * z
    ]]></literal>
    <justification jstring="[hyper(63,a,8527,a,b,10011,a)].">
      <j1 rule="hyper" parents="63 8527 10011"/>
    </justification>
  </clause>

  <clause id="10035">
    <literal><![CDATA[
      ((x \ y) * x) * (y \ z) = K(x \ y,x) * z
    ]]></literal>
    <justification jstring="[hyper(34,a,9218,a,b,10011,a)].">
      <j1 rule="hyper" parents="34 9218 10011"/>
    </justification>
  </clause>

  <clause id="10036">
    <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(1676(a,1),10016(a,2,1))].">
      <j1 rule="para" parents="1676 10016"/>
    </justification>
  </clause>

  <clause id="10038">
    <literal><![CDATA[
      K(x \ y,x) * (y \ z) = (x * (y / x)) \ z
    ]]></literal>
    <justification jstring="[para(10(a,1),10024(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 10024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10039">
    <literal><![CDATA[
      ((x \ y) * x) \ (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ y) * z = u
    ]]></literal>
    <justification jstring="[para(10025(a,1),575(a,1))].">
      <j1 rule="para" parents="10025 575"/>
    </justification>
  </clause>

  <clause id="10040">
    <literal><![CDATA[
      T(x,y) * ((x * y) \ z) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (x * ((y * x) \ z)) = w
    ]]></literal>
    <justification jstring="[para(10026(a,2),564(a,1))].">
      <j1 rule="para" parents="10026 564"/>
    </justification>
  </clause>

  <clause id="10041">
    <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(6864(a,1),10026(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6864 10026"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10042">
    <literal><![CDATA[
      K(x \ y,x) * (y * z) = ((x \ y) * x) * z
    ]]></literal>
    <justification jstring="[hyper(575,a,10035,a),flip(a)].">
      <j1 rule="hyper" parents="575 10035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10043">
    <literal><![CDATA[
      (x \ y) / (y \ (y / x)) = (x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(123,a,4407,a(flip),b,10035,a)].">
      <j1 rule="hyper" parents="123 4407 10035"/>
    </justification>
  </clause>

  <clause id="10044">
    <literal><![CDATA[
      x \ (K(y,y \ x) * z) = ((y \ x) * y) \ z
    ]]></literal>
    <justification jstring="[hyper(121,a,4558,a(flip),b,10035,a),flip(a)].">
      <j1 rule="hyper" parents="121 4558 10035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10045">
    <literal><![CDATA[
      ((x \ y) * x) \ (x \ y) = y \ (y / x)
    ]]></literal>
    <justification jstring="[hyper(121,a,4407,a(flip),b,10035,a)].">
      <j1 rule="hyper" parents="121 4407 10035"/>
    </justification>
  </clause>

  <clause id="10046">
    <literal><![CDATA[
      L(x \ 1,x,x \ y) = y \ (y / x)
    ]]></literal>
    <justification jstring="[hyper(424,a,10043,a)].">
      <j1 rule="hyper" parents="424 10043"/>
    </justification>
  </clause>

  <clause id="10047">
    <literal><![CDATA[
      x * L(y \ 1,y,y \ z) = x * (z \ (z / y))
    ]]></literal>
    <justification jstring="[hyper(126,a,10046,a,b,9,a)].">
      <j1 rule="hyper" parents="126 10046 9"/>
    </justification>
  </clause>

  <clause id="10048">
    <literal><![CDATA[
      R((x / y) / x,z,u) * x = x * R(L(y \ 1,y,y \ x),z,u)
    ]]></literal>
    <justification jstring="[para(10046(a,2),675(a,2,2,1))].">
      <j1 rule="para" parents="10046 675"/>
    </justification>
  </clause>

  <clause id="10049">
    <literal><![CDATA[
      x \ (x / y) != z \ u
    ]]></literal>
    <literal><![CDATA[
      z * L(y \ 1,y,y \ x) = u
    ]]></literal>
    <justification jstring="[para(10045(a,1),656(a,1))].">
      <j1 rule="para" parents="10045 656"/>
    </justification>
  </clause>

  <clause id="10050">
    <literal><![CDATA[
      ((x \ y) * x) * (y \ z) = y * ((x * (y / x)) \ z)
    ]]></literal>
    <justification jstring="[para(10038(a,1),10011(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10038 10011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10051">
    <literal><![CDATA[
      K((x * T(y,x * y)) \ z,x * y) * (z * u) = (((x * y) \ z) * (x * y)) * u
    ]]></literal>
    <justification jstring="[para(7604(a,2),10042(a,1,1))].">
      <j1 rule="para" parents="7604 10042"/>
    </justification>
  </clause>

  <clause id="10053">
    <literal><![CDATA[
      x * (((y \ x) * y) \ z) != u * w
    ]]></literal>
    <literal><![CDATA[
      (K(y,y \ x) * z) / w = u
    ]]></literal>
    <justification jstring="[para(10044(a,1),362(a,1,2))].">
      <j1 rule="para" parents="10044 362"/>
    </justification>
  </clause>

  <clause id="10054">
    <literal><![CDATA[
      K(x,T(T(((y \ z) * y) \ u,w),K(y,y \ z) * u)) = K(x,T((K(y,y \ z) * u) / z,w))
    ]]></literal>
    <justification jstring="[para(10044(a,1),7656(a,1,2,1,1))].">
      <j1 rule="para" parents="10044 7656"/>
    </justification>
  </clause>

  <clause id="10055">
    <literal><![CDATA[
      K(x,x \ 1) * y != z
    ]]></literal>
    <literal><![CDATA[
      ((x \ 1) * x) \ y = z
    ]]></literal>
    <justification jstring="[para(166(a,1),10027(a,1,2))].">
      <j1 rule="para" parents="166 10027"/>
    </justification>
  </clause>

  <clause id="10056">
    <literal><![CDATA[
      (x * (1 / x)) * y != z
    ]]></literal>
    <literal><![CDATA[
      ((x \ 1) * x) \ y = z
    ]]></literal>
    <justification jstring="[para(2098(a,1),10055(a,1,1))].">
      <j1 rule="para" parents="2098 10055"/>
    </justification>
  </clause>

  <clause id="10057">
    <literal><![CDATA[
      ((x \ 1) * x) \ y = y * (x * (1 / x))
    ]]></literal>
    <justification jstring="[hyper(10056,a,2409,a)].">
      <j1 rule="hyper" parents="10056 2409"/>
    </justification>
  </clause>

  <clause id="10058">
    <literal><![CDATA[
      ((x \ 1) * x) \ y = (x * (1 / x)) * y
    ]]></literal>
    <justification jstring="[hyper(10056,a,xx)].">
      <j1 rule="hyper" parents="10056"/>
    </justification>
  </clause>

  <clause id="10059">
    <literal><![CDATA[
      (x * (1 / x)) \ (((x \ 1) * x) \ y) = y
    ]]></literal>
    <justification jstring="[hyper(121,a,10057,a,b,2409,a)].">
      <j1 rule="hyper" parents="121 10057 2409"/>
    </justification>
  </clause>

  <clause id="10060">
    <literal><![CDATA[
      (((x \ 1) * x) \ y) / z = y / ((x * (1 / x)) \ z)
    ]]></literal>
    <justification jstring="[para(10057(a,2),2433(a,1,1))].">
      <j1 rule="para" parents="10057 2433"/>
    </justification>
  </clause>

  <clause id="10061">
    <literal><![CDATA[
      (((x \ 1) * x) \ y) \ z = (x * (1 / x)) \ (y \ z)
    ]]></literal>
    <justification jstring="[para(10057(a,2),2638(a,1,1))].">
      <j1 rule="para" parents="10057 2638"/>
    </justification>
  </clause>

  <clause id="10062">
    <literal><![CDATA[
      (x * (1 / x)) \ (y * T(x,x \ 1)) = y * x
    ]]></literal>
    <justification jstring="[hyper(121,a,7725,a(flip),b,10058,a(flip))].">
      <j1 rule="hyper" parents="121 7725 10058"/>
    </justification>
  </clause>

  <clause id="10063">
    <literal><![CDATA[
      ((x * (1 / x)) \ y) \ z = y \ (((x \ 1) * x) \ z)
    ]]></literal>
    <justification jstring="[para(10058(a,2),2793(a,2,2))].">
      <j1 rule="para" parents="10058 2793"/>
    </justification>
  </clause>

  <clause id="10064">
    <literal><![CDATA[
      (((x \ 1) * x) \ y) \ z = y \ ((x * (1 / x)) \ z)
    ]]></literal>
    <justification jstring="[para(10058(a,2),2794(a,1,1))].">
      <j1 rule="para" parents="10058 2794"/>
    </justification>
  </clause>

  <clause id="10065">
    <literal><![CDATA[
      (((x \ 1) * x) \ y) / z = (x * (1 / x)) * (y / z)
    ]]></literal>
    <justification jstring="[para(10058(a,2),2795(a,1,1))].">
      <j1 rule="para" parents="10058 2795"/>
    </justification>
  </clause>

  <clause id="10066">
    <literal><![CDATA[
      (x * (1 / x)) \ y != z
    ]]></literal>
    <literal><![CDATA[
      ((x \ 1) * x) \ z = y
    ]]></literal>
    <justification jstring="[para(10059(a,1),47(a,1)),flip(a)].">
      <j1 rule="para" parents="10059 47"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10067">
    <literal><![CDATA[
      (x / ((y \ 1) \ 1)) * y = (y * (1 / y)) \ x
    ]]></literal>
    <justification jstring="[para(460(a,1),10062(a,1,2)),flip(a)].">
      <j1 rule="para" parents="460 10062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10068">
    <literal><![CDATA[
      (x * y) * (K(x,y) * z) = (T(x,y) * y) * z
    ]]></literal>
    <justification jstring="[para(4372(a,1),10022(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4372 10022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10069">
    <literal><![CDATA[
      (T(x,y) * (y * z)) \ ((T(x,y) * y) * z) = a(x,y,K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(10068(a,1),5035(a,1,2))].">
      <j1 rule="para" parents="10068 5035"/>
    </justification>
  </clause>

  <clause id="10070">
    <literal><![CDATA[
      L(x,y,x) \ (T(x * y,x) \ z) = x \ ((y * x) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,8510,a,b,10031,a)].">
      <j1 rule="hyper" parents="63 8510 10031"/>
    </justification>
  </clause>

  <clause id="10071">
    <literal><![CDATA[
      x * ((y * (x / y)) \ z) = K(y \ x,y) * z
    ]]></literal>
    <justification jstring="[hyper(63,a,10035,a(flip),b,10050,a),flip(a)].">
      <j1 rule="hyper" parents="63 10035 10050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10072">
    <literal><![CDATA[
      (x * ((x * y) / x)) \ y = (x * y) \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(121,a,4333,a(flip),b,10071,a),flip(a)].">
      <j1 rule="hyper" parents="121 4333 10071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10073">
    <literal><![CDATA[
      (x * (y / x)) \ (K(x,x \ y) * (y * z)) = z
    ]]></literal>
    <justification jstring="[hyper(34,a,4558,a(flip),b,10071,a),flip(a)].">
      <j1 rule="hyper" parents="34 4558 10071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10074">
    <literal><![CDATA[
      L(x,y,K(z,z \ y)) = x
    ]]></literal>
    <justification jstring="[hyper(4634,a,10073,a)].">
      <j1 rule="hyper" parents="4634 10073"/>
    </justification>
  </clause>

  <clause id="10075">
    <literal><![CDATA[
      K(x,x \ y) * (y * z) = (x * (y / x)) * z
    ]]></literal>
    <justification jstring="[hyper(142,a,10073,a),flip(a)].">
      <j1 rule="hyper" parents="142 10073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10076">
    <literal><![CDATA[
      L(x,y * z,K(z,y)) = x
    ]]></literal>
    <justification jstring="[para(4394(a,1),10074(a,1,3))].">
      <j1 rule="para" parents="4394 10074"/>
    </justification>
  </clause>

  <clause id="10077">
    <literal><![CDATA[
      L(x,T(y,z),z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5716,a(flip),b,10076,a)].">
      <j1 rule="hyper" parents="63 5716 10076"/>
    </justification>
  </clause>

  <clause id="10078">
    <literal><![CDATA[
      L(x,y,z * K(y,z)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5715,a(flip),b,10076,a)].">
      <j1 rule="hyper" parents="63 5715 10076"/>
    </justification>
  </clause>

  <clause id="10079">
    <literal><![CDATA[
      L(x,y * z,K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(10076(a,1),50(a,2))].">
      <j1 rule="para" parents="10076 50"/>
    </justification>
  </clause>

  <clause id="10080">
    <literal><![CDATA[
      K(x,y) * ((y * x) * z) = (x * y) * z
    ]]></literal>
    <justification jstring="[para(10076(a,1),4353(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10076 4353"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10082">
    <literal><![CDATA[
      L(x,y,z) = (y * z) \ (z * (T(y,z) * x))
    ]]></literal>
    <justification jstring="[hyper(63,a,245,a,b,10077,a),flip(a)].">
      <j1 rule="hyper" parents="63 245 10077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10083">
    <literal><![CDATA[
      L(x,y / z,z) = L(x,z \ y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,4845,a(flip),b,10077,a)].">
      <j1 rule="hyper" parents="63 4845 10077"/>
    </justification>
  </clause>

  <clause id="10084">
    <literal><![CDATA[
      L(T(x,y) \ z,x,y) = (x * y) \ (y * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,520,a(flip),b,10077,a),flip(a)].">
      <j1 rule="hyper" parents="63 520 10077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10085">
    <literal><![CDATA[
      (x * y) * L(z,x,y) = y * (T(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(126,a,10077,a(flip),b,245,a)].">
      <j1 rule="hyper" parents="126 10077 245"/>
    </justification>
  </clause>

  <clause id="10087">
    <literal><![CDATA[
      L(x,(y \ z) \ z,y \ z) = L(x,y,y \ z)
    ]]></literal>
    <justification jstring="[para(112(a,1),10077(a,1,2))].">
      <j1 rule="para" parents="112 10077"/>
    </justification>
  </clause>

  <clause id="10090">
    <literal><![CDATA[
      L(x,y,T(z,y)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(4271(a,1),10078(a,1,3)),flip(a)].">
      <j1 rule="para" parents="4271 10078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10091">
    <literal><![CDATA[
      L(x,y,z / y) = L(x,y,y \ z)
    ]]></literal>
    <justification jstring="[para(4292(a,1),10078(a,1,3))].">
      <j1 rule="para" parents="4292 10078"/>
    </justification>
  </clause>

  <clause id="10092">
    <literal><![CDATA[
      L(x,y,z \ K(y,z \ 1)) = L(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[para(4726(a,1),10078(a,1,3))].">
      <j1 rule="para" parents="4726 10078"/>
    </justification>
  </clause>

  <clause id="10094">
    <literal><![CDATA[
      L(x,T(y,z),z) = L(x,y,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(333,a,10077,a,b,10090,a)].">
      <j1 rule="hyper" parents="333 10077 10090"/>
    </justification>
  </clause>

  <clause id="10095">
    <literal><![CDATA[
      L(T(x,y) \ 1,x,T(y,x)) = (x * y) \ y
    ]]></literal>
    <justification jstring="[hyper(333,a,5087,a(flip),b,10090,a),flip(a)].">
      <j1 rule="hyper" parents="333 5087 10090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10096">
    <literal><![CDATA[
      L(T(x,y),z,T(u,z)) = T(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(333,a,25,a(flip),b,10090,a),flip(a)].">
      <j1 rule="hyper" parents="333 25 10090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10097">
    <literal><![CDATA[
      L(K(x,y),z,T(u,K(x,w) * z)) = L(K(x,y),K(x,w) * z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,7833,a(flip),b,10090,a)].">
      <j1 rule="hyper" parents="63 7833 10090"/>
    </justification>
  </clause>

  <clause id="10098">
    <literal><![CDATA[
      L(x,y \ z,(y \ z) \ z) = L(x,y \ z,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,1645,a(flip),b,10090,a)].">
      <j1 rule="hyper" parents="63 1645 10090"/>
    </justification>
  </clause>

  <clause id="10099">
    <literal><![CDATA[
      L(x,T(y,z),z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(5716(a,1),10079(a,1))].">
      <j1 rule="para" parents="5716 10079"/>
    </justification>
  </clause>

  <clause id="10100">
    <literal><![CDATA[
      (x * (y / x)) * L(z,x \ y,x) = x * ((y / x) * z)
    ]]></literal>
    <justification jstring="[hyper(126,a,10083,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="126 10083 18"/>
    </justification>
  </clause>

  <clause id="10101">
    <literal><![CDATA[
      L(x,y / z,(y / z) \ y) = L(x,z \ y,z)
    ]]></literal>
    <justification jstring="[hyper(5590,a,10091,a),flip(a)].">
      <j1 rule="hyper" parents="5590 10091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10102">
    <literal><![CDATA[
      L(x \ y,x,x \ z) = z \ ((z / x) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,517,a(flip),b,10091,a),flip(a)].">
      <j1 rule="hyper" parents="63 517 10091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10103">
    <literal><![CDATA[
      x * L(y,z,z \ x) = (x / z) * (z * y)
    ]]></literal>
    <justification jstring="[hyper(126,a,10091,a(flip),b,100,a)].">
      <j1 rule="hyper" parents="126 10091 100"/>
    </justification>
  </clause>

  <clause id="10104">
    <literal><![CDATA[
      (x / y) * (y * T(z,x)) = L(z,y,y \ x) * x
    ]]></literal>
    <justification jstring="[para(10091(a,1),789(a,2,1))].">
      <j1 rule="para" parents="10091 789"/>
    </justification>
  </clause>

  <clause id="10105">
    <literal><![CDATA[
      (x * T(y,(x / z) * z)) / a(x / z,z,T(y,(x / z) * z)) = L(y,z,z \ x) * ((x / z) * z)
    ]]></literal>
    <justification jstring="[para(10091(a,1),979(a,2,1))].">
      <j1 rule="para" parents="10091 979"/>
    </justification>
  </clause>

  <clause id="10106">
    <literal><![CDATA[
      L(x,y,T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(10094(a,1),10099(a,1))].">
      <j1 rule="para" parents="10094 10099"/>
    </justification>
  </clause>

  <clause id="10107">
    <literal><![CDATA[
      (x * y) \ (K(x,y) * z) = (y * x) \ z
    ]]></literal>
    <justification jstring="[hyper(631,a,10080,a)].">
      <j1 rule="hyper" parents="631 10080"/>
    </justification>
  </clause>

  <clause id="10108">
    <literal><![CDATA[
      (x * y) * ((y * x) \ z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(343,a,10080,a),flip(a)].">
      <j1 rule="hyper" parents="343 10080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10109">
    <literal><![CDATA[
      T(x,y) * ((y * x) * z) = x * ((x * y) * z)
    ]]></literal>
    <justification jstring="[hyper(126,a,10080,a(flip),b,4550,a)].">
      <j1 rule="hyper" parents="126 10080 4550"/>
    </justification>
  </clause>

  <clause id="10110">
    <literal><![CDATA[
      K(x,(x * y) / x) * ((((x * y) / x) * x) * z) = (T(x,y) * y) * z
    ]]></literal>
    <justification jstring="[para(3311(a,2),10080(a,2,1))].">
      <j1 rule="para" parents="3311 10080"/>
    </justification>
  </clause>

  <clause id="10112">
    <literal><![CDATA[
      K(x \ ((y * z) * u),z) = K(x \ ((z * y) * u),z)
    ]]></literal>
    <justification jstring="[para(10080(a,1),9573(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10080 9573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10113">
    <literal><![CDATA[
      K(x,y \ ((x * z) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ ((z * x) * u)) = w
    ]]></literal>
    <justification jstring="[para(10080(a,1),9589(a,1,2,2))].">
      <j1 rule="para" parents="10080 9589"/>
    </justification>
  </clause>

  <clause id="10114">
    <literal><![CDATA[
      T(L(x,y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(T(x,u),y,z) = w
    ]]></literal>
    <justification jstring="[para(10096(a,1),10106(a,1))].">
      <j1 rule="para" parents="10096 10106"/>
    </justification>
  </clause>

  <clause id="10115">
    <literal><![CDATA[
      (x * y) \ (T(x,y) * z) = (y * x) \ (x * z)
    ]]></literal>
    <justification jstring="[para(4273(a,1),10107(a,1,2))].">
      <j1 rule="para" parents="4273 10107"/>
    </justification>
  </clause>

  <clause id="10117">
    <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(333,a,3711,a,b,10108,a)].">
      <j1 rule="hyper" parents="333 3711 10108"/>
    </justification>
  </clause>

  <clause id="10118">
    <literal><![CDATA[
      (x * y) \ (x * (T(y,x) * z)) = K(y,x) * L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(126,a,10082,a,b,10010,a),flip(a)].">
      <j1 rule="hyper" parents="126 10082 10010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10119">
    <literal><![CDATA[
      (x * y) \ (y * (x * z)) = L(K(y,x) * z,x,y)
    ]]></literal>
    <justification jstring="[para(4250(a,1),10082(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4250 10082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10120">
    <literal><![CDATA[
      (K(x,y) * z) \ (z * (K(x,T(y,z)) * u)) = L(u,K(x,y),z)
    ]]></literal>
    <justification jstring="[para(6365(a,2),10082(a,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="6365 10082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10121">
    <literal><![CDATA[
      (x * y) * L(K(z \ x,z),x,y) = y * (K(x,y) * ((z \ x) * z))
    ]]></literal>
    <justification jstring="[para(4538(a,2),10085(a,2,2))].">
      <j1 rule="para" parents="4538 10085"/>
    </justification>
  </clause>

  <clause id="10122">
    <literal><![CDATA[
      L(T((x / y) \ 1,y * (x / y)) \ 1,(x / y) \ 1,T(y * (x / y),(x / y) \ 1)) = (((y \ x) \ 1) * x) \ (y * (x / y))
    ]]></literal>
    <justification jstring="[para(5744(a,1),10095(a,2,1))].">
      <j1 rule="para" parents="5744 10095"/>
    </justification>
  </clause>

  <clause id="10123">
    <literal><![CDATA[
      L(T(x,y),y,y \ z) = z \ ((z / y) * (x * y))
    ]]></literal>
    <justification jstring="[para(22(a,2),10102(a,1,1))].">
      <j1 rule="para" parents="22 10102"/>
    </justification>
  </clause>

  <clause id="10124">
    <literal><![CDATA[
      L(T(x,y) \ z,T(x,y),T(x,y) \ y) = y \ ((T(y,x) / x) * z)
    ]]></literal>
    <justification jstring="[para(3625(a,2),10102(a,2,2,1))].">
      <j1 rule="para" parents="3625 10102"/>
    </justification>
  </clause>

  <clause id="10125">
    <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(5990(a,1),10102(a,1,3))].">
      <j1 rule="para" parents="5990 10102"/>
    </justification>
  </clause>

  <clause id="10126">
    <literal><![CDATA[
      L(T(x,y),z,T(x,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(T(x,y),z,x) = w
    ]]></literal>
    <justification jstring="[para(6581(a,2),10114(a,1))].">
      <j1 rule="para" parents="6581 10114"/>
    </justification>
  </clause>

  <clause id="10127">
    <literal><![CDATA[
      K(x,x \ y) * (z * y) = (x * (y / x)) * T(z,y)
    ]]></literal>
    <justification jstring="[hyper(595,a,10075,a)].">
      <j1 rule="hyper" parents="595 10075"/>
    </justification>
  </clause>

  <clause id="10128">
    <literal><![CDATA[
      (x * (x * y)) \ (x * ((x * y) * z)) = L(z,y * x,T(x,y))
    ]]></literal>
    <justification jstring="[para(10109(a,1),3714(a,1,2))].">
      <j1 rule="para" parents="10109 3714"/>
    </justification>
  </clause>

  <clause id="10129">
    <literal><![CDATA[
      L(K(x,T(y,z)),u,u \ z) * z = (z / u) * (u * K(x,y))
    ]]></literal>
    <justification jstring="[para(6896(a,1),10104(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6896 10104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10130">
    <literal><![CDATA[
      (x * R(y,z,y)) \ ((y * x) * y) != u
    ]]></literal>
    <literal><![CDATA[
      L(T(y,x),z,y) = u
    ]]></literal>
    <justification jstring="[para(9326(a,2),10126(a,1))].">
      <j1 rule="para" parents="9326 10126"/>
    </justification>
  </clause>

  <clause id="10131">
    <literal><![CDATA[
      (x * y) / ((y * (1 / y)) \ z) = (x * T(y,y \ 1)) / z
    ]]></literal>
    <justification jstring="[para(7725(a,1),10060(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7725 10060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10132">
    <literal><![CDATA[
      (x * (1 / x)) \ (y \ z) = y \ ((x * (1 / x)) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,10061,a(flip),b,10064,a)].">
      <j1 rule="hyper" parents="63 10061 10064"/>
    </justification>
  </clause>

  <clause id="10133">
    <literal><![CDATA[
      (x * y) \ ((x * (1 / x)) \ z) = (T(x,x \ 1) * y) \ z
    ]]></literal>
    <justification jstring="[para(4720(a,1),10064(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4720 10064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10134">
    <literal><![CDATA[
      (((x \ 1) * x) \ y) / z = ((x \ 1) * x) \ (y / z)
    ]]></literal>
    <justification jstring="[hyper(333,a,10058,a,b,10065,a),flip(a)].">
      <j1 rule="hyper" parents="333 10058 10065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10135">
    <literal><![CDATA[
      L(x,K(y,y \ z) * ((u * z) \ 1),w) = L(x,(y * (z / y)) * T(u,z),w)
    ]]></literal>
    <justification jstring="[para(10127(a,1),2634(a,2,2))].">
      <j1 rule="para" parents="10127 2634"/>
    </justification>
  </clause>

  <clause id="10136">
    <literal><![CDATA[
      ((x \ 1) * x) \ (y \ ((x * (1 / x)) \ z)) = y \ z
    ]]></literal>
    <justification jstring="[hyper(10066,a,10132,a)].">
      <j1 rule="hyper" parents="10066 10132"/>
    </justification>
  </clause>

  <clause id="10137">
    <literal><![CDATA[
      (x * (1 / x)) \ (y \ 1) = y \ ((x \ 1) * x)
    ]]></literal>
    <justification jstring="[para(4480(a,1),10132(a,2,2))].">
      <j1 rule="para" parents="4480 10132"/>
    </justification>
  </clause>

  <clause id="10138">
    <literal><![CDATA[
      (x \ 1) \ (((y \ 1) * y) \ z) = (x \ ((y \ 1) * y)) \ z
    ]]></literal>
    <justification jstring="[para(10137(a,1),10063(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10137 10063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10139">
    <literal><![CDATA[
      ((x \ 1) * x) \ ((y * x) / z) = (y * T(x,x \ 1)) / z
    ]]></literal>
    <justification jstring="[para(7725(a,1),10134(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7725 10134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10140">
    <literal><![CDATA[
      ((x \ 1) * x) \ (y \ z) = y \ (((x \ 1) * x) \ z)
    ]]></literal>
    <justification jstring="[para(10059(a,1),10136(a,1,2,2))].">
      <j1 rule="para" parents="10059 10136"/>
    </justification>
  </clause>

  <clause id="10141">
    <literal><![CDATA[
      x \ (((y \ 1) * y) \ (x * z)) = ((y \ 1) * y) \ z
    ]]></literal>
    <justification jstring="[para(9(a,1),10140(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9 10140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10142">
    <literal><![CDATA[
      ((x \ 1) * x) \ (y * ((x \ 1) * z)) = y * L(x \ z,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(126,a,99,a,b,10141,a),flip(a)].">
      <j1 rule="hyper" parents="126 99 10141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10143">
    <literal><![CDATA[
      L(K(x \ y,x),z,y) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,10042,a,b,10034,a),flip(a)].">
      <j1 rule="hyper" parents="35 10042 10034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10144">
    <literal><![CDATA[
      (x * y) * K(z \ x,z) = x * (y * K(z \ x,z))
    ]]></literal>
    <justification jstring="[hyper(126,a,10143,a(flip),b,3220,a(flip))].">
      <j1 rule="hyper" parents="126 10143 3220"/>
    </justification>
  </clause>

  <clause id="10146">
    <literal><![CDATA[
      (K(x,y) * (z / K(x,y))) * L(u,K(x,y) \ z,K(x,y)) = K(x,y) * ((z * K(y,x)) * u)
    ]]></literal>
    <justification jstring="[para(5994(a,1),10100(a,2,2,1))].">
      <j1 rule="para" parents="5994 10100"/>
    </justification>
  </clause>

  <clause id="10147">
    <literal><![CDATA[
      L(K(x,y) * z,x,y) = K(x,y) * L(z,x,y)
    ]]></literal>
    <justification jstring="[hyper(4526,a,10118,a)].">
      <j1 rule="hyper" parents="4526 10118"/>
    </justification>
  </clause>

  <clause id="10148">
    <literal><![CDATA[
      x * L(K(x,y) * z,x,y) = T(x,y) * L(z,x,y)
    ]]></literal>
    <justification jstring="[hyper(126,a,10147,a,b,4515,a)].">
      <j1 rule="hyper" parents="126 10147 4515"/>
    </justification>
  </clause>

  <clause id="10149">
    <literal><![CDATA[
      (T(x \ (x / y),(x \ (x / y)) \ 1) * T(x,y \ 1)) \ z = (x / y) \ (((x \ (x / y)) * (1 / (x \ (x / y)))) \ z)
    ]]></literal>
    <justification jstring="[para(5838(a,1),10133(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5838 10133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10150">
    <literal><![CDATA[
      ((x \ 1) * x) \ ((y \ 1) \ z) = (y \ ((x \ 1) * x)) \ z
    ]]></literal>
    <justification jstring="[hyper(63,a,10140,a,b,10138,a)].">
      <j1 rule="hyper" parents="63 10140 10138"/>
    </justification>
  </clause>

  <clause id="10151">
    <literal><![CDATA[
      T(x,(y * T(z,z \ 1)) / u) = T(x,(y * z) / u)
    ]]></literal>
    <justification jstring="[para(10139(a,1),3190(a,1,2))].">
      <j1 rule="para" parents="10139 3190"/>
    </justification>
  </clause>

  <clause id="10152">
    <literal><![CDATA[
      x / y != K(z,z \ u) * (u \ w)
    ]]></literal>
    <literal><![CDATA[
      (((z \ u) * z) \ w) * y = x
    ]]></literal>
    <justification jstring="[para(10(a,1),10033(a,2,2,1))].">
      <j1 rule="para" parents="10 10033"/>
    </justification>
  </clause>

  <clause id="10153">
    <literal><![CDATA[
      L(x,y * z,T(z,y)) = L(x,z * y,z)
    ]]></literal>
    <justification jstring="[hyper(504,a,10128,a),flip(a)].">
      <j1 rule="hyper" parents="504 10128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10154">
    <literal><![CDATA[
      L(K(x,y),z,T(u,K(x,w) * z)) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(333,a,7833,a(flip),b,10097,a),flip(a)].">
      <j1 rule="hyper" parents="333 7833 10097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10156">
    <literal><![CDATA[
      x * R(L(y \ 1,y,y \ x),z,u) = x * R(x \ (x / y),z,u)
    ]]></literal>
    <justification jstring="[hyper(903,a,10048,a),flip(a)].">
      <j1 rule="hyper" parents="903 10048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10157">
    <literal><![CDATA[
      (((x \ y) * x) \ z) * K(y,((x \ y) * x) \ z) = (K(x,x \ y) * z) / y
    ]]></literal>
    <justification jstring="[hyper(10053,a,4291,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="10053 4291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10158">
    <literal><![CDATA[
      a(x,y,K(x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      a(T(x,y),y,z) = u
    ]]></literal>
    <justification jstring="[para(10069(a,1),752(a,1))].">
      <j1 rule="para" parents="10069 752"/>
    </justification>
  </clause>

  <clause id="10159">
    <literal><![CDATA[
      ((x \ 1) * x) \ (y * ((x \ 1) * z)) = y * ((1 / x) * z)
    ]]></literal>
    <justification jstring="[para(2655(a,1),10142(a,2,2))].">
      <j1 rule="para" parents="2655 10142"/>
    </justification>
  </clause>

  <clause id="10160">
    <literal><![CDATA[
      ((T(x,y) \ 1) \ 1) * ((x \ 1) * z) = T(x,y) * ((1 / x) * z)
    ]]></literal>
    <justification jstring="[hyper(3515,a,10159,a)].">
      <j1 rule="hyper" parents="3515 10159"/>
    </justification>
  </clause>

  <clause id="10161">
    <literal><![CDATA[
      x * R(x \ (x / y),z,u) = x * L(R(y \ 1,z,u),y,y \ x)
    ]]></literal>
    <justification jstring="[para(29(a,1),10156(a,1,2)),flip(a)].">
      <j1 rule="para" parents="29 10156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10162">
    <literal><![CDATA[
      (x / y) \ (x * R(x \ (x / y),z,u)) = y * R(y \ 1,z,u)
    ]]></literal>
    <justification jstring="[hyper(121,a,10161,a,b,10103,a(flip))].">
      <j1 rule="hyper" parents="121 10161 10103"/>
    </justification>
  </clause>

  <clause id="10164">
    <literal><![CDATA[
      (x \ y) \ (y * R(y \ (y / T(x,x \ y)),z,u)) = T(x,x \ y) * R(T(x,x \ y) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(281(a,1),10162(a,1,1))].">
      <j1 rule="para" parents="281 10162"/>
    </justification>
  </clause>

  <clause id="10165">
    <literal><![CDATA[
      K(x,y) * ((((x * y) / x) * x) * z) = (T(x,y) * y) * z
    ]]></literal>
    <justification jstring="[para(4369(a,1),10110(a,1,1))].">
      <j1 rule="para" parents="4369 10110"/>
    </justification>
  </clause>

  <clause id="10166">
    <literal><![CDATA[
      K(x,y) * ((x * y) * z) = (T(x,y) * y) * z
    ]]></literal>
    <justification jstring="[para(12(a,1),10165(a,1,2,1))].">
      <j1 rule="para" parents="12 10165"/>
    </justification>
  </clause>

  <clause id="10167">
    <literal><![CDATA[
      ((x * y) / x) \ ((y * x) * z) = y \ ((T(y,x) * x) * z)
    ]]></literal>
    <justification jstring="[hyper(121,a,10166,a(flip),b,4236,a),flip(a)].">
      <j1 rule="hyper" parents="121 10166 4236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10169">
    <literal><![CDATA[
      L(K(x,y \ ((z \ u) * x)),z \ u,z) = K((x \ 1) \ 1,(z * (L(y,x \ 1,x) / x)) \ u)
    ]]></literal>
    <justification jstring="[para(9980(a,1),9898(a,1,1))].">
      <j1 rule="para" parents="9980 9898"/>
    </justification>
  </clause>

  <clause id="10170">
    <literal><![CDATA[
      K(x,y) * (((x * y) \ y) * z) = ((y * x) \ y) * z
    ]]></literal>
    <justification jstring="[para(7119(a,1),10029(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7119 10029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10171">
    <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(6968(a,1),10125(a,2,2,1))].">
      <j1 rule="para" parents="6968 10125"/>
    </justification>
  </clause>

  <clause id="10172">
    <literal><![CDATA[
      K(L(x,y,z),u \ L(K(x,w),v5,v6)) = K(L(x,y,z),u \ 1)
    ]]></literal>
    <justification jstring="[hyper(333,a,4948,a(flip),b,9443,a),flip(a)].">
      <j1 rule="hyper" parents="333 4948 9443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10173">
    <literal><![CDATA[
      K(x,(y * (z / (x \ 1))) \ u) = K(x,(y * z) \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(9982,a,9983,a)].">
      <j1 rule="hyper" parents="9982 9983"/>
    </justification>
  </clause>

  <clause id="10174">
    <literal><![CDATA[
      K(x,(y * ((x \ 1) * z)) \ (x \ u)) = K(x,(y * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,9864,a(flip),b,10173,a),flip(a)].">
      <j1 rule="hyper" parents="63 9864 10173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10175">
    <literal><![CDATA[
      K(x,(y * ((x \ 1) * z)) \ T(u,x)) = K(x,(y * z) \ (u * x))
    ]]></literal>
    <justification jstring="[para(22(a,2),10174(a,1,2,2))].">
      <j1 rule="para" parents="22 10174"/>
    </justification>
  </clause>

  <clause id="10176">
    <literal><![CDATA[
      K(x,(y * ((x \ 1) * z)) \ u) = K(x,(y * z) \ (u * x))
    ]]></literal>
    <justification jstring="[hyper(7528,a,10175,a)].">
      <j1 rule="hyper" parents="7528 10175"/>
    </justification>
  </clause>

  <clause id="10177">
    <literal><![CDATA[
      K((L(x,y,x) * y) \ z,y * x) * (z * u) = (((y * x) \ z) * (y * x)) * u
    ]]></literal>
    <justification jstring="[para(3686(a,1),10051(a,1,1,1,1))].">
      <j1 rule="para" parents="3686 10051"/>
    </justification>
  </clause>

  <clause id="10178">
    <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(9891(a,2),7074(a,1))].">
      <j1 rule="para" parents="9891 7074"/>
    </justification>
  </clause>

  <clause id="10179">
    <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(63,a,9491,a(flip),b,9691,a),flip(a)].">
      <j1 rule="hyper" parents="63 9491 9691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10181">
    <literal><![CDATA[
      K(x,L(y,K(x,z) * u,w)) = K(x,(w * u) \ (w * (u * y)))
    ]]></literal>
    <justification jstring="[hyper(63,a,7661,a(flip),b,10179,a),flip(a)].">
      <j1 rule="hyper" parents="63 7661 10179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10183">
    <literal><![CDATA[
      K(x,L(y,K(x,z) * u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(18(a,2),10181(a,2,2))].">
      <j1 rule="para" parents="18 10181"/>
    </justification>
  </clause>

  <clause id="10184">
    <literal><![CDATA[
      K(x,L(y,K(x,z) \ u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(10(a,1),10183(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 10183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10185">
    <literal><![CDATA[
      K(L(x,K(y,z) * u,w),y) = (y \ 1) / (y \ K(y,L(x,u,w)))
    ]]></literal>
    <justification jstring="[para(10183(a,1),4688(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10183 4688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10186">
    <literal><![CDATA[
      K(L(x,K(y,z) * u,w),y) = K(L(x,u,w),y)
    ]]></literal>
    <justification jstring="[hyper(333,a,4688,a(flip),b,10185,a),flip(a)].">
      <j1 rule="hyper" parents="333 4688 10185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10187">
    <literal><![CDATA[
      K(L(x,T(y,z),u),z) = K(L(x,y,u),z)
    ]]></literal>
    <justification jstring="[para(4224(a,1),10186(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4224 10186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10188">
    <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(6695,a,9530,a),flip(a)].">
      <j1 rule="hyper" parents="6695 9530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10189">
    <literal><![CDATA[
      K(L(x,y,z),T(u \ L(x,y,z),L(K(x,w),v5,v6))) = K(L(x,y,z),u \ (L(x,y,z) * L(K(x,w),v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(63,a,9995,a(flip),b,9665,a),flip(a)].">
      <j1 rule="hyper" parents="63 9995 9665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10190">
    <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(178(a,1),9705(a,2,1,2))].">
      <j1 rule="para" parents="178 9705"/>
    </justification>
  </clause>

  <clause id="10191">
    <literal><![CDATA[
      L(K(x,y),L(y,z,u),w) = K(x,y)
    ]]></literal>
    <justification jstring="[para(1815(a,1),10190(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1815 10190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10192">
    <literal><![CDATA[
      a(x,L(y,z,u),K(w,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(120,a,10191,a,b,9744,a),flip(a)].">
      <j1 rule="hyper" parents="120 10191 9744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10193">
    <literal><![CDATA[
      K((x \ 1) * L(y,z,u),y) = K(x \ L(y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,7300,a(flip),b,10191,a)].">
      <j1 rule="hyper" parents="63 7300 10191"/>
    </justification>
  </clause>

  <clause id="10194">
    <literal><![CDATA[
      K((x \ y) \ L(z,u,w),z) = K(y \ (x * L(z,u,w)),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,6282,a(flip),b,10191,a),flip(a)].">
      <j1 rule="hyper" parents="63 6282 10191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10195">
    <literal><![CDATA[
      L(K(x,y),L(x,z,u),w) = (((v5 \ v6) \ v6) * K(y,x)) \ T(v5,v5 \ v6)
    ]]></literal>
    <justification jstring="[para(10191(a,1),9444(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10191 9444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10196">
    <literal><![CDATA[
      L(K(x,y),L(x,z,u),w) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,5992,a(flip),b,10195,a),flip(a)].">
      <j1 rule="hyper" parents="333 5992 10195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10197">
    <literal><![CDATA[
      K(x,(y \ z) \ L(x,u,w)) = K(x,z \ (y * L(x,u,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,9513,a(flip),b,10196,a),flip(a)].">
      <j1 rule="hyper" parents="63 9513 10196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10198">
    <literal><![CDATA[
      R(K(x,x \ y),z,T(y,K(x,x \ y) * z)) = (y * (K(x,x \ y) * z)) / (y * z)
    ]]></literal>
    <justification jstring="[para(111(a,1),9759(a,2,2))].">
      <j1 rule="para" parents="111 9759"/>
    </justification>
  </clause>

  <clause id="10199">
    <literal><![CDATA[
      R(K(x,x \ y),z,T(y,K(x,x \ y) * z)) = K(x,(y * z) / (y * ((x \ y) \ z)))
    ]]></literal>
    <justification jstring="[hyper(333,a,9939,a,b,10198,a),flip(a)].">
      <j1 rule="hyper" parents="333 9939 10198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10200">
    <literal><![CDATA[
      K(x,(y * z) / (y * ((x \ y) \ z))) = R(K(x,x \ y),z,T(y,z))
    ]]></literal>
    <justification jstring="[para(9758(a,1),10199(a,1,3)),flip(a)].">
      <j1 rule="para" parents="9758 10199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10202">
    <literal><![CDATA[
      K(x,L(y,z \ 1,z) \ z) = K(x,((((z \ x) \ x) \ 1) * y) \ 1)
    ]]></literal>
    <justification jstring="[para(9167(a,1),9787(a,1,2,1))].">
      <j1 rule="para" parents="9167 9787"/>
    </justification>
  </clause>

  <clause id="10203">
    <literal><![CDATA[
      K(x,((((y \ x) \ x) \ 1) * z) \ 1) = K(x,((y \ 1) * z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(5950,a,10202,a),flip(a)].">
      <j1 rule="hyper" parents="5950 10202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10205">
    <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(9(a,1),9798(a,1,2,1))].">
      <j1 rule="para" parents="9 9798"/>
    </justification>
  </clause>

  <clause id="10207">
    <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(18(a,2),10205(a,1,2))].">
      <j1 rule="para" parents="18 10205"/>
    </justification>
  </clause>

  <clause id="10208">
    <literal><![CDATA[
      K(L(x,y * z,u),z) = K(x,L(L(z,y,x),x * y,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,9538,a(flip),b,10207,a)].">
      <j1 rule="hyper" parents="63 9538 10207"/>
    </justification>
  </clause>

  <clause id="10209">
    <literal><![CDATA[
      K(L(x,y * z,u),z) = K(x,L(z,x * y,u))
    ]]></literal>
    <justification jstring="[hyper(333,a,9477,a(flip),b,10208,a),flip(a)].">
      <j1 rule="hyper" parents="333 9477 10208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10212">
    <literal><![CDATA[
      K(L(x,(x \ y) * z,u),z) = K(x,L(z,y,u))
    ]]></literal>
    <justification jstring="[para(10(a,1),10209(a,2,2,2))].">
      <j1 rule="para" parents="10 10209"/>
    </justification>
  </clause>

  <clause id="10213">
    <literal><![CDATA[
      K(x,L(y * ((z * y) \ z),u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(63,a,8395,a(flip),b,10212,a),flip(a)].">
      <j1 rule="hyper" parents="63 8395 10212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10214">
    <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(3744(a,1),10212(a,1,1,2))].">
      <j1 rule="para" parents="3744 10212"/>
    </justification>
  </clause>

  <clause id="10215">
    <literal><![CDATA[
      K(x,y \ K(z,L(x,u,w))) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(10212(a,1),7426(a,1,2,2))].">
      <j1 rule="para" parents="10212 7426"/>
    </justification>
  </clause>

  <clause id="10216">
    <literal><![CDATA[
      K(x,a(y,z,z \ 1) \ 1) = 1
    ]]></literal>
    <justification jstring="[hyper(63,a,7694,a(flip),b,10213,a)].">
      <j1 rule="hyper" parents="63 7694 10213"/>
    </justification>
  </clause>

  <clause id="10218">
    <literal><![CDATA[
      T(x,a(y,z,z \ 1) \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(56,a,10216,a)].">
      <j1 rule="hyper" parents="56 10216"/>
    </justification>
  </clause>

  <clause id="10219">
    <literal><![CDATA[
      K(x,(T(L(x,y,z),u) \ w) \ 1) = K(x,w \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,7696,a(flip),b,10215,a),flip(a)].">
      <j1 rule="hyper" parents="63 7696 10215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10220">
    <literal><![CDATA[
      K(x,y \ K(z,L(L(x,u,w),v5,v6))) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(10212(a,1),10215(a,1,2,2))].">
      <j1 rule="para" parents="10212 10215"/>
    </justification>
  </clause>

  <clause id="10221">
    <literal><![CDATA[
      K(x,(L(T(x,y),z,u) \ w) \ 1) = K(x,w \ L(x,z,u))
    ]]></literal>
    <justification jstring="[para(25(a,2),10219(a,1,2,1,1))].">
      <j1 rule="para" parents="25 10219"/>
    </justification>
  </clause>

  <clause id="10222">
    <literal><![CDATA[
      K(x,y \ L(T(x,z),u,w)) = K(x,y \ L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(5853,a,10221,a)].">
      <j1 rule="hyper" parents="5853 10221"/>
    </justification>
  </clause>

  <clause id="10223">
    <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(1099(a,1),10222(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="1099 10222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10224">
    <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(1100(a,1),10222(a,1,2,2,1))].">
      <j1 rule="para" parents="1100 10222"/>
    </justification>
  </clause>

  <clause id="10225">
    <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(6337,a,10214,a)].">
      <j1 rule="hyper" parents="6337 10214"/>
    </justification>
  </clause>

  <clause id="10227">
    <literal><![CDATA[
      K(x,L(R(y,x \ z,y),z,u)) = K(L(x,y * (x \ z),u),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,10187,a(flip),b,10225,a),flip(a)].">
      <j1 rule="hyper" parents="63 10187 10225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10228">
    <literal><![CDATA[
      T(x,K(y,z)) * L(u,K(y,z) \ x,K(y,z)) = K(y,z) * ((x * K(z,y)) * u)
    ]]></literal>
    <justification jstring="[para(7095(a,1),10146(a,1,1))].">
      <j1 rule="para" parents="7095 10146"/>
    </justification>
  </clause>

  <clause id="10229">
    <literal><![CDATA[
      T(x,K(y,z)) * L(u,K(z,y) * x,K(y,z)) = K(y,z) * ((x * K(z,y)) * u)
    ]]></literal>
    <justification jstring="[para(4567(a,1),10228(a,1,2,2))].">
      <j1 rule="para" parents="4567 10228"/>
    </justification>
  </clause>

  <clause id="10230">
    <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(333,a,9869,a(flip),b,10188,a),flip(a)].">
      <j1 rule="hyper" parents="333 9869 10188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10232">
    <literal><![CDATA[
      K((((L(x,y,z) \ u) \ w) \ w) \ w,x) = K((L(x,y,z) * w) / u,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,6922,a(flip),b,10230,a),flip(a)].">
      <j1 rule="hyper" parents="333 6922 10230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10233">
    <literal><![CDATA[
      K((((L(x,y,z) \ u) \ w) \ w) \ w,x) = K((u / w) \ L(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(333,a,9761,a(flip),b,10232,a),flip(a)].">
      <j1 rule="hyper" parents="333 9761 10232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10234">
    <literal><![CDATA[
      K(x / (L(y,z,u) \ w),y) = K((w / x) \ L(y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(7204,a,10233,a)].">
      <j1 rule="hyper" parents="7204 10233"/>
    </justification>
  </clause>

  <clause id="10235">
    <literal><![CDATA[
      K(L(x,y,z),u \ ((1 / x) \ L(K(x,w),v5,v6))) = K(L(x,y,z),(x \ u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(333,a,10172,a(flip),b,9762,a),flip(a)].">
      <j1 rule="hyper" parents="333 10172 9762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10237">
    <literal><![CDATA[
      K(L(x,y,z),u \ ((1 / x) \ L(K(x,w),v5,v6))) = K(L(x,y,z),u \ x)
    ]]></literal>
    <justification jstring="[hyper(333,a,5766,a(flip),b,10235,a),flip(a)].">
      <j1 rule="hyper" parents="333 5766 10235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10238">
    <literal><![CDATA[
      K(L(x,y,z),u \ (x * L(K(x,w),v5,v6))) = K(L(x,y,z),u \ x)
    ]]></literal>
    <justification jstring="[para(4664(a,1),10237(a,1,2,2))].">
      <j1 rule="para" parents="4664 10237"/>
    </justification>
  </clause>

  <clause id="10239">
    <literal><![CDATA[
      (x / (1 / y)) * (1 / T(y,y \ (x / (1 / y)))) = (T(x,y) / (1 / y)) * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(582,a,10036,a)].">
      <j1 rule="hyper" parents="582 10036"/>
    </justification>
  </clause>

  <clause id="10241">
    <literal><![CDATA[
      (x / (1 / y)) * (1 / T(y,(x / (1 / y)) / y)) = (T(x,y) / (1 / y)) * (1 / y)
    ]]></literal>
    <justification jstring="[para(3633(a,2),10239(a,1,2,2))].">
      <j1 rule="para" parents="3633 10239"/>
    </justification>
  </clause>

  <clause id="10242">
    <literal><![CDATA[
      (T(x,y) / (1 / y)) * (1 / y) = (x / (1 / y)) * (1 / T(y,x))
    ]]></literal>
    <justification jstring="[para(6530(a,1),10241(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6530 10241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10243">
    <literal><![CDATA[
      T(x,y) / (1 / T(y,x)) = x / (1 / y)
    ]]></literal>
    <justification jstring="[hyper(410,a,10242,a)].">
      <j1 rule="hyper" parents="410 10242"/>
    </justification>
  </clause>

  <clause id="10245">
    <literal><![CDATA[
      T(x,y / x) / (1 / (x \ y)) = x / (1 / (y / x))
    ]]></literal>
    <justification jstring="[para(113(a,1),10243(a,1,2,2))].">
      <j1 rule="para" parents="113 10243"/>
    </justification>
  </clause>

  <clause id="10246">
    <literal><![CDATA[
      (x / (1 / (x \ y))) / x = x \ (x / (1 / (y / x)))
    ]]></literal>
    <justification jstring="[para(10245(a,1),3670(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10245 3670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10247">
    <literal><![CDATA[
      T((x / (1 / (x \ y))) / x,1 / (y / x)) = x \ (x / ((y / x) \ 1))
    ]]></literal>
    <justification jstring="[para(10246(a,2),2888(a,1,1))].">
      <j1 rule="para" parents="10246 2888"/>
    </justification>
  </clause>

  <clause id="10248">
    <literal><![CDATA[
      x * ((x / ((x \ y) \ 1)) / x) = x / ((y / x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(8983,a,10247,a)].">
      <j1 rule="hyper" parents="8983 10247"/>
    </justification>
  </clause>

  <clause id="10249">
    <literal><![CDATA[
      K((x \ 1) \ 1,(y * (L(z,x \ 1,x) / x)) \ u) = K(x,(y * (x \ z)) \ u)
    ]]></literal>
    <justification jstring="[hyper(9850,a,10169,a),flip(a)].">
      <j1 rule="hyper" parents="9850 10169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10250">
    <literal><![CDATA[
      K(x,(y * (L(z,x \ 1,x) / x)) \ u) = K(x,(y * (x \ z)) \ u)
    ]]></literal>
    <justification jstring="[hyper(3382,a,10249,a)].">
      <j1 rule="hyper" parents="3382 10249"/>
    </justification>
  </clause>

  <clause id="10251">
    <literal><![CDATA[
      K(x,(y * (x \ L(z,x \ 1,x))) \ u) = K(x,(y * (x \ z)) \ u)
    ]]></literal>
    <justification jstring="[hyper(9974,a,10250,a)].">
      <j1 rule="hyper" parents="9974 10250"/>
    </justification>
  </clause>

  <clause id="10252">
    <literal><![CDATA[
      K(x,(y * ((x \ 1) * z)) \ u) = K(x,(y * (x \ z)) \ u)
    ]]></literal>
    <justification jstring="[para(439(a,1),10251(a,1,2,1,2))].">
      <j1 rule="para" parents="439 10251"/>
    </justification>
  </clause>

  <clause id="10253">
    <literal><![CDATA[
      K(x,(y * (x \ z)) \ u) = K(x,(y * z) \ (u * x))
    ]]></literal>
    <justification jstring="[hyper(63,a,10176,a(flip),b,10252,a),flip(a)].">
      <j1 rule="hyper" parents="63 10176 10252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10254">
    <literal><![CDATA[
      K(x,(y * (z / x)) \ u) = K(x,(y * z) \ (u * x))
    ]]></literal>
    <justification jstring="[hyper(7652,a,10253,a)].">
      <j1 rule="hyper" parents="7652 10253"/>
    </justification>
  </clause>

  <clause id="10255">
    <literal><![CDATA[
      L(K(x,y \ ((z \ u) * x)),z \ u,z) = K(x,(z * y) \ (u * x))
    ]]></literal>
    <justification jstring="[hyper(63,a,9703,a,b,10253,a)].">
      <j1 rule="hyper" parents="63 9703 10253"/>
    </justification>
  </clause>

  <clause id="10256">
    <literal><![CDATA[
      K(x,(y * (x \ 1)) \ z) = K(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[para(8(a,1),10253(a,2,2,1))].">
      <j1 rule="para" parents="8 10253"/>
    </justification>
  </clause>

  <clause id="10257">
    <literal><![CDATA[
      K(x,((y * K(x \ z,y)) * z) \ (u * x)) = K(x,((x \ z) * y) \ u)
    ]]></literal>
    <justification jstring="[para(4291(a,1),10253(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4291 10253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10258">
    <literal><![CDATA[
      K(x,(y * z) \ (u * x)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * (z / x)) \ u) = w
    ]]></literal>
    <justification jstring="[para(10253(a,1),7652(a,1))].">
      <j1 rule="para" parents="10253 7652"/>
    </justification>
  </clause>

  <clause id="10259">
    <literal><![CDATA[
      L(K(x,(x \ 1) \ y),y,z) = K(x,z \ ((z * y) * x))
    ]]></literal>
    <justification jstring="[hyper(9764,a,10256,a)].">
      <j1 rule="hyper" parents="9764 10256"/>
    </justification>
  </clause>

  <clause id="10260">
    <literal><![CDATA[
      K(x,((x \ 1) * y) \ z) = K(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[hyper(63,a,9863,a,b,10256,a)].">
      <j1 rule="hyper" parents="63 9863 10256"/>
    </justification>
  </clause>

  <clause id="10261">
    <literal><![CDATA[
      K(x,y \ ((x \ 1) \ z)) = K(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[hyper(63,a,9489,a(flip),b,10260,a)].">
      <j1 rule="hyper" parents="63 9489 10260"/>
    </justification>
  </clause>

  <clause id="10262">
    <literal><![CDATA[
      K(T(x,y),y \ (z * T(x,y))) = K(x,z / ((x \ 1) * y))
    ]]></literal>
    <justification jstring="[hyper(63,a,8704,a(flip),b,10260,a),flip(a)].">
      <j1 rule="hyper" parents="63 8704 10260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10263">
    <literal><![CDATA[
      K(x,x \ ((x \ 1) \ y)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,4394,a(flip),b,10261,a),flip(a)].">
      <j1 rule="hyper" parents="333 4394 10261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10264">
    <literal><![CDATA[
      K(x,y) * ((x \ 1) \ y) = x * (((x \ 1) \ y) / x)
    ]]></literal>
    <justification jstring="[hyper(125,a,10263,a(flip),b,4535,a)].">
      <j1 rule="hyper" parents="125 10263 4535"/>
    </justification>
  </clause>

  <clause id="10267">
    <literal><![CDATA[
      (x \ 1) / (x \ K(x,(y * z) \ (u * x))) = K((y * (z / x)) \ u,x)
    ]]></literal>
    <justification jstring="[para(10254(a,1),4688(a,1,2,2))].">
      <j1 rule="para" parents="10254 4688"/>
    </justification>
  </clause>

  <clause id="10268">
    <literal><![CDATA[
      L(K(x,(y * z) \ ((u \ w) * x)),u \ w,u) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(u * (y * (z / x))) \ w) = v5
    ]]></literal>
    <justification jstring="[para(10254(a,1),9697(a,1,1))].">
      <j1 rule="para" parents="10254 9697"/>
    </justification>
  </clause>

  <clause id="10269">
    <literal><![CDATA[
      (T(x,y) \ 1) \ y = x * (((x \ 1) \ y) / x)
    ]]></literal>
    <justification jstring="[hyper(63,a,5242,a(flip),b,10264,a)].">
      <j1 rule="hyper" parents="63 5242 10264"/>
    </justification>
  </clause>

  <clause id="10270">
    <literal><![CDATA[
      L(K(x,x * y),y,z) = K(x,z \ ((z * y) * x))
    ]]></literal>
    <justification jstring="[para(9479(a,1),10259(a,1,1))].">
      <j1 rule="para" parents="9479 10259"/>
    </justification>
  </clause>

  <clause id="10271">
    <literal><![CDATA[
      L(K(x,x * (y \ z)),y \ z,y) = K(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[para(10(a,1),10270(a,2,2,2,1))].">
      <j1 rule="para" parents="10 10270"/>
    </justification>
  </clause>

  <clause id="10272">
    <literal><![CDATA[
      L(K(x,y * x),y,z) = K(x,z \ ((z * y) * x))
    ]]></literal>
    <justification jstring="[para(4636(a,2),10270(a,1,1))].">
      <j1 rule="para" parents="4636 10270"/>
    </justification>
  </clause>

  <clause id="10273">
    <literal><![CDATA[
      K(x,y \ ((y * z) * x)) * a(y,z,K(x,x * z)) = K(x,x * z)
    ]]></literal>
    <justification jstring="[para(10270(a,1),9744(a,1,1))].">
      <j1 rule="para" parents="10270 9744"/>
    </justification>
  </clause>

  <clause id="10274">
    <literal><![CDATA[
      L(K(L(x,y,z),y * L(x,y,z)),y,z) = K(L(x,y,z),y * x)
    ]]></literal>
    <justification jstring="[para(310(a,1),10272(a,2,2))].">
      <j1 rule="para" parents="310 10272"/>
    </justification>
  </clause>

  <clause id="10275">
    <literal><![CDATA[
      K(x,(y * T(x,z)) / z) = K(x,y / ((x \ 1) * z))
    ]]></literal>
    <justification jstring="[hyper(7073,a,10262,a)].">
      <j1 rule="hyper" parents="7073 10262"/>
    </justification>
  </clause>

  <clause id="10276">
    <literal><![CDATA[
      K(x,y / ((x \ 1) * z)) = K(x,y / (x \ z))
    ]]></literal>
    <justification jstring="[hyper(9685,a,10275,a),flip(a)].">
      <j1 rule="hyper" parents="9685 10275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10277">
    <literal><![CDATA[
      K(x,(((x \ 1) * y) * z) / (x \ z)) = K(T(x,x \ 1),R(y,x \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,6930,a(flip),b,10276,a),flip(a)].">
      <j1 rule="hyper" parents="63 6930 10276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10279">
    <literal><![CDATA[
      L(K(L(x,y,z),y * L(x,y,z)),y,z) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(333,a,6547,a(flip),b,10274,a),flip(a)].">
      <j1 rule="hyper" parents="333 6547 10274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10281">
    <literal><![CDATA[
      K(x,x * y) * K(z \ ((z * y) * x),x) = a(z,y,K(x,x * y))
    ]]></literal>
    <justification jstring="[hyper(34,a,4573,a,b,10273,a)].">
      <j1 rule="hyper" parents="34 4573 10273"/>
    </justification>
  </clause>

  <clause id="10282">
    <literal><![CDATA[
      L(K(x * y,x),y,z) = K(z \ ((z * y) * x),x)
    ]]></literal>
    <justification jstring="[hyper(34,a,9729,a,b,10281,a)].">
      <j1 rule="hyper" parents="34 9729 10281"/>
    </justification>
  </clause>

  <clause id="10283">
    <literal><![CDATA[
      L(K(x * (y \ z),x),y \ z,y) = K(y \ (z * x),x)
    ]]></literal>
    <justification jstring="[para(10(a,1),10282(a,2,1,2,1))].">
      <j1 rule="para" parents="10 10282"/>
    </justification>
  </clause>

  <clause id="10284">
    <literal><![CDATA[
      K(x,(((K(y,x \ z) / y) \ 1) * z) \ (u * x)) = K(x,((x \ z) * y) \ u)
    ]]></literal>
    <justification jstring="[para(4727(a,2),10257(a,1,2,1,1))].">
      <j1 rule="para" parents="4727 10257"/>
    </justification>
  </clause>

  <clause id="10285">
    <literal><![CDATA[
      K((x * (y / z)) \ u,z) = K((x * y) \ (u * z),z)
    ]]></literal>
    <justification jstring="[hyper(4730,a,10267,a),flip(a)].">
      <j1 rule="hyper" parents="4730 10267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10286">
    <literal><![CDATA[
      K((x * (y \ z)) \ u,y) = K((x * z) \ (u * y),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,7605,a(flip),b,10285,a)].">
      <j1 rule="hyper" parents="63 7605 10285"/>
    </justification>
  </clause>

  <clause id="10287">
    <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(10286(a,1),9014(a,1,1,2,2))].">
      <j1 rule="para" parents="10286 9014"/>
    </justification>
  </clause>

  <clause id="10288">
    <literal><![CDATA[
      K(x,(((x \ 1) * y) * z) / (x \ z)) = K(x,R(y,x \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(333,a,3350,a(flip),b,10277,a),flip(a)].">
      <j1 rule="hyper" parents="333 3350 10277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10289">
    <literal><![CDATA[
      K(x,(y / (((x \ 1) * z) * y)) \ x) = K(x,R(z,x \ 1,y))
    ]]></literal>
    <justification jstring="[hyper(9631,a,10288,a)].">
      <j1 rule="hyper" parents="9631 10288"/>
    </justification>
  </clause>

  <clause id="10290">
    <literal><![CDATA[
      R(K(x,(x \ 1) \ y),y,z) = K(x,(z / (((x \ 1) * ((x \ 1) \ y)) * z)) \ x)
    ]]></literal>
    <justification jstring="[hyper(333,a,8063,a,b,10289,a)].">
      <j1 rule="hyper" parents="333 8063 10289"/>
    </justification>
  </clause>

  <clause id="10291">
    <literal><![CDATA[
      K(x,((1 / (K(y,x \ z) / y)) * z) \ (u * x)) = K(x,((x \ z) * y) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,4802,a,b,10284,a)].">
      <j1 rule="hyper" parents="63 4802 10284"/>
    </justification>
  </clause>

  <clause id="10292">
    <literal><![CDATA[
      R(K(x,x * y),y,z) = K(x,(z / (((x \ 1) * ((x \ 1) \ y)) * z)) \ x)
    ]]></literal>
    <justification jstring="[para(9479(a,1),10290(a,1,1))].">
      <j1 rule="para" parents="9479 10290"/>
    </justification>
  </clause>

  <clause id="10293">
    <literal><![CDATA[
      R(K(x,x * y),y,z) = K(x,(z / (y * z)) \ x)
    ]]></literal>
    <justification jstring="[para(10(a,1),10292(a,2,2,1,2,1))].">
      <j1 rule="para" parents="10 10292"/>
    </justification>
  </clause>

  <clause id="10294">
    <literal><![CDATA[
      K(x,R(y \ 1,y,z) \ x) = R(K(x,x * y),y,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,4874,a,b,10293,a)].">
      <j1 rule="hyper" parents="333 4874 10293"/>
    </justification>
  </clause>

  <clause id="10296">
    <literal><![CDATA[
      T(x,R(y \ 1,y,z) \ x) = x * R(K(x,x * y),y,z)
    ]]></literal>
    <justification jstring="[hyper(126,a,10294,a(flip),b,4215,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="126 10294 4215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10297">
    <literal><![CDATA[
      K(x,(y * (z * (u / x))) \ w) = K(x,(y * (z * u)) \ (w * x))
    ]]></literal>
    <justification jstring="[hyper(10268,a,10255,a)].">
      <j1 rule="hyper" parents="10268 10255"/>
    </justification>
  </clause>

  <clause id="10298">
    <literal><![CDATA[
      K(x,(y * (z / x)) \ (u \ (y * (z / x)))) = K(x,(u * (y * z)) \ ((y * (x \ z)) * x))
    ]]></literal>
    <justification jstring="[hyper(63,a,9663,a(flip),b,10297,a)].">
      <j1 rule="hyper" parents="63 9663 10297"/>
    </justification>
  </clause>

  <clause id="10299">
    <literal><![CDATA[
      K(x,(y * (z * u)) \ ((z * (x \ u)) * x)) = K(x,T(y \ 1,z * (u / x)))
    ]]></literal>
    <justification jstring="[hyper(7977,a,10298,a),flip(a)].">
      <j1 rule="hyper" parents="7977 10298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10300">
    <literal><![CDATA[
      K(x,(y * (z * u)) \ ((z * (x \ u)) * x)) = K(x,T(y \ 1,z * u))
    ]]></literal>
    <justification jstring="[hyper(333,a,9804,a(flip),b,10299,a),flip(a)].">
      <j1 rule="hyper" parents="333 9804 10299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10301">
    <literal><![CDATA[
      K(x,T((y / (z * u)) \ 1,z * u)) = K(x,y \ ((z * (x \ u)) * x))
    ]]></literal>
    <justification jstring="[para(12(a,1),10300(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12 10300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10302">
    <literal><![CDATA[
      K(x,y \ ((z * (x \ u)) * x)) = K(x,((z * u) \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,6492,a(flip),b,10301,a),flip(a)].">
      <j1 rule="hyper" parents="63 6492 10301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10303">
    <literal><![CDATA[
      K(x,y \ ((z * (x \ u)) * x)) = K(x,y \ (z * u))
    ]]></literal>
    <justification jstring="[hyper(333,a,5766,a(flip),b,10302,a),flip(a)].">
      <j1 rule="hyper" parents="333 5766 10302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10304">
    <literal><![CDATA[
      K(x,y \ ((x \ y) * z)) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,9612,a(flip),b,10303,a),flip(a)].">
      <j1 rule="hyper" parents="63 9612 10303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10305">
    <literal><![CDATA[
      K(x,x \ (y * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (x \ z)) = u
    ]]></literal>
    <justification jstring="[para(10303(a,1),4479(a,1))].">
      <j1 rule="para" parents="10303 4479"/>
    </justification>
  </clause>

  <clause id="10306">
    <literal><![CDATA[
      L(K(x,x \ y),y,x \ z) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,9559,a,b,10304,a)].">
      <j1 rule="hyper" parents="63 9559 10304"/>
    </justification>
  </clause>

  <clause id="10308">
    <literal><![CDATA[
      L(K(x,x \ y),y,z) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(9(a,1),10306(a,1,3))].">
      <j1 rule="para" parents="9 10306"/>
    </justification>
  </clause>

  <clause id="10310">
    <literal><![CDATA[
      K(x,y \ (x \ (y * z))) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,9542,a(flip),b,10308,a)].">
      <j1 rule="hyper" parents="63 9542 10308"/>
    </justification>
  </clause>

  <clause id="10311">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (y * (u * (z / u)))) = K(u,u \ L(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,9088,a(flip),b,10308,a)].">
      <j1 rule="hyper" parents="63 9088 10308"/>
    </justification>
  </clause>

  <clause id="10312">
    <literal><![CDATA[
      a(x,y,K(z \ y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(120,a,10308,a(flip),b,9731,a),flip(a)].">
      <j1 rule="hyper" parents="120 10308 9731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10313">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (y * (u * (z / u)))) = L(K(u,u \ z),y * z,x)
    ]]></literal>
    <justification jstring="[para(10308(a,1),4668(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10308 4668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10314">
    <literal><![CDATA[
      L(K(x \ y,x),y,z) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(52,a,10312,a)].">
      <j1 rule="hyper" parents="52 10312"/>
    </justification>
  </clause>

  <clause id="10315">
    <literal><![CDATA[
      K((x * y) \ z,y) = K(y \ (x \ z),y)
    ]]></literal>
    <justification jstring="[hyper(8475,a,10314,a)].">
      <j1 rule="hyper" parents="8475 10314"/>
    </justification>
  </clause>

  <clause id="10317">
    <literal><![CDATA[
      K((x \ y) \ z,x \ y) = K(y \ (x * z),x \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,6282,a(flip),b,10314,a),flip(a)].">
      <j1 rule="hyper" parents="63 6282 10314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10318">
    <literal><![CDATA[
      (x * y) * K(z \ y,z) = x * ((z \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(126,a,10314,a(flip),b,480,a)].">
      <j1 rule="hyper" parents="126 10314 480"/>
    </justification>
  </clause>

  <clause id="10319">
    <literal><![CDATA[
      (x * y) * L(K(z \ x,z),x,u) = x * (y * K(z \ x,z))
    ]]></literal>
    <justification jstring="[para(10314(a,2),10144(a,1,2))].">
      <j1 rule="para" parents="10314 10144"/>
    </justification>
  </clause>

  <clause id="10321">
    <literal><![CDATA[
      T(x,y \ (x \ (y * z))) = T(x,x \ z)
    ]]></literal>
    <justification jstring="[hyper(124,a,10310,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 10310 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10322">
    <literal><![CDATA[
      K(x,y \ (x \ z)) = K(x,x \ (y \ z))
    ]]></literal>
    <justification jstring="[para(10(a,1),10310(a,1,2,2,2))].">
      <j1 rule="para" parents="10 10310"/>
    </justification>
  </clause>

  <clause id="10323">
    <literal><![CDATA[
      K(x,x \ (y \ (x * z))) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(70(a,1),10310(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="70 10310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10324">
    <literal><![CDATA[
      (x * y) * K(z,z \ y) = x * (z * (y / z))
    ]]></literal>
    <justification jstring="[para(10310(a,1),9649(a,1,2))].">
      <j1 rule="para" parents="10310 9649"/>
    </justification>
  </clause>

  <clause id="10325">
    <literal><![CDATA[
      K(x \ (y \ (z * x)),x) = K(y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,7484,a(flip),b,10315,a),flip(a)].">
      <j1 rule="hyper" parents="63 7484 10315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10326">
    <literal><![CDATA[
      K(x \ (y \ z),y) = K(y \ (x \ z),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,6555,a(flip),b,10315,a)].">
      <j1 rule="hyper" parents="63 6555 10315"/>
    </justification>
  </clause>

  <clause id="10327">
    <literal><![CDATA[
      K(x \ (y \ z),x) * z = z * K(z / (y * x),x)
    ]]></literal>
    <justification jstring="[para(10315(a,1),6889(a,1,1))].">
      <j1 rule="para" parents="10315 6889"/>
    </justification>
  </clause>

  <clause id="10328">
    <literal><![CDATA[
      K(x,(x * y) \ z) = K(x,x \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(9648,a,10322,a)].">
      <j1 rule="hyper" parents="9648 10322"/>
    </justification>
  </clause>

  <clause id="10329">
    <literal><![CDATA[
      K(x,x \ ((y * (x \ z)) \ u)) = K(x,(y * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,9975,a(flip),b,10322,a),flip(a)].">
      <j1 rule="hyper" parents="63 9975 10322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10330">
    <literal><![CDATA[
      x \ K(y,y \ (x \ 1)) = y * ((x \ 1) / y)
    ]]></literal>
    <justification jstring="[hyper(121,a,10322,a(flip),b,7876,a)].">
      <j1 rule="hyper" parents="121 10322 7876"/>
    </justification>
  </clause>

  <clause id="10331">
    <literal><![CDATA[
      K(x,K(y,z \ (y \ u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z \ u)) = w
    ]]></literal>
    <justification jstring="[para(10322(a,2),7049(a,1,2))].">
      <j1 rule="para" parents="10322 7049"/>
    </justification>
  </clause>

  <clause id="10332">
    <literal><![CDATA[
      K(x,K(y,z \ (y * u))) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[para(10323(a,1),6954(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10323 6954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10333">
    <literal><![CDATA[
      K(x,x \ (y \ (z * x))) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,9611,a(flip),b,10328,a),flip(a)].">
      <j1 rule="hyper" parents="63 9611 10328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10334">
    <literal><![CDATA[
      K(x,x \ (y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (x \ z)) = u
    ]]></literal>
    <justification jstring="[para(10328(a,1),9700(a,1))].">
      <j1 rule="para" parents="10328 9700"/>
    </justification>
  </clause>

  <clause id="10335">
    <literal><![CDATA[
      K(x,K(y,z \ (u * y))) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[para(10333(a,1),6954(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10333 6954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10336">
    <literal><![CDATA[
      R(x,y,K(z \ y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(881,a,10318,a)].">
      <j1 rule="hyper" parents="881 10318"/>
    </justification>
  </clause>

  <clause id="10338">
    <literal><![CDATA[
      R(x,y / z,z) = R(x,z \ y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,8871,a(flip),b,10336,a),flip(a)].">
      <j1 rule="hyper" parents="63 8871 10336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10339">
    <literal><![CDATA[
      R(x,y * z,K(z,y)) = x
    ]]></literal>
    <justification jstring="[para(9(a,1),10336(a,1,3,1))].">
      <j1 rule="para" parents="9 10336"/>
    </justification>
  </clause>

  <clause id="10340">
    <literal><![CDATA[
      R(x,y,T(z,y)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(8655,a,10339,a)].">
      <j1 rule="hyper" parents="8655 10339"/>
    </justification>
  </clause>

  <clause id="10341">
    <literal><![CDATA[
      (x * (y * z)) * K(z,y) = x * (z * y)
    ]]></literal>
    <justification jstring="[para(10339(a,1),545(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10339 545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10343">
    <literal><![CDATA[
      R(x,T(y,z),z) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,7867,a,b,10340,a)].">
      <j1 rule="hyper" parents="63 7867 10340"/>
    </justification>
  </clause>

  <clause id="10344">
    <literal><![CDATA[
      R(x,y,z / y) = R(x,y,y \ z)
    ]]></literal>
    <justification jstring="[para(113(a,1),10340(a,1,3)),flip(a)].">
      <j1 rule="para" parents="113 10340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10345">
    <literal><![CDATA[
      R(x,y,z) * (z * y) = (x * y) * T(z,y)
    ]]></literal>
    <justification jstring="[para(10340(a,1),532(a,1,1))].">
      <j1 rule="para" parents="10340 532"/>
    </justification>
  </clause>

  <clause id="10347">
    <literal><![CDATA[
      R(x,y,K(z,T(u,y))) = R(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(6365(a,2),10340(a,1,3))].">
      <j1 rule="para" parents="6365 10340"/>
    </justification>
  </clause>

  <clause id="10349">
    <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(7618(a,1),10343(a,1,2))].">
      <j1 rule="para" parents="7618 10343"/>
    </justification>
  </clause>

  <clause id="10351">
    <literal><![CDATA[
      ((x * (y / z)) * z) / y = R(x,z \ y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,109,a,b,10338,a)].">
      <j1 rule="hyper" parents="63 109 10338"/>
    </justification>
  </clause>

  <clause id="10352">
    <literal><![CDATA[
      R(K(x,(y / (z / u)) \ x),u \ z,u) = K(x,z / ((x \ y) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,9629,a(flip),b,10338,a),flip(a)].">
      <j1 rule="hyper" parents="63 9629 10338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10353">
    <literal><![CDATA[
      R(K(x,(y / z) / u),z \ y,z) = K(x,y / (u * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,5646,a(flip),b,10338,a),flip(a)].">
      <j1 rule="hyper" parents="63 5646 10338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10354">
    <literal><![CDATA[
      R(x / (y / z),z \ y,z) = (x * z) / y
    ]]></literal>
    <justification jstring="[hyper(63,a,556,a(flip),b,10338,a),flip(a)].">
      <j1 rule="hyper" parents="63 556 10338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10355">
    <literal><![CDATA[
      R(x,y \ z,y) * z = (x * (z / y)) * y
    ]]></literal>
    <justification jstring="[hyper(125,a,10338,a(flip),b,109,a)].">
      <j1 rule="hyper" parents="125 10338 109"/>
    </justification>
  </clause>

  <clause id="10356">
    <literal><![CDATA[
      K(x,L(y,x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(7327,a,10341,a)].">
      <j1 rule="hyper" parents="7327 10341"/>
    </justification>
  </clause>

  <clause id="10357">
    <literal><![CDATA[
      K(L(x,y,z),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(7302,a,10341,a)].">
      <j1 rule="hyper" parents="7302 10341"/>
    </justification>
  </clause>

  <clause id="10358">
    <literal><![CDATA[
      (x / (y * z)) * (z * y) = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(339,a,10341,a),flip(a)].">
      <j1 rule="hyper" parents="339 10341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10359">
    <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(6591(a,1),10341(a,2,2))].">
      <j1 rule="para" parents="6591 10341"/>
    </justification>
  </clause>

  <clause id="10360">
    <literal><![CDATA[
      T(x,L(y,x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(124,a,10356,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 10356 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10361">
    <literal><![CDATA[
      T(x,L(y,x,z)) = x * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(126,a,10356,a(flip),b,4215,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="126 10356 4215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10365">
    <literal><![CDATA[
      K(L(x,y,z),y) = (u * T(y,x)) \ (u * y)
    ]]></literal>
    <justification jstring="[hyper(333,a,5482,a,b,10357,a),flip(a)].">
      <j1 rule="hyper" parents="333 5482 10357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10366">
    <literal><![CDATA[
      L(x,y,z) * K(x,y) = L(T(x,y),y,z)
    ]]></literal>
    <justification jstring="[hyper(126,a,10357,a(flip),b,4283,a)].">
      <j1 rule="hyper" parents="126 10357 4283"/>
    </justification>
  </clause>

  <clause id="10367">
    <literal><![CDATA[
      K(L(x,1 / y,z),y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(2597(a,2),10357(a,1,1))].">
      <j1 rule="para" parents="2597 10357"/>
    </justification>
  </clause>

  <clause id="10372">
    <literal><![CDATA[
      L(x,y,z) * T(y,x) = y * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(126,a,10360,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="126 10360 22"/>
    </justification>
  </clause>

  <clause id="10373">
    <literal><![CDATA[
      T(L(x,y,z),(z * (y * x)) \ ((z * y) * u)) = T(L(x,y,z),L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(524(a,1),10360(a,1,2))].">
      <j1 rule="para" parents="524 10360"/>
    </justification>
  </clause>

  <clause id="10374">
    <literal><![CDATA[
      L(x,y,z) = (z * T(y,x)) \ (z * (T(y,x) * x))
    ]]></literal>
    <justification jstring="[para(10360(a,1),8697(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10360 8697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10375">
    <literal><![CDATA[
      T(x,L(y,x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = u
    ]]></literal>
    <justification jstring="[para(10361(a,2),4285(a,1))].">
      <j1 rule="para" parents="10361 4285"/>
    </justification>
  </clause>

  <clause id="10376">
    <literal><![CDATA[
      K((x * (1 / y)) \ z,y) = K((1 / y) \ (x \ z),y)
    ]]></literal>
    <justification jstring="[para(311(a,1),10367(a,1,1))].">
      <j1 rule="para" parents="311 10367"/>
    </justification>
  </clause>

  <clause id="10377">
    <literal><![CDATA[
      T(x,y \ (x \ (y * z))) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,x \ z) = u
    ]]></literal>
    <justification jstring="[para(7877(a,1),10375(a,1))].">
      <j1 rule="para" parents="7877 10375"/>
    </justification>
  </clause>

  <clause id="10378">
    <literal><![CDATA[
      (x * T(y,z)) / (y * z) = (x * y) / (z * y)
    ]]></literal>
    <justification jstring="[hyper(123,a,5984,a(flip),b,10358,a)].">
      <j1 rule="hyper" parents="123 5984 10358"/>
    </justification>
  </clause>

  <clause id="10379">
    <literal><![CDATA[
      L(x,y,z) * (K(x,y) * u) = L(T(x,y),y,z) * u
    ]]></literal>
    <justification jstring="[para(10366(a,1),3839(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10366 3839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10380">
    <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(10372(a,1),1262(a,1,2,2))].">
      <j1 rule="para" parents="10372 1262"/>
    </justification>
  </clause>

  <clause id="10381">
    <literal><![CDATA[
      (x * T(y,z)) / (y * z) = R(x / z,z,y)
    ]]></literal>
    <justification jstring="[hyper(123,a,152,a(flip),b,10345,a)].">
      <j1 rule="hyper" parents="123 152 10345"/>
    </justification>
  </clause>

  <clause id="10382">
    <literal><![CDATA[
      K((x * y) * T(z,y),z * y) != u
    ]]></literal>
    <literal><![CDATA[
      K((z * y) * R(x,y,z),z * y) = u
    ]]></literal>
    <justification jstring="[para(10345(a,1),7447(a,1,1))].">
      <j1 rule="para" parents="10345 7447"/>
    </justification>
  </clause>

  <clause id="10383">
    <literal><![CDATA[
      R(x / (y / (y * K(z,u))),K(u,z),y * K(z,u)) = (x * (y * K(z,u))) / y
    ]]></literal>
    <justification jstring="[para(5990(a,1),10354(a,1,2))].">
      <j1 rule="para" parents="5990 10354"/>
    </justification>
  </clause>

  <clause id="10384">
    <literal><![CDATA[
      R(x * K(y,z),z \ (z * y),z) = ((x * y) * z) / (z * y)
    ]]></literal>
    <justification jstring="[para(7662(a,1),10354(a,1,1))].">
      <j1 rule="para" parents="7662 10354"/>
    </justification>
  </clause>

  <clause id="10385">
    <literal><![CDATA[
      K(L(x,y,z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(10365(a,2),5488(a,1))].">
      <j1 rule="para" parents="10365 5488"/>
    </justification>
  </clause>

  <clause id="10386">
    <literal><![CDATA[
      K(x,L(y,x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(7326(a,1),10385(a,1))].">
      <j1 rule="para" parents="7326 10385"/>
    </justification>
  </clause>

  <clause id="10387">
    <literal><![CDATA[
      R(R(x,y,x) / x,x,z) = (z * R(x,y,x)) / (z * x)
    ]]></literal>
    <justification jstring="[para(6343(a,1),10381(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6343 10381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10389">
    <literal><![CDATA[
      K(x,((y \ z) \ u) \ y) * K(x,K(y,z \ u)) = K(x,y / ((y \ z) \ u))
    ]]></literal>
    <justification jstring="[para(10332(a,1),9502(a,1,2))].">
      <j1 rule="para" parents="10332 9502"/>
    </justification>
  </clause>

  <clause id="10390">
    <literal><![CDATA[
      K(x,K(y,z \ u)) * K(x,y \ ((y \ z) \ u)) = K(x,((y \ z) \ u) / y)
    ]]></literal>
    <justification jstring="[para(10332(a,1),9503(a,1,1))].">
      <j1 rule="para" parents="10332 9503"/>
    </justification>
  </clause>

  <clause id="10391">
    <literal><![CDATA[
      K(x,K(y,z \ (u * y))) = K(y,K(x,z \ u))
    ]]></literal>
    <justification jstring="[hyper(333,a,6785,a,b,10335,a),flip(a)].">
      <j1 rule="hyper" parents="333 6785 10335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10392">
    <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(1510(a,1),10335(a,1,2,2))].">
      <j1 rule="para" parents="1510 10335"/>
    </justification>
  </clause>

  <clause id="10393">
    <literal><![CDATA[
      K(x,K(y,z \ (u * x))) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(6798,a,10391,a)].">
      <j1 rule="hyper" parents="6798 10391"/>
    </justification>
  </clause>

  <clause id="10394">
    <literal><![CDATA[
      K(x,K(y,z \ (u * x))) = K(x,K(y,u \ z))
    ]]></literal>
    <justification jstring="[hyper(333,a,7167,a,b,10393,a),flip(a)].">
      <j1 rule="hyper" parents="333 7167 10393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10396">
    <literal><![CDATA[
      K(x,K(y,(z * x) \ u)) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(7195,a,10394,a)].">
      <j1 rule="hyper" parents="7195 10394"/>
    </justification>
  </clause>

  <clause id="10397">
    <literal><![CDATA[
      K(x,K(y,(z / x) \ u)) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[para(12(a,1),10396(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="12 10396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10398">
    <literal><![CDATA[
      K(x,K(y,(x \ z) \ u)) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,7523,a(flip),b,10397,a)].">
      <j1 rule="hyper" parents="63 7523 10397"/>
    </justification>
  </clause>

  <clause id="10399">
    <literal><![CDATA[
      K(x,K(y,z \ (x \ u))) = K(x,K(y,u \ z))
    ]]></literal>
    <justification jstring="[hyper(7195,a,10398,a)].">
      <j1 rule="hyper" parents="7195 10398"/>
    </justification>
  </clause>

  <clause id="10400">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z \ u)) = K(x,T(y,(x \ z) \ u))
    ]]></literal>
    <justification jstring="[para(10398(a,1),6761(a,1,2))].">
      <j1 rule="para" parents="10398 6761"/>
    </justification>
  </clause>

  <clause id="10401">
    <literal><![CDATA[
      K(x,K(y,z \ (x \ u))) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(333,a,7167,a,b,10399,a),flip(a)].">
      <j1 rule="hyper" parents="333 7167 10399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10402">
    <literal><![CDATA[
      K((T(x,y) * z) \ u,K(x,w)) = K(x,K(w,u \ z))
    ]]></literal>
    <justification jstring="[hyper(63,a,9767,a,b,10399,a)].">
      <j1 rule="hyper" parents="63 9767 10399"/>
    </justification>
  </clause>

  <clause id="10403">
    <literal><![CDATA[
      K(x,K(y,z \ (x * u))) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[para(9(a,1),10401(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="9 10401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10404">
    <literal><![CDATA[
      L(x,T(y,x),z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,18,a,b,10374,a)].">
      <j1 rule="hyper" parents="333 18 10374"/>
    </justification>
  </clause>

  <clause id="10406">
    <literal><![CDATA[
      L(x,y / x,z) = L(x,x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,4845,a(flip),b,10404,a)].">
      <j1 rule="hyper" parents="63 4845 10404"/>
    </justification>
  </clause>

  <clause id="10409">
    <literal><![CDATA[
      L(x,x \ y,z) = (z * (y / x)) \ (z * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,101,a(flip),b,10406,a),flip(a)].">
      <j1 rule="hyper" parents="63 101 10406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10410">
    <literal><![CDATA[
      (x * y) / L(z,z \ y,x) = x * (y / z)
    ]]></literal>
    <justification jstring="[hyper(197,a,10406,a(flip),b,101,a(flip))].">
      <j1 rule="hyper" parents="197 10406 101"/>
    </justification>
  </clause>

  <clause id="10411">
    <literal><![CDATA[
      K(x,T(L(y,y \ z,u),u * z)) = K(x,(u * z) / (u * (z / y)))
    ]]></literal>
    <justification jstring="[para(10409(a,2),6902(a,1,2,1))].">
      <j1 rule="para" parents="10409 6902"/>
    </justification>
  </clause>

  <clause id="10412">
    <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(10409(a,2),6971(a,1,1,2))].">
      <j1 rule="para" parents="10409 6971"/>
    </justification>
  </clause>

  <clause id="10413">
    <literal><![CDATA[
      T(x * (y / z),L(z,z \ y,x)) = L(z,z \ y,x) \ (x * y)
    ]]></literal>
    <justification jstring="[para(10410(a,1),113(a,1,1))].">
      <j1 rule="para" parents="10410 113"/>
    </justification>
  </clause>

  <clause id="10414">
    <literal><![CDATA[
      T(x,y \ (x \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,x \ (y \ z)) = u
    ]]></literal>
    <justification jstring="[para(10(a,1),10377(a,1,2,2,2))].">
      <j1 rule="para" parents="10 10377"/>
    </justification>
  </clause>

  <clause id="10415">
    <literal><![CDATA[
      K((x / y) \ z,y \ x) = K(x \ (y * z),y \ x)
    ]]></literal>
    <justification jstring="[hyper(7448,a,10317,a)].">
      <j1 rule="hyper" parents="7448 10317"/>
    </justification>
  </clause>

  <clause id="10416">
    <literal><![CDATA[
      K(L(x,y,z),L(x,y,z) \ ((u * (x \ (1 / L(x,y,z)))) \ w)) = K(L(x,y,z),(u * (1 / x)) \ w)
    ]]></literal>
    <justification jstring="[para(5387(a,1),10329(a,1,2,2,1,2))].">
      <j1 rule="para" parents="5387 10329"/>
    </justification>
  </clause>

  <clause id="10417">
    <literal><![CDATA[
      K(L(x,y,z),x \ ((u * (x \ w)) \ v5)) = L(K(x,(u * w) \ v5),y * x,z)
    ]]></literal>
    <justification jstring="[para(10329(a,1),6298(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10329 6298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10418">
    <literal><![CDATA[
      L(x,y,z) * L(K(x,y) * u,x,y) = L(T(x,y),y,z) * L(u,x,y)
    ]]></literal>
    <justification jstring="[para(10147(a,2),10379(a,1,2))].">
      <j1 rule="para" parents="10147 10379"/>
    </justification>
  </clause>

  <clause id="10419">
    <literal><![CDATA[
      K(x,K(y,(T(x,z) * u) \ w)) = K(x,K(y,w \ u))
    ]]></literal>
    <justification jstring="[hyper(6825,a,10402,a)].">
      <j1 rule="hyper" parents="6825 10402"/>
    </justification>
  </clause>

  <clause id="10420">
    <literal><![CDATA[
      K(x \ (y * z),y \ x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z / (x / y),y \ x) = u
    ]]></literal>
    <justification jstring="[para(10415(a,1),7209(a,1))].">
      <j1 rule="para" parents="10415 7209"/>
    </justification>
  </clause>

  <clause id="10421">
    <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(9149(a,1),10419(a,1,2,2))].">
      <j1 rule="para" parents="9149 10419"/>
    </justification>
  </clause>

  <clause id="10422">
    <literal><![CDATA[
      (x * R(y,z,y)) / (x * y) = R(a(y,z,y),y,x)
    ]]></literal>
    <justification jstring="[para(8213(a,1),10387(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8213 10387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10423">
    <literal><![CDATA[
      R(a(x,y,x),x,z) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,9324,a(flip),b,10422,a),flip(a)].">
      <j1 rule="hyper" parents="63 9324 10422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10425">
    <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(63,a,542,a,b,10423,a)].">
      <j1 rule="hyper" parents="63 542 10423"/>
    </justification>
  </clause>

  <clause id="10426">
    <literal><![CDATA[
      K(x,T(y,(x \ z) \ u)) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(6764,a,10400,a),flip(a)].">
      <j1 rule="hyper" parents="6764 10400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10427">
    <literal><![CDATA[
      K(x,T(y,z \ (x * u))) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,7199,a(flip),b,10426,a)].">
      <j1 rule="hyper" parents="63 7199 10426"/>
    </justification>
  </clause>

  <clause id="10428">
    <literal><![CDATA[
      K(x,T(x \ y,y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(x \ y,z)) = u
    ]]></literal>
    <justification jstring="[para(10426(a,1),6364(a,1))].">
      <j1 rule="para" parents="10426 6364"/>
    </justification>
  </clause>

  <clause id="10429">
    <literal><![CDATA[
      K(x,T(y,z \ (x \ u))) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[para(10(a,1),10427(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="10 10427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10430">
    <literal><![CDATA[
      K(x,T(T(x \ y,z),u \ y)) = K(x,T(T(x \ y,z),u))
    ]]></literal>
    <justification jstring="[hyper(7587,a,10429,a),flip(a)].">
      <j1 rule="hyper" parents="7587 10429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10431">
    <literal><![CDATA[
      K(x,T(T(x \ y,z),y \ u)) = K(x,T(T(x \ y,z),u))
    ]]></literal>
    <justification jstring="[hyper(7286,a,10430,a)].">
      <j1 rule="hyper" parents="7286 10430"/>
    </justification>
  </clause>

  <clause id="10432">
    <literal><![CDATA[
      K(x,T(T(x \ y,z),y * u)) = K(x,T(T(x \ y,z),u))
    ]]></literal>
    <justification jstring="[para(9(a,1),10431(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 10431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10433">
    <literal><![CDATA[
      L(K(x,T(T(x \ y,z),z)),z,y) = (y * (K(x,x \ y) * z)) / (y * z)
    ]]></literal>
    <justification jstring="[para(10432(a,1),7901(a,1,1))].">
      <j1 rule="para" parents="10432 7901"/>
    </justification>
  </clause>

  <clause id="10434">
    <literal><![CDATA[
      x * (K(y,x) * ((z \ y) * z)) = y * (x * K(z \ y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,10121,a(flip),b,10319,a)].">
      <j1 rule="hyper" parents="63 10121 10319"/>
    </justification>
  </clause>

  <clause id="10435">
    <literal><![CDATA[
      K(x,y) * (y * ((z \ x) * z)) = x * (y * K(z \ x,z))
    ]]></literal>
    <justification jstring="[hyper(4918,a,10434,a)].">
      <j1 rule="hyper" parents="4918 10434"/>
    </justification>
  </clause>

  <clause id="10437">
    <literal><![CDATA[
      (x * K(y \ z,y)) * z = x * ((y \ z) * y)
    ]]></literal>
    <justification jstring="[hyper(34,a,9756,a,b,10435,a)].">
      <j1 rule="hyper" parents="34 9756 10435"/>
    </justification>
  </clause>

  <clause id="10438">
    <literal><![CDATA[
      R(x,K(y \ z,y),z) = x
    ]]></literal>
    <justification jstring="[hyper(4196,a,10437,a)].">
      <j1 rule="hyper" parents="4196 10437"/>
    </justification>
  </clause>

  <clause id="10439">
    <literal><![CDATA[
      R(x,K(y,y \ z),z) = x
    ]]></literal>
    <justification jstring="[para(4377(a,1),10438(a,1,2))].">
      <j1 rule="para" parents="4377 10438"/>
    </justification>
  </clause>

  <clause id="10440">
    <literal><![CDATA[
      (x * K(y,y \ z)) * z = x * (y * (z / y))
    ]]></literal>
    <justification jstring="[para(10439(a,1),4633(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10439 4633"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10441">
    <literal><![CDATA[
      (x * K(y,y \ z)) * z = (x * z) * K(y,y \ z)
    ]]></literal>
    <justification jstring="[hyper(333,a,10324,a,b,10440,a),flip(a)].">
      <j1 rule="hyper" parents="333 10324 10440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10442">
    <literal><![CDATA[
      (x * K(y,y \ z)) \ (x * (y * (z / y))) = z
    ]]></literal>
    <justification jstring="[hyper(129,a,10440,a)].">
      <j1 rule="hyper" parents="129 10440"/>
    </justification>
  </clause>

  <clause id="10443">
    <literal><![CDATA[
      L(x,K(y,y \ x),z) = x
    ]]></literal>
    <justification jstring="[hyper(4635,a,10442,a)].">
      <j1 rule="hyper" parents="4635 10442"/>
    </justification>
  </clause>

  <clause id="10444">
    <literal><![CDATA[
      L(x * y,K(y,x),z) = x * y
    ]]></literal>
    <justification jstring="[para(4394(a,1),10443(a,1,2))].">
      <j1 rule="para" parents="4394 10443"/>
    </justification>
  </clause>

  <clause id="10445">
    <literal><![CDATA[
      (x * (y * z)) / (z * y) = x * K(y,z)
    ]]></literal>
    <justification jstring="[para(10444(a,1),4204(a,1,2))].">
      <j1 rule="para" parents="10444 4204"/>
    </justification>
  </clause>

  <clause id="10446">
    <literal><![CDATA[
      (x / (y * z)) * K(y,z) = x / (z * y)
    ]]></literal>
    <justification jstring="[hyper(422,a,10445,a),flip(a)].">
      <j1 rule="hyper" parents="422 10445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10448">
    <literal><![CDATA[
      ((x / y) * (z * y)) / (y * z) = x / T(y,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,5450,a(flip),b,10445,a),flip(a)].">
      <j1 rule="hyper" parents="333 5450 10445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10449">
    <literal><![CDATA[
      (x * y) * T(z * K(y,x),x * y) = z * (y * x)
    ]]></literal>
    <justification jstring="[hyper(291,a,10445,a)].">
      <j1 rule="hyper" parents="291 10445"/>
    </justification>
  </clause>

  <clause id="10450">
    <literal><![CDATA[
      (x * K(y,z)) * (z * y) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (x * (y * z)) = w
    ]]></literal>
    <justification jstring="[para(10445(a,1),414(a,1,1))].">
      <j1 rule="para" parents="10445 414"/>
    </justification>
  </clause>

  <clause id="10451">
    <literal><![CDATA[
      (x * K(y,z)) / (z * y) = (x / (z * y)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(10358(a,1),10445(a,1,1))].">
      <j1 rule="para" parents="10358 10445"/>
    </justification>
  </clause>

  <clause id="10453">
    <literal><![CDATA[
      (x / (y * z)) * (z * K(y,z)) = (x / (z * y)) * z
    ]]></literal>
    <justification jstring="[hyper(125,a,10446,a(flip),b,7669,a)].">
      <j1 rule="hyper" parents="125 10446 7669"/>
    </justification>
  </clause>

  <clause id="10454">
    <literal><![CDATA[
      (x / y) * K(y / z,z) = x / (z * (y / z))
    ]]></literal>
    <justification jstring="[para(12(a,1),10446(a,1,1,2))].">
      <j1 rule="para" parents="12 10446"/>
    </justification>
  </clause>

  <clause id="10455">
    <literal><![CDATA[
      K(x,y / (z * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (x * z)) = u
    ]]></literal>
    <justification jstring="[para(10446(a,1),7456(a,1,2))].">
      <j1 rule="para" parents="10446 7456"/>
    </justification>
  </clause>

  <clause id="10456">
    <literal><![CDATA[
      (x / T(y,z)) * (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      (x / y) * (z * y) = u
    ]]></literal>
    <justification jstring="[para(10448(a,1),264(a,1,1)),flip(b)].">
      <j1 rule="para" parents="10448 264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10457">
    <literal><![CDATA[
      1 / ((x * ((x / y) \ 1)) / x) = x / (x * (y / x))
    ]]></literal>
    <justification jstring="[hyper(63,a,8041,a,b,10454,a)].">
      <j1 rule="hyper" parents="63 8041 10454"/>
    </justification>
  </clause>

  <clause id="10458">
    <literal><![CDATA[
      (x / y) * K(z \ y,z) = x / (z * (y / z))
    ]]></literal>
    <justification jstring="[para(4375(a,1),10454(a,1,2))].">
      <j1 rule="para" parents="4375 10454"/>
    </justification>
  </clause>

  <clause id="10459">
    <literal><![CDATA[
      R(K(x,x \ y),z,y) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(9896,a,10441,a)].">
      <j1 rule="hyper" parents="9896 10441"/>
    </justification>
  </clause>

  <clause id="10461">
    <literal><![CDATA[
      (x * (y * z)) * K(z,L(y,z,x)) = (y * z) * T(x * K(z,y),y * z)
    ]]></literal>
    <justification jstring="[hyper(333,a,7301,a,b,10449,a)].">
      <j1 rule="hyper" parents="333 7301 10449"/>
    </justification>
  </clause>

  <clause id="10462">
    <literal><![CDATA[
      (x * ((x / y) \ 1)) / x = (x / (x * (y / x))) \ 1
    ]]></literal>
    <justification jstring="[hyper(192,a,10457,a),flip(a)].">
      <j1 rule="hyper" parents="192 10457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10463">
    <literal><![CDATA[
      x / (x * (((y / x) \ 1) \ 1)) = ((x * ((x / y) \ 1)) / x) \ 1
    ]]></literal>
    <justification jstring="[para(10462(a,2),2824(a,2,1))].">
      <j1 rule="para" parents="10462 2824"/>
    </justification>
  </clause>

  <clause id="10464">
    <literal><![CDATA[
      ((x * y) * z) / (z * y) = R(x * K(y,z),y,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),10384(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9 10384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10465">
    <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(6390(a,1),10464(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6390 10464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10466">
    <literal><![CDATA[
      ((x * K(y,z)) * z) \ (x * (y * z)) = L(y,z,x * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(10450,a,97,a(flip))].">
      <j1 rule="hyper" parents="10450 97"/>
    </justification>
  </clause>

  <clause id="10467">
    <literal><![CDATA[
      (x * (y * K(z,y))) \ (x * (z * y)) = L(z,y,x * K(z,y))
    ]]></literal>
    <justification jstring="[para(5417(a,1),10466(a,1,1))].">
      <j1 rule="para" parents="5417 10466"/>
    </justification>
  </clause>

  <clause id="10468">
    <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(6365(a,2),10349(a,1,2))].">
      <j1 rule="para" parents="6365 10349"/>
    </justification>
  </clause>

  <clause id="10469">
    <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(10392(a,2),7195(a,1))].">
      <j1 rule="para" parents="10392 7195"/>
    </justification>
  </clause>

  <clause id="10474">
    <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(8735(a,2),10463(a,2,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8735 10463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10475">
    <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(10468(a,1),8828(a,2,1))].">
      <j1 rule="para" parents="10468 8828"/>
    </justification>
  </clause>

  <clause id="10477">
    <literal><![CDATA[
      K(x,L(T(y,z * u),y \ u,z)) = K(x,(z * u) / (z * (u / y)))
    ]]></literal>
    <justification jstring="[para(25(a,2),10411(a,1,2))].">
      <j1 rule="para" parents="25 10411"/>
    </justification>
  </clause>

  <clause id="10478">
    <literal><![CDATA[
      L(K(x,x \ y),z * y,u) = K(x,x \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,10311,a(flip),b,10313,a),flip(a)].">
      <j1 rule="hyper" parents="63 10311 10313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10480">
    <literal><![CDATA[
      (x * (K(y,y \ x) * z)) / (x * z) = L(K(y,y \ x),z,x)
    ]]></literal>
    <justification jstring="[para(6900(a,1),10433(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6900 10433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10481">
    <literal><![CDATA[
      K(x,(y * z) / (y * ((x \ y) \ z))) = L(K(x,x \ y),z,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,9939,a,b,10480,a)].">
      <j1 rule="hyper" parents="63 9939 10480"/>
    </justification>
  </clause>

  <clause id="10483">
    <literal><![CDATA[
      R(K(x,x \ y),z,T(y,z)) = L(K(x,x \ y),z,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,10200,a(flip),b,10481,a)].">
      <j1 rule="hyper" parents="63 10200 10481"/>
    </justification>
  </clause>

  <clause id="10484">
    <literal><![CDATA[
      R(K(x,x \ y),z,y) = L(K(x,x \ y),z,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,10340,a(flip),b,10483,a)].">
      <j1 rule="hyper" parents="63 10340 10483"/>
    </justification>
  </clause>

  <clause id="10485">
    <literal><![CDATA[
      L(K(x,x \ y),z,y) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,10459,a(flip),b,10484,a),flip(a)].">
      <j1 rule="hyper" parents="63 10459 10484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10487">
    <literal><![CDATA[
      K(x,x \ L(y,z,y)) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,10478,a(flip),b,10485,a)].">
      <j1 rule="hyper" parents="63 10478 10485"/>
    </justification>
  </clause>

  <clause id="10488">
    <literal><![CDATA[
      L(K(x,y),T(z,y * x),y * x) = K(x,L(y,x,z))
    ]]></literal>
    <justification jstring="[hyper(8334,a,10461,a)].">
      <j1 rule="hyper" parents="8334 10461"/>
    </justification>
  </clause>

  <clause id="10489">
    <literal><![CDATA[
      K(x,L(y,x,((y * x) * z) / (y * x))) = L(K(x,y),z,y * x)
    ]]></literal>
    <justification jstring="[para(238(a,1),10488(a,1,2)),flip(a)].">
      <j1 rule="para" parents="238 10488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10490">
    <literal><![CDATA[
      L(K(x,y),z,y * x) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(10386,a,10489,a),flip(a)].">
      <j1 rule="hyper" parents="10386 10489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10492">
    <literal><![CDATA[
      K(x,R(y,x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,9943,a(flip),b,10490,a)].">
      <j1 rule="hyper" parents="63 9943 10490"/>
    </justification>
  </clause>

  <clause id="10494">
    <literal><![CDATA[
      T(x,R(y,x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(124,a,10492,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 10492 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10495">
    <literal><![CDATA[
      K(R(x,y,z),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,7965,a,b,10492,a)].">
      <j1 rule="hyper" parents="63 7965 10492"/>
    </justification>
  </clause>

  <clause id="10496">
    <literal><![CDATA[
      K(x,y / (z * x)) = K(x,x \ (y / z))
    ]]></literal>
    <justification jstring="[hyper(63,a,8461,a(flip),b,10492,a)].">
      <j1 rule="hyper" parents="63 8461 10492"/>
    </justification>
  </clause>

  <clause id="10497">
    <literal><![CDATA[
      K(x,R(R(y,x,z),u,w)) = K(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[para(31(a,1),10492(a,1,2))].">
      <j1 rule="para" parents="31 10492"/>
    </justification>
  </clause>

  <clause id="10499">
    <literal><![CDATA[
      K(1 / x,T(y / (1 / x),z)) = K(1 / x,T(y * x,z))
    ]]></literal>
    <justification jstring="[para(663(a,1),10492(a,1,2)),flip(a)].">
      <j1 rule="para" parents="663 10492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10500">
    <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(562(a,1),10494(a,1,2))].">
      <j1 rule="para" parents="562 10494"/>
    </justification>
  </clause>

  <clause id="10502">
    <literal><![CDATA[
      K(R(x,y,z),y) = K(u \ (u * x),y)
    ]]></literal>
    <justification jstring="[hyper(333,a,705,a,b,10495,a),flip(a)].">
      <j1 rule="hyper" parents="333 705 10495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10503">
    <literal><![CDATA[
      K(x / (y * z),z) = K(z \ (x / y),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,9086,a(flip),b,10495,a)].">
      <j1 rule="hyper" parents="63 9086 10495"/>
    </justification>
  </clause>

  <clause id="10505">
    <literal><![CDATA[
      K(x,y) / R(x,y,y \ 1) = 1 / ((y * x) * (y \ 1))
    ]]></literal>
    <justification jstring="[para(10495(a,1),4665(a,1,1))].">
      <j1 rule="para" parents="10495 4665"/>
    </justification>
  </clause>

  <clause id="10506">
    <literal><![CDATA[
      K(R(x,y,z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(10502(a,2),4614(a,1))].">
      <j1 rule="para" parents="10502 4614"/>
    </justification>
  </clause>

  <clause id="10507">
    <literal><![CDATA[
      K(x,R(y,x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(7965(a,1),10506(a,1))].">
      <j1 rule="para" parents="7965 10506"/>
    </justification>
  </clause>

  <clause id="10508">
    <literal><![CDATA[
      K(x,y / (z * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ (y / z)) = u
    ]]></literal>
    <justification jstring="[para(8461(a,1),10507(a,1))].">
      <j1 rule="para" parents="8461 10507"/>
    </justification>
  </clause>

  <clause id="10509">
    <literal><![CDATA[
      K(x,y / (x * z)) = K(x,x \ (y / z))
    ]]></literal>
    <justification jstring="[hyper(10455,a,10496,a)].">
      <j1 rule="hyper" parents="10455 10496"/>
    </justification>
  </clause>

  <clause id="10511">
    <literal><![CDATA[
      K(x,x \ ((x * y) / z)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(63,a,9637,a(flip),b,10496,a),flip(a)].">
      <j1 rule="hyper" parents="63 9637 10496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10512">
    <literal><![CDATA[
      K(x,y / ((z * x) * u)) = K(x,x \ (y / (z * u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,9070,a(flip),b,10496,a)].">
      <j1 rule="hyper" parents="63 9070 10496"/>
    </justification>
  </clause>

  <clause id="10514">
    <literal><![CDATA[
      K((x \ y) / z,x) = K(x \ (y / z),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,9672,a,b,10503,a)].">
      <j1 rule="hyper" parents="63 9672 10503"/>
    </justification>
  </clause>

  <clause id="10515">
    <literal><![CDATA[
      K(x / (y * z),y) = K(y \ (x / z),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,7791,a(flip),b,10503,a)].">
      <j1 rule="hyper" parents="63 7791 10503"/>
    </justification>
  </clause>

  <clause id="10516">
    <literal><![CDATA[
      K(x \ (y \ z),x) * z = z * K(x \ (z / y),x)
    ]]></literal>
    <justification jstring="[para(10503(a,1),10327(a,2,2))].">
      <j1 rule="para" parents="10503 10327"/>
    </justification>
  </clause>

  <clause id="10517">
    <literal><![CDATA[
      x * K(x,x \ (y / (z * u))) = T(x,y / ((x * z) * u))
    ]]></literal>
    <justification jstring="[para(10509(a,1),9077(a,1,2))].">
      <j1 rule="para" parents="10509 9077"/>
    </justification>
  </clause>

  <clause id="10518">
    <literal><![CDATA[
      K(x,x \ ((y \ 1) \ (x * z))) = K(x,z / T(y \ 1,y * (x * z)))
    ]]></literal>
    <justification jstring="[para(3934(a,1),10511(a,1,2,2))].">
      <j1 rule="para" parents="3934 10511"/>
    </justification>
  </clause>

  <clause id="10519">
    <literal><![CDATA[
      K(x \ (y / z),x) * z = z * K(z \ (x \ y),x)
    ]]></literal>
    <justification jstring="[para(10514(a,1),6476(a,1,1))].">
      <j1 rule="para" parents="10514 6476"/>
    </justification>
  </clause>

  <clause id="10520">
    <literal><![CDATA[
      R(K(x,R(y,x,z)),(y * x) * z,u) = K(x,R(y,x * z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,5656,a,b,10497,a)].">
      <j1 rule="hyper" parents="63 5656 10497"/>
    </justification>
  </clause>

  <clause id="10522">
    <literal><![CDATA[
      K(x,y / (x * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ (y / z)) = u
    ]]></literal>
    <justification jstring="[para(7920(a,1),10508(a,1))].">
      <j1 rule="para" parents="7920 10508"/>
    </justification>
  </clause>

  <clause id="10523">
    <literal><![CDATA[
      K(x,x \ (y / ((x \ z) * u))) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,8146,a(flip),b,10512,a),flip(a)].">
      <j1 rule="hyper" parents="63 8146 10512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10524">
    <literal><![CDATA[
      K(x \ (y / z),T(x,z)) = K(z \ (x \ y),x)
    ]]></literal>
    <justification jstring="[hyper(6496,a,10519,a)].">
      <j1 rule="hyper" parents="6496 10519"/>
    </justification>
  </clause>

  <clause id="10525">
    <literal><![CDATA[
      K(x \ (y / z),T(x,y)) = K(z \ (x \ y),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,7959,a(flip),b,10524,a)].">
      <j1 rule="hyper" parents="63 7959 10524"/>
    </justification>
  </clause>

  <clause id="10526">
    <literal><![CDATA[
      K(T(x,y),x \ (y / z)) = (u * K(z \ (x \ y),x)) \ u
    ]]></literal>
    <justification jstring="[para(10525(a,1),5990(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10525 5990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10527">
    <literal><![CDATA[
      K(x,(x * y) / (z * u)) = K(x,y / ((x \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,10511,a(flip),b,10523,a),flip(a)].">
      <j1 rule="hyper" parents="63 10511 10523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10528">
    <literal><![CDATA[
      K(x,y / ((x \ z) * u)) = K(x,((z * u) / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(5663,a,10527,a),flip(a)].">
      <j1 rule="hyper" parents="5663 10527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10529">
    <literal><![CDATA[
      1 / ((x * (L(x,y,z) \ 1)) * (x \ 1)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,4022,a(flip),b,10505,a),flip(a)].">
      <j1 rule="hyper" parents="63 4022 10505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10531">
    <literal><![CDATA[
      1 / ((L(x,y,z) \ x) * (x \ 1)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(1260(a,1),10529(a,1,2,1))].">
      <j1 rule="para" parents="1260 10529"/>
    </justification>
  </clause>

  <clause id="10532">
    <literal><![CDATA[
      (L(x,y,z) \ x) * (x \ 1) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(192,a,10531,a),flip(a)].">
      <j1 rule="hyper" parents="192 10531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10533">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ (L(x,y,z) \ 1) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(129,a,10532,a)].">
      <j1 rule="hyper" parents="129 10532"/>
    </justification>
  </clause>

  <clause id="10534">
    <literal><![CDATA[
      (L(x \ 1,y,z) \ (x \ 1)) * T(1 / (1 / x),x \ 1) = K(x \ 1,x) * (L(x \ 1,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(10532(a,1),3537(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10532 3537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10535">
    <literal><![CDATA[
      (1 / (x * L(x \ 1,y,z))) \ (L(x \ 1,y,z) \ 1) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(3264(a,2),10533(a,1,1))].">
      <j1 rule="para" parents="3264 10533"/>
    </justification>
  </clause>

  <clause id="10536">
    <literal><![CDATA[
      T(x,y / ((x * z) * u)) = T(x,x \ (y / (z * u)))
    ]]></literal>
    <justification jstring="[hyper(4285,a,10517,a),flip(a)].">
      <j1 rule="hyper" parents="4285 10517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10540">
    <literal><![CDATA[
      K(T(x,y),x \ (y / z)) = K(x,z \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(333,a,5990,a(flip),b,10526,a),flip(a)].">
      <j1 rule="hyper" parents="333 5990 10526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10541">
    <literal><![CDATA[
      K(x,T(x \ (y / z),y)) = K(x,z \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(6695,a,10540,a)].">
      <j1 rule="hyper" parents="6695 10540"/>
    </justification>
  </clause>

  <clause id="10542">
    <literal><![CDATA[
      K(x \ (y / z),x) \ y = y * K(x,z \ (x \ y))
    ]]></literal>
    <justification jstring="[para(10540(a,1),6356(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10540 6356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10543">
    <literal><![CDATA[
      K(x,(y \ z) \ (x \ z)) = K(x,T(x \ y,z))
    ]]></literal>
    <justification jstring="[para(76(a,1),10541(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="76 10541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10544">
    <literal><![CDATA[
      R(K(x,y),(y * x) * z,u) = K(x,R(y,x * z,u))
    ]]></literal>
    <justification jstring="[para(10492(a,1),10520(a,1,1))].">
      <j1 rule="para" parents="10492 10520"/>
    </justification>
  </clause>

  <clause id="10546">
    <literal><![CDATA[
      K(x,y / T(z \ 1,z * (x * y))) = K(x,(z \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,10323,a(flip),b,10518,a),flip(a)].">
      <j1 rule="hyper" parents="63 10323 10518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10547">
    <literal><![CDATA[
      K(L(x,y,z),x \ ((u * (x \ w)) \ v5)) = K(L(x,y,z),(u * w) \ v5)
    ]]></literal>
    <justification jstring="[hyper(333,a,6298,a(flip),b,10417,a),flip(a)].">
      <j1 rule="hyper" parents="333 6298 10417"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10548">
    <literal><![CDATA[
      L(T(x,(y * (z * x)) \ ((y * z) * u)),z,y) = T(L(x,z,y),L(x,z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(10114,a,10373,a)].">
      <j1 rule="hyper" parents="10114 10373"/>
    </justification>
  </clause>

  <clause id="10549">
    <literal><![CDATA[
      R(x / K(y,T(z,u)),K(y,z),u * K(z,y)) = (x * (u * K(z,y))) / u
    ]]></literal>
    <justification jstring="[para(6968(a,1),10383(a,1,1,2))].">
      <j1 rule="para" parents="6968 10383"/>
    </justification>
  </clause>

  <clause id="10550">
    <literal><![CDATA[
      R(x * K(y,T(z,u)),K(z,y),u * K(y,z)) = (x * (u * K(y,z))) / u
    ]]></literal>
    <justification jstring="[para(6424(a,1),10549(a,1,1))].">
      <j1 rule="para" parents="6424 10549"/>
    </justification>
  </clause>

  <clause id="10551">
    <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(333,a,8764,a(flip),b,10475,a),flip(a)].">
      <j1 rule="hyper" parents="333 8764 10475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10552">
    <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(6370(a,1),10551(a,1,1,2))].">
      <j1 rule="para" parents="6370 10551"/>
    </justification>
  </clause>

  <clause id="10553">
    <literal><![CDATA[
      (x * K(y,T(z,u))) * (u * K(z,y)) = (x * K(y,z)) * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(6887(a,1),10552(a,1,2))].">
      <j1 rule="para" parents="6887 10552"/>
    </justification>
  </clause>

  <clause id="10554">
    <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(7916(a,2),10553(a,1,1))].">
      <j1 rule="para" parents="7916 10553"/>
    </justification>
  </clause>

  <clause id="10555">
    <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(63,a,27,a,b,10500,a)].">
      <j1 rule="hyper" parents="63 27 10500"/>
    </justification>
  </clause>

  <clause id="10556">
    <literal><![CDATA[
      L(T(x,(y * z) \ (x \ ((y * z) * u))),z,y) = T(L(x,z,y),L(x,z,y) \ u)
    ]]></literal>
    <justification jstring="[para(7632(a,1),10548(a,1,1))].">
      <j1 rule="para" parents="7632 10548"/>
    </justification>
  </clause>

  <clause id="10557">
    <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(333,a,3633,a(flip),b,10555,a),flip(a)].">
      <j1 rule="hyper" parents="333 3633 10555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10558">
    <literal><![CDATA[
      T(L(x,y,z),L(x,y,z) \ u) = L(T(x,x \ u),y,z)
    ]]></literal>
    <justification jstring="[para(10321(a,1),10556(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10321 10556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10559">
    <literal><![CDATA[
      T(x,L(x,y,z) \ u) = T(x,x \ u)
    ]]></literal>
    <justification jstring="[hyper(150,a,10558,a)].">
      <j1 rule="hyper" parents="150 10558"/>
    </justification>
  </clause>

  <clause id="10560">
    <literal><![CDATA[
      (L(x,y,z) \ u) / (L(T(x,x \ w),y,z) \ u) = K(L(x,y,z),L(x,y,z) \ w)
    ]]></literal>
    <justification jstring="[para(10558(a,1),4631(a,1,2,1))].">
      <j1 rule="para" parents="10558 4631"/>
    </justification>
  </clause>

  <clause id="10564">
    <literal><![CDATA[
      T(x,L(x,y,z) \ x) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(10559(a,2),210(a,1))].">
      <j1 rule="para" parents="10559 210"/>
    </justification>
  </clause>

  <clause id="10566">
    <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(333,a,27,a,b,10557,a),flip(a)].">
      <j1 rule="hyper" parents="333 27 10557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10567">
    <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(10536(a,1),10566(a,1,1))].">
      <j1 rule="para" parents="10536 10566"/>
    </justification>
  </clause>

  <clause id="10568">
    <literal><![CDATA[
      R(T(x,R(x,y,z) \ u),y,z) = R(T(x,x \ u),y,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),10567(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11 10567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10569">
    <literal><![CDATA[
      R(T(x,x \ y),z,u) = (R(x,z,u) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(63,a,323,a(flip),b,10568,a),flip(a)].">
      <j1 rule="hyper" parents="63 323 10568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10570">
    <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(10568(a,1),4722(a,1,2,1))].">
      <j1 rule="para" parents="10568 4722"/>
    </justification>
  </clause>

  <clause id="10571">
    <literal><![CDATA[
      R((x \ y) \ y,z,u) = (R(x,z,u) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(63,a,1047,a(flip),b,10569,a)].">
      <j1 rule="hyper" parents="63 1047 10569"/>
    </justification>
  </clause>

  <clause id="10572">
    <literal><![CDATA[
      (R(x,y,z) \ (x * u)) \ (x * u) = R(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),10569(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 10569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10573">
    <literal><![CDATA[
      (R(x / y,z,u) \ x) \ x = R(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(332(a,1),10569(a,1,1)),flip(a)].">
      <j1 rule="para" parents="332 10569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10575">
    <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(10571(a,2),3046(a,1,1))].">
      <j1 rule="para" parents="10571 3046"/>
    </justification>
  </clause>

  <clause id="10576">
    <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(4951(a,1),10571(a,2,1))].">
      <j1 rule="para" parents="4951 10571"/>
    </justification>
  </clause>

  <clause id="10577">
    <literal><![CDATA[
      x / (x / R(y \ x,z,u)) = R(x / y,z,u)
    ]]></literal>
    <justification jstring="[para(10573(a,1),193(a,1,2,2))].">
      <j1 rule="para" parents="10573 193"/>
    </justification>
  </clause>

  <clause id="10578">
    <literal><![CDATA[
      K(x * R(1 / y,z,u),w) = K(x * R(y \ 1,z,u),w)
    ]]></literal>
    <justification jstring="[para(10573(a,1),4758(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10573 4758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10579">
    <literal><![CDATA[
      K(x,R(x / y,z,u) \ w) = K(x,R(y \ x,z,u) \ w)
    ]]></literal>
    <justification jstring="[para(10573(a,1),5579(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10573 5579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10580">
    <literal><![CDATA[
      R(x / (x / y),z,u) = x / (x / R(y,z,u))
    ]]></literal>
    <justification jstring="[para(79(a,1),10577(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="79 10577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10581">
    <literal><![CDATA[
      R(x / (x / y),z,u) \ x = x / R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(192,a,10580,a(flip))].">
      <j1 rule="hyper" parents="192 10580"/>
    </justification>
  </clause>

  <clause id="10583">
    <literal><![CDATA[
      R(T(1 / (1 / x),y),z,u) \ 1 = 1 / R(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(2384(a,1),10581(a,1,1,1))].">
      <j1 rule="para" parents="2384 10581"/>
    </justification>
  </clause>

  <clause id="10585">
    <literal><![CDATA[
      R(T(x,R(x,y,z) * u),y,z) = (x * u) \ (x * (R(x,y,z) * u))
    ]]></literal>
    <justification jstring="[para(1514(a,1),10572(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1514 10572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10586">
    <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(10578(a,1),5711(a,1,1,1))].">
      <j1 rule="para" parents="10578 5711"/>
    </justification>
  </clause>

  <clause id="10587">
    <literal><![CDATA[
      1 / R(T(x,(1 / x) * y),1 / x,y) = (((1 / x) * y) \ y) \ 1
    ]]></literal>
    <justification jstring="[para(779(a,1),10583(a,1,1)),flip(a)].">
      <j1 rule="para" parents="779 10583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10588">
    <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(333,a,246,a(flip),b,10585,a),flip(a)].">
      <j1 rule="hyper" parents="333 246 10585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10589">
    <literal><![CDATA[
      R(T(x,R(x,y,z) * u),y,z) = L(R(T(x,u),y,z),u,x)
    ]]></literal>
    <justification jstring="[para(27(a,2),10588(a,2,1))].">
      <j1 rule="para" parents="27 10588"/>
    </justification>
  </clause>

  <clause id="10591">
    <literal><![CDATA[
      T(x,R(x,y,z) * u) = T(x,x * u)
    ]]></literal>
    <justification jstring="[hyper(42,a,637,a(flip),b,10589,a),flip(a)].">
      <j1 rule="hyper" parents="42 637 10589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10592">
    <literal><![CDATA[
      T(x,x * (R(x,y,z) \ u)) = T(x,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),10591(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 10591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10594">
    <literal><![CDATA[
      K(R(x,y,z) * u,R(x,w,v5)) = R(T(x,x * u),w,v5) \ R(x,w,v5)
    ]]></literal>
    <attribute><![CDATA[
      label(flip_matches_hint)
    ]]></attribute>
    <justification jstring="[para(10591(a,1),4230(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10591 4230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10595">
    <literal><![CDATA[
      T(x,x * (R(x,y,z) \ u)) = x * K(x,u)
    ]]></literal>
    <justification jstring="[hyper(333,a,4222,a(flip),b,10592,a),flip(a)].">
      <j1 rule="hyper" parents="333 4222 10592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10596">
    <literal><![CDATA[
      K(x,x * (R(x,y,z) \ u)) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(4305,a,10595,a)].">
      <j1 rule="hyper" parents="4305 10595"/>
    </justification>
  </clause>

  <clause id="10598">
    <literal><![CDATA[
      K(x,K(y,R(y,z,u) \ w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[para(10596(a,1),6874(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10596 6874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10599">
    <literal><![CDATA[
      K(x,K(y,R(x \ y,z,u) \ w)) = K(x,K(x \ y,w))
    ]]></literal>
    <justification jstring="[hyper(7202,a,10598,a)].">
      <j1 rule="hyper" parents="7202 10598"/>
    </justification>
  </clause>

  <clause id="10601">
    <literal><![CDATA[
      K(x,K(y,R(x \ y,z,u) \ w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(333,a,7037,a(flip),b,10599,a),flip(a)].">
      <j1 rule="hyper" parents="333 7037 10599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10602">
    <literal><![CDATA[
      K(x,K(y,R(y \ x,z,u) \ w)) = K(y,K(x,w))
    ]]></literal>
    <justification jstring="[hyper(6798,a,10601,a)].">
      <j1 rule="hyper" parents="6798 10601"/>
    </justification>
  </clause>

  <clause id="10603">
    <literal><![CDATA[
      K(x,K(y,R(y \ x,z,u) \ w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(333,a,6785,a,b,10602,a),flip(a)].">
      <j1 rule="hyper" parents="333 6785 10602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10604">
    <literal><![CDATA[
      1 / R(T(x,(1 / x) * y),x \ 1,y) = (((1 / x) * y) \ y) \ 1
    ]]></literal>
    <justification jstring="[para(1937(a,1),10587(a,1,2))].">
      <j1 rule="para" parents="1937 10587"/>
    </justification>
  </clause>

  <clause id="10605">
    <literal><![CDATA[
      1 / R(T(x,(x \ 1) * y),x \ 1,y) = (((1 / x) * y) \ y) \ 1
    ]]></literal>
    <justification jstring="[para(2648(a,1),10604(a,1,2,1))].">
      <j1 rule="para" parents="2648 10604"/>
    </justification>
  </clause>

  <clause id="10606">
    <literal><![CDATA[
      (((1 / x) * (y * x)) \ (y * x)) \ 1 = 1 / R(T(x,y),x \ 1,y * x)
    ]]></literal>
    <justification jstring="[para(3928(a,1),10605(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3928 10605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10607">
    <literal><![CDATA[
      K(R(x,y,z) * u,R(x,w,v5)) = K(x * u,R(x,w,v5))
    ]]></literal>
    <justification jstring="[hyper(333,a,4230,a(flip),b,10594,a),flip(a)].">
      <j1 rule="hyper" parents="333 4230 10594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10609">
    <literal><![CDATA[
      K(x * R(y,z,u),R(y,z,u)) = K(y * x,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(7452,a,10607,a)].">
      <j1 rule="hyper" parents="7452 10607"/>
    </justification>
  </clause>

  <clause id="10610">
    <literal><![CDATA[
      K(x * R(y,z,u),R(y,z,u)) = K(x * y,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(333,a,9997,a,b,10609,a),flip(a)].">
      <j1 rule="hyper" parents="333 9997 10609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10611">
    <literal><![CDATA[
      1 / R(T(x,y),x \ 1,y * x) = (L(y,x,x \ 1) \ (x * y)) \ 1
    ]]></literal>
    <justification jstring="[para(3991(a,1),10606(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3991 10606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10612">
    <literal><![CDATA[
      ((L(x,y,y \ 1) \ (y * x)) \ 1) \ 1 = R(T(y,x),y \ 1,x * y)
    ]]></literal>
    <justification jstring="[hyper(192,a,10611,a)].">
      <j1 rule="hyper" parents="192 10611"/>
    </justification>
  </clause>

  <clause id="10613">
    <literal><![CDATA[
      ((x \ 1) * (x * y)) \ (x * y) = R(T(x,y),x \ 1,y * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,3534,a(flip),b,10612,a)].">
      <j1 rule="hyper" parents="63 3534 10612"/>
    </justification>
  </clause>

  <clause id="10617">
    <literal><![CDATA[
      K(L(x,y,z),L(x,y,z) \ u) = K(L(x,y,z),x \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,4725,a(flip),b,10560,a),flip(a)].">
      <j1 rule="hyper" parents="63 4725 10560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10618">
    <literal><![CDATA[
      K(R(x,y,z) \ u,R(x,y,z)) = K(x \ u,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,4722,a(flip),b,10570,a),flip(a)].">
      <j1 rule="hyper" parents="63 4722 10570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10619">
    <literal><![CDATA[
      K(R(x,y,z) \ 1,R(x,y,z)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,3042,a(flip),b,10618,a),flip(a)].">
      <j1 rule="hyper" parents="333 3042 10618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10620">
    <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(10618(a,1),4190(a,1,1,2))].">
      <j1 rule="para" parents="10618 4190"/>
    </justification>
  </clause>

  <clause id="10621">
    <literal><![CDATA[
      K(R(x,y,z) \ 1,R(x,y,z)) = K(x \ 1,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(333,a,3042,a,b,10619,a),flip(a)].">
      <j1 rule="hyper" parents="333 3042 10619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10623">
    <literal><![CDATA[
      (x \ (1 / R(y,z,u))) * K(y \ 1,y) = x \ (R(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(10619(a,1),1918(a,1,2))].">
      <j1 rule="para" parents="10619 1918"/>
    </justification>
  </clause>

  <clause id="10625">
    <literal><![CDATA[
      K(x \ 1,R(x,y,z)) \ 1 = R(x,u,w) * (1 / R(x,u,w))
    ]]></literal>
    <justification jstring="[para(10621(a,1),2122(a,1,1))].">
      <j1 rule="para" parents="10621 2122"/>
    </justification>
  </clause>

  <clause id="10629">
    <literal><![CDATA[
      K(R(x,y,z),x \ 1) = R(x,u,w) * (1 / R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(4382,a,10625,a)].">
      <j1 rule="hyper" parents="4382 10625"/>
    </justification>
  </clause>

  <clause id="10630">
    <literal><![CDATA[
      R(x,y,z) * (1 / R(x,y,z)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(10506,a,10629,a),flip(a)].">
      <j1 rule="hyper" parents="10506 10629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10631">
    <literal><![CDATA[
      (1 / x) \ (1 / R(x,y,z)) = (x \ 1) \ (R(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(5178,a,10623,a)].">
      <j1 rule="hyper" parents="5178 10623"/>
    </justification>
  </clause>

  <clause id="10633">
    <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(111(a,1),10380(a,1,1,1))].">
      <j1 rule="para" parents="111 10380"/>
    </justification>
  </clause>

  <clause id="10634">
    <literal><![CDATA[
      K(L(x,y,z),x * T(y,x)) = K(x,y * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(1824,a,10633,a),flip(a)].">
      <j1 rule="hyper" parents="1824 10633"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10635">
    <literal><![CDATA[
      K(L(x,y,z),y * x) = K(x,y * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(111(a,1),10634(a,1,2))].">
      <j1 rule="para" parents="111 10634"/>
    </justification>
  </clause>

  <clause id="10636">
    <literal><![CDATA[
      K(x,y * L(x,y,z)) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(6548,a,10635,a),flip(a)].">
      <j1 rule="hyper" parents="6548 10635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10638">
    <literal><![CDATA[
      L(K(x,x * y),z * x,u) = K(L(x,z,u),y * L(x,y,w))
    ]]></literal>
    <justification jstring="[para(10636(a,1),6298(a,1,1))].">
      <j1 rule="para" parents="10636 6298"/>
    </justification>
  </clause>

  <clause id="10639">
    <literal><![CDATA[
      K(L(x,y,z),u * L(x,u,w)) = K(L(x,y,z),x * u)
    ]]></literal>
    <justification jstring="[hyper(9539,a,10638,a),flip(a)].">
      <j1 rule="hyper" parents="9539 10638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10640">
    <literal><![CDATA[
      L(K(L(x,y,z),x * y),y,z) = K(x,x * y)
    ]]></literal>
    <justification jstring="[para(10639(a,1),10279(a,1,1))].">
      <j1 rule="para" parents="10639 10279"/>
    </justification>
  </clause>

  <clause id="10641">
    <literal><![CDATA[
      L(K(x,x * y),y,z) = K(x,x * y)
    ]]></literal>
    <justification jstring="[para(7782(a,1),10640(a,1,1))].">
      <j1 rule="para" parents="7782 10640"/>
    </justification>
  </clause>

  <clause id="10643">
    <literal><![CDATA[
      1 / L(K(x,x * y),y,z) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(197,a,10641,a,b,4367,a)].">
      <j1 rule="hyper" parents="197 10641 4367"/>
    </justification>
  </clause>

  <clause id="10644">
    <literal><![CDATA[
      K(x,y \ (z * x)) = K(x,x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(63,a,10271,a(flip),b,10641,a)].">
      <j1 rule="hyper" parents="63 10271 10641"/>
    </justification>
  </clause>

  <clause id="10645">
    <literal><![CDATA[
      K(x,y \ ((y * z) * x)) = K(x,x * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,10270,a(flip),b,10641,a)].">
      <j1 rule="hyper" parents="63 10270 10641"/>
    </justification>
  </clause>

  <clause id="10647">
    <literal><![CDATA[
      K(x,(y * (z / x)) \ u) = K(x,x * ((y * z) \ u))
    ]]></literal>
    <justification jstring="[hyper(10258,a,10644,a)].">
      <j1 rule="hyper" parents="10258 10644"/>
    </justification>
  </clause>

  <clause id="10648">
    <literal><![CDATA[
      K(x,(y \ z) \ x) = K(x,x * (z \ y))
    ]]></literal>
    <justification jstring="[hyper(9556,a,10644,a)].">
      <j1 rule="hyper" parents="9556 10644"/>
    </justification>
  </clause>

  <clause id="10650">
    <literal><![CDATA[
      K(x,x * (y \ (x \ z))) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,9593,a(flip),b,10644,a),flip(a)].">
      <j1 rule="hyper" parents="63 9593 10644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10651">
    <literal><![CDATA[
      K(x,y \ (x * z)) = K(x,x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(63,a,9592,a(flip),b,10644,a)].">
      <j1 rule="hyper" parents="63 9592 10644"/>
    </justification>
  </clause>

  <clause id="10652">
    <literal><![CDATA[
      K(x,y * (L(y,z,u) \ x)) = K(x,x * (L(y,z,u) \ y))
    ]]></literal>
    <justification jstring="[para(1258(a,1),10644(a,1,2))].">
      <j1 rule="para" parents="1258 10644"/>
    </justification>
  </clause>

  <clause id="10653">
    <literal><![CDATA[
      L(K(x,x * (y \ z)),u * x,w) = K(L(x,u,w),y \ (z * x))
    ]]></literal>
    <justification jstring="[para(10644(a,1),6298(a,1,1))].">
      <j1 rule="para" parents="10644 6298"/>
    </justification>
  </clause>

  <clause id="10655">
    <literal><![CDATA[
      K(x,y \ ((y * z) * x)) = K(x,z * x)
    ]]></literal>
    <justification jstring="[hyper(333,a,4636,a,b,10645,a),flip(a)].">
      <j1 rule="hyper" parents="333 4636 10645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10656">
    <literal><![CDATA[
      K(x,(y / R(y,z,u)) \ x) = K(x,x * (y \ R(y,z,u)))
    ]]></literal>
    <justification jstring="[para(3019(a,2),10648(a,1,2,1))].">
      <j1 rule="para" parents="3019 10648"/>
    </justification>
  </clause>

  <clause id="10657">
    <literal><![CDATA[
      K(x,R(x,y,z) \ u) = K(x,x \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,10596,a(flip),b,10650,a),flip(a)].">
      <j1 rule="hyper" parents="63 10596 10650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10658">
    <literal><![CDATA[
      K(x,x \ ((x * R(T(x,y),z,u)) / w)) = K(x,w \ x)
    ]]></literal>
    <justification jstring="[hyper(10178,a,10657,a),flip(a)].">
      <j1 rule="hyper" parents="10178 10657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10659">
    <literal><![CDATA[
      K(x / y,(x * (y \ 1)) \ z) = K(x / y,(x / y) \ z)
    ]]></literal>
    <justification jstring="[para(554(a,1),10657(a,1,2,1))].">
      <j1 rule="para" parents="554 10657"/>
    </justification>
  </clause>

  <clause id="10660">
    <literal><![CDATA[
      K(x,x \ (y * z)) = K(x,(x \ y) * z)
    ]]></literal>
    <justification jstring="[para(529(a,1),10657(a,1,2)),flip(a)].">
      <j1 rule="para" parents="529 10657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10661">
    <literal><![CDATA[
      K(x,y * ((x * y) \ z)) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[para(364(a,1),10657(a,1,2))].">
      <j1 rule="para" parents="364 10657"/>
    </justification>
  </clause>

  <clause id="10662">
    <literal><![CDATA[
      K(x / y,(x / y) \ z) * K(x,K(y,R(x / y,u,w) \ z)) = K(y \ x,R(x / y,u,w) \ z)
    ]]></literal>
    <justification jstring="[para(10657(a,1),7629(a,1,1))].">
      <j1 rule="para" parents="10657 7629"/>
    </justification>
  </clause>

  <clause id="10663">
    <literal><![CDATA[
      L(K(x,y * x),y,z) = K(x,y * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,10272,a,b,10655,a)].">
      <j1 rule="hyper" parents="63 10272 10655"/>
    </justification>
  </clause>

  <clause id="10665">
    <literal><![CDATA[
      a(x,y,K(y * z,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(120,a,10663,a(flip),b,9731,a),flip(a)].">
      <j1 rule="hyper" parents="120 10663 9731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10666">
    <literal><![CDATA[
      a(x,y,K(z,y \ z)) = 1
    ]]></literal>
    <justification jstring="[para(10(a,1),10665(a,1,3,1))].">
      <j1 rule="para" parents="10 10665"/>
    </justification>
  </clause>

  <clause id="10667">
    <literal><![CDATA[
      K(x,(x \ y) * z) = K(x,y * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(10305,a,10660,a),flip(a)].">
      <j1 rule="hyper" parents="10305 10660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10668">
    <literal><![CDATA[
      T(x,(x \ y) * z) = T(x,y * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(124,a,10667,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 10667 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10669">
    <literal><![CDATA[
      T(x,(y / x) * z) = T(x,y * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(7446,a,10668,a)].">
      <j1 rule="hyper" parents="7446 10668"/>
    </justification>
  </clause>

  <clause id="10670">
    <literal><![CDATA[
      L(K(x * y,x),y,z) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(9454,a,10643,a)].">
      <j1 rule="hyper" parents="9454 10643"/>
    </justification>
  </clause>

  <clause id="10671">
    <literal><![CDATA[
      1 / ((x * (y \ T(y * z,y))) \ (x * z)) = K(y * z,y)
    ]]></literal>
    <justification jstring="[para(9521(a,2),10643(a,1,2))].">
      <j1 rule="para" parents="9521 10643"/>
    </justification>
  </clause>

  <clause id="10672">
    <literal><![CDATA[
      K(x \ (y * z),z) = K(z * (x \ y),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,10283,a(flip),b,10670,a)].">
      <j1 rule="hyper" parents="63 10283 10670"/>
    </justification>
  </clause>

  <clause id="10673">
    <literal><![CDATA[
      K((x \ y) \ z,z) = K(z * (y \ x),z)
    ]]></literal>
    <justification jstring="[hyper(6295,a,10672,a)].">
      <j1 rule="hyper" parents="6295 10672"/>
    </justification>
  </clause>

  <clause id="10675">
    <literal><![CDATA[
      K((x * (y \ z)) \ u,y) = K(y * ((x * z) \ u),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,10286,a,b,10672,a)].">
      <j1 rule="hyper" parents="63 10286 10672"/>
    </justification>
  </clause>

  <clause id="10676">
    <literal><![CDATA[
      K(x \ (y * z),y) = K(y * (x \ z),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,9575,a(flip),b,10672,a)].">
      <j1 rule="hyper" parents="63 9575 10672"/>
    </justification>
  </clause>

  <clause id="10677">
    <literal><![CDATA[
      K(x * ((y * x) \ z),x) = K(y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,7484,a(flip),b,10672,a),flip(a)].">
      <j1 rule="hyper" parents="63 7484 10672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10678">
    <literal><![CDATA[
      L(x * K(x * (y \ z),x),u,w) / L(x,u,w) = K(y \ (z * x),L(x,u,w))
    ]]></literal>
    <justification jstring="[para(10672(a,1),4947(a,1,1,1,2))].">
      <j1 rule="para" parents="10672 4947"/>
    </justification>
  </clause>

  <clause id="10679">
    <literal><![CDATA[
      K(x * (y \ z),x) * K(x,y \ z) = a(x,(z \ y) \ 1,x)
    ]]></literal>
    <justification jstring="[para(10672(a,1),9366(a,1,1))].">
      <j1 rule="para" parents="10672 9366"/>
    </justification>
  </clause>

  <clause id="10680">
    <literal><![CDATA[
      L(x * K(x * ((y * z) \ u),x),w,v5) \ L(x,w,v5) = K(L(x,w,v5),(y * (x \ z)) \ u)
    ]]></literal>
    <justification jstring="[para(10675(a,1),4948(a,1,1,1,2))].">
      <j1 rule="para" parents="10675 4948"/>
    </justification>
  </clause>

  <clause id="10681">
    <literal><![CDATA[
      K(x,R(T(x,y),z,u) / w) = K(x,w \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,10511,a(flip),b,10658,a)].">
      <j1 rule="hyper" parents="63 10511 10658"/>
    </justification>
  </clause>

  <clause id="10682">
    <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(63,a,9620,a,b,10656,a)].">
      <j1 rule="hyper" parents="63 9620 10656"/>
    </justification>
  </clause>

  <clause id="10683">
    <literal><![CDATA[
      T(K(x * y,T(x,z)),z) = 1 / ((u * (x \ T(x * y,x))) \ (u * y))
    ]]></literal>
    <justification jstring="[hyper(333,a,6896,a,b,10671,a)].">
      <j1 rule="hyper" parents="333 6896 10671"/>
    </justification>
  </clause>

  <clause id="10685">
    <literal><![CDATA[
      a(x,(y \ z) \ 1,x) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,z \ y,x) = u
    ]]></literal>
    <justification jstring="[para(10679(a,1),8260(a,1))].">
      <j1 rule="para" parents="10679 8260"/>
    </justification>
  </clause>

  <clause id="10686">
    <literal><![CDATA[
      K(L(x,y,z),u \ (w * x)) = K(L(x,y,z),x * (u \ w))
    ]]></literal>
    <justification jstring="[hyper(9539,a,10653,a),flip(a)].">
      <j1 rule="hyper" parents="9539 10653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10687">
    <literal><![CDATA[
      K(L(x,y,z),u \ (x * w)) = K(L(x,y,z),x * (u \ w))
    ]]></literal>
    <justification jstring="[hyper(9945,a,10686,a)].">
      <j1 rule="hyper" parents="9945 10686"/>
    </justification>
  </clause>

  <clause id="10688">
    <literal><![CDATA[
      K(L(x,y,z),x * (u \ L(K(x,w),v5,v6))) = K(L(x,y,z),u \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,10238,a(flip),b,10687,a),flip(a)].">
      <j1 rule="hyper" parents="63 10238 10687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10689">
    <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(6957(a,2),10683(a,1,1))].">
      <j1 rule="para" parents="6957 10683"/>
    </justification>
  </clause>

  <clause id="10690">
    <literal><![CDATA[
      K(x \ (y * z),L(z,u,w)) = K(z * (x \ y),L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(5171,a,10678,a),flip(a)].">
      <j1 rule="hyper" parents="5171 10678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10691">
    <literal><![CDATA[
      K((x \ y) \ z,L(z,u,w)) = K(z * (y \ x),L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,9536,a,b,10690,a)].">
      <j1 rule="hyper" parents="63 9536 10690"/>
    </justification>
  </clause>

  <clause id="10692">
    <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(1510(a,1),10682(a,1,2,1))].">
      <j1 rule="para" parents="1510 10682"/>
    </justification>
  </clause>

  <clause id="10693">
    <literal><![CDATA[
      K(x,T(R(y,z,u) * (y \ x),y)) = K(x,x * (y \ R(y,z,u)))
    ]]></literal>
    <justification jstring="[para(177(a,1),10692(a,1,2,2))].">
      <j1 rule="para" parents="177 10692"/>
    </justification>
  </clause>

  <clause id="10694">
    <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(7332,a,10689,a),flip(a)].">
      <j1 rule="hyper" parents="7332 10689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10698">
    <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(333,a,8345,a(flip),b,10576,a),flip(a)].">
      <j1 rule="hyper" parents="333 8345 10576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10699">
    <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(8343(a,1),10698(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8343 10698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10700">
    <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(10699(a,1),9321(a,1,2))].">
      <j1 rule="para" parents="10699 9321"/>
    </justification>
  </clause>

  <clause id="10701">
    <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(4949(a,1),10620(a,1,1))].">
      <j1 rule="para" parents="4949 10620"/>
    </justification>
  </clause>

  <clause id="10702">
    <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(63,a,27,a,b,10701,a)].">
      <j1 rule="hyper" parents="63 27 10701"/>
    </justification>
  </clause>

  <clause id="10703">
    <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(4190(a,1),10702(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4190 10702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10704">
    <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(333,a,29,a(flip),b,10703,a),flip(a)].">
      <j1 rule="hyper" parents="333 29 10703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10705">
    <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(10704(a,1),1179(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10704 1179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10707">
    <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(6763(a,1),10465(a,1,1,2))].">
      <j1 rule="para" parents="6763 10465"/>
    </justification>
  </clause>

  <clause id="10709">
    <literal><![CDATA[
      K(L(x,y,z),(u * (x \ w)) \ v5) = K(L(x,y,z),x * ((u * w) \ v5))
    ]]></literal>
    <justification jstring="[hyper(6098,a,10680,a),flip(a)].">
      <j1 rule="hyper" parents="6098 10680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10710">
    <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(5205(a,1),10359(a,1,1,2))].">
      <j1 rule="para" parents="5205 10359"/>
    </justification>
  </clause>

  <clause id="10711">
    <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(7517(a,1),10710(a,1,2))].">
      <j1 rule="para" parents="7517 10710"/>
    </justification>
  </clause>

  <clause id="10712">
    <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(6785(a,1),10711(a,1,2))].">
      <j1 rule="para" parents="6785 10711"/>
    </justification>
  </clause>

  <clause id="10714">
    <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(10712(a,1),9416(a,1,2,2))].">
      <j1 rule="para" parents="10712 9416"/>
    </justification>
  </clause>

  <clause id="10715">
    <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(63,a,9441,a(flip),b,10714,a),flip(a)].">
      <j1 rule="hyper" parents="63 9441 10714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10717">
    <literal><![CDATA[
      K(x,y * (z * (x * (T(T(x,u),u) \ w)))) = K(x,y * (z * w))
    ]]></literal>
    <justification jstring="[hyper(333,a,9516,a(flip),b,10715,a),flip(a)].">
      <j1 rule="hyper" parents="333 9516 10715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10719">
    <literal><![CDATA[
      L(K(x,(y \ 1) \ (z \ u)),z \ u,z) = K(x,(z * ((((y \ x) / x) * y) * (1 / y))) \ u)
    ]]></literal>
    <justification jstring="[para(9668(a,1),9899(a,1,1))].">
      <j1 rule="para" parents="9668 9899"/>
    </justification>
  </clause>

  <clause id="10720">
    <literal><![CDATA[
      K(x,(y * ((((z \ x) / x) * z) * (1 / z))) \ u) = K(x,(y * (z \ 1)) \ u)
    ]]></literal>
    <justification jstring="[hyper(9697,a,10719,a),flip(a)].">
      <j1 rule="hyper" parents="9697 10719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10721">
    <literal><![CDATA[
      K(x,(y * ((z \ x) / x)) \ u) = K(x,(y * (z \ 1)) \ u)
    ]]></literal>
    <justification jstring="[para(2221(a,1),10720(a,1,2,1,2))].">
      <j1 rule="para" parents="2221 10720"/>
    </justification>
  </clause>

  <clause id="10722">
    <literal><![CDATA[
      K(x,(y * (z \ x)) \ (u * x)) = K(x,(y * (z \ 1)) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,10254,a(flip),b,10721,a)].">
      <j1 rule="hyper" parents="63 10254 10721"/>
    </justification>
  </clause>

  <clause id="10723">
    <literal><![CDATA[
      K(x,(y * ((z \ x) \ 1)) \ u) = K(x,(y * z) \ (u * x))
    ]]></literal>
    <justification jstring="[hyper(63,a,5576,a(flip),b,10722,a),flip(a)].">
      <j1 rule="hyper" parents="63 5576 10722"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10724">
    <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(4945(a,1),10723(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4945 10723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10725">
    <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(12(a,1),9813(a,2,1))].">
      <j1 rule="para" parents="12 9813"/>
    </justification>
  </clause>

  <clause id="10726">
    <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(333,a,5459,a,b,10725,a)].">
      <j1 rule="hyper" parents="333 5459 10725"/>
    </justification>
  </clause>

  <clause id="10727">
    <literal><![CDATA[
      K(x,y * (((1 / z) * (K(x,u) * z)) * z)) = K(x,y * ((z \ 1) \ K(u,x)))
    ]]></literal>
    <justification jstring="[hyper(63,a,10717,a(flip),b,9894,a)].">
      <j1 rule="hyper" parents="63 10717 9894"/>
    </justification>
  </clause>

  <clause id="10728">
    <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(7547(a,1),10727(a,1,2,2))].">
      <j1 rule="para" parents="7547 10727"/>
    </justification>
  </clause>

  <clause id="10729">
    <literal><![CDATA[
      K(x,y * ((z \ 1) \ K(u,x))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,9433,a(flip),b,10728,a),flip(a)].">
      <j1 rule="hyper" parents="63 9433 10728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10731">
    <literal><![CDATA[
      K(x,y * (z \ K(u,x))) = K(x,y * (z \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,5020,a(flip),b,10729,a)].">
      <j1 rule="hyper" parents="63 5020 10729"/>
    </justification>
  </clause>

  <clause id="10732">
    <literal><![CDATA[
      K(x,y * (K(z,x) / u)) = K(x,y * (u \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,9095,a,b,10731,a)].">
      <j1 rule="hyper" parents="63 9095 10731"/>
    </justification>
  </clause>

  <clause id="10733">
    <literal><![CDATA[
      K((x * (y \ 1)) \ 1,K(z,u)) = K(z,K(u,x * (y \ K(w,u))))
    ]]></literal>
    <justification jstring="[para(10731(a,2),7163(a,2,2))].">
      <j1 rule="para" parents="10731 7163"/>
    </justification>
  </clause>

  <clause id="10735">
    <literal><![CDATA[
      K(x,K(y,z * (u \ K(w,y)))) = K(x,K(y,z * (u \ 1)))
    ]]></literal>
    <justification jstring="[hyper(7175,a,10733,a),flip(a)].">
      <j1 rule="hyper" parents="7175 10733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10736">
    <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(7423(a,1),10735(a,1,2))].">
      <j1 rule="para" parents="7423 10735"/>
    </justification>
  </clause>

  <clause id="10737">
    <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(385(a,1),10736(a,2,2,2))].">
      <j1 rule="para" parents="385 10736"/>
    </justification>
  </clause>

  <clause id="10738">
    <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(63,a,7816,a,b,10737,a)].">
      <j1 rule="hyper" parents="63 7816 10737"/>
    </justification>
  </clause>

  <clause id="10739">
    <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(333,a,6785,a,b,10738,a),flip(a)].">
      <j1 rule="hyper" parents="333 6785 10738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10740">
    <literal><![CDATA[
      (x * T(y,(x / z) * z)) / a(x / z,z,T(y,(x / z) * z)) = L(y,z,z \ x) * x
    ]]></literal>
    <justification jstring="[para(12(a,1),10105(a,2,2))].">
      <j1 rule="para" parents="12 10105"/>
    </justification>
  </clause>

  <clause id="10741">
    <literal><![CDATA[
      (x * T(y,x)) / a(x / z,z,T(y,(x / z) * z)) = L(y,z,z \ x) * x
    ]]></literal>
    <justification jstring="[para(12(a,1),10740(a,1,1,2,2))].">
      <j1 rule="para" parents="12 10740"/>
    </justification>
  </clause>

  <clause id="10742">
    <literal><![CDATA[
      (x * y) / a(y / z,z,T(x,(y / z) * z)) = L(x,z,z \ y) * y
    ]]></literal>
    <justification jstring="[para(111(a,1),10741(a,1,1))].">
      <j1 rule="para" parents="111 10741"/>
    </justification>
  </clause>

  <clause id="10743">
    <literal><![CDATA[
      (x \ y) \ (y * R(y \ (x \ y),z,u)) = T(x,x \ y) * R(T(x,x \ y) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(281(a,1),10164(a,1,2,2,1,2))].">
      <j1 rule="para" parents="281 10164"/>
    </justification>
  </clause>

  <clause id="10744">
    <literal><![CDATA[
      T(x * R(x \ 1,y,z),x \ u) = (x \ u) \ (u * R(u \ (x \ u),y,z))
    ]]></literal>
    <justification jstring="[hyper(333,a,1795,a(flip),b,10743,a)].">
      <j1 rule="hyper" parents="333 1795 10743"/>
    </justification>
  </clause>

  <clause id="10745">
    <literal><![CDATA[
      K(L(x,y,z),x \ ((u * (x \ (1 / L(x,y,z)))) \ w)) = K(L(x,y,z),(u * (1 / x)) \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,10617,a(flip),b,10416,a)].">
      <j1 rule="hyper" parents="63 10617 10416"/>
    </justification>
  </clause>

  <clause id="10746">
    <literal><![CDATA[
      K(L(x,y,z),(u * (1 / L(x,y,z))) \ w) = K(L(x,y,z),(u * (1 / x)) \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,10547,a(flip),b,10745,a)].">
      <j1 rule="hyper" parents="63 10547 10745"/>
    </justification>
  </clause>

  <clause id="10747">
    <literal><![CDATA[
      K(L(x,y,z),L(x,y,z) * ((u * 1) \ w)) = K(L(x,y,z),(u * (1 / x)) \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,10647,a(flip),b,10746,a)].">
      <j1 rule="hyper" parents="63 10647 10746"/>
    </justification>
  </clause>

  <clause id="10748">
    <literal><![CDATA[
      K(L(x,y,z),L(x,y,z) * (u \ w)) = K(L(x,y,z),(u * (1 / x)) \ w)
    ]]></literal>
    <justification jstring="[para(8(a,1),10747(a,1,2,2,1))].">
      <j1 rule="para" parents="8 10747"/>
    </justification>
  </clause>

  <clause id="10749">
    <literal><![CDATA[
      K(L(x,y,z),L(x,y,z) * (u \ w)) = K(L(x,y,z),(u * (x \ 1)) \ w)
    ]]></literal>
    <justification jstring="[hyper(333,a,5021,a(flip),b,10748,a),flip(a)].">
      <j1 rule="hyper" parents="333 5021 10748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10750">
    <literal><![CDATA[
      K(L(x,y,z),L(x,y,z) * (u \ w)) = K(L(x,y,z),x * ((u * 1) \ w))
    ]]></literal>
    <justification jstring="[hyper(333,a,10709,a(flip),b,10749,a),flip(a)].">
      <j1 rule="hyper" parents="333 10709 10749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10751">
    <literal><![CDATA[
      K(L(x,y,z),L(x,y,z) * (u \ w)) = K(L(x,y,z),x * (u \ w))
    ]]></literal>
    <justification jstring="[para(8(a,1),10750(a,2,2,2,1))].">
      <j1 rule="para" parents="8 10750"/>
    </justification>
  </clause>

  <clause id="10752">
    <literal><![CDATA[
      (L(x \ 1,y,z) \ (x \ 1)) * T(1 / (1 / x),x \ 1) = L(x \ 1,y,z) \ K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,2437,a(flip),b,10534,a),flip(a)].">
      <j1 rule="hyper" parents="333 2437 10534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10753">
    <literal><![CDATA[
      (L(x \ 1,y,z) \ (x \ 1)) * T(1 / (1 / x),x \ 1) = (x \ 1) * (L(x \ 1,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(333,a,1273,a(flip),b,10752,a),flip(a)].">
      <j1 rule="hyper" parents="333 1273 10752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10754">
    <literal><![CDATA[
      (L(x \ 1,y,z) \ (x \ 1)) * x = (x \ 1) * (L(x \ 1,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(1904(a,1),10753(a,1,2))].">
      <j1 rule="para" parents="1904 10753"/>
    </justification>
  </clause>

  <clause id="10755">
    <literal><![CDATA[
      (L(x \ 1,y,z) \ (x \ 1)) \ (L(1 / x,y,z) \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(121,a,2922,a(flip),b,10754,a)].">
      <j1 rule="hyper" parents="121 2922 10754"/>
    </justification>
  </clause>

  <clause id="10756">
    <literal><![CDATA[
      T(x,x \ (L(x \ 1,y,z) \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,9151,a(flip),b,10755,a)].">
      <j1 rule="hyper" parents="63 9151 10755"/>
    </justification>
  </clause>

  <clause id="10758">
    <literal><![CDATA[
      T(x,x \ (((y * x) \ y) \ 1)) = x
    ]]></literal>
    <justification jstring="[para(227(a,1),10756(a,1,2,2,1))].">
      <j1 rule="para" parents="227 10756"/>
    </justification>
  </clause>

  <clause id="10759">
    <literal><![CDATA[
      (1 / ((x * y) \ x)) / y = y \ (1 / ((x * y) \ x))
    ]]></literal>
    <justification jstring="[para(10758(a,1),3186(a,1,2))].">
      <j1 rule="para" parents="10758 3186"/>
    </justification>
  </clause>

  <clause id="10760">
    <literal><![CDATA[
      T((1 / ((x * y) \ x)) * K(y,z),y) = (y \ (1 / ((x * y) \ x))) * T(y,z)
    ]]></literal>
    <justification jstring="[para(10759(a,1),6746(a,2,1))].">
      <j1 rule="para" parents="10759 6746"/>
    </justification>
  </clause>

  <clause id="10761">
    <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(3861(a,1),10700(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3861 10700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10762">
    <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(333,a,5022,a(flip),b,10724,a),flip(a)].">
      <j1 rule="hyper" parents="333 5022 10724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10763">
    <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(76(a,1),10762(a,2,2,1,2))].">
      <j1 rule="para" parents="76 10762"/>
    </justification>
  </clause>

  <clause id="10765">
    <literal><![CDATA[
      K(x,((1 / (K(y,x \ z) / y)) * z) \ (u * x)) = K(x,(((z \ x) \ 1) * y) \ u)
    ]]></literal>
    <justification jstring="[para(5766(a,1),10763(a,1,2,1,1,2,1))].">
      <j1 rule="para" parents="5766 10763"/>
    </justification>
  </clause>

  <clause id="10766">
    <literal><![CDATA[
      K(x,(((y \ x) \ 1) * z) \ u) = K(x,((x \ y) * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,10291,a(flip),b,10765,a),flip(a)].">
      <j1 rule="hyper" parents="63 10291 10765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10767">
    <literal><![CDATA[
      K(x,((x \ (y \ x)) * z) \ 1) = K(x,((y \ 1) * z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,10203,a(flip),b,10766,a),flip(a)].">
      <j1 rule="hyper" parents="63 10203 10766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10768">
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ 1) = K(x,((y \ x) * z) \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,9992,a(flip),b,10767,a),flip(a)].">
      <j1 rule="hyper" parents="63 9992 10767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10769">
    <literal><![CDATA[
      K(x,((y \ x) * (y / z)) \ x) = L(K(x,z),y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,9718,a(flip),b,10768,a),flip(a)].">
      <j1 rule="hyper" parents="63 9718 10768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10770">
    <literal><![CDATA[
      L(K(x,y),z,z \ 1) = L(K(x,y),z,z \ x)
    ]]></literal>
    <justification jstring="[hyper(9848,a,10769,a),flip(a)].">
      <j1 rule="hyper" parents="9848 10769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10771">
    <literal><![CDATA[
      K(R(x \ y,z,u),w \ (y / x)) = K(R(x \ y,z,u),w \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(6099,a,9656,a),flip(a)].">
      <j1 rule="hyper" parents="6099 9656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10772">
    <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(4421(a,1),10771(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4421 10771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10773">
    <literal><![CDATA[
      a((x \ y) \ y,z,(x \ y) \ y) = K(x * z,T(T(x,y),u)) * K((x \ y) \ y,T(z,u))
    ]]></literal>
    <justification jstring="[para(8896(a,1),9888(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8896 9888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10774">
    <literal><![CDATA[
      a((x \ y) \ y,z,(x \ y) \ y) = K(x * z,T(T(x,y),u)) * K(x,T(T(z,u),y))
    ]]></literal>
    <justification jstring="[para(6373(a,1),10773(a,2,2))].">
      <j1 rule="para" parents="6373 10773"/>
    </justification>
  </clause>

  <clause id="10776">
    <literal><![CDATA[
      K(x * y,T(T(x,z),u)) * K(x,T(T(y,u),z)) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,9372,a(flip),b,10774,a),flip(a)].">
      <j1 rule="hyper" parents="63 9372 10774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10778">
    <literal><![CDATA[
      K(x * y,T(T(x,z),u)) * K(x,T(T(y,z),u)) = a(x,y,x)
    ]]></literal>
    <justification jstring="[para(23(a,1),10776(a,1,1,2))].">
      <j1 rule="para" parents="23 10776"/>
    </justification>
  </clause>

  <clause id="10779">
    <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(4623(a,1),9889(a,1,1))].">
      <j1 rule="para" parents="4623 9889"/>
    </justification>
  </clause>

  <clause id="10780">
    <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(8222(a,1),10425(a,1,1,1))].">
      <j1 rule="para" parents="8222 10425"/>
    </justification>
  </clause>

  <clause id="10781">
    <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(453(a,1),10780(a,1,1))].">
      <j1 rule="para" parents="453 10780"/>
    </justification>
  </clause>

  <clause id="10782">
    <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(333,a,1179,a(flip),b,10705,a),flip(a)].">
      <j1 rule="hyper" parents="333 1179 10705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10783">
    <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(27(a,2),10782(a,2,3))].">
      <j1 rule="para" parents="27 10782"/>
    </justification>
  </clause>

  <clause id="10784">
    <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(8963(a,1),10779(a,1,1))].">
      <j1 rule="para" parents="8963 10779"/>
    </justification>
  </clause>

  <clause id="10785">
    <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(4965(a,1),10784(a,1,2))].">
      <j1 rule="para" parents="4965 10784"/>
    </justification>
  </clause>

  <clause id="10786">
    <literal><![CDATA[
      K((x \ y) \ z,x / y) * K(x / y,z) = a((y / x) \ 1,z,(y / x) \ 1)
    ]]></literal>
    <justification jstring="[para(7304(a,1),10785(a,1,2))].">
      <j1 rule="para" parents="7304 10785"/>
    </justification>
  </clause>

  <clause id="10787">
    <literal><![CDATA[
      K(L(x,y,z),T(u \ L(x,y,z),L(K(x,w),v5,v6))) = K(L(x,y,z),L(x,y,z) * (u \ L(K(x,w),v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(333,a,10651,a(flip),b,10189,a),flip(a)].">
      <j1 rule="hyper" parents="333 10651 10189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10788">
    <literal><![CDATA[
      K(L(x,y,z),T(u \ L(x,y,z),L(K(x,w),v5,v6))) = K(L(x,y,z),x * (u \ L(K(x,w),v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(333,a,10751,a(flip),b,10787,a),flip(a)].">
      <j1 rule="hyper" parents="333 10751 10787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10789">
    <literal><![CDATA[
      K(L(x,y,z),T(u \ L(x,y,z),L(K(x,w),v5,v6))) = K(L(x,y,z),u \ x)
    ]]></literal>
    <justification jstring="[hyper(333,a,10688,a(flip),b,10788,a),flip(a)].">
      <j1 rule="hyper" parents="333 10688 10788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10791">
    <literal><![CDATA[
      K(L(x,y,z),u \ L(x,y,z)) = K(L(x,y,z),u \ x)
    ]]></literal>
    <justification jstring="[para(2407(a,1),10789(a,1,2))].">
      <j1 rule="para" parents="2407 10789"/>
    </justification>
  </clause>

  <clause id="10792">
    <literal><![CDATA[
      K(x \ L(y,z,u),L(y,z,u)) = (w * K(L(y,z,u),x \ y)) \ w
    ]]></literal>
    <justification jstring="[para(10791(a,1),5990(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10791 5990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10793">
    <literal><![CDATA[
      K(x \ L(y,z,u),L(y,z,u)) = K(x \ y,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(333,a,5990,a(flip),b,10792,a),flip(a)].">
      <j1 rule="hyper" parents="333 5990 10792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10794">
    <literal><![CDATA[
      T(L(x,y,z) * K((u \ 1) \ x,L(x,y,z)),u) = u \ T(L(x,y,z) * u,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(10793(a,1),5972(a,1,1,2))].">
      <j1 rule="para" parents="10793 5972"/>
    </justification>
  </clause>

  <clause id="10795">
    <literal><![CDATA[
      T(L(x,y,z) * K(x * (1 \ u),L(x,y,z)),u) = u \ T(L(x,y,z) * u,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(10691(a,1),10794(a,1,1,2))].">
      <j1 rule="para" parents="10691 10794"/>
    </justification>
  </clause>

  <clause id="10796">
    <literal><![CDATA[
      T(L(x,y,z) * K(x * u,L(x,y,z)),u) = u \ T(L(x,y,z) * u,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(65(a,1),10795(a,1,1,2,1,2))].">
      <j1 rule="para" parents="65 10795"/>
    </justification>
  </clause>

  <clause id="10797">
    <literal><![CDATA[
      T(L(x * K(x * y,x),z,u),y) = y \ T(L(x,z,u) * y,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(4941(a,1),10796(a,1,1))].">
      <j1 rule="para" parents="4941 10796"/>
    </justification>
  </clause>

  <clause id="10798">
    <literal><![CDATA[
      L(T(x * K(x * y,x),y),z,u) = y \ T(L(x,z,u) * y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(10114,a,10797,a)].">
      <j1 rule="hyper" parents="10114 10797"/>
    </justification>
  </clause>

  <clause id="10799">
    <literal><![CDATA[
      x \ T(L(y,z,u) * x,L(y,z,u)) = L(R(y,x,y),z,u)
    ]]></literal>
    <justification jstring="[para(4650(a,1),10798(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4650 10798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10800">
    <literal><![CDATA[
      R(L(x,y,z),u,L(x,y,z)) = L(R(x,u,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(3751,a,10799,a)].">
      <j1 rule="hyper" parents="3751 10799"/>
    </justification>
  </clause>

  <clause id="10801">
    <literal><![CDATA[
      R(x,y,L(x,z,u)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(41,a,29,a(flip),b,10800,a(flip))].">
      <j1 rule="hyper" parents="41 29 10800"/>
    </justification>
  </clause>

  <clause id="10802">
    <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(10800(a,1),6337(a,1,2))].">
      <j1 rule="para" parents="10800 6337"/>
    </justification>
  </clause>

  <clause id="10803">
    <literal><![CDATA[
      T(x * K(y * x,x),y) = R(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(333,a,4425,a,b,10801,a)].">
      <j1 rule="hyper" parents="333 4425 10801"/>
    </justification>
  </clause>

  <clause id="10806">
    <literal><![CDATA[
      K(x * L(y,z,u),y) = (w * T(y,x)) \ (w * R(y,x,y))
    ]]></literal>
    <justification jstring="[para(10801(a,1),8785(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10801 8785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10807">
    <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(10801(a,1),9368(a,1,1,2,2))].">
      <j1 rule="para" parents="10801 9368"/>
    </justification>
  </clause>

  <clause id="10808">
    <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(10610(a,1),10803(a,1,1,2))].">
      <j1 rule="para" parents="10610 10803"/>
    </justification>
  </clause>

  <clause id="10809">
    <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(10227(a,1),10802(a,1))].">
      <j1 rule="para" parents="10227 10802"/>
    </justification>
  </clause>

  <clause id="10810">
    <literal><![CDATA[
      K(x * L(y,z,u),y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,6523,a(flip),b,10806,a),flip(a)].">
      <j1 rule="hyper" parents="333 6523 10806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10812">
    <literal><![CDATA[
      K(x * L(y,z,u),y) = K(x,y) * a(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,8243,a,b,10810,a),flip(a)].">
      <j1 rule="hyper" parents="333 8243 10810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10813">
    <literal><![CDATA[
      K(x \ L(y,z,u),y) = K(y * (x \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,10193,a(flip),b,10810,a)].">
      <j1 rule="hyper" parents="63 10193 10810"/>
    </justification>
  </clause>

  <clause id="10814">
    <literal><![CDATA[
      K(x * (L(x,y,z) \ u),x) = K(u,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,9420,a(flip),b,10810,a),flip(a)].">
      <j1 rule="hyper" parents="63 9420 10810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10815">
    <literal><![CDATA[
      K(x * (y * z),z) = K(z * (x * y),z)
    ]]></literal>
    <justification jstring="[para(97(a,1),10810(a,1,1))].">
      <j1 rule="para" parents="97 10810"/>
    </justification>
  </clause>

  <clause id="10818">
    <literal><![CDATA[
      T(x,x * (L(x,y,z) \ u)) = (w * K(u,x)) \ (w * x)
    ]]></literal>
    <justification jstring="[para(10814(a,1),5447(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10814 5447"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10819">
    <literal><![CDATA[
      K(x * (y * z),y) = K(y * (x * z),y)
    ]]></literal>
    <justification jstring="[hyper(7459,a,10815,a)].">
      <j1 rule="hyper" parents="7459 10815"/>
    </justification>
  </clause>

  <clause id="10821">
    <literal><![CDATA[
      K(x \ L(y,z,u),y) = K(x \ y,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,5939,a(flip),b,10813,a),flip(a)].">
      <j1 rule="hyper" parents="333 5939 10813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10822">
    <literal><![CDATA[
      K(x / (L(y,z,u) \ w),y) = K((w / x) \ y,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,10234,a,b,10821,a)].">
      <j1 rule="hyper" parents="63 10234 10821"/>
    </justification>
  </clause>

  <clause id="10823">
    <literal><![CDATA[
      K(x \ (y * L(z,u,w)),z) = K((y \ x) \ z,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,10194,a(flip),b,10821,a)].">
      <j1 rule="hyper" parents="63 10194 10821"/>
    </justification>
  </clause>

  <clause id="10824">
    <literal><![CDATA[
      (L(x,y,z) * K((u \ x) \ x,x)) * u = (x \ (L(x,y,z) * u)) * x
    ]]></literal>
    <justification jstring="[para(10821(a,1),7787(a,1,1,2))].">
      <j1 rule="para" parents="10821 7787"/>
    </justification>
  </clause>

  <clause id="10827">
    <literal><![CDATA[
      K(x \ (y * L(z,u,w)),z) = K(z * (x \ y),z)
    ]]></literal>
    <justification jstring="[hyper(333,a,10673,a(flip),b,10823,a),flip(a)].">
      <j1 rule="hyper" parents="333 10673 10823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10828">
    <literal><![CDATA[
      K(x \ (y * L(x,z,u)),x) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,5917,a(flip),b,10823,a),flip(a)].">
      <j1 rule="hyper" parents="333 5917 10823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10829">
    <literal><![CDATA[
      K(x \ (y * L(x,z,u)),x) != w
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = w
    ]]></literal>
    <justification jstring="[para(10823(a,2),5919(a,1))].">
      <j1 rule="para" parents="10823 5919"/>
    </justification>
  </clause>

  <clause id="10830">
    <literal><![CDATA[
      K(x / L(y,z,u),y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[para(12(a,1),10828(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="12 10828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10831">
    <literal><![CDATA[
      T(x * L(y,z,u),K(x,y)) = x * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(10828(a,1),4195(a,1,2))].">
      <j1 rule="para" parents="10828 4195"/>
    </justification>
  </clause>

  <clause id="10832">
    <literal><![CDATA[
      K(x \ (y * (z * x)),x) != u
    ]]></literal>
    <literal><![CDATA[
      K(y * z,x) = u
    ]]></literal>
    <justification jstring="[para(97(a,1),10829(a,1,1,2))].">
      <j1 rule="para" parents="97 10829"/>
    </justification>
  </clause>

  <clause id="10833">
    <literal><![CDATA[
      T(x * ((y * z) \ (y * u)),K(x,z \ u)) = x * L(z \ u,z,y)
    ]]></literal>
    <justification jstring="[para(99(a,1),10831(a,1,1,2))].">
      <j1 rule="para" parents="99 10831"/>
    </justification>
  </clause>

  <clause id="10834">
    <literal><![CDATA[
      K(x \ (y * (z * u)),u) = K(u * (x \ (y * z)),u)
    ]]></literal>
    <justification jstring="[para(97(a,1),10827(a,1,1,2))].">
      <j1 rule="para" parents="97 10827"/>
    </justification>
  </clause>

  <clause id="10835">
    <literal><![CDATA[
      K(x \ (y * (x * z)),x) = K(y * z,x)
    ]]></literal>
    <justification jstring="[hyper(10832,a,9584,a),flip(a)].">
      <j1 rule="hyper" parents="10832 9584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10836">
    <literal><![CDATA[
      K(x \ (y * z),x) = K(y * (x \ z),x)
    ]]></literal>
    <justification jstring="[para(10(a,1),10835(a,1,1,2,2))].">
      <j1 rule="para" parents="10 10835"/>
    </justification>
  </clause>

  <clause id="10837">
    <literal><![CDATA[
      K(x \ (y \ (z * (u * y))),y) = K(y * ((x * y) \ (z * u)),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,6555,a(flip),b,10834,a)].">
      <j1 rule="hyper" parents="63 6555 10834"/>
    </justification>
  </clause>

  <clause id="10838">
    <literal><![CDATA[
      T(x,x * (L(x,y,z) \ u)) = T(x,u)
    ]]></literal>
    <justification jstring="[hyper(333,a,5447,a(flip),b,10818,a),flip(a)].">
      <j1 rule="hyper" parents="333 5447 10818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10839">
    <literal><![CDATA[
      T(x,L(x,y,z) * u) = T(x,x * u)
    ]]></literal>
    <justification jstring="[para(9(a,1),10838(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 10838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10840">
    <literal><![CDATA[
      (x * (L(x,y,z) \ u)) \ (x * u) = L(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(10838(a,1),1694(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10838 1694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10841">
    <literal><![CDATA[
      T(x,L(x,y,z) * u) = x * K(x,x * u)
    ]]></literal>
    <justification jstring="[hyper(333,a,4222,a(flip),b,10839,a),flip(a)].">
      <j1 rule="hyper" parents="333 4222 10839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10842">
    <literal><![CDATA[
      K(x,L(x,y,z) * u) = K(x,x * u)
    ]]></literal>
    <justification jstring="[hyper(4305,a,10841,a)].">
      <j1 rule="hyper" parents="4305 10841"/>
    </justification>
  </clause>

  <clause id="10843">
    <literal><![CDATA[
      K(x,K(y,L(y,z,u) * w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[para(10842(a,2),6874(a,1,2))].">
      <j1 rule="para" parents="10842 6874"/>
    </justification>
  </clause>

  <clause id="10844">
    <literal><![CDATA[
      (x * (L(x,y,z) \ (x \ u))) \ (x * (x \ u)) = L((x \ u) \ u,y,z)
    ]]></literal>
    <justification jstring="[para(112(a,1),10840(a,2,1))].">
      <j1 rule="para" parents="112 10840"/>
    </justification>
  </clause>

  <clause id="10846">
    <literal><![CDATA[
      K(x \ (y \ (z * (u * y))),y) = K(x \ (z * u),y)
    ]]></literal>
    <justification jstring="[hyper(333,a,10677,a(flip),b,10837,a),flip(a)].">
      <j1 rule="hyper" parents="333 10677 10837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10847">
    <literal><![CDATA[
      K(L(x,y * z,u),y) = K((u * z) \ (u * (z * x)),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,9971,a(flip),b,10846,a)].">
      <j1 rule="hyper" parents="63 9971 10846"/>
    </justification>
  </clause>

  <clause id="10848">
    <literal><![CDATA[
      K(L(x,y * z,u),y) = K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(18(a,2),10847(a,2,1))].">
      <j1 rule="para" parents="18 10847"/>
    </justification>
  </clause>

  <clause id="10849">
    <literal><![CDATA[
      K(L(x,x \ y,z),u) = K(x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(10809,a,10848,a),flip(a)].">
      <j1 rule="hyper" parents="10809 10848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10850">
    <literal><![CDATA[
      K(L(x,x \ y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(u,y,z)) = w
    ]]></literal>
    <justification jstring="[para(10848(a,1),10809(a,1))].">
      <j1 rule="para" parents="10848 10809"/>
    </justification>
  </clause>

  <clause id="10851">
    <literal><![CDATA[
      L(K(x,y),z,u) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,7780,a(flip),b,10849,a)].">
      <j1 rule="hyper" parents="63 7780 10849"/>
    </justification>
  </clause>

  <clause id="10852">
    <literal><![CDATA[
      K(x,L(y,T(x,z),u)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(5435(a,1),10849(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5435 10849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10853">
    <literal><![CDATA[
      K(x,(y * T(x,z)) \ u) = K(x,T(x,z) \ (y \ u))
    ]]></literal>
    <justification jstring="[para(311(a,1),10852(a,1,2))].">
      <j1 rule="para" parents="311 10852"/>
    </justification>
  </clause>

  <clause id="10854">
    <literal><![CDATA[
      K(x,(y * (z \ u)) \ (y * u)) = K(x,L(T(z,u),u,y))
    ]]></literal>
    <justification jstring="[hyper(9765,a,10851,a)].">
      <j1 rule="hyper" parents="9765 10851"/>
    </justification>
  </clause>

  <clause id="10855">
    <literal><![CDATA[
      K(x,L(y \ z,z,u)) = K(x,(u * y) \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(9568,a,10851,a),flip(a)].">
      <j1 rule="hyper" parents="9568 10851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10856">
    <literal><![CDATA[
      K(x,L(y,z * x,u)) = K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(9539,a,10851,a),flip(a)].">
      <j1 rule="hyper" parents="9539 10851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10857">
    <literal><![CDATA[
      K(x \ (y \ z),L(u,y \ z,y)) = K((y * x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(8475,a,10851,a),flip(a)].">
      <j1 rule="hyper" parents="8475 10851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10858">
    <literal><![CDATA[
      x * L(K(x,y),z,u) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(126,a,10851,a,b,4215,a(flip))].">
      <j1 rule="hyper" parents="126 10851 4215"/>
    </justification>
  </clause>

  <clause id="10859">
    <literal><![CDATA[
      K(L(x,y,z),u) \ w = L(K(u,x),y,z) * w
    ]]></literal>
    <justification jstring="[hyper(125,a,10851,a,b,4564,a),flip(a)].">
      <j1 rule="hyper" parents="125 10851 4564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10860">
    <literal><![CDATA[
      K(x,y) * a(z,u,K(y,x)) = K(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,9731,a,b,10851,a)].">
      <j1 rule="hyper" parents="63 9731 10851"/>
    </justification>
  </clause>

  <clause id="10861">
    <literal><![CDATA[
      K(x,L(y,y \ z,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,9722,a,b,10851,a)].">
      <j1 rule="hyper" parents="63 9722 10851"/>
    </justification>
  </clause>

  <clause id="10862">
    <literal><![CDATA[
      K(x,L(y,z / y,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,9453,a,b,10851,a)].">
      <j1 rule="hyper" parents="63 9453 10851"/>
    </justification>
  </clause>

  <clause id="10863">
    <literal><![CDATA[
      L(K(x,y),z,u) \ 1 = K(y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,9448,a,b,10851,a)].">
      <j1 rule="hyper" parents="63 9448 10851"/>
    </justification>
  </clause>

  <clause id="10864">
    <literal><![CDATA[
      L(K(x,y),z,z \ x) = K(x,L(y,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,10770,a(flip),b,10851,a)].">
      <j1 rule="hyper" parents="63 10770 10851"/>
    </justification>
  </clause>

  <clause id="10865">
    <literal><![CDATA[
      K(x,L(y / z,z,u)) = K(x,L(y / z,y,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,9727,a(flip),b,10851,a)].">
      <j1 rule="hyper" parents="63 9727 10851"/>
    </justification>
  </clause>

  <clause id="10866">
    <literal><![CDATA[
      K(x,L(y,y * z,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,9721,a(flip),b,10851,a),flip(a)].">
      <j1 rule="hyper" parents="63 9721 10851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10867">
    <literal><![CDATA[
      K(x,L((y \ z) \ u,u,y)) = K(x,z \ (y * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,9513,a(flip),b,10851,a),flip(a)].">
      <j1 rule="hyper" parents="63 9513 10851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10868">
    <literal><![CDATA[
      K(x,L(y \ z,z,u)) = K(x,L(y \ z,y,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,9458,a(flip),b,10851,a),flip(a)].">
      <j1 rule="hyper" parents="63 9458 10851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10869">
    <literal><![CDATA[
      K((x \ 1) \ (x \ y),L(z,y / x,x)) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,9110,a(flip),b,10851,a),flip(a)].">
      <j1 rule="hyper" parents="63 9110 10851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10870">
    <literal><![CDATA[
      K(x \ y,L(z,y,y \ 1)) = K(((y \ 1) * x) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,6281,a(flip),b,10851,a),flip(a)].">
      <j1 rule="hyper" parents="63 6281 10851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10871">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,u) = K(x \ 1,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,5369,a(flip),b,10851,a)].">
      <j1 rule="hyper" parents="63 5369 10851"/>
    </justification>
  </clause>

  <clause id="10872">
    <literal><![CDATA[
      x * K(y,L(z,u \ x,u)) = u * ((u \ x) * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(126,a,10851,a(flip),b,98,a)].">
      <j1 rule="hyper" parents="126 10851 98"/>
    </justification>
  </clause>

  <clause id="10873">
    <literal><![CDATA[
      (x * y) * K(z,L(u,x,y)) = y * (T(x,y) * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(126,a,10851,a(flip),b,10082,a(flip))].">
      <j1 rule="hyper" parents="126 10851 10082"/>
    </justification>
  </clause>

  <clause id="10874">
    <literal><![CDATA[
      (x * y) * K(z,L(u,y,x)) = x * (y * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(126,a,10851,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="126 10851 18"/>
    </justification>
  </clause>

  <clause id="10875">
    <literal><![CDATA[
      L(K(x,y \ (z \ u)),y,z) = K(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[para(311(a,1),10851(a,2,2))].">
      <j1 rule="para" parents="311 10851"/>
    </justification>
  </clause>

  <clause id="10876">
    <literal><![CDATA[
      L(K(x,(y \ z) \ u),y \ z,y) = K(x,z \ (y * u))
    ]]></literal>
    <justification jstring="[para(515(a,1),10851(a,2,2))].">
      <j1 rule="para" parents="515 10851"/>
    </justification>
  </clause>

  <clause id="10878">
    <literal><![CDATA[
      (x * y) * K(z,L(u,y,x)) != w * v5
    ]]></literal>
    <literal><![CDATA[
      w \ (x * (y * K(z,u))) = v5
    ]]></literal>
    <justification jstring="[para(10851(a,1),626(a,1,2))].">
      <j1 rule="para" parents="10851 626"/>
    </justification>
  </clause>

  <clause id="10879">
    <literal><![CDATA[
      ((x * y) / x) * L(((x * y) / x) \ y,z,u) = ((x * y) * K(y,L(x,z,u))) / x
    ]]></literal>
    <justification jstring="[para(10851(a,1),1835(a,2,1,2))].">
      <j1 rule="para" parents="10851 1835"/>
    </justification>
  </clause>

  <clause id="10880">
    <literal><![CDATA[
      ((x * y) / x) * L(((x * y) / x) \ y,z,u) = K(y,L(x,z,u)) * ((x * y) / x)
    ]]></literal>
    <justification jstring="[para(10851(a,1),4410(a,2,1))].">
      <j1 rule="para" parents="10851 4410"/>
    </justification>
  </clause>

  <clause id="10881">
    <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(10851(a,1),7551(a,1,2))].">
      <j1 rule="para" parents="10851 7551"/>
    </justification>
  </clause>

  <clause id="10882">
    <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(10851(a,1),8475(a,1))].">
      <j1 rule="para" parents="10851 8475"/>
    </justification>
  </clause>

  <clause id="10883">
    <literal><![CDATA[
      K(x,y) * K(y,L(x,z,u)) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(10851(a,1),9729(a,1,2))].">
      <j1 rule="para" parents="10851 9729"/>
    </justification>
  </clause>

  <clause id="10884">
    <literal><![CDATA[
      K(x,L(y,z,u)) * K(y,x) = a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[para(10851(a,1),9732(a,1,1))].">
      <j1 rule="para" parents="10851 9732"/>
    </justification>
  </clause>

  <clause id="10885">
    <literal><![CDATA[
      K(x,L(y,z,u)) * a(u,z,K(x,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(10851(a,1),9744(a,1,1))].">
      <j1 rule="para" parents="10851 9744"/>
    </justification>
  </clause>

  <clause id="10886">
    <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(10851(a,1),9697(a,1))].">
      <j1 rule="para" parents="10851 9697"/>
    </justification>
  </clause>

  <clause id="10887">
    <literal><![CDATA[
      x * K(y,L(z,u,u \ x)) = (x / u) * (u * K(y,z))
    ]]></literal>
    <justification jstring="[para(10851(a,1),10103(a,1,2))].">
      <j1 rule="para" parents="10851 10103"/>
    </justification>
  </clause>

  <clause id="10889">
    <literal><![CDATA[
      K(x,K(L(x,y,z),u) * w) = K(x,w)
    ]]></literal>
    <justification jstring="[para(10856(a,1),7406(a,1,2,1))].">
      <j1 rule="para" parents="10856 7406"/>
    </justification>
  </clause>

  <clause id="10890">
    <literal><![CDATA[
      K(x,L(x,y,z) * u) = K(x,u * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(4201(a,1),10889(a,1,2))].">
      <j1 rule="para" parents="4201 10889"/>
    </justification>
  </clause>

  <clause id="10891">
    <literal><![CDATA[
      K(x,y) \ L(K(x,y),z,u) = T(y,x) \ T(y,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(10858(a,1),5542(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10858 5542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10892">
    <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(10861(a,1),10412(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10861 10412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10893">
    <literal><![CDATA[
      K(x,L(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x,y),z,u) = w
    ]]></literal>
    <justification jstring="[para(10862(a,1),9534(a,1))].">
      <j1 rule="para" parents="10862 9534"/>
    </justification>
  </clause>

  <clause id="10894">
    <literal><![CDATA[
      L(K(x,y),z,u) = K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(39,a,4367,a,b,10863,a),flip(a)].">
      <j1 rule="hyper" parents="39 4367 10863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10895">
    <literal><![CDATA[
      K(x,(y * (z \ u)) \ (y * u)) = K(L(x,u,y),T(z,u))
    ]]></literal>
    <justification jstring="[hyper(9765,a,10894,a)].">
      <j1 rule="hyper" parents="9765 10894"/>
    </justification>
  </clause>

  <clause id="10896">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) = K(y,K(z,L(x,u,w)))
    ]]></literal>
    <justification jstring="[hyper(333,a,6788,a,b,10894,a),flip(a)].">
      <j1 rule="hyper" parents="333 6788 10894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10897">
    <literal><![CDATA[
      (x * (y * K(z,u))) \ (x * y) = K(L(u,y,x),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,9450,a,b,10894,a)].">
      <j1 rule="hyper" parents="63 9450 10894"/>
    </justification>
  </clause>

  <clause id="10898">
    <literal><![CDATA[
      K(L(x,y,z),u) = K(x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,10851,a(flip),b,10894,a),flip(a)].">
      <j1 rule="hyper" parents="63 10851 10894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10899">
    <literal><![CDATA[
      K(L(x,y,z),T(y,u)) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,6457,a(flip),b,10894,a),flip(a)].">
      <j1 rule="hyper" parents="63 6457 10894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10900">
    <literal><![CDATA[
      K(L(K(x,y),z,u),w) = K(w,K(y,L(x,z,u)))
    ]]></literal>
    <justification jstring="[para(10894(a,2),5296(a,1,1))].">
      <j1 rule="para" parents="10894 5296"/>
    </justification>
  </clause>

  <clause id="10901">
    <literal><![CDATA[
      K(x,L(K(y,z),u,w)) = K(x,K(z,L(y,u,w)))
    ]]></literal>
    <justification jstring="[para(10894(a,2),6800(a,1,2))].">
      <j1 rule="para" parents="10894 6800"/>
    </justification>
  </clause>

  <clause id="10902">
    <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(10894(a,2),6825(a,1))].">
      <j1 rule="para" parents="10894 6825"/>
    </justification>
  </clause>

  <clause id="10904">
    <literal><![CDATA[
      K(x,y) * K(L(y,z,u),x) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(10894(a,1),9729(a,1,2))].">
      <j1 rule="para" parents="10894 9729"/>
    </justification>
  </clause>

  <clause id="10905">
    <literal><![CDATA[
      K(x,L(y,z * x,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,10856,a,b,10898,a)].">
      <j1 rule="hyper" parents="63 10856 10898"/>
    </justification>
  </clause>

  <clause id="10906">
    <literal><![CDATA[
      K(x,L(y,x \ z,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,10849,a(flip),b,10898,a),flip(a)].">
      <j1 rule="hyper" parents="63 10849 10898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10907">
    <literal><![CDATA[
      K(x \ (y \ z),L(u,x,y)) = K((y * x) \ z,u)
    ]]></literal>
    <justification jstring="[para(311(a,1),10898(a,1,1)),flip(a)].">
      <j1 rule="para" parents="311 10898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10908">
    <literal><![CDATA[
      K((x \ 1) \ y,L(z,x \ 1,x)) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(514(a,1),10898(a,1,1)),flip(a)].">
      <j1 rule="para" parents="514 10898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10909">
    <literal><![CDATA[
      K((x \ y) \ z,L(u,x \ y,x)) = K(y \ (x * z),u)
    ]]></literal>
    <justification jstring="[para(515(a,1),10898(a,1,1)),flip(a)].">
      <j1 rule="para" parents="515 10898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10910">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (y \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(y,L(x,z,u)) \ w = v5
    ]]></literal>
    <justification jstring="[para(10898(a,1),4697(a,1,1))].">
      <j1 rule="para" parents="10898 4697"/>
    </justification>
  </clause>

  <clause id="10911">
    <literal><![CDATA[
      L(T(x,y),z,u) * (L(x,z,u) \ w) = K(x,L(y,z,u)) * w
    ]]></literal>
    <justification jstring="[para(10898(a,1),4537(a,2,1))].">
      <j1 rule="para" parents="10898 4537"/>
    </justification>
  </clause>

  <clause id="10912">
    <literal><![CDATA[
      x * (K(y,L(x,z,u)) * K(w,L(y,z,u))) = (L(y,z,u) * x) / T(L(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(10898(a,1),5471(a,1,2,1))].">
      <j1 rule="para" parents="10898 5471"/>
    </justification>
  </clause>

  <clause id="10913">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) = K(z,K(x,L(y,u,w)))
    ]]></literal>
    <justification jstring="[para(10898(a,1),6788(a,1,2))].">
      <j1 rule="para" parents="10898 6788"/>
    </justification>
  </clause>

  <clause id="10914">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) = K(x,K(z,L(y,u,w)))
    ]]></literal>
    <justification jstring="[para(10898(a,1),6800(a,1,2))].">
      <j1 rule="para" parents="10898 6800"/>
    </justification>
  </clause>

  <clause id="10916">
    <literal><![CDATA[
      K(x * K(y,L(x,z,u)),w) = K(x,T(w,L(y,z,u)))
    ]]></literal>
    <justification jstring="[para(10898(a,1),6935(a,1,1,2))].">
      <j1 rule="para" parents="10898 6935"/>
    </justification>
  </clause>

  <clause id="10917">
    <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(10898(a,1),6836(a,1,2))].">
      <j1 rule="para" parents="10898 6836"/>
    </justification>
  </clause>

  <clause id="10918">
    <literal><![CDATA[
      ((x * y) * K(z,L(u,y,x))) \ (x * (y * T(z,u))) = L(z,y,x)
    ]]></literal>
    <justification jstring="[para(10898(a,1),6063(a,1,1,2))].">
      <j1 rule="para" parents="10898 6063"/>
    </justification>
  </clause>

  <clause id="10919">
    <literal><![CDATA[
      (L(x,y,z) * (u * K(x,L(w,y,z)))) / L(T(x,w),y,z) = (L(x,y,z) * u) / L(x,y,z)
    ]]></literal>
    <justification jstring="[para(10898(a,1),6205(a,1,1,2,2))].">
      <j1 rule="para" parents="10898 6205"/>
    </justification>
  </clause>

  <clause id="10920">
    <literal><![CDATA[
      K((x * y) / (x * z),z) = K(z \ y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(8418,a,10899,a)].">
      <j1 rule="hyper" parents="8418 10899"/>
    </justification>
  </clause>

  <clause id="10921">
    <literal><![CDATA[
      K(x \ y,L(z,y,u)) = K(x \ y,L(z,x,u))
    ]]></literal>
    <justification jstring="[para(10(a,1),10905(a,1,2,2))].">
      <j1 rule="para" parents="10 10905"/>
    </justification>
  </clause>

  <clause id="10922">
    <literal><![CDATA[
      K(x,L(y,z / x,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(12(a,1),10905(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 10905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10923">
    <literal><![CDATA[
      K(x,L(y,x * z,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(9(a,1),10906(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 10906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10924">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) = v5
    ]]></literal>
    <justification jstring="[para(10851(a,1),10893(a,1,2))].">
      <j1 rule="para" parents="10851 10893"/>
    </justification>
  </clause>

  <clause id="10925">
    <literal><![CDATA[
      K(L(x,y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x,u),y,z) = w
    ]]></literal>
    <justification jstring="[para(10898(a,2),10893(a,1))].">
      <j1 rule="para" parents="10898 10893"/>
    </justification>
  </clause>

  <clause id="10926">
    <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(6788(a,2),10925(a,1))].">
      <j1 rule="para" parents="6788 10925"/>
    </justification>
  </clause>

  <clause id="10927">
    <literal><![CDATA[
      L(K(x,y),z,u) \ R(T(x,L(y,z,u)),w,x) = R(x,w,x)
    ]]></literal>
    <justification jstring="[hyper(121,a,6562,a(flip),b,10859,a(flip))].">
      <j1 rule="hyper" parents="121 6562 10859"/>
    </justification>
  </clause>

  <clause id="10928">
    <literal><![CDATA[
      a(x,y,K(z,u)) * K(u,z) = K(u,L(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,8771,a(flip),b,10860,a)].">
      <j1 rule="hyper" parents="63 8771 10860"/>
    </justification>
  </clause>

  <clause id="10929">
    <literal><![CDATA[
      a(x,y,K(z,u)) * K(z,L(u,y,x)) = K(z,u)
    ]]></literal>
    <justification jstring="[hyper(126,a,10860,a(flip),b,9793,a)].">
      <j1 rule="hyper" parents="126 10860 9793"/>
    </justification>
  </clause>

  <clause id="10930">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1)) = K(x,L(y,z,z \ x))
    ]]></literal>
    <justification jstring="[hyper(63,a,10851,a(flip),b,10864,a),flip(a)].">
      <j1 rule="hyper" parents="63 10851 10864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10931">
    <literal><![CDATA[
      K(x,L(T(y,z) \ u,u,z)) = K(x,(y * z) \ (z * u))
    ]]></literal>
    <justification jstring="[para(520(a,1),10868(a,2,2))].">
      <j1 rule="para" parents="520 10868"/>
    </justification>
  </clause>

  <clause id="10932">
    <literal><![CDATA[
      a(x,y * z,K(z,u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,9739,a(flip),b,10883,a)].">
      <j1 rule="hyper" parents="63 9739 10883"/>
    </justification>
  </clause>

  <clause id="10933">
    <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(10883(a,1),4590(a,1,2))].">
      <j1 rule="para" parents="10883 4590"/>
    </justification>
  </clause>

  <clause id="10934">
    <literal><![CDATA[
      a(x,y * z,K(u,K(w,z))) = a(x,y,K(z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(6788(a,2),10932(a,1,3))].">
      <j1 rule="para" parents="6788 10932"/>
    </justification>
  </clause>

  <clause id="10935">
    <literal><![CDATA[
      T(x,L(y,z,u)) * K(y,x) = x * a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(126,a,10884,a(flip),b,4515,a),flip(a)].">
      <j1 rule="hyper" parents="126 10884 4515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10936">
    <literal><![CDATA[
      a(x,y,K(z,u)) * T(u,z) = T(u,L(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(125,a,10884,a(flip),b,5448,a)].">
      <j1 rule="hyper" parents="125 10884 5448"/>
    </justification>
  </clause>

  <clause id="10937">
    <literal><![CDATA[
      K(x,y * L(x,z,u)) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,10842,a(flip),b,10890,a),flip(a)].">
      <j1 rule="hyper" parents="63 10842 10890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10938">
    <literal><![CDATA[
      K(x,K(y,z * L(y,u,w))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(10890(a,1),10843(a,1,2))].">
      <j1 rule="para" parents="10890 10843"/>
    </justification>
  </clause>

  <clause id="10941">
    <literal><![CDATA[
      K(x \ 1,(x \ 1) * (y * x)) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(392(a,1),10937(a,1,2)),flip(a)].">
      <j1 rule="para" parents="392 10937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10943">
    <literal><![CDATA[
      K(x,K(y,z * (u * y))) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[para(97(a,1),10938(a,1,2,2))].">
      <j1 rule="para" parents="97 10938"/>
    </justification>
  </clause>

  <clause id="10944">
    <literal><![CDATA[
      K(x,K(y / z,L(u,y,w))) = K(x,K(u,L(y / z,z,w)))
    ]]></literal>
    <justification jstring="[para(9727(a,1),10901(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9727 10901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10945">
    <literal><![CDATA[
      a(x,y * z,K(u,z)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,9736,a(flip),b,10904,a)].">
      <j1 rule="hyper" parents="63 9736 10904"/>
    </justification>
  </clause>

  <clause id="10946">
    <literal><![CDATA[
      (x * y) / T(x,L(y,z,u)) = y * a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(10904(a,1),5471(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10904 5471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10947">
    <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(10900(a,1),10904(a,1,2))].">
      <j1 rule="para" parents="10900 10904"/>
    </justification>
  </clause>

  <clause id="10948">
    <literal><![CDATA[
      a(x,y / z,K(u,z)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[para(12(a,1),10945(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12 10945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10949">
    <literal><![CDATA[
      x / T(x / y,L(y,z,u)) = y * a(u,z,K(y \ x,y))
    ]]></literal>
    <justification jstring="[para(10945(a,1),9973(a,2,2))].">
      <j1 rule="para" parents="10945 9973"/>
    </justification>
  </clause>

  <clause id="10951">
    <literal><![CDATA[
      K(x,K(y,L(z \ 1,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(y,K(z,L(x,u,w))) = v5
    ]]></literal>
    <justification jstring="[para(10913(a,1),7181(a,1))].">
      <j1 rule="para" parents="10913 7181"/>
    </justification>
  </clause>

  <clause id="10952">
    <literal><![CDATA[
      K(x,K(y,L(z,1 / u,w))) = K(x,K(z,L(y,u,w)))
    ]]></literal>
    <justification jstring="[para(2597(a,1),10914(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2597 10914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10953">
    <literal><![CDATA[
      K(x \ ((y * z) / y),x) = K(x \ z,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,10503,a(flip),b,10920,a)].">
      <j1 rule="hyper" parents="63 10503 10920"/>
    </justification>
  </clause>

  <clause id="10954">
    <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(10928(a,1),5998(a,1,1))].">
      <j1 rule="para" parents="10928 5998"/>
    </justification>
  </clause>

  <clause id="10956">
    <literal><![CDATA[
      K(x,y) * K(L(y,z,u),x) != w
    ]]></literal>
    <literal><![CDATA[
      a(u,z,K(x,y)) = w
    ]]></literal>
    <justification jstring="[para(10929(a,1),5998(a,1,1))].">
      <j1 rule="para" parents="10929 5998"/>
    </justification>
  </clause>

  <clause id="10957">
    <literal><![CDATA[
      a(x,T(y,z),K(u,y \ L(y,w,v5))) * K(u,L(y \ L(y,w,v5),y,x)) = K(u,y \ L(y,w,v5))
    ]]></literal>
    <justification jstring="[para(9173(a,1),10929(a,1,2,2))].">
      <j1 rule="para" parents="9173 10929"/>
    </justification>
  </clause>

  <clause id="10958">
    <literal><![CDATA[
      K(x,L(y,z \ x,(z \ x) \ 1)) = K(x,L(y,z \ x,z))
    ]]></literal>
    <justification jstring="[para(10098(a,1),10930(a,2,2))].">
      <j1 rule="para" parents="10098 10930"/>
    </justification>
  </clause>

  <clause id="10959">
    <literal><![CDATA[
      K(x,K(y / z,u * z)) = K(x,K(y / z,u * y))
    ]]></literal>
    <justification jstring="[para(9437(a,1),10943(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9437 10943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10960">
    <literal><![CDATA[
      L(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(7780(a,1),10850(a,1))].">
      <j1 rule="para" parents="7780 10850"/>
    </justification>
  </clause>

  <clause id="10961">
    <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(9458(a,1),10960(a,1))].">
      <j1 rule="para" parents="9458 10960"/>
    </justification>
  </clause>

  <clause id="10962">
    <literal><![CDATA[
      (x * (y * K(z,u))) \ (x * y) != w
    ]]></literal>
    <literal><![CDATA[
      K(u,L(z,y,x)) = w
    ]]></literal>
    <justification jstring="[para(9450(a,2),10960(a,1))].">
      <j1 rule="para" parents="9450 10960"/>
    </justification>
  </clause>

  <clause id="10963">
    <literal><![CDATA[
      K(L(x,y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(u,y,z)) = w
    ]]></literal>
    <justification jstring="[para(10894(a,1),10960(a,1))].">
      <j1 rule="para" parents="10894 10960"/>
    </justification>
  </clause>

  <clause id="10964">
    <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(5147(a,1),10855(a,2,2,2))].">
      <j1 rule="para" parents="5147 10855"/>
    </justification>
  </clause>

  <clause id="10965">
    <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(398(a,1),10867(a,1,2,1,1))].">
      <j1 rule="para" parents="398 10867"/>
    </justification>
  </clause>

  <clause id="10966">
    <literal><![CDATA[
      ((x * y) / z) \ (x * (y * K(z,u))) = T(z,L(u,y,x))
    ]]></literal>
    <justification jstring="[hyper(121,a,10874,a(flip),b,5974,a)].">
      <j1 rule="hyper" parents="121 10874 5974"/>
    </justification>
  </clause>

  <clause id="10967">
    <literal><![CDATA[
      (x * y) * z != x * (y * K(u,w))
    ]]></literal>
    <literal><![CDATA[
      K(u,L(w,y,x)) = z
    ]]></literal>
    <justification jstring="[para(10874(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="10874 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10968">
    <literal><![CDATA[
      (L(x,y,z) \ x) * K(u,L(w,L(x,y,z) \ 1,x)) = x * ((L(x,y,z) \ 1) * K(u,w))
    ]]></literal>
    <justification jstring="[para(1260(a,1),10874(a,1,1))].">
      <j1 rule="para" parents="1260 10874"/>
    </justification>
  </clause>

  <clause id="10969">
    <literal><![CDATA[
      ((x * y) / z) \ (x * (y * K(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      T(z,L(u,y,x)) = w
    ]]></literal>
    <justification jstring="[para(10874(a,1),5985(a,1,2))].">
      <j1 rule="para" parents="10874 5985"/>
    </justification>
  </clause>

  <clause id="10971">
    <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(6426(a,1),10874(a,2,2))].">
      <j1 rule="para" parents="6426 10874"/>
    </justification>
  </clause>

  <clause id="10972">
    <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(10874(a,1),7488(a,2,2,1))].">
      <j1 rule="para" parents="10874 7488"/>
    </justification>
  </clause>

  <clause id="10973">
    <literal><![CDATA[
      K(x,y / (z * (u * K(x,w)))) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[para(10874(a,1),7925(a,1,2,2))].">
      <j1 rule="para" parents="10874 7925"/>
    </justification>
  </clause>

  <clause id="10974">
    <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(10874(a,1),9680(a,2,2,1))].">
      <j1 rule="para" parents="10874 9680"/>
    </justification>
  </clause>

  <clause id="10975">
    <literal><![CDATA[
      (x * y) * K(z,K(u,L(w,y,x))) = x * (y * K(z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(10851(a,1),10874(a,1,2,2))].">
      <j1 rule="para" parents="10851 10874"/>
    </justification>
  </clause>

  <clause id="10976">
    <literal><![CDATA[
      (x * (y / z)) * K(z,L(u,y,x)) = x * ((y / z) * K(z,u))
    ]]></literal>
    <justification jstring="[para(10922(a,1),10874(a,1,2))].">
      <j1 rule="para" parents="10922 10874"/>
    </justification>
  </clause>

  <clause id="10977">
    <literal><![CDATA[
      (x * (y * z)) / L(T(z,u),y,x) = x * (y * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(39,a,8005,a,b,10897,a)].">
      <j1 rule="hyper" parents="39 8005 10897"/>
    </justification>
  </clause>

  <clause id="10978">
    <literal><![CDATA[
      K((x \ 1) \ y,x * z) = K(x * y,(x \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(514(a,1),10908(a,1,2))].">
      <j1 rule="para" parents="514 10908"/>
    </justification>
  </clause>

  <clause id="10979">
    <literal><![CDATA[
      K(x,(y * T(x,z)) \ u) = K(x,x \ (y \ u))
    ]]></literal>
    <justification jstring="[hyper(333,a,7410,a(flip),b,10853,a),flip(a)].">
      <j1 rule="hyper" parents="333 7410 10853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10982">
    <literal><![CDATA[
      T(x * K(y,x),L(y,z,u)) = x * a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,9206,a,b,10935,a)].">
      <j1 rule="hyper" parents="63 9206 10935"/>
    </justification>
  </clause>

  <clause id="10983">
    <literal><![CDATA[
      K(x,y / (z * ((u / x) * w))) = K(x,y / (z * ((x \ u) * w)))
    ]]></literal>
    <justification jstring="[para(5966(a,1),10973(a,1,2,2,2))].">
      <j1 rule="para" parents="5966 10973"/>
    </justification>
  </clause>

  <clause id="10984">
    <literal><![CDATA[
      K(x * y,(x \ 1) \ (x \ z)) = K((x \ 1) \ y,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),10978(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 10978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10985">
    <literal><![CDATA[
      T(x * a(y,z,K(u,x)),u) = T(x,L(u,z,y))
    ]]></literal>
    <justification jstring="[para(10982(a,1),4320(a,1,1))].">
      <j1 rule="para" parents="10982 4320"/>
    </justification>
  </clause>

  <clause id="10986">
    <literal><![CDATA[
      T(x * a(y,z,K(u,x)),u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,L(u,z,y)) = w
    ]]></literal>
    <justification jstring="[para(10982(a,1),4424(a,1,1))].">
      <j1 rule="para" parents="10982 4424"/>
    </justification>
  </clause>

  <clause id="10987">
    <literal><![CDATA[
      K((x \ 1) \ (x \ y),z) = K(y,(x \ 1) \ (x \ z))
    ]]></literal>
    <justification jstring="[para(10(a,1),10984(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 10984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10988">
    <literal><![CDATA[
      K(x,(y \ 1) \ (y \ L(z,x / y,y))) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,10869,a(flip),b,10987,a),flip(a)].">
      <j1 rule="hyper" parents="63 10869 10987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10989">
    <literal><![CDATA[
      K(x,L((y \ 1) \ (y \ z),x / y,y)) = K(x,z)
    ]]></literal>
    <justification jstring="[para(1535(a,2),10988(a,1,2))].">
      <j1 rule="para" parents="1535 10988"/>
    </justification>
  </clause>

  <clause id="10990">
    <literal><![CDATA[
      K(x,L((y \ 1) \ (y \ z),y \ x,y)) = K(x,z)
    ]]></literal>
    <justification jstring="[para(10083(a,1),10989(a,1,2))].">
      <j1 rule="para" parents="10083 10989"/>
    </justification>
  </clause>

  <clause id="10991">
    <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(6049(a,1),10854(a,1,2,1))].">
      <j1 rule="para" parents="6049 10854"/>
    </justification>
  </clause>

  <clause id="10992">
    <literal><![CDATA[
      K(x \ (T(y,x) \ z),L(u,T(y,x) \ z,T(y,x))) = K((y * ((y * x) / y)) \ z,u)
    ]]></literal>
    <justification jstring="[para(3311(a,1),10857(a,2,1,1))].">
      <j1 rule="para" parents="3311 10857"/>
    </justification>
  </clause>

  <clause id="10993">
    <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(63,a,10987,a(flip),b,10870,a)].">
      <j1 rule="hyper" parents="63 10987 10870"/>
    </justification>
  </clause>

  <clause id="10994">
    <literal><![CDATA[
      x * ((x \ y) * K(z,(x \ y) \ u)) = y * K(z,y \ (x * u))
    ]]></literal>
    <justification jstring="[para(515(a,1),10872(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="515 10872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10995">
    <literal><![CDATA[
      T(x * (T(y,x) * K(z,u)),K(z,L(u,y,x))) != w
    ]]></literal>
    <literal><![CDATA[
      K(z,L(u,y,x)) * (y * x) = w
    ]]></literal>
    <justification jstring="[para(10873(a,1),6860(a,1,1))].">
      <j1 rule="para" parents="10873 6860"/>
    </justification>
  </clause>

  <clause id="10996">
    <literal><![CDATA[
      x \ (y * K(z,y \ (x * u))) = (x \ y) * K(z,(x \ y) \ u)
    ]]></literal>
    <justification jstring="[para(10876(a,1),495(a,1,2,2))].">
      <j1 rule="para" parents="10876 495"/>
    </justification>
  </clause>

  <clause id="10997">
    <literal><![CDATA[
      (x / y) * (y * K(z,T(u,y))) = x * K(z,x \ ((x / y) * (u * y)))
    ]]></literal>
    <justification jstring="[para(10123(a,1),10887(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10123 10887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10998">
    <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(6785(a,1),10902(a,1,1))].">
      <j1 rule="para" parents="6785 10902"/>
    </justification>
  </clause>

  <clause id="11001">
    <literal><![CDATA[
      K(x,K(L(y,z,u),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,L(w,z,u))) = v5
    ]]></literal>
    <justification jstring="[para(6800(a,1),10917(a,1))].">
      <j1 rule="para" parents="6800 10917"/>
    </justification>
  </clause>

  <clause id="11003">
    <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(3792(a,1),10931(a,2,2,1))].">
      <j1 rule="para" parents="3792 10931"/>
    </justification>
  </clause>

  <clause id="11004">
    <literal><![CDATA[
      a(x,y * z,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(9745(a,1),10954(a,1))].">
      <j1 rule="para" parents="9745 10954"/>
    </justification>
  </clause>

  <clause id="11005">
    <literal><![CDATA[
      a(x,y * z,K(u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(9736(a,1),10956(a,1))].">
      <j1 rule="para" parents="9736 10956"/>
    </justification>
  </clause>

  <clause id="11006">
    <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(10998,a,9730,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="10998 9730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11007">
    <literal><![CDATA[
      K(x,y) \ L(K(x,y),z,u) = K(y,L(x,z,u)) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,4842,a(flip),b,10891,a),flip(a)].">
      <j1 rule="hyper" parents="333 4842 10891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11008">
    <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(522(a,1),10944(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="522 10944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11009">
    <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(10949(a,1),8191(a,2,2))].">
      <j1 rule="para" parents="10949 8191"/>
    </justification>
  </clause>

  <clause id="11010">
    <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(63,a,9855,a(flip),b,11006,a)].">
      <j1 rule="hyper" parents="63 9855 11006"/>
    </justification>
  </clause>

  <clause id="11011">
    <literal><![CDATA[
      K(x,y) \ K(x,L(y,z,u)) = K(y,L(x,z,u)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(10851(a,1),11007(a,1,2))].">
      <j1 rule="para" parents="10851 11007"/>
    </justification>
  </clause>

  <clause id="11012">
    <literal><![CDATA[
      K(x,L(y,z,u)) * K(y,x) = K(x,y) * K(y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(4580,a,11011,a),flip(a)].">
      <j1 rule="hyper" parents="4580 11011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11013">
    <literal><![CDATA[
      x * (K(x,y) * K(y,L(x,z,u))) = T(x,L(y,z,u)) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(126,a,11012,a(flip),b,4515,a)].">
      <j1 rule="hyper" parents="126 11012 4515"/>
    </justification>
  </clause>

  <clause id="11014">
    <literal><![CDATA[
      L(T(x,y),z,u) \ T(x,L(y,z,u)) = L(x,z,u) \ x
    ]]></literal>
    <justification jstring="[hyper(121,a,4274,a,b,10911,a)].">
      <j1 rule="hyper" parents="121 4274 10911"/>
    </justification>
  </clause>

  <clause id="11015">
    <literal><![CDATA[
      L(x * K(y,x),z,u) \ (x * K(y,x)) = L(x,z,u) \ T(x * K(y,x),L(y,z,u))
    ]]></literal>
    <justification jstring="[para(4239(a,1),11014(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4239 11014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11017">
    <literal><![CDATA[
      K(x \ (y \ z),L(u,x,y)) != w
    ]]></literal>
    <literal><![CDATA[
      K((y * x) \ z,u) = w
    ]]></literal>
    <justification jstring="[para(10921(a,1),10882(a,1))].">
      <j1 rule="para" parents="10921 10882"/>
    </justification>
  </clause>

  <clause id="11018">
    <literal><![CDATA[
      (x * (y * K(z,u))) \ (x * (y * T(z,u))) = L(z,y,x)
    ]]></literal>
    <justification jstring="[para(10874(a,1),10918(a,1,1))].">
      <j1 rule="para" parents="10874 10918"/>
    </justification>
  </clause>

  <clause id="11019">
    <literal><![CDATA[
      L(x,y * K(x,z),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(6069,a,11018,a)].">
      <j1 rule="hyper" parents="6069 11018"/>
    </justification>
  </clause>

  <clause id="11020">
    <literal><![CDATA[
      L(x,y,z) = (z * (y * K(x,y))) \ (z * (x * y))
    ]]></literal>
    <justification jstring="[para(111(a,1),11018(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="111 11018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11021">
    <literal><![CDATA[
      L(x,y \ T(z,x),u) = L(x,y \ z,u)
    ]]></literal>
    <justification jstring="[para(6244(a,1),11019(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6244 11019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11022">
    <literal><![CDATA[
      L(x,K(x,y) * z,u) = L(x,z,u)
    ]]></literal>
    <justification jstring="[para(6390(a,1),11019(a,1,2))].">
      <j1 rule="para" parents="6390 11019"/>
    </justification>
  </clause>

  <clause id="11024">
    <literal><![CDATA[
      L(x,T(y,x) \ z,u) = L(x,y \ z,u)
    ]]></literal>
    <justification jstring="[para(7339(a,1),11019(a,1,2))].">
      <j1 rule="para" parents="7339 11019"/>
    </justification>
  </clause>

  <clause id="11027">
    <literal><![CDATA[
      L(T(x,y),K(x,z) * u,w) = L(T(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(6901(a,1),11022(a,1,2,1))].">
      <j1 rule="para" parents="6901 11022"/>
    </justification>
  </clause>

  <clause id="11028">
    <literal><![CDATA[
      K(x,y \ z) \ T(x,(y \ z) * x) = L(x,y \ T(z,x),x)
    ]]></literal>
    <justification jstring="[hyper(333,a,4732,a,b,11021,a)].">
      <j1 rule="hyper" parents="333 4732 11021"/>
    </justification>
  </clause>

  <clause id="11029">
    <literal><![CDATA[
      T(x,y) * L(y,z \ x,z) = z * ((z \ T(x,y)) * y)
    ]]></literal>
    <justification jstring="[hyper(126,a,11021,a(flip),b,98,a)].">
      <j1 rule="hyper" parents="126 11021 98"/>
    </justification>
  </clause>

  <clause id="11030">
    <literal><![CDATA[
      L(x,(y \ T(x,y \ x)) \ z,u) = L(x,(y \ x) \ z,u)
    ]]></literal>
    <justification jstring="[para(3368(a,1),11024(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3368 11024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11031">
    <literal><![CDATA[
      L(T(x,y),T(x,z) \ u,w) = L(T(x,y),x \ u,w)
    ]]></literal>
    <justification jstring="[para(4518(a,1),11027(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4518 11027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11033">
    <literal><![CDATA[
      L(x,y,z * K(x,y)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,10467,a(flip),b,11020,a)].">
      <j1 rule="hyper" parents="333 10467 11020"/>
    </justification>
  </clause>

  <clause id="11035">
    <literal><![CDATA[
      L(x,y,T((y * x) \ z,K(x,y))) = L(x,y,(x * y) \ z)
    ]]></literal>
    <justification jstring="[para(10030(a,2),11033(a,1,3))].">
      <j1 rule="para" parents="10030 11033"/>
    </justification>
  </clause>

  <clause id="11037">
    <literal><![CDATA[
      K(x,L(T(y,z),y \ u,w)) = K(x,L(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(11031(a,1),10861(a,1,2))].">
      <j1 rule="para" parents="11031 10861"/>
    </justification>
  </clause>

  <clause id="11038">
    <literal><![CDATA[
      K(x,(y * z) / (y * (z / u))) = K(x,L(T(u,y * z),z,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,10477,a(flip),b,11037,a)].">
      <j1 rule="hyper" parents="63 10477 11037"/>
    </justification>
  </clause>

  <clause id="11039">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) * K(x,K(z,y)) = a(w,u,K(x,K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(5313,a,10947,a)].">
      <j1 rule="hyper" parents="5313 10947"/>
    </justification>
  </clause>

  <clause id="11040">
    <literal><![CDATA[
      K(x,y / (x * ((x \ z) * u))) = K(x,x \ (y / ((z / x) * u)))
    ]]></literal>
    <justification jstring="[hyper(10522,a,10983,a),flip(a)].">
      <j1 rule="hyper" parents="10522 10983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11041">
    <literal><![CDATA[
      L(x,y,z) * (x \ ((L(x,y,z) \ x) * K(u,(L(x,y,z) \ x) \ w))) = K(u,x \ (L(x,y,z) * w))
    ]]></literal>
    <justification jstring="[hyper(1270,a,10994,a)].">
      <j1 rule="hyper" parents="1270 10994"/>
    </justification>
  </clause>

  <clause id="11042">
    <literal><![CDATA[
      K(x / (y \ z),u) \ (y \ z) = y \ (z * K(u,z \ (y * x)))
    ]]></literal>
    <justification jstring="[hyper(333,a,6517,a,b,10996,a)].">
      <j1 rule="hyper" parents="333 6517 10996"/>
    </justification>
  </clause>

  <clause id="11044">
    <literal><![CDATA[
      K(K(L(x,y,z) \ 1,u) \ 1,w) = K(w,K(x,L(u,y,z)))
    ]]></literal>
    <justification jstring="[hyper(10951,a,11010,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="10951 11010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11045">
    <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(8511(a,1),11044(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="8511 11044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11046">
    <literal><![CDATA[
      T(x,L(y,z,u)) * K(y,x) = T(x,y) * K(y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(4684,a,11013,a),flip(a)].">
      <j1 rule="hyper" parents="4684 11013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11047">
    <literal><![CDATA[
      T(x * K(y,L(x,z,u)),y) = T(x,L(y,z,u)) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,6650,a,b,11046,a)].">
      <j1 rule="hyper" parents="333 6650 11046"/>
    </justification>
  </clause>

  <clause id="11048">
    <literal><![CDATA[
      K(x,x \ (y / ((z / x) * u))) = K(x,x \ (y / ((x \ z) * u)))
    ]]></literal>
    <justification jstring="[hyper(10522,a,11040,a),flip(a)].">
      <j1 rule="hyper" parents="10522 11040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11049">
    <literal><![CDATA[
      K(x / (y \ z),u) \ (y \ z) = y \ (K((y * x) / z,u) \ z)
    ]]></literal>
    <justification jstring="[para(6517(a,2),11042(a,2,2))].">
      <j1 rule="para" parents="6517 11042"/>
    </justification>
  </clause>

  <clause id="11051">
    <literal><![CDATA[
      T(x / (y \ z),u) \ x = y \ (K((y * x) / z,u) \ z)
    ]]></literal>
    <justification jstring="[hyper(4914,a,11049,a)].">
      <j1 rule="hyper" parents="4914 11049"/>
    </justification>
  </clause>

  <clause id="11052">
    <literal><![CDATA[
      T(1 / (x \ y),z) \ 1 = x \ (K(x / y,z) \ y)
    ]]></literal>
    <justification jstring="[para(8(a,1),11051(a,2,2,1,1,1))].">
      <j1 rule="para" parents="8 11051"/>
    </justification>
  </clause>

  <clause id="11053">
    <literal><![CDATA[
      T(1 / (x \ (x / y)),z) \ 1 = x \ (K(y,T(z,x)) \ (x / y))
    ]]></literal>
    <justification jstring="[para(6927(a,1),11052(a,2,2,1))].">
      <j1 rule="para" parents="6927 11052"/>
    </justification>
  </clause>

  <clause id="11054">
    <literal><![CDATA[
      T(1 / (x \ (x / y)),z) \ 1 = x \ ((x / y) * K(z,y))
    ]]></literal>
    <justification jstring="[para(6991(a,1),11053(a,2,2))].">
      <j1 rule="para" parents="6991 11053"/>
    </justification>
  </clause>

  <clause id="11055">
    <literal><![CDATA[
      T(1 / (x \ (x / y)),z) \ 1 = x \ (x / T(y,z))
    ]]></literal>
    <justification jstring="[para(5450(a,1),11054(a,2,2))].">
      <j1 rule="para" parents="5450 11054"/>
    </justification>
  </clause>

  <clause id="11056">
    <literal><![CDATA[
      K(x,y) \ (z \ (z / x)) = z \ (z / T(x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,8286,a(flip),b,11055,a)].">
      <j1 rule="hyper" parents="63 8286 11055"/>
    </justification>
  </clause>

  <clause id="11057">
    <literal><![CDATA[
      K(x,y) * ((z \ (z / y)) * u) = (z \ (z / T(y,x))) * u
    ]]></literal>
    <justification jstring="[para(11056(a,1),5798(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11056 5798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11058">
    <literal><![CDATA[
      K(x,y) \ ((z \ (z / x)) * u) = (z \ (z / T(x,y))) * u
    ]]></literal>
    <justification jstring="[hyper(4585,a,11057,a)].">
      <j1 rule="hyper" parents="4585 11057"/>
    </justification>
  </clause>

  <clause id="11059">
    <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(9408(a,1),10881(a,1,1))].">
      <j1 rule="para" parents="9408 10881"/>
    </justification>
  </clause>

  <clause id="11060">
    <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(333,a,9406,a(flip),b,11059,a),flip(a)].">
      <j1 rule="hyper" parents="333 9406 11059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11061">
    <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(6857,a,11060,a)].">
      <j1 rule="hyper" parents="6857 11060"/>
    </justification>
  </clause>

  <clause id="11062">
    <literal><![CDATA[
      L(a(x,y,x),z * x,u) = a(L(x,z,u),y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,9325,a(flip),b,10807,a)].">
      <j1 rule="hyper" parents="63 9325 10807"/>
    </justification>
  </clause>

  <clause id="11064">
    <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(12(a,1),11062(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12 11062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11065">
    <literal><![CDATA[
      (x \ (L(x,y,z) * u)) * x = (L(x,y,z) * K(u,x)) * u
    ]]></literal>
    <justification jstring="[para(5917(a,1),10824(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5917 10824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11066">
    <literal><![CDATA[
      (x \ (L(x,y,z) * u)) * x = L(x,y,z) * T(u,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,5982,a(flip),b,11065,a),flip(a)].">
      <j1 rule="hyper" parents="333 5982 11065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11067">
    <literal><![CDATA[
      (L(x,y,z) * (x \ u)) * x = L(x,y,z) * T(u,x)
    ]]></literal>
    <justification jstring="[para(1254(a,1),11066(a,1,1))].">
      <j1 rule="para" parents="1254 11066"/>
    </justification>
  </clause>

  <clause id="11068">
    <literal><![CDATA[
      (x / y) \ (L(y,z,u) * (y \ x)) = x \ (L(y,z,u) * T(x,y))
    ]]></literal>
    <justification jstring="[para(11067(a,1),8737(a,2,2))].">
      <j1 rule="para" parents="11067 8737"/>
    </justification>
  </clause>

  <clause id="11069">
    <literal><![CDATA[
      (x / y) \ (L(y,z,u) * (y \ x)) = T(L(y,z,u) * K(x,y),x)
    ]]></literal>
    <justification jstring="[hyper(333,a,6054,a,b,11068,a),flip(a)].">
      <j1 rule="hyper" parents="333 6054 11068"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11070">
    <literal><![CDATA[
      (L(x,y,z) \ u) \ (x * (x \ u)) = L((x \ u) \ u,y,z)
    ]]></literal>
    <justification jstring="[para(1259(a,1),10844(a,1,1))].">
      <j1 rule="para" parents="1259 10844"/>
    </justification>
  </clause>

  <clause id="11071">
    <literal><![CDATA[
      L((x \ y) \ y,z,u) = (L(x,z,u) \ y) \ y
    ]]></literal>
    <justification jstring="[para(10(a,1),11070(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 11070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11072">
    <literal><![CDATA[
      (L(x / y,z,u) \ x) \ x = L(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(79(a,1),11071(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="79 11071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11074">
    <literal><![CDATA[
      x / L(y \ x,z,u) = L(x / y,z,u) \ x
    ]]></literal>
    <justification jstring="[hyper(198,a,11072,a)].">
      <j1 rule="hyper" parents="198 11072"/>
    </justification>
  </clause>

  <clause id="11075">
    <literal><![CDATA[
      L(L(x \ 1,y,z),L(x,y,z),L(x \ 1,y,z)) = L(1 / x,y,z)
    ]]></literal>
    <justification jstring="[hyper(39,a,8236,a,b,11074,a(flip))].">
      <j1 rule="hyper" parents="39 8236 11074"/>
    </justification>
  </clause>

  <clause id="11076">
    <literal><![CDATA[
      L(x / (x / y),z,u) \ x = x / L(y,z,u)
    ]]></literal>
    <justification jstring="[para(79(a,1),11074(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="79 11074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11077">
    <literal><![CDATA[
      L(x / (x / y),z,u) = x / (x / L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(198,a,11076,a),flip(a)].">
      <j1 rule="hyper" parents="198 11076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11078">
    <literal><![CDATA[
      L(x / (x / y),y,x) = x / (x * (1 / y))
    ]]></literal>
    <justification jstring="[hyper(197,a,2607,a(flip),b,11076,a),flip(a)].">
      <j1 rule="hyper" parents="197 2607 11076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11079">
    <literal><![CDATA[
      T(x / (x / L(y,z,u)),x / y) = L((x / y) \ x,z,u)
    ]]></literal>
    <justification jstring="[para(11077(a,1),260(a,1,1))].">
      <j1 rule="para" parents="11077 260"/>
    </justification>
  </clause>

  <clause id="11080">
    <literal><![CDATA[
      K(x,L(y / (y / z),u,w)) = K(x,T(L(z,u,w),y))
    ]]></literal>
    <justification jstring="[para(11077(a,2),6979(a,1,2))].">
      <j1 rule="para" parents="11077 6979"/>
    </justification>
  </clause>

  <clause id="11081">
    <literal><![CDATA[
      T(x / (x / L(y,z,u)),x / y) = L(y,z,u)
    ]]></literal>
    <justification jstring="[para(79(a,1),11079(a,2,1))].">
      <j1 rule="para" parents="79 11079"/>
    </justification>
  </clause>

  <clause id="11082">
    <literal><![CDATA[
      T(T(x / (x / L(y,z,u)),w),x / y) = T(L(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(11081(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11081 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11084">
    <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(11075(a,1),8525(a,1,2,1))].">
      <j1 rule="para" parents="11075 8525"/>
    </justification>
  </clause>

  <clause id="11085">
    <literal><![CDATA[
      K(x,L(L(1 / y,y,z),z * y,u)) = K(x,1 / L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(333,a,6279,a(flip),b,11084,a),flip(a)].">
      <j1 rule="hyper" parents="333 6279 11084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11086">
    <literal><![CDATA[
      x * K(y,x \ ((x / z) * (u * z))) = (x / z) * (K(y,u) * z)
    ]]></literal>
    <justification jstring="[hyper(6401,a,10997,a),flip(a)].">
      <j1 rule="hyper" parents="6401 10997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11102">
    <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(3150(a,1),10965(a,1,2))].">
      <j1 rule="para" parents="3150 10965"/>
    </justification>
  </clause>

  <clause id="11103">
    <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(4367(a,1),11045(a,2,1))].">
      <j1 rule="para" parents="4367 11045"/>
    </justification>
  </clause>

  <clause id="11104">
    <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(333,a,6763,a(flip),b,11103,a),flip(a)].">
      <j1 rule="hyper" parents="333 6763 11103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11105">
    <literal><![CDATA[
      K(x,K(y / (z \ 1),L(u,z \ 1,z))) = K(u,K(x,T(z * y,z)))
    ]]></literal>
    <justification jstring="[hyper(333,a,7155,a(flip),b,11104,a),flip(a)].">
      <j1 rule="hyper" parents="333 7155 11104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11106">
    <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(4949(a,1),10808(a,1,1))].">
      <j1 rule="para" parents="4949 10808"/>
    </justification>
  </clause>

  <clause id="11107">
    <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(4543(a,1),11106(a,1,1,1,2))].">
      <j1 rule="para" parents="4543 11106"/>
    </justification>
  </clause>

  <clause id="11108">
    <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(63,a,27,a,b,11107,a)].">
      <j1 rule="hyper" parents="63 27 11107"/>
    </justification>
  </clause>

  <clause id="11109">
    <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(4650(a,1),11108(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4650 11108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11110">
    <literal><![CDATA[
      R(R(x,y,z),u,R(x,y,z)) = R(R(x,u,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,10801,a(flip),b,11109,a)].">
      <j1 rule="hyper" parents="63 10801 11109"/>
    </justification>
  </clause>

  <clause id="11111">
    <literal><![CDATA[
      R(x,y,R(x,z,u)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(42,a,31,a,b,11110,a(flip))].">
      <j1 rule="hyper" parents="42 31 11110"/>
    </justification>
  </clause>

  <clause id="11113">
    <literal><![CDATA[
      R(x,y,R(x,z,u)) = x * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,8214,a,b,11111,a),flip(a)].">
      <j1 rule="hyper" parents="333 8214 11111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11115">
    <literal><![CDATA[
      K(x,R(y,z,R(y,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(11111(a,2),6336(a,1,2))].">
      <j1 rule="para" parents="11111 6336"/>
    </justification>
  </clause>

  <clause id="11116">
    <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(11111(a,1),10781(a,1,1,1,1))].">
      <j1 rule="para" parents="11111 10781"/>
    </justification>
  </clause>

  <clause id="11117">
    <literal><![CDATA[
      K(T(x,y),T(z,y)) = K(x,R(z,u,R(T(z,y),w,v5)))
    ]]></literal>
    <justification jstring="[hyper(7071,a,11115,a),flip(a)].">
      <j1 rule="hyper" parents="7071 11115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11120">
    <literal><![CDATA[
      a(x,y,R(x,z,u)) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(34,a,8794,a,b,11113,a(flip))].">
      <j1 rule="hyper" parents="34 8794 11113"/>
    </justification>
  </clause>

  <clause id="11122">
    <literal><![CDATA[
      K(x,R(y,z,R(T(y,u),w,v5))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(7063,a,11117,a),flip(a)].">
      <j1 rule="hyper" parents="7063 11117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11124">
    <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(11122(a,1),8893(a,1,1))].">
      <j1 rule="para" parents="11122 8893"/>
    </justification>
  </clause>

  <clause id="11126">
    <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(11116(a,1),9338(a,1))].">
      <j1 rule="para" parents="11116 9338"/>
    </justification>
  </clause>

  <clause id="11128">
    <literal><![CDATA[
      ((x * y) / x) * L(((x * y) / x) \ y,z,u) = (x * T(y,L(x,z,u))) / x
    ]]></literal>
    <justification jstring="[para(5984(a,1),10879(a,2,1))].">
      <j1 rule="para" parents="5984 10879"/>
    </justification>
  </clause>

  <clause id="11129">
    <literal><![CDATA[
      ((x * y) / x) * L(((x * y) / x) \ y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      T((x * y) / x,L(x,z,u)) = w
    ]]></literal>
    <justification jstring="[para(11128(a,2),479(a,1))].">
      <j1 rule="para" parents="11128 479"/>
    </justification>
  </clause>

  <clause id="11130">
    <literal><![CDATA[
      ((x * y) / x) * L(((x * y) / x) \ y,z,u) = T(y,L(x,z,u)) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,4542,a(flip),b,10880,a),flip(a)].">
      <j1 rule="hyper" parents="333 4542 10880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11131">
    <literal><![CDATA[
      ((x * y) / x) * L(((x * y) / x) \ y,z,u) = T(y * K(x,L(y,z,u)),x)
    ]]></literal>
    <justification jstring="[hyper(333,a,11047,a,b,11130,a),flip(a)].">
      <j1 rule="hyper" parents="333 11047 11130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11132">
    <literal><![CDATA[
      x * (K(y,L(x,z,u)) * K(w,L(y,z,u))) = (L(y,z,u) * x) / L(T(y,w),z,u)
    ]]></literal>
    <justification jstring="[para(25(a,2),10912(a,2,2))].">
      <j1 rule="para" parents="25 10912"/>
    </justification>
  </clause>

  <clause id="11133">
    <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(4697,a,11124,a)].">
      <j1 rule="hyper" parents="4697 11124"/>
    </justification>
  </clause>

  <clause id="11134">
    <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(8860(a,1),11124(a,1,2,2))].">
      <j1 rule="para" parents="8860 11124"/>
    </justification>
  </clause>

  <clause id="11135">
    <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(8796,a,11133,a)].">
      <j1 rule="hyper" parents="8796 11133"/>
    </justification>
  </clause>

  <clause id="11136">
    <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(8798(a,1),11134(a,1,2))].">
      <j1 rule="para" parents="8798 11134"/>
    </justification>
  </clause>

  <clause id="11137">
    <literal><![CDATA[
      x \ R(x,y,R(T(x,z),u,w)) = a(x,y,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(4590,a,11136,a),flip(a)].">
      <j1 rule="hyper" parents="4590 11136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11138">
    <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(11136(a,1),4590(a,1))].">
      <j1 rule="para" parents="11136 4590"/>
    </justification>
  </clause>

  <clause id="11140">
    <literal><![CDATA[
      a(T(x,y),z,R(T(x,y),u,w)) = a(x,z,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,11135,a,b,11137,a)].">
      <j1 rule="hyper" parents="63 11135 11137"/>
    </justification>
  </clause>

  <clause id="11142">
    <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(11135(a,2),11138(a,1))].">
      <j1 rule="para" parents="11135 11138"/>
    </justification>
  </clause>

  <clause id="11143">
    <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(11038(a,1),10892(a,1,2))].">
      <j1 rule="para" parents="11038 10892"/>
    </justification>
  </clause>

  <clause id="11144">
    <literal><![CDATA[
      K((x * ((x * y) / x)) \ z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K((T(x,y) * y) \ z,u) = w
    ]]></literal>
    <justification jstring="[para(10992(a,1),10882(a,1))].">
      <j1 rule="para" parents="10992 10882"/>
    </justification>
  </clause>

  <clause id="11145">
    <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(11069(a,1),11009(a,1,2))].">
      <j1 rule="para" parents="11069 11009"/>
    </justification>
  </clause>

  <clause id="11146">
    <literal><![CDATA[
      x \ (x * a(y,z,K(x \ u,x))) = K(L(x,z,y),u) * K(u,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,6665,a(flip),b,11145,a),flip(a)].">
      <j1 rule="hyper" parents="63 6665 11145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11147">
    <literal><![CDATA[
      x \ (x * a(y,z,K(x \ u,x))) = K(x,L(u,z,y)) * K(u,x)
    ]]></literal>
    <justification jstring="[para(10898(a,1),11146(a,2,1))].">
      <j1 rule="para" parents="10898 11146"/>
    </justification>
  </clause>

  <clause id="11148">
    <literal><![CDATA[
      x \ (x * a(y,z,K(x \ u,x))) = a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(333,a,10884,a(flip),b,11147,a),flip(a)].">
      <j1 rule="hyper" parents="333 10884 11147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11149">
    <literal><![CDATA[
      a(x,y,K(z \ u,z)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(344,a,11148,a),flip(a)].">
      <j1 rule="hyper" parents="344 11148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11150">
    <literal><![CDATA[
      x * a(y,z,K(u \ w,u)) = x * a(y,z,K(w,u))
    ]]></literal>
    <justification jstring="[para(11148(a,1),155(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11148 155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11152">
    <literal><![CDATA[
      a(x,y,K(z * u,z)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[para(9(a,1),11149(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="9 11149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11153">
    <literal><![CDATA[
      a(x,y,K(z,u \ z)) = a(x,y,K(u,u \ z))
    ]]></literal>
    <justification jstring="[para(4377(a,1),11149(a,1,3)),flip(a)].">
      <j1 rule="para" parents="4377 11149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11154">
    <literal><![CDATA[
      a(x,y,K(z \ 1,u)) = a(x,y,K(z \ u,u))
    ]]></literal>
    <justification jstring="[para(4974(a,1),11149(a,1,3))].">
      <j1 rule="para" parents="4974 11149"/>
    </justification>
  </clause>

  <clause id="11155">
    <literal><![CDATA[
      a(x,y,K(z \ (u * w),w)) = a(x,y,K(z \ u,w))
    ]]></literal>
    <justification jstring="[para(10325(a,1),11149(a,1,3)),flip(a)].">
      <j1 rule="para" parents="10325 11149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11156">
    <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(11152(a,2),9793(a,1,1))].">
      <j1 rule="para" parents="11152 9793"/>
    </justification>
  </clause>

  <clause id="11157">
    <literal><![CDATA[
      a(x,y,K(z,z * u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(9795,a,11156,a)].">
      <j1 rule="hyper" parents="9795 11156"/>
    </justification>
  </clause>

  <clause id="11158">
    <literal><![CDATA[
      a(x,y,K(z,z \ u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(10(a,1),11157(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="10 11157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11159">
    <literal><![CDATA[
      a(x,y,K(z,u * z)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(4636(a,2),11157(a,1,3))].">
      <j1 rule="para" parents="4636 11157"/>
    </justification>
  </clause>

  <clause id="11160">
    <literal><![CDATA[
      a(x,y,K(z,u \ z)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,11153,a,b,11158,a)].">
      <j1 rule="hyper" parents="63 11153 11158"/>
    </justification>
  </clause>

  <clause id="11161">
    <literal><![CDATA[
      a(x,y,K(z \ u,u)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[para(4643(a,1),11160(a,1,3)),flip(a)].">
      <j1 rule="para" parents="4643 11160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11162">
    <literal><![CDATA[
      a(x,y,K(z \ 1,u)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,11154,a,b,11161,a)].">
      <j1 rule="hyper" parents="63 11154 11161"/>
    </justification>
  </clause>

  <clause id="11163">
    <literal><![CDATA[
      a(x,y,K(z \ u,w)) = a(x,y,K(w,u \ z))
    ]]></literal>
    <justification jstring="[para(5852(a,1),11162(a,1,3))].">
      <j1 rule="para" parents="5852 11162"/>
    </justification>
  </clause>

  <clause id="11164">
    <literal><![CDATA[
      T((x * y) / x,L(x,z,u)) = T(y * K(x,L(y,z,u)),x)
    ]]></literal>
    <justification jstring="[hyper(11129,a,11131,a)].">
      <j1 rule="hyper" parents="11129 11131"/>
    </justification>
  </clause>

  <clause id="11165">
    <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(1535(a,2),10993(a,1,2))].">
      <j1 rule="para" parents="1535 10993"/>
    </justification>
  </clause>

  <clause id="11170">
    <literal><![CDATA[
      K(x,L((y \ 1) \ (y \ z),y \ x,y)) = K((((y \ x) \ 1) * (y \ 1)) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,10958,a(flip),b,11165,a)].">
      <j1 rule="hyper" parents="63 10958 11165"/>
    </justification>
  </clause>

  <clause id="11171">
    <literal><![CDATA[
      K((((x \ y) \ 1) * (x \ 1)) \ 1,z) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,10990,a(flip),b,11170,a),flip(a)].">
      <j1 rule="hyper" parents="63 10990 11170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11173">
    <literal><![CDATA[
      (1 / (x \ y)) * (x \ T(y,z)) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5358,a(flip),b,11171,a)].">
      <j1 rule="hyper" parents="63 5358 11171"/>
    </justification>
  </clause>

  <clause id="11174">
    <literal><![CDATA[
      K(((((x \ 1) \ y) \ 1) * x) \ 1,z) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5009,a(flip),b,11171,a)].">
      <j1 rule="hyper" parents="63 5009 11171"/>
    </justification>
  </clause>

  <clause id="11175">
    <literal><![CDATA[
      (1 / (x \ y)) \ K(y,z) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(121,a,11171,a(flip),b,5358,a(flip))].">
      <j1 rule="hyper" parents="121 11171 5358"/>
    </justification>
  </clause>

  <clause id="11176">
    <literal><![CDATA[
      1 / ((T(x,y) / z) \ x) = K(x,y) / z
    ]]></literal>
    <justification jstring="[hyper(466,a,11173,a),flip(a)].">
      <j1 rule="hyper" parents="466 11173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11178">
    <literal><![CDATA[
      (1 / x) * (y \ T(y * x,z)) = K(y * x,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),11173(a,1,1,2))].">
      <j1 rule="para" parents="9 11173"/>
    </justification>
  </clause>

  <clause id="11179">
    <literal><![CDATA[
      T(x,y) / ((1 / z) \ x) = K(x,y) / z
    ]]></literal>
    <justification jstring="[para(11174(a,1),8723(a,2,1))].">
      <j1 rule="para" parents="11174 8723"/>
    </justification>
  </clause>

  <clause id="11180">
    <literal><![CDATA[
      T(x,y) / ((1 / y) \ x) = 1 / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,4225,a(flip),b,11179,a),flip(a)].">
      <j1 rule="hyper" parents="333 4225 11179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11181">
    <literal><![CDATA[
      (K(x,y) / z) \ T(x,y) = (1 / z) \ x
    ]]></literal>
    <justification jstring="[hyper(192,a,11179,a)].">
      <j1 rule="hyper" parents="192 11179"/>
    </justification>
  </clause>

  <clause id="11182">
    <literal><![CDATA[
      (1 / (x \ K(y,z))) \ y = x \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(36,a,183,a,b,11179,a),flip(a)].">
      <j1 rule="hyper" parents="36 183 11179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11184">
    <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(8400(a,1),11180(a,2,2))].">
      <j1 rule="para" parents="8400 11180"/>
    </justification>
  </clause>

  <clause id="11185">
    <literal><![CDATA[
      K(x,((y \ 1) * (z \ 1)) \ 1) = 1 / K(z * y,x)
    ]]></literal>
    <justification jstring="[para(11178(a,1),5357(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11178 5357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11186">
    <literal><![CDATA[
      K(x,((y \ 1) * (z \ 1)) \ 1) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(333,a,4371,a(flip),b,11185,a),flip(a)].">
      <j1 rule="hyper" parents="333 4371 11185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11187">
    <literal><![CDATA[
      (1 / x) \ K(y,z * x) = x * K(y,(z \ 1) \ x)
    ]]></literal>
    <justification jstring="[para(11186(a,1),9717(a,1,2))].">
      <j1 rule="para" parents="11186 9717"/>
    </justification>
  </clause>

  <clause id="11188">
    <literal><![CDATA[
      x * K(y,((z / x) \ 1) \ x) = (1 / x) \ K(y,z)
    ]]></literal>
    <justification jstring="[para(12(a,1),11187(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 11187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11189">
    <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(7680(a,1),11184(a,1,1))].">
      <j1 rule="para" parents="7680 11184"/>
    </justification>
  </clause>

  <clause id="11190">
    <literal><![CDATA[
      L(x,y,z) * (x \ ((L(x,y,z) \ x) * K(u,(L(x,y,z) \ x) \ w))) = K(u,L(x,y,z) * (x \ w))
    ]]></literal>
    <justification jstring="[para(1254(a,1),11041(a,2,2))].">
      <j1 rule="para" parents="1254 11041"/>
    </justification>
  </clause>

  <clause id="11191">
    <literal><![CDATA[
      (((x * y) \ x) \ 1) / ((y \ 1) \ 1) = 1 / (y * ((x * y) \ x))
    ]]></literal>
    <justification jstring="[para(10535(a,1),11189(a,1,2))].">
      <j1 rule="para" parents="10535 11189"/>
    </justification>
  </clause>

  <clause id="11192">
    <literal><![CDATA[
      (1 / ((x * y) \ x)) / y = 1 / (y * ((x * y) \ x))
    ]]></literal>
    <justification jstring="[hyper(63,a,5224,a(flip),b,11191,a)].">
      <j1 rule="hyper" parents="63 5224 11191"/>
    </justification>
  </clause>

  <clause id="11193">
    <literal><![CDATA[
      (1 / ((x * y) \ x)) / y = (y * ((x * y) \ x)) \ 1
    ]]></literal>
    <justification jstring="[hyper(333,a,8398,a(flip),b,11192,a),flip(a)].">
      <j1 rule="hyper" parents="333 8398 11192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11194">
    <literal><![CDATA[
      ((x * ((y * x) \ y)) \ 1) \ (1 / ((y * x) \ y)) = x
    ]]></literal>
    <justification jstring="[hyper(192,a,11193,a)].">
      <j1 rule="hyper" parents="192 11193"/>
    </justification>
  </clause>

  <clause id="11195">
    <literal><![CDATA[
      (x * ((y * x) \ y)) \ 1 = x \ (1 / ((y * x) \ y))
    ]]></literal>
    <justification jstring="[hyper(63,a,10759,a(flip),b,11193,a),flip(a)].">
      <j1 rule="hyper" parents="63 10759 11193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11196">
    <literal><![CDATA[
      ((x * ((y * x) \ y)) \ 1) * T(x,z) = T(x,z) / (x * ((y * x) \ y))
    ]]></literal>
    <justification jstring="[para(11194(a,1),4141(a,1,2,1))].">
      <j1 rule="para" parents="11194 4141"/>
    </justification>
  </clause>

  <clause id="11197">
    <literal><![CDATA[
      ((x * ((y * x) \ y)) \ 1) * T(x,z) = (x * ((y * x) \ y)) \ T(x,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,8398,a(flip),b,11196,a),flip(a)].">
      <j1 rule="hyper" parents="333 8398 11196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11198">
    <literal><![CDATA[
      (x \ (1 / ((y * x) \ y))) * T(x,z) = (x * ((y * x) \ y)) \ T(x,z)
    ]]></literal>
    <justification jstring="[para(11195(a,1),11197(a,1,1))].">
      <j1 rule="para" parents="11195 11197"/>
    </justification>
  </clause>

  <clause id="11199">
    <literal><![CDATA[
      T((1 / ((x * y) \ x)) * K(y,z),y) = (y * ((x * y) \ x)) \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,10760,a,b,11198,a)].">
      <j1 rule="hyper" parents="63 10760 11198"/>
    </justification>
  </clause>

  <clause id="11200">
    <literal><![CDATA[
      T(T(1 / ((x * y) \ x),z),y) = (y * ((x * y) \ x)) \ T(y,z)
    ]]></literal>
    <justification jstring="[para(5881(a,1),11199(a,1,1))].">
      <j1 rule="para" parents="5881 11199"/>
    </justification>
  </clause>

  <clause id="11201">
    <literal><![CDATA[
      (x * ((y * x) \ y)) \ T(x,z) = T(1 / ((y * x) \ y),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,4986,a(flip),b,11200,a),flip(a)].">
      <j1 rule="hyper" parents="63 4986 11200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11202">
    <literal><![CDATA[
      1 / ((x * T(y,z)) \ x) = T(1 / ((x * y) \ x),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,8407,a(flip),b,11201,a)].">
      <j1 rule="hyper" parents="63 8407 11201"/>
    </justification>
  </clause>

  <clause id="11203">
    <literal><![CDATA[
      T(1 / ((x * y) \ x),z) \ 1 = (x * T(y,z)) \ x
    ]]></literal>
    <justification jstring="[hyper(192,a,11202,a)].">
      <j1 rule="hyper" parents="192 11202"/>
    </justification>
  </clause>

  <clause id="11204">
    <literal><![CDATA[
      T(((x * y) \ x) \ 1,z) = ((x * T(y,z)) \ x) \ 1
    ]]></literal>
    <justification jstring="[para(11203(a,1),2383(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11203 2383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11205">
    <literal><![CDATA[
      T(((x * y) \ x) \ 1,x) = ((y * x) \ x) \ 1
    ]]></literal>
    <justification jstring="[para(111(a,1),11204(a,2,1,1))].">
      <j1 rule="para" parents="111 11204"/>
    </justification>
  </clause>

  <clause id="11206">
    <literal><![CDATA[
      (((x \ y) * x) \ x) \ 1 = T((y \ x) \ 1,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),11205(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 11205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11207">
    <literal><![CDATA[
      L(x,T(((y * z) \ z) \ 1,z),u) = L(x,((z * y) \ z) \ 1,u)
    ]]></literal>
    <justification jstring="[para(11205(a,1),4844(a,1,2,1))].">
      <j1 rule="para" parents="11205 4844"/>
    </justification>
  </clause>

  <clause id="11208">
    <literal><![CDATA[
      (x \ T(y,y \ x)) \ 1 = T((x \ y) \ 1,y)
    ]]></literal>
    <justification jstring="[para(5040(a,1),11206(a,1,1))].">
      <j1 rule="para" parents="5040 11206"/>
    </justification>
  </clause>

  <clause id="11209">
    <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(9(a,1),10772(a,2,1,1))].">
      <j1 rule="para" parents="9 10772"/>
    </justification>
  </clause>

  <clause id="11210">
    <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(333,a,8313,a(flip),b,11209,a),flip(a)].">
      <j1 rule="hyper" parents="333 8313 11209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11212">
    <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(9(a,1),11210(a,1,1,1))].">
      <j1 rule="para" parents="9 11210"/>
    </justification>
  </clause>

  <clause id="11213">
    <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(9(a,1),11212(a,1,2,2))].">
      <j1 rule="para" parents="9 11212"/>
    </justification>
  </clause>

  <clause id="11214">
    <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(5372(a,1),11213(a,1,2,1,3))].">
      <j1 rule="para" parents="5372 11213"/>
    </justification>
  </clause>

  <clause id="11216">
    <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(333,a,6322,a(flip),b,10223,a),flip(a)].">
      <j1 rule="hyper" parents="333 6322 10223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11218">
    <literal><![CDATA[
      K((x \ y) \ T(y,x),z \ L((x \ y) \ T(y,x),u,w)) = K(x,z \ L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(333,a,10222,a(flip),b,11216,a),flip(a)].">
      <j1 rule="hyper" parents="333 10222 11216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11220">
    <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(10253(a,1),10287(a,1,2,1,1))].">
      <j1 rule="para" parents="10253 10287"/>
    </justification>
  </clause>

  <clause id="11222">
    <literal><![CDATA[
      K(x,T((y * (x \ z)) \ u,w)) = K(x,T((y * z) \ (u * x),w))
    ]]></literal>
    <justification jstring="[hyper(63,a,9014,a(flip),b,11220,a),flip(a)].">
      <j1 rule="hyper" parents="63 9014 11220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11223">
    <literal><![CDATA[
      K(x,T((y * z) \ (u * x),y * z)) = K(x,u / (y * (x \ z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,9808,a(flip),b,11222,a),flip(a)].">
      <j1 rule="hyper" parents="63 9808 11222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11224">
    <literal><![CDATA[
      K(x,(y * x) / (z * u)) = K(x,y / (z * (x \ u)))
    ]]></literal>
    <justification jstring="[hyper(7076,a,11223,a)].">
      <j1 rule="hyper" parents="7076 11223"/>
    </justification>
  </clause>

  <clause id="11225">
    <literal><![CDATA[
      K(x,y / (z * (x \ u))) = K(x,((z * u) / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(9645,a,11224,a),flip(a)].">
      <j1 rule="hyper" parents="9645 11224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11226">
    <literal><![CDATA[
      R(K(x,((y * z) / (u / w)) \ x),w \ u,w) = K(x,u / ((y * (x \ z)) * w))
    ]]></literal>
    <justification jstring="[para(11225(a,1),10353(a,1,1))].">
      <j1 rule="para" parents="11225 10353"/>
    </justification>
  </clause>

  <clause id="11227">
    <literal><![CDATA[
      K(x,y / ((x \ (z * u)) * w)) = K(x,y / ((z * (x \ u)) * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,10352,a(flip),b,11226,a)].">
      <j1 rule="hyper" parents="63 10352 11226"/>
    </justification>
  </clause>

  <clause id="11228">
    <literal><![CDATA[
      K(x,y / ((z * (x \ u)) * w)) = K(x,(((z * u) * w) / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,10528,a(flip),b,11227,a),flip(a)].">
      <j1 rule="hyper" parents="63 10528 11227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11229">
    <literal><![CDATA[
      K(x,(((y * z) * u) / (z * u)) \ x) = R(K(x,y \ x),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,5692,a(flip),b,11228,a),flip(a)].">
      <j1 rule="hyper" parents="63 5692 11228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11230">
    <literal><![CDATA[
      K(x,(((y * x) * z) / u) \ x) = K(x,u / (y * z))
    ]]></literal>
    <justification jstring="[para(173(a,1),11228(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="173 11228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11231">
    <literal><![CDATA[
      K(x,(y * x) / ((z * x) * u)) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,9621,a,b,11230,a)].">
      <j1 rule="hyper" parents="63 9621 11230"/>
    </justification>
  </clause>

  <clause id="11232">
    <literal><![CDATA[
      R(K(x,y \ x),z,u) = K(x,R(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[para(20(a,2),11229(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="20 11229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11233">
    <literal><![CDATA[
      K(x,R(y \ x,z,u) \ x) = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(4643(a,1),11232(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4643 11232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11234">
    <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(10579(a,1),11232(a,1,1))].">
      <j1 rule="para" parents="10579 11232"/>
    </justification>
  </clause>

  <clause id="11235">
    <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(11233(a,1),11234(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11233 11234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11247">
    <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(4567(a,1),9816(a,1,1,2,2))].">
      <j1 rule="para" parents="4567 9816"/>
    </justification>
  </clause>

  <clause id="11248">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,x / y) * K((x \ y) \ 1,T(z,T(x,y))) = a((x \ y) \ 1,z,(x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(6905(a,1),9887(a,1,1))].">
      <j1 rule="para" parents="6905 9887"/>
    </justification>
  </clause>

  <clause id="11249">
    <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(63,a,9492,a(flip),b,10421,a),flip(a)].">
      <j1 rule="hyper" parents="63 9492 10421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11250">
    <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(6798,a,11249,a)].">
      <j1 rule="hyper" parents="6798 11249"/>
    </justification>
  </clause>

  <clause id="11252">
    <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(9646(a,1),11250(a,1,2))].">
      <j1 rule="para" parents="9646 11250"/>
    </justification>
  </clause>

  <clause id="11253">
    <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(10331,a,11252,a)].">
      <j1 rule="hyper" parents="10331 11252"/>
    </justification>
  </clause>

  <clause id="11254">
    <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(4532(a,1),11247(a,1,1,2))].">
      <j1 rule="para" parents="4532 11247"/>
    </justification>
  </clause>

  <clause id="11255">
    <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(10184(a,1),11254(a,1,2))].">
      <j1 rule="para" parents="10184 11254"/>
    </justification>
  </clause>

  <clause id="11256">
    <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(9722(a,1),11255(a,1,2))].">
      <j1 rule="para" parents="9722 11255"/>
    </justification>
  </clause>

  <clause id="11258">
    <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(4567(a,1),11256(a,2,2,1,1))].">
      <j1 rule="para" parents="4567 11256"/>
    </justification>
  </clause>

  <clause id="11259">
    <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(6844(a,1),11258(a,2,2,1))].">
      <j1 rule="para" parents="6844 11258"/>
    </justification>
  </clause>

  <clause id="11260">
    <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(6186(a,2),11259(a,2,2))].">
      <j1 rule="para" parents="6186 11259"/>
    </justification>
  </clause>

  <clause id="11261">
    <literal><![CDATA[
      (x * (K(y,z) * u)) * L(K(z,y),u,x) = x * T(u,K(y,z))
    ]]></literal>
    <justification jstring="[para(12(a,1),11260(a,2,2,1))].">
      <j1 rule="para" parents="12 11260"/>
    </justification>
  </clause>

  <clause id="11262">
    <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(11261(a,1),5277(a,1,1,2))].">
      <j1 rule="para" parents="11261 5277"/>
    </justification>
  </clause>

  <clause id="11263">
    <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(6140(a,1),10041(a,2,2,1))].">
      <j1 rule="para" parents="6140 10041"/>
    </justification>
  </clause>

  <clause id="11264">
    <literal><![CDATA[
      (T(x \ (x / y),(x \ (x / y)) \ 1) * T(x,y \ 1)) \ z = (x / y) \ (K(x \ (x / y),(x / y) \ x) \ z)
    ]]></literal>
    <justification jstring="[para(2936(a,1),10149(a,2,2,1))].">
      <j1 rule="para" parents="2936 10149"/>
    </justification>
  </clause>

  <clause id="11265">
    <literal><![CDATA[
      (T(x \ (x / y),(x \ (x / y)) \ 1) * T(x,y \ 1)) \ z = (x / y) \ (K(x \ (x / y),y) \ z)
    ]]></literal>
    <justification jstring="[para(79(a,1),11264(a,2,2,1,2))].">
      <j1 rule="para" parents="79 11264"/>
    </justification>
  </clause>

  <clause id="11266">
    <literal><![CDATA[
      (T(x \ (x / y),(x \ (x / y)) \ 1) * T(x,y \ 1)) \ z = (x / y) \ (((y \ 1) * y) \ z)
    ]]></literal>
    <justification jstring="[para(2973(a,1),11265(a,2,2,1))].">
      <j1 rule="para" parents="2973 11265"/>
    </justification>
  </clause>

  <clause id="11267">
    <literal><![CDATA[
      (x / y) \ (((y \ 1) * y) \ z) = ((((x \ (x / y)) \ 1) \ 1) * T(x,y \ 1)) \ z
    ]]></literal>
    <justification jstring="[para(112(a,1),11266(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="112 11266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11269">
    <literal><![CDATA[
      (x / y) \ (((y \ 1) * y) \ z) = ((x \ (x / ((y \ 1) \ 1))) * T(x,y \ 1)) \ z
    ]]></literal>
    <justification jstring="[para(2892(a,1),11267(a,2,1,1))].">
      <j1 rule="para" parents="2892 11267"/>
    </justification>
  </clause>

  <clause id="11270">
    <literal><![CDATA[
      (x / y) \ (((y \ 1) * y) \ z) = (x / ((y \ 1) \ 1)) \ z
    ]]></literal>
    <justification jstring="[para(5486(a,1),11269(a,2,1))].">
      <j1 rule="para" parents="5486 11269"/>
    </justification>
  </clause>

  <clause id="11271">
    <literal><![CDATA[
      R(x,(((y / z) \ 1) \ 1) \ (((z \ 1) * z) \ u),w) = R(x,(y / ((z \ 1) \ 1)) \ u,w)
    ]]></literal>
    <justification jstring="[para(11270(a,1),3157(a,2,2))].">
      <j1 rule="para" parents="11270 3157"/>
    </justification>
  </clause>

  <clause id="11272">
    <literal><![CDATA[
      R(x,(((y / z) \ 1) \ ((z \ 1) * z)) \ u,w) = R(x,(y / ((z \ 1) \ 1)) \ u,w)
    ]]></literal>
    <justification jstring="[para(10138(a,1),11271(a,1,2))].">
      <j1 rule="para" parents="10138 11271"/>
    </justification>
  </clause>

  <clause id="11279">
    <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(8165(a,1),11263(a,2,2,1,2))].">
      <j1 rule="para" parents="8165 11263"/>
    </justification>
  </clause>

  <clause id="11280">
    <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(20(a,2),1833(a,2,2,1,1))].">
      <j1 rule="para" parents="20 1833"/>
    </justification>
  </clause>

  <clause id="11281">
    <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(1631(a,1),11280(a,1,1))].">
      <j1 rule="para" parents="1631 11280"/>
    </justification>
  </clause>

  <clause id="11282">
    <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(1603(a,1),11281(a,1,1,1))].">
      <j1 rule="para" parents="1603 11281"/>
    </justification>
  </clause>

  <clause id="11283">
    <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(544,a,11282,a),flip(a)].">
      <j1 rule="hyper" parents="544 11282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11284">
    <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(788(a,1),11283(a,2,1,2))].">
      <j1 rule="para" parents="788 11283"/>
    </justification>
  </clause>

  <clause id="11285">
    <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(1518(a,1),11284(a,1,2))].">
      <j1 rule="para" parents="1518 11284"/>
    </justification>
  </clause>

  <clause id="11286">
    <literal><![CDATA[
      R(x,y,z) * ((1 / x) * (R(x,y,z) \ x)) = R(x * (1 / x),y,z)
    ]]></literal>
    <justification jstring="[para(199(a,1),11285(a,2,1,2))].">
      <j1 rule="para" parents="199 11285"/>
    </justification>
  </clause>

  <clause id="11287">
    <literal><![CDATA[
      R(x,y,z) * ((1 / x) * (R(x,y,z) \ x)) = R(K(x,x \ 1),y,z)
    ]]></literal>
    <justification jstring="[para(2098(a,2),11286(a,2,1))].">
      <j1 rule="para" parents="2098 11286"/>
    </justification>
  </clause>

  <clause id="11288">
    <literal><![CDATA[
      R(x,y,z) * ((1 / x) * (R(x,y,z) \ x)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(333,a,2781,a(flip),b,11287,a),flip(a)].">
      <j1 rule="hyper" parents="333 2781 11287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11290">
    <literal><![CDATA[
      (1 / x) * (R(x,y,z) \ x) = 1 / R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(34,a,10630,a,b,11288,a),flip(a)].">
      <j1 rule="hyper" parents="34 10630 11288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11291">
    <literal><![CDATA[
      (1 / x) \ (1 / R(x,y,z)) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(129,a,11290,a)].">
      <j1 rule="hyper" parents="129 11290"/>
    </justification>
  </clause>

  <clause id="11292">
    <literal><![CDATA[
      (x \ 1) \ (R(x,y,z) \ 1) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,10631,a(flip),b,11291,a)].">
      <j1 rule="hyper" parents="63 10631 11291"/>
    </justification>
  </clause>

  <clause id="11293">
    <literal><![CDATA[
      T(R(x,y,z) \ x,x \ 1) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,5681,a,b,11292,a)].">
      <j1 rule="hyper" parents="63 5681 11292"/>
    </justification>
  </clause>

  <clause id="11294">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ 1 = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,4047,a(flip),b,11292,a)].">
      <j1 rule="hyper" parents="63 4047 11292"/>
    </justification>
  </clause>

  <clause id="11295">
    <literal><![CDATA[
      R(x,y,R(x,z,u)) \ x = a(x,y,R(x,z,u)) \ 1
    ]]></literal>
    <justification jstring="[para(8795(a,1),11294(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8795 11294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11296">
    <literal><![CDATA[
      K(R(x,y,z) \ x,x \ 1) = 1
    ]]></literal>
    <justification jstring="[hyper(55,a,11293,a)].">
      <j1 rule="hyper" parents="55 11293"/>
    </justification>
  </clause>

  <clause id="11297">
    <literal><![CDATA[
      T(1 / x,R(x,y,z) \ x) = 1 / x
    ]]></literal>
    <justification jstring="[para(11296(a,1),4870(a,1,1,1))].">
      <j1 rule="para" parents="11296 4870"/>
    </justification>
  </clause>

  <clause id="11298">
    <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(11297(a,1),1795(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11297 1795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11299">
    <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(5162(a,1),11295(a,2,1))].">
      <j1 rule="para" parents="5162 11295"/>
    </justification>
  </clause>

  <clause id="11300">
    <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(8743(a,1),11299(a,1,1))].">
      <j1 rule="para" parents="8743 11299"/>
    </justification>
  </clause>

  <clause id="11301">
    <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(8971(a,1),11300(a,2,1))].">
      <j1 rule="para" parents="8971 11300"/>
    </justification>
  </clause>

  <clause id="11302">
    <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(63,a,11295,a(flip),b,11301,a)].">
      <j1 rule="hyper" parents="63 11295 11301"/>
    </justification>
  </clause>

  <clause id="11303">
    <literal><![CDATA[
      a(R(x,y,z),u,x) \ 1 = a(x,u,R(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(11140(a,1),11302(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11140 11302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11304">
    <literal><![CDATA[
      a(R(x,y,z),u,x) = a(x,u,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(48,a,11303,a)].">
      <j1 rule="hyper" parents="48 11303"/>
    </justification>
  </clause>

  <clause id="11306">
    <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(333,a,5265,a,b,11304,a)].">
      <j1 rule="hyper" parents="333 5265 11304"/>
    </justification>
  </clause>

  <clause id="11308">
    <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(11297(a,1),11298(a,2,2,1,1))].">
      <j1 rule="para" parents="11297 11298"/>
    </justification>
  </clause>

  <clause id="11309">
    <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(79(a,1),11308(a,2,2,1))].">
      <j1 rule="para" parents="79 11308"/>
    </justification>
  </clause>

  <clause id="11311">
    <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(333,a,3023,a(flip),b,11309,a),flip(a)].">
      <j1 rule="hyper" parents="333 3023 11309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11312">
    <literal><![CDATA[
      T((1 / x) * R(x,y,z),R(x,u,w) \ x) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(79(a,1),11311(a,1,1,2,1))].">
      <j1 rule="para" parents="79 11311"/>
    </justification>
  </clause>

  <clause id="11313">
    <literal><![CDATA[
      T(x \ R(x,y,z),R(x,u,w) \ x) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(3023(a,1),11312(a,1,1))].">
      <j1 rule="para" parents="3023 11312"/>
    </justification>
  </clause>

  <clause id="11314">
    <literal><![CDATA[
      ((x \ R(x,y,z)) \ 1) \ 1 = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(5814,a,11313,a)].">
      <j1 rule="hyper" parents="5814 11313"/>
    </justification>
  </clause>

  <clause id="11315">
    <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(11314(a,1),10575(a,1,1,1))].">
      <j1 rule="para" parents="11314 10575"/>
    </justification>
  </clause>

  <clause id="11316">
    <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(835,a,11315,a)].">
      <j1 rule="hyper" parents="835 11315"/>
    </justification>
  </clause>

  <clause id="11317">
    <literal><![CDATA[
      T((x * (y * z)) \ ((x * y) * z),x) = (((x * (y * z)) \ ((x * y) * z)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(107(a,1),11316(a,1,1,2))].">
      <j1 rule="para" parents="107 11316"/>
    </justification>
  </clause>

  <clause id="11318">
    <literal><![CDATA[
      (((x * (y * z)) \ ((x * y) * z)) \ 1) \ 1 = T(a(x,y,z),x)
    ]]></literal>
    <justification jstring="[para(14(a,2),11317(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14 11317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11319">
    <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(8950(a,1),11306(a,1,1,2))].">
      <j1 rule="para" parents="8950 11306"/>
    </justification>
  </clause>

  <clause id="11320">
    <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(667(a,1),11319(a,1,1))].">
      <j1 rule="para" parents="667 11319"/>
    </justification>
  </clause>

  <clause id="11321">
    <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(252(a,1),11320(a,1,2)),flip(a)].">
      <j1 rule="para" parents="252 11320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11322">
    <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(333,a,1179,a(flip),b,11321,a),flip(a)].">
      <j1 rule="hyper" parents="333 1179 11321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11323">
    <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(27(a,2),11322(a,2,3))].">
      <j1 rule="para" parents="27 11322"/>
    </justification>
  </clause>

  <clause id="11324">
    <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(63,a,11304,a(flip),b,11323,a)].">
      <j1 rule="hyper" parents="63 11304 11323"/>
    </justification>
  </clause>

  <clause id="11325">
    <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(11142,a,11324,a)].">
      <j1 rule="hyper" parents="11142 11324"/>
    </justification>
  </clause>

  <clause id="11327">
    <literal><![CDATA[
      a(x,x \ y,R(T(x,y),z,u)) = a(x,x \ y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,9194,a(flip),b,11325,a),flip(a)].">
      <j1 rule="hyper" parents="63 9194 11325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11329">
    <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(63,a,10783,a,b,11327,a)].">
      <j1 rule="hyper" parents="63 10783 11327"/>
    </justification>
  </clause>

  <clause id="11330">
    <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(8487,a,11329,a)].">
      <j1 rule="hyper" parents="8487 11329"/>
    </justification>
  </clause>

  <clause id="11331">
    <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(11330(a,1),10761(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11330 10761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11332">
    <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(22(a,2),11331(a,2,2,2))].">
      <j1 rule="para" parents="22 11331"/>
    </justification>
  </clause>

  <clause id="11333">
    <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(8853(a,1),11332(a,2,2))].">
      <j1 rule="para" parents="8853 11332"/>
    </justification>
  </clause>

  <clause id="11337">
    <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(5507(a,1),7541(a,1,1,1))].">
      <j1 rule="para" parents="5507 7541"/>
    </justification>
  </clause>

  <clause id="11338">
    <literal><![CDATA[
      L((x \ y) \ y,T(x,y) \ y,(x \ y) \ y) = T(x,x * (y / T(x,y)))
    ]]></literal>
    <justification jstring="[para(3626(a,1),11337(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3626 11337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11339">
    <literal><![CDATA[
      L((x \ y) \ y,T(x,y) \ y,(x \ y) \ y) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,3805,a(flip),b,11338,a),flip(a)].">
      <j1 rule="hyper" parents="333 3805 11338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11340">
    <literal><![CDATA[
      K(x,x \ ((y \ z) \ z)) = K(x,x \ T(y,z))
    ]]></literal>
    <justification jstring="[para(11339(a,1),10487(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11339 10487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11341">
    <literal><![CDATA[
      K(x,(y \ z) \ (x \ z)) = K(x,x \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(10334,a,11340,a)].">
      <j1 rule="hyper" parents="10334 11340"/>
    </justification>
  </clause>

  <clause id="11342">
    <literal><![CDATA[
      K(x,T(x \ y,z)) = K(x,x \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,10543,a(flip),b,11341,a)].">
      <j1 rule="hyper" parents="63 10543 11341"/>
    </justification>
  </clause>

  <clause id="11343">
    <literal><![CDATA[
      K(K(x,y) * z,z \ x) = K(z,T(z \ x,y))
    ]]></literal>
    <justification jstring="[hyper(333,a,8924,a,b,11342,a)].">
      <j1 rule="hyper" parents="333 8924 11342"/>
    </justification>
  </clause>

  <clause id="11344">
    <literal><![CDATA[
      T(x,T(x \ y,z)) = T(x,x \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(124,a,11342,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 11342 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11345">
    <literal><![CDATA[
      K(x,x \ T(x * y,z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(9(a,1),11342(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 11342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11346">
    <literal><![CDATA[
      K(x,T(y,z) / x) = K(x,T(y / x,z))
    ]]></literal>
    <justification jstring="[para(4082(a,1),11345(a,1,2))].">
      <j1 rule="para" parents="4082 11345"/>
    </justification>
  </clause>

  <clause id="11347">
    <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(1865(a,1),11346(a,2,2,1))].">
      <j1 rule="para" parents="1865 11346"/>
    </justification>
  </clause>

  <clause id="11348">
    <literal><![CDATA[
      K(x,T(x \ y,z)) * (K(y,z) * x) = T(K(y,z) * x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(125,a,11343,a(flip),b,4261,a(flip))].">
      <j1 rule="hyper" parents="125 11343 4261"/>
    </justification>
  </clause>

  <clause id="11349">
    <literal><![CDATA[
      T(K(x,y) * z,z \ x) = T(z,z \ x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,8110,a(flip),b,11348,a),flip(a)].">
      <j1 rule="hyper" parents="63 8110 11348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11350">
    <literal><![CDATA[
      (x \ y) * T(K(y,z) * x,x \ y) = (y / x) * (x * K(y,z))
    ]]></literal>
    <justification jstring="[para(11349(a,2),4982(a,1,2))].">
      <j1 rule="para" parents="11349 4982"/>
    </justification>
  </clause>

  <clause id="11351">
    <literal><![CDATA[
      (K(x,y) * z) * (z \ x) = (x / z) * (z * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(300,a,11350,a)].">
      <j1 rule="hyper" parents="300 11350"/>
    </justification>
  </clause>

  <clause id="11352">
    <literal><![CDATA[
      ((x / y) * (y * K(x,z))) / T(x,z) = a(K(x,z),y,y \ x)
    ]]></literal>
    <justification jstring="[para(11351(a,1),8862(a,1,1))].">
      <j1 rule="para" parents="11351 8862"/>
    </justification>
  </clause>

  <clause id="11353">
    <literal><![CDATA[
      ((x / y) * (y * K(z,x))) \ ((z * x) / z) = T(a(K(x,z),y,y \ x),x)
    ]]></literal>
    <justification jstring="[para(11352(a,1),10726(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11352 10726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11354">
    <literal><![CDATA[
      K(x \ 1,T(y * x,z)) = K(x \ 1,T(y,z) * x)
    ]]></literal>
    <justification jstring="[para(1869(a,1),11347(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1869 11347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11355">
    <literal><![CDATA[
      ((x / y) * (y * K(z,x))) \ ((z * x) / z) = a(K(x,z),y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(333,a,7914,a(flip),b,11353,a),flip(a)].">
      <j1 rule="hyper" parents="333 7914 11353"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11356">
    <literal><![CDATA[
      a(K(x,y),z,z \ x) = a(x / z,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,4428,a(flip),b,11355,a),flip(a)].">
      <j1 rule="hyper" parents="63 4428 11355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11357">
    <literal><![CDATA[
      a(K(x * y,z),y,y \ (x * y)) = a(x,y,K(z,x * y))
    ]]></literal>
    <justification jstring="[para(11(a,1),11356(a,2,1))].">
      <j1 rule="para" parents="11 11356"/>
    </justification>
  </clause>

  <clause id="11358">
    <literal><![CDATA[
      a(K(x * y,z),y,T(x,y)) = a(x,y,K(z,x * y))
    ]]></literal>
    <justification jstring="[para(22(a,2),11357(a,1,3))].">
      <j1 rule="para" parents="22 11357"/>
    </justification>
  </clause>

  <clause id="11359">
    <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(11358(a,1),4350(a,1,2))].">
      <j1 rule="para" parents="11358 4350"/>
    </justification>
  </clause>

  <clause id="11360">
    <literal><![CDATA[
      (K(x * y,z) * y) * T(x,y) = x * (y * K(x * y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,9914,a(flip),b,11359,a),flip(a)].">
      <j1 rule="hyper" parents="63 9914 11359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11361">
    <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(333,a,453,a(flip),b,8958,a),flip(a)].">
      <j1 rule="hyper" parents="333 453 8958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11362">
    <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(63,a,1553,a(flip),b,11361,a)].">
      <j1 rule="hyper" parents="63 1553 11361"/>
    </justification>
  </clause>

  <clause id="11363">
    <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(4587(a,1),11362(a,1,1,2,1))].">
      <j1 rule="para" parents="4587 11362"/>
    </justification>
  </clause>

  <clause id="11364">
    <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(4993(a,1),11363(a,1,1,2,1))].">
      <j1 rule="para" parents="4993 11363"/>
    </justification>
  </clause>

  <clause id="11365">
    <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(6926(a,1),11364(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6926 11364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11366">
    <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(63,a,3840,a(flip),b,11365,a),flip(a)].">
      <j1 rule="hyper" parents="63 3840 11365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11368">
    <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(11366(a,1),1523(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="11366 1523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11369">
    <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(4567(a,1),11368(a,1,1))].">
      <j1 rule="para" parents="4567 11368"/>
    </justification>
  </clause>

  <clause id="11370">
    <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(8775(a,1),11369(a,1,1))].">
      <j1 rule="para" parents="8775 11369"/>
    </justification>
  </clause>

  <clause id="11371">
    <literal><![CDATA[
      R(K(x,y),R(T(x,z),u,w),v5) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(304,a,11370,a),flip(a)].">
      <j1 rule="hyper" parents="304 11370"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11374">
    <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(63,a,5645,a(flip),b,11371,a)].">
      <j1 rule="hyper" parents="63 5645 11371"/>
    </justification>
  </clause>

  <clause id="11375">
    <literal><![CDATA[
      R(K(x,y),R(x,z,u),w) = K(x,y)
    ]]></literal>
    <justification jstring="[para(110(a,1),11371(a,1,2,1))].">
      <j1 rule="para" parents="110 11371"/>
    </justification>
  </clause>

  <clause id="11376">
    <literal><![CDATA[
      K(x,(R(x,y,z) * u) / w) = K(x,R(x,y,z) / (w / u))
    ]]></literal>
    <justification jstring="[hyper(63,a,5647,a(flip),b,11375,a)].">
      <j1 rule="hyper" parents="63 5647 11375"/>
    </justification>
  </clause>

  <clause id="11377">
    <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(333,a,6473,a(flip),b,11374,a),flip(a)].">
      <j1 rule="hyper" parents="333 6473 11374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11378">
    <literal><![CDATA[
      K(x,y \ R(T(x,z),u,w)) = K(x,R(x,u,w) * (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,8813,a(flip),b,11377,a),flip(a)].">
      <j1 rule="hyper" parents="63 8813 11377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11380">
    <literal><![CDATA[
      K(x,R(x,y,z) * (u \ 1)) = K(x,u \ R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,7425,a(flip),b,11378,a),flip(a)].">
      <j1 rule="hyper" parents="63 7425 11378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11381">
    <literal><![CDATA[
      K(x,y \ R(T(x,z),u,w)) = K(x,y \ R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,11378,a,b,11380,a)].">
      <j1 rule="hyper" parents="63 11378 11380"/>
    </justification>
  </clause>

  <clause id="11382">
    <literal><![CDATA[
      K(x,R(T(x,y),z,u) / w) = K(x,w \ R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(7226,a,11381,a)].">
      <j1 rule="hyper" parents="7226 11381"/>
    </justification>
  </clause>

  <clause id="11384">
    <literal><![CDATA[
      K(x,y \ R(x,z,u)) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,10681,a(flip),b,11382,a),flip(a)].">
      <j1 rule="hyper" parents="63 10681 11382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11385">
    <literal><![CDATA[
      K(x,y \ ((z * x) * (z \ 1))) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(9642,a,11384,a)].">
      <j1 rule="hyper" parents="9642 11384"/>
    </justification>
  </clause>

  <clause id="11388">
    <literal><![CDATA[
      K(x,y \ (z * R(x,u,w))) = K(x,(z \ y) \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,9550,a(flip),b,11384,a)].">
      <j1 rule="hyper" parents="63 9550 11384"/>
    </justification>
  </clause>

  <clause id="11389">
    <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(63,a,8346,a(flip),b,11385,a)].">
      <j1 rule="hyper" parents="63 8346 11385"/>
    </justification>
  </clause>

  <clause id="11391">
    <literal><![CDATA[
      K(x,y \ (z * R(x,u,w))) = K(x,x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(333,a,10648,a(flip),b,11388,a),flip(a)].">
      <j1 rule="hyper" parents="333 10648 11388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11392">
    <literal><![CDATA[
      K(x,y \ (R(x,z,u) * w)) = K(x,x * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(63,a,9837,a,b,11391,a)].">
      <j1 rule="hyper" parents="63 9837 11391"/>
    </justification>
  </clause>

  <clause id="11393">
    <literal><![CDATA[
      K(x,(y / R(x,z,u)) \ w) = K(x,x * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(63,a,8747,a,b,11391,a)].">
      <j1 rule="hyper" parents="63 8747 11391"/>
    </justification>
  </clause>

  <clause id="11394">
    <literal><![CDATA[
      K(x,y \ ((x * z) * u)) = K(x,x * (y \ (z * u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,9839,a(flip),b,11391,a)].">
      <j1 rule="hyper" parents="63 9839 11391"/>
    </justification>
  </clause>

  <clause id="11396">
    <literal><![CDATA[
      K(x,y \ (x \ ((x * z) * u))) = K(x,x * (y \ (x \ (z * u))))
    ]]></literal>
    <justification jstring="[para(1520(a,1),11392(a,1,2,2))].">
      <j1 rule="para" parents="1520 11392"/>
    </justification>
  </clause>

  <clause id="11398">
    <literal><![CDATA[
      K(x,y \ ((z * x) * u)) = K(x,x * (y \ (z * u)))
    ]]></literal>
    <justification jstring="[hyper(10113,a,11394,a)].">
      <j1 rule="hyper" parents="10113 11394"/>
    </justification>
  </clause>

  <clause id="11400">
    <literal><![CDATA[
      K(x,y \ ((z * u) * x)) = K(x,y \ ((x * z) * u))
    ]]></literal>
    <justification jstring="[hyper(333,a,10644,a,b,11394,a)].">
      <j1 rule="hyper" parents="333 10644 11394"/>
    </justification>
  </clause>

  <clause id="11401">
    <literal><![CDATA[
      K(x,x \ ((y * x) * z)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(10(a,1),11398(a,2,2))].">
      <j1 rule="para" parents="10 11398"/>
    </justification>
  </clause>

  <clause id="11402">
    <literal><![CDATA[
      K(x,y * ((y * x) \ z)) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[para(10(a,1),11401(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 11401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11403">
    <literal><![CDATA[
      K(x \ y,(x \ y) \ z) = K(x \ y,x * (y \ z))
    ]]></literal>
    <justification jstring="[para(10(a,1),11402(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10 11402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11404">
    <literal><![CDATA[
      x * K(y \ z,y * (z \ x)) = (y \ z) * (x / (y \ z))
    ]]></literal>
    <justification jstring="[hyper(126,a,11403,a(flip),b,4460,a)].">
      <j1 rule="hyper" parents="126 11403 4460"/>
    </justification>
  </clause>

  <clause id="11405">
    <literal><![CDATA[
      K(x,y \ (x \ ((x * z) * u))) = K(x,y \ (z * u))
    ]]></literal>
    <justification jstring="[hyper(333,a,10650,a(flip),b,11396,a),flip(a)].">
      <j1 rule="hyper" parents="333 10650 11396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11406">
    <literal><![CDATA[
      K(x,y \ (x \ (z * u))) = K(x,y \ ((x \ z) * u))
    ]]></literal>
    <justification jstring="[para(10(a,1),11405(a,1,2,2,2,1))].">
      <j1 rule="para" parents="10 11405"/>
    </justification>
  </clause>

  <clause id="11407">
    <literal><![CDATA[
      K(x,y \ (x \ (z * y))) = K(x,T(x \ z,y))
    ]]></literal>
    <justification jstring="[para(22(a,2),11406(a,2,2))].">
      <j1 rule="para" parents="22 11406"/>
    </justification>
  </clause>

  <clause id="11408">
    <literal><![CDATA[
      K(x,T(x \ y,y \ (x * z))) = K(x,(y \ (x * z)) \ z)
    ]]></literal>
    <justification jstring="[para(70(a,1),11407(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="70 11407"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11409">
    <literal><![CDATA[
      K(x,T(x \ y,y \ z)) = K(x,(y \ (x * z)) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,10427,a(flip),b,11408,a)].">
      <j1 rule="hyper" parents="63 10427 11408"/>
    </justification>
  </clause>

  <clause id="11410">
    <literal><![CDATA[
      K(x,(y \ (x * z)) \ z) = K(x,T(x \ y,z))
    ]]></literal>
    <justification jstring="[hyper(10428,a,11409,a),flip(a)].">
      <j1 rule="hyper" parents="10428 11409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11411">
    <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(63,a,6322,a(flip),b,10224,a),flip(a)].">
      <j1 rule="hyper" parents="63 6322 10224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11413">
    <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(7839(a,1),7842(a,1,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="7839 7842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11414">
    <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(9(a,1),11413(a,2,1,2,1))].">
      <j1 rule="para" parents="9 11413"/>
    </justification>
  </clause>

  <clause id="11416">
    <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(7839(a,1),11414(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7839 11414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11417">
    <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(2009(a,1),11416(a,2,2))].">
      <j1 rule="para" parents="2009 11416"/>
    </justification>
  </clause>

  <clause id="11418">
    <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(63,a,8471,a,b,11417,a)].">
      <j1 rule="hyper" parents="63 8471 11417"/>
    </justification>
  </clause>

  <clause id="11419">
    <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(269,a,11418,a),flip(a)].">
      <j1 rule="hyper" parents="269 11418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11420">
    <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(4571(a,1),11418(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4571 11418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11421">
    <literal><![CDATA[
      x / a(K(y,z),u,u \ 1) = x * a(K(z,y),u,u \ 1)
    ]]></literal>
    <justification jstring="[para(4571(a,1),11420(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4571 11420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11422">
    <literal><![CDATA[
      a(K(x,y),z,z \ 1) \ 1 = a(K(y,x),z,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(3984,a,11421,a)].">
      <j1 rule="hyper" parents="3984 11421"/>
    </justification>
  </clause>

  <clause id="11423">
    <literal><![CDATA[
      T(x,a(K(y,z),u,u \ 1)) = x
    ]]></literal>
    <justification jstring="[para(11422(a,1),10218(a,1,2))].">
      <j1 rule="para" parents="11422 10218"/>
    </justification>
  </clause>

  <clause id="11424">
    <literal><![CDATA[
      T(x,a(K(y,z),u \ 1,u)) = x
    ]]></literal>
    <justification jstring="[para(3277(a,1),11423(a,1,2))].">
      <j1 rule="para" parents="3277 11423"/>
    </justification>
  </clause>

  <clause id="11425">
    <literal><![CDATA[
      T(a(K(x,y),z \ 1,z),u) = a(K(x,y),z \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(54,a,11424,a)].">
      <j1 rule="hyper" parents="54 11424"/>
    </justification>
  </clause>

  <clause id="11426">
    <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(333,a,3281,a,b,11425,a),flip(a)].">
      <j1 rule="hyper" parents="333 3281 11425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11427">
    <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(4589(a,2),11426(a,1,1))].">
      <j1 rule="para" parents="4589 11426"/>
    </justification>
  </clause>

  <clause id="11428">
    <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(63,a,8680,a,b,11427,a)].">
      <j1 rule="hyper" parents="63 8680 11427"/>
    </justification>
  </clause>

  <clause id="11429">
    <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(63,a,6409,a,b,11428,a)].">
      <j1 rule="hyper" parents="63 6409 11428"/>
    </justification>
  </clause>

  <clause id="11430">
    <literal><![CDATA[
      K(x,K(y,R(z,u \ 1,u))) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(8975,a,11429,a)].">
      <j1 rule="hyper" parents="8975 11429"/>
    </justification>
  </clause>

  <clause id="11431">
    <literal><![CDATA[
      K(x,K(y,R(z,u,u \ 1))) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(1929(a,1),11430(a,1,2,2))].">
      <j1 rule="para" parents="1929 11430"/>
    </justification>
  </clause>

  <clause id="11432">
    <literal><![CDATA[
      K(x,K(y,R(z,u,u \ 1))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(333,a,6800,a,b,11431,a),flip(a)].">
      <j1 rule="hyper" parents="333 6800 11431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11434">
    <literal><![CDATA[
      K(x,K(y,R(z,u,u \ K(w,x)))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,10739,a,b,11431,a)].">
      <j1 rule="hyper" parents="63 10739 11431"/>
    </justification>
  </clause>

  <clause id="11435">
    <literal><![CDATA[
      K(x,K(y,z * (u \ 1))) = K(x,K(y,z / u))
    ]]></literal>
    <justification jstring="[para(554(a,1),11432(a,1,2,2))].">
      <j1 rule="para" parents="554 11432"/>
    </justification>
  </clause>

  <clause id="11437">
    <literal><![CDATA[
      T(x,K(y,z * (u \ 1))) = T(x,K(y,z / u))
    ]]></literal>
    <justification jstring="[hyper(124,a,11435,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 11435 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11438">
    <literal><![CDATA[
      K(x,K(y,z * (1 / u))) = K(x,K(y,z / u))
    ]]></literal>
    <justification jstring="[para(4785(a,2),11435(a,1,2))].">
      <j1 rule="para" parents="4785 11435"/>
    </justification>
  </clause>

  <clause id="11439">
    <literal><![CDATA[
      K(x,K(y,z / (u \ 1))) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[para(4786(a,1),11435(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4786 11435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11440">
    <literal><![CDATA[
      T(T(x,y),K(y,z / u)) = T(x,T(y,(z * (u \ 1)) \ 1))
    ]]></literal>
    <justification jstring="[hyper(7197,a,11437,a),flip(a)].">
      <j1 rule="hyper" parents="7197 11437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11441">
    <literal><![CDATA[
      T(x,K(y,z / (u \ 1))) = T(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[para(4786(a,1),11437(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4786 11437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11443">
    <literal><![CDATA[
      K(x,K(y,(z \ 1) / u)) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(7214,a,11439,a)].">
      <j1 rule="hyper" parents="7214 11439"/>
    </justification>
  </clause>

  <clause id="11444">
    <literal><![CDATA[
      K(x,K(y / (z \ 1),u)) = K(x,K(u,y * z))
    ]]></literal>
    <justification jstring="[hyper(6836,a,11439,a)].">
      <j1 rule="hyper" parents="6836 11439"/>
    </justification>
  </clause>

  <clause id="11445">
    <literal><![CDATA[
      K(x,K(T(y,z),z * u)) = K(x,K(y,(u \ 1) \ z))
    ]]></literal>
    <justification jstring="[para(6353(a,1),11439(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6353 11439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11446">
    <literal><![CDATA[
      T(x \ 1,K(y,z * x)) = T(x \ 1,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(7060,a,11441,a),flip(a)].">
      <j1 rule="hyper" parents="7060 11441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11447">
    <literal><![CDATA[
      T(x,K(y,(z * (u \ 1)) * u)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(11(a,1),11441(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11 11441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11448">
    <literal><![CDATA[
      K(x,K(y,(z \ 1) / (u / z))) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(12(a,1),11443(a,2,2,2))].">
      <j1 rule="para" parents="12 11443"/>
    </justification>
  </clause>

  <clause id="11449">
    <literal><![CDATA[
      K(x,K(y,(1 / z) / u)) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[para(4794(a,2),11443(a,1,2))].">
      <j1 rule="para" parents="4794 11443"/>
    </justification>
  </clause>

  <clause id="11450">
    <literal><![CDATA[
      K(x,K(y / (z \ 1),u)) = K(x,K(y * z,u))
    ]]></literal>
    <justification jstring="[hyper(333,a,6800,a,b,11444,a),flip(a)].">
      <j1 rule="hyper" parents="333 6800 11444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11452">
    <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(11446(a,1),4405(a,1,1))].">
      <j1 rule="para" parents="11446 4405"/>
    </justification>
  </clause>

  <clause id="11453">
    <literal><![CDATA[
      K(x,K(y,(z \ 1) / (u / z))) = K(y,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(6798,a,11448,a)].">
      <j1 rule="hyper" parents="6798 11448"/>
    </justification>
  </clause>

  <clause id="11454">
    <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(11449(a,1),10934(a,1,3))].">
      <j1 rule="para" parents="11449 10934"/>
    </justification>
  </clause>

  <clause id="11455">
    <literal><![CDATA[
      K(x,K(y * z,L(u,z \ 1,z))) = K(u,K(x,T(z * y,z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,11105,a(flip),b,11450,a),flip(a)].">
      <j1 rule="hyper" parents="63 11105 11450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11456">
    <literal><![CDATA[
      K(x,K(y / (z \ 1),u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,y * z)) = w
    ]]></literal>
    <justification jstring="[para(11450(a,2),6836(a,1))].">
      <j1 rule="para" parents="11450 6836"/>
    </justification>
  </clause>

  <clause id="11457">
    <literal><![CDATA[
      K(x,(T(y,z) / u) / (y / u)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,7187,a(flip),b,11453,a)].">
      <j1 rule="hyper" parents="63 7187 11453"/>
    </justification>
  </clause>

  <clause id="11459">
    <literal><![CDATA[
      K(x,K(y,z)) * (z / u) = T(z,K(x,y)) / u
    ]]></literal>
    <justification jstring="[para(11457(a,1),8410(a,1,1))].">
      <j1 rule="para" parents="11457 8410"/>
    </justification>
  </clause>

  <clause id="11460">
    <literal><![CDATA[
      R(K(x,K(y,z)),z / u,u) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(11457(a,1),8754(a,1,1))].">
      <j1 rule="para" parents="11457 8754"/>
    </justification>
  </clause>

  <clause id="11461">
    <literal><![CDATA[
      R(K(x,K(y,z)),y / u,u) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(6800(a,1),11460(a,1,1))].">
      <j1 rule="para" parents="6800 11460"/>
    </justification>
  </clause>

  <clause id="11463">
    <literal><![CDATA[
      K(x,K(y,R(z,x / u,u))) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,7814,a(flip),b,11461,a)].">
      <j1 rule="hyper" parents="63 7814 11461"/>
    </justification>
  </clause>

  <clause id="11464">
    <literal><![CDATA[
      K(x,K(y,R(z,u,u \ x))) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(76(a,1),11463(a,1,2,2,2))].">
      <j1 rule="para" parents="76 11463"/>
    </justification>
  </clause>

  <clause id="11465">
    <literal><![CDATA[
      K(x,K(y,z)) * (T(z,K(x,y)) / u) = z / u
    ]]></literal>
    <justification jstring="[hyper(6832,a,11459,a)].">
      <j1 rule="hyper" parents="6832 11459"/>
    </justification>
  </clause>

  <clause id="11466">
    <literal><![CDATA[
      T(x,K(y,z)) / (u \ x) = K(y,K(z,x)) * u
    ]]></literal>
    <justification jstring="[para(76(a,1),11459(a,1,2)),flip(a)].">
      <j1 rule="para" parents="76 11459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11468">
    <literal><![CDATA[
      K(x,K(y,z)) * (T(x,K(z,y)) / u) = x / u
    ]]></literal>
    <justification jstring="[para(6762(a,1),11465(a,1,1))].">
      <j1 rule="para" parents="6762 11465"/>
    </justification>
  </clause>

  <clause id="11469">
    <literal><![CDATA[
      T(x,K(y,z)) / (u \ x) = K(x,K(y,z)) * u
    ]]></literal>
    <justification jstring="[para(6788(a,1),11466(a,2,1))].">
      <j1 rule="para" parents="6788 11466"/>
    </justification>
  </clause>

  <clause id="11470">
    <literal><![CDATA[
      K((T(x,y) / z) / (x / z),u) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(8412,a,11468,a)].">
      <j1 rule="hyper" parents="8412 11468"/>
    </justification>
  </clause>

  <clause id="11471">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) \ T(x,K(y,z)) = u \ x
    ]]></literal>
    <justification jstring="[hyper(192,a,11469,a)].">
      <j1 rule="hyper" parents="192 11469"/>
    </justification>
  </clause>

  <clause id="11472">
    <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(9209(a,1),11470(a,1,1,1,1))].">
      <j1 rule="para" parents="9209 11470"/>
    </justification>
  </clause>

  <clause id="11473">
    <literal><![CDATA[
      L(x \ y,x,K(y,K(z,u))) = x \ y
    ]]></literal>
    <justification jstring="[hyper(4349,a,11471,a)].">
      <j1 rule="hyper" parents="4349 11471"/>
    </justification>
  </clause>

  <clause id="11474">
    <literal><![CDATA[
      a(K(x,K(y,z)),u,u \ x) = 1
    ]]></literal>
    <justification jstring="[hyper(53,a,11473,a)].">
      <j1 rule="hyper" parents="53 11473"/>
    </justification>
  </clause>

  <clause id="11475">
    <literal><![CDATA[
      a(K(x * y,K(z,u)),x,y) = 1
    ]]></literal>
    <justification jstring="[para(9(a,1),11474(a,1,3))].">
      <j1 rule="para" parents="9 11474"/>
    </justification>
  </clause>

  <clause id="11476">
    <literal><![CDATA[
      a(K(K(x,y),z),u,u \ z) = 1
    ]]></literal>
    <justification jstring="[para(5296(a,2),11474(a,1,1))].">
      <j1 rule="para" parents="5296 11474"/>
    </justification>
  </clause>

  <clause id="11477">
    <literal><![CDATA[
      a(K(x,K(y,z * u)),z,u) = 1
    ]]></literal>
    <justification jstring="[para(6762(a,1),11475(a,1,1))].">
      <j1 rule="para" parents="6762 11475"/>
    </justification>
  </clause>

  <clause id="11478">
    <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(333,a,6822,a,b,11476,a),flip(a)].">
      <j1 rule="hyper" parents="333 6822 11476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11480">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * (u \ K(w,z)) = K(w,z) * K(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(11434(a,1),8855(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11434 8855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11482">
    <literal><![CDATA[
      K(x,K(y,T(z * u,z))) = K(x,K(y,(u \ 1) \ z))
    ]]></literal>
    <justification jstring="[para(6370(a,1),11445(a,1,2))].">
      <j1 rule="para" parents="6370 11445"/>
    </justification>
  </clause>

  <clause id="11483">
    <literal><![CDATA[
      T(x,T(y,(z * (u \ 1)) \ 1)) = T(x,T(y,z / u))
    ]]></literal>
    <justification jstring="[hyper(7056,a,11440,a),flip(a)].">
      <j1 rule="hyper" parents="7056 11440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11484">
    <literal><![CDATA[
      T(x,T(y,z * (u \ 1))) = T(x,T(y,z / u))
    ]]></literal>
    <justification jstring="[hyper(7273,a,11483,a)].">
      <j1 rule="hyper" parents="7273 11483"/>
    </justification>
  </clause>

  <clause id="11485">
    <literal><![CDATA[
      T(x,T(y,z * (u \ 1))) = x * K(x,T(y,z / u))
    ]]></literal>
    <justification jstring="[hyper(333,a,4222,a(flip),b,11484,a),flip(a)].">
      <j1 rule="hyper" parents="333 4222 11484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11486">
    <literal><![CDATA[
      K(x,T(y,z * (u \ 1))) = K(x,T(y,z / u))
    ]]></literal>
    <justification jstring="[hyper(4305,a,11485,a)].">
      <j1 rule="hyper" parents="4305 11485"/>
    </justification>
  </clause>

  <clause id="11487">
    <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(11486(a,1),11389(a,1,1))].">
      <j1 rule="para" parents="11486 11389"/>
    </justification>
  </clause>

  <clause id="11488">
    <literal><![CDATA[
      K(x,K(y,T(z * (u / z),z))) = K(y,K(u,L(x,z \ 1,z)))
    ]]></literal>
    <justification jstring="[para(12(a,1),11455(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12 11455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11489">
    <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(11464(a,1),11478(a,2,2))].">
      <j1 rule="para" parents="11464 11478"/>
    </justification>
  </clause>

  <clause id="11490">
    <literal><![CDATA[
      K(x,K(y,T(z * (u / z),z))) = K(x,K(u,L(y,z \ 1,z)))
    ]]></literal>
    <justification jstring="[hyper(6798,a,11488,a)].">
      <j1 rule="hyper" parents="6798 11488"/>
    </justification>
  </clause>

  <clause id="11491">
    <literal><![CDATA[
      K(x,K(y,((z / u) \ 1) \ u)) = K(x,K(z,L(y,u \ 1,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,11482,a(flip),b,11490,a)].">
      <j1 rule="hyper" parents="63 11482 11490"/>
    </justification>
  </clause>

  <clause id="11492">
    <literal><![CDATA[
      (x / y) \ T(x,K(z,u)) = y * K(z,K(x,L(u,y \ 1,y)))
    ]]></literal>
    <justification jstring="[para(11491(a,1),7766(a,2,2))].">
      <j1 rule="para" parents="11491 7766"/>
    </justification>
  </clause>

  <clause id="11493">
    <literal><![CDATA[
      (x / y) \ T(x,K(z,u)) = y * K(x,K(z,L(u,y \ 1,y)))
    ]]></literal>
    <justification jstring="[para(6785(a,1),11492(a,2,2))].">
      <j1 rule="para" parents="6785 11492"/>
    </justification>
  </clause>

  <clause id="11494">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * (u \ K(y,z)) = T(K(y,z),x)
    ]]></literal>
    <justification jstring="[hyper(333,a,6793,a(flip),b,11480,a),flip(a)].">
      <j1 rule="hyper" parents="333 6793 11480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11496">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * (u \ K(x,y)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(6788(a,2),11494(a,1,1,1))].">
      <j1 rule="para" parents="6788 11494"/>
    </justification>
  </clause>

  <clause id="11497">
    <literal><![CDATA[
      K(x,T(y,z)) / (u \ K(x,y)) = K(x,K(y,z)) * u
    ]]></literal>
    <justification jstring="[hyper(123,a,6365,a,b,11496,a)].">
      <j1 rule="hyper" parents="123 6365 11496"/>
    </justification>
  </clause>

  <clause id="11498">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(x,y) / u) = K(x,T(y,z)) / u
    ]]></literal>
    <justification jstring="[para(79(a,1),11497(a,1,2)),flip(a)].">
      <j1 rule="para" parents="79 11497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11499">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(x,T(y,z)) / u) = K(x,y) / u
    ]]></literal>
    <justification jstring="[hyper(6832,a,11498,a)].">
      <j1 rule="hyper" parents="6832 11498"/>
    </justification>
  </clause>

  <clause id="11500">
    <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(11499(a,1),6019(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11499 6019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11501">
    <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(6763(a,2),11500(a,2,2))].">
      <j1 rule="para" parents="6763 11500"/>
    </justification>
  </clause>

  <clause id="11502">
    <literal><![CDATA[
      K(x,(K(y,z) / u) / (u \ 1)) = K(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(34,a,8914,a,b,11501,a)].">
      <j1 rule="hyper" parents="34 8914 11501"/>
    </justification>
  </clause>

  <clause id="11504">
    <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(6788(a,2),11489(a,2,2))].">
      <j1 rule="para" parents="6788 11489"/>
    </justification>
  </clause>

  <clause id="11505">
    <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(5296(a,1),11504(a,1,1))].">
      <j1 rule="para" parents="5296 11504"/>
    </justification>
  </clause>

  <clause id="11506">
    <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(6947(a,1),11487(a,1,1,2))].">
      <j1 rule="para" parents="6947 11487"/>
    </justification>
  </clause>

  <clause id="11507">
    <literal><![CDATA[
      K(x,((y \ (z * x)) * (z \ 1)) \ x) = R(K(x,y),z * x,z \ 1)
    ]]></literal>
    <justification jstring="[para(4639(a,1),11506(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4639 11506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11508">
    <literal><![CDATA[
      K(x,((y \ (z * x)) * (z \ 1)) \ x) = K(R(x,z,z \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(333,a,7963,a(flip),b,11507,a),flip(a)].">
      <j1 rule="hyper" parents="333 7963 11507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11510">
    <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(529(a,1),11508(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="529 11508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11511">
    <literal><![CDATA[
      R(K(R(x,y,y \ 1),z),y,x) = K(x,(((z \ y) * x) * (y \ 1)) \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,5651,a(flip),b,11510,a)].">
      <j1 rule="hyper" parents="63 5651 11510"/>
    </justification>
  </clause>

  <clause id="11512">
    <literal><![CDATA[
      K(x,(((y \ z) * x) * (z \ 1)) \ x) = K(R(x,z,z \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(6330,a,11511,a)].">
      <j1 rule="hyper" parents="6330 11511"/>
    </justification>
  </clause>

  <clause id="11513">
    <literal><![CDATA[
      K(x,((y \ z) * (z \ 1)) \ (x \ x)) = K(R(x,z,z \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,9986,a(flip),b,11512,a)].">
      <j1 rule="hyper" parents="63 9986 11512"/>
    </justification>
  </clause>

  <clause id="11515">
    <literal><![CDATA[
      K(x,((y \ z) * (z \ 1)) \ 1) = K(R(x,z,z \ 1),y)
    ]]></literal>
    <justification jstring="[para(66(a,1),11513(a,1,2,2))].">
      <j1 rule="para" parents="66 11513"/>
    </justification>
  </clause>

  <clause id="11516">
    <literal><![CDATA[
      R(K(x,y),z,z \ 1) = K(R(x,z,z \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,5673,a(flip),b,11515,a)].">
      <j1 rule="hyper" parents="63 5673 11515"/>
    </justification>
  </clause>

  <clause id="11518">
    <literal><![CDATA[
      R(K(x,y),z,z \ 1) \ 1 = K(y,R(x,z,z \ 1))
    ]]></literal>
    <justification jstring="[para(11516(a,2),4367(a,1,1))].">
      <j1 rule="para" parents="11516 4367"/>
    </justification>
  </clause>

  <clause id="11519">
    <literal><![CDATA[
      R(K(x,y),z,z \ 1) = K(x,R(y,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(5640,a,11518,a)].">
      <j1 rule="hyper" parents="5640 11518"/>
    </justification>
  </clause>

  <clause id="11520">
    <literal><![CDATA[
      K(x,(y * z) * (z \ 1)) = R(K(x,y),z,z \ 1)
    ]]></literal>
    <justification jstring="[para(385(a,2),11519(a,2,2)),flip(a)].">
      <j1 rule="para" parents="385 11519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11521">
    <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(4707(a,2),11472(a,1,1))].">
      <j1 rule="para" parents="4707 11472"/>
    </justification>
  </clause>

  <clause id="11522">
    <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(7045,a,11521,a)].">
      <j1 rule="hyper" parents="7045 11521"/>
    </justification>
  </clause>

  <clause id="11523">
    <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(11456,a,11522,a)].">
      <j1 rule="hyper" parents="11456 11522"/>
    </justification>
  </clause>

  <clause id="11524">
    <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(12(a,1),11523(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 11523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11525">
    <literal><![CDATA[
      K(x,K(y * z,z \ L(z,u,w))) = K(x,K(z * y,z \ L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(6783,a,11524,a)].">
      <j1 rule="hyper" parents="6783 11524"/>
    </justification>
  </clause>

  <clause id="11526">
    <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(1953(a,1),9821(a,2,1,2))].">
      <j1 rule="para" parents="1953 9821"/>
    </justification>
  </clause>

  <clause id="11527">
    <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(449(a,1),11526(a,1,1,2,2))].">
      <j1 rule="para" parents="449 11526"/>
    </justification>
  </clause>

  <clause id="11528">
    <literal><![CDATA[
      K(x * T((y * z) \ z,y),y \ 1) = K(x * R(y \ 1,y,z),y \ 1)
    ]]></literal>
    <justification jstring="[para(2868(a,1),11527(a,1,1,2))].">
      <j1 rule="para" parents="2868 11527"/>
    </justification>
  </clause>

  <clause id="11529">
    <literal><![CDATA[
      K(x * R(y \ 1,y,z),y \ 1) = K(x * ((y * z) \ z),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,4865,a(flip),b,11528,a),flip(a)].">
      <j1 rule="hyper" parents="63 4865 11528"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11530">
    <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(6763(a,1),11452(a,1,2,1,2))].">
      <j1 rule="para" parents="6763 11452"/>
    </justification>
  </clause>

  <clause id="11531">
    <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(7144(a,1),11530(a,1,2,1,2))].">
      <j1 rule="para" parents="7144 11530"/>
    </justification>
  </clause>

  <clause id="11532">
    <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(6871(a,1),11531(a,1,2,1,2))].">
      <j1 rule="para" parents="6871 11531"/>
    </justification>
  </clause>

  <clause id="11533">
    <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(4258(a,2),11532(a,1,2,1))].">
      <j1 rule="para" parents="4258 11532"/>
    </justification>
  </clause>

  <clause id="11534">
    <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(5097,a,11533,a)].">
      <j1 rule="hyper" parents="5097 11533"/>
    </justification>
  </clause>

  <clause id="11535">
    <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(7174(a,1),11534(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7174 11534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11536">
    <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(1343(a,1),11535(a,2,2))].">
      <j1 rule="para" parents="1343 11535"/>
    </justification>
  </clause>

  <clause id="11537">
    <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(333,a,6830,a(flip),b,11536,a),flip(a)].">
      <j1 rule="hyper" parents="333 6830 11536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11538">
    <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(333,a,2869,a(flip),b,11537,a),flip(a)].">
      <j1 rule="hyper" parents="333 2869 11537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11539">
    <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(1264(a,1),11538(a,1,1))].">
      <j1 rule="para" parents="1264 11538"/>
    </justification>
  </clause>

  <clause id="11540">
    <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(11539(a,1),6839(a,1,2))].">
      <j1 rule="para" parents="11539 6839"/>
    </justification>
  </clause>

  <clause id="11541">
    <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(7052,a,11540,a),flip(a)].">
      <j1 rule="hyper" parents="7052 11540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11542">
    <literal><![CDATA[
      K(x \ L(x,y,z),K(u * x,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(u,K(w,x \ L(x,y,z))) = v5
    ]]></literal>
    <justification jstring="[para(11541(a,2),6825(a,1))].">
      <j1 rule="para" parents="11541 6825"/>
    </justification>
  </clause>

  <clause id="11543">
    <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(11542,a,11524,a),flip(a)].">
      <j1 rule="hyper" parents="11542 11524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11544">
    <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(333,a,6785,a,b,11543,a),flip(a)].">
      <j1 rule="hyper" parents="333 6785 11543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11545">
    <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(63,a,11525,a,b,11544,a)].">
      <j1 rule="hyper" parents="63 11525 11544"/>
    </justification>
  </clause>

  <clause id="11546">
    <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(4567(a,1),8648(a,1,1,1))].">
      <j1 rule="para" parents="4567 8648"/>
    </justification>
  </clause>

  <clause id="11547">
    <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(9(a,1),9832(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 9832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11548">
    <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(333,a,6373,a(flip),b,11547,a),flip(a)].">
      <j1 rule="hyper" parents="333 6373 11547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11550">
    <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(333,a,7950,a(flip),b,11548,a),flip(a)].">
      <j1 rule="hyper" parents="333 7950 11548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11551">
    <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(6695,a,11550,a)].">
      <j1 rule="hyper" parents="6695 11550"/>
    </justification>
  </clause>

  <clause id="11552">
    <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(63,a,9806,a(flip),b,11551,a)].">
      <j1 rule="hyper" parents="63 9806 11551"/>
    </justification>
  </clause>

  <clause id="11553">
    <literal><![CDATA[
      K(x,T((R(x,y,z) \ u) \ w,w)) = K(x,(R(x,y,z) * w) / u)
    ]]></literal>
    <justification jstring="[hyper(63,a,7948,a(flip),b,11552,a)].">
      <j1 rule="hyper" parents="63 7948 11552"/>
    </justification>
  </clause>

  <clause id="11554">
    <literal><![CDATA[
      K(x,(R(x,y,z) * u) / w) = K(x,u / (R(x,y,z) \ w))
    ]]></literal>
    <justification jstring="[hyper(7225,a,11553,a),flip(a)].">
      <j1 rule="hyper" parents="7225 11553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11557">
    <literal><![CDATA[
      K(x,R(x,y,z) / (u / w)) = K(x,w / (R(x,y,z) \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,11376,a(flip),b,11554,a)].">
      <j1 rule="hyper" parents="63 11376 11554"/>
    </justification>
  </clause>

  <clause id="11558">
    <literal><![CDATA[
      K(x,(y * z) / (R(x,y,z) \ u)) = K(x,((x * y) * z) / u)
    ]]></literal>
    <justification jstring="[para(107(a,1),11554(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="107 11554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11559">
    <literal><![CDATA[
      K(x,y / (R(x,z,u) \ w)) = K(x,(w / y) \ R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(5958,a,11557,a),flip(a)].">
      <j1 rule="hyper" parents="5958 11557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11560">
    <literal><![CDATA[
      K(x,y / (R(x,z,u) \ w)) = K(x,(w / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(333,a,11384,a(flip),b,11559,a),flip(a)].">
      <j1 rule="hyper" parents="333 11384 11559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11561">
    <literal><![CDATA[
      K(x,(y * R(x,z,u)) / w) = K(x,(w / y) \ R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,7807,a,b,11559,a)].">
      <j1 rule="hyper" parents="63 7807 11559"/>
    </justification>
  </clause>

  <clause id="11563">
    <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(63,a,9129,a,b,11561,a)].">
      <j1 rule="hyper" parents="63 9129 11561"/>
    </justification>
  </clause>

  <clause id="11564">
    <literal><![CDATA[
      K(x,((x * y) * z) / u) = K(x,(u / (y * z)) \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,11560,a(flip),b,11558,a),flip(a)].">
      <j1 rule="hyper" parents="63 11560 11558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11566">
    <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(20(a,2),11563(a,2,2,1))].">
      <j1 rule="para" parents="20 11563"/>
    </justification>
  </clause>

  <clause id="11567">
    <literal><![CDATA[
      K(x,R(y,z,u) \ R(x,z,u)) = K(R(x,z,u),y \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,8092,a(flip),b,11566,a),flip(a)].">
      <j1 rule="hyper" parents="63 8092 11566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11569">
    <literal><![CDATA[
      K(R(x,y,z),u \ x) = K(x,R(u,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,11384,a(flip),b,11567,a),flip(a)].">
      <j1 rule="hyper" parents="63 11384 11567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11571">
    <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(63,a,11214,a(flip),b,11569,a),flip(a)].">
      <j1 rule="hyper" parents="63 11214 11569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11572">
    <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(63,a,11235,a(flip),b,11571,a)].">
      <j1 rule="hyper" parents="63 11235 11571"/>
    </justification>
  </clause>

  <clause id="11573">
    <literal><![CDATA[
      R(K(x,y),z,u) = K(R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(4889(a,1),11572(a,1,1))].">
      <j1 rule="para" parents="4889 11572"/>
    </justification>
  </clause>

  <clause id="11574">
    <literal><![CDATA[
      R(K(x,y),z,u) \ 1 = K(y,R(x,z,u))
    ]]></literal>
    <justification jstring="[para(11573(a,2),4367(a,1,1))].">
      <j1 rule="para" parents="11573 4367"/>
    </justification>
  </clause>

  <clause id="11576">
    <literal><![CDATA[
      R(K(x,y),z,u) = K(x,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(5640,a,11574,a)].">
      <j1 rule="hyper" parents="5640 11574"/>
    </justification>
  </clause>

  <clause id="11577">
    <literal><![CDATA[
      K(x,R(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      R(K(x,y),z,u) = w
    ]]></literal>
    <justification jstring="[para(11574(a,1),5640(a,1))].">
      <j1 rule="para" parents="11574 5640"/>
    </justification>
  </clause>

  <clause id="11578">
    <literal><![CDATA[
      K(x,R(y,z,u)) * 1 = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(333,a,8,a,b,11576,a)].">
      <j1 rule="hyper" parents="333 8 11576"/>
    </justification>
  </clause>

  <clause id="11579">
    <literal><![CDATA[
      K(R(x,y,z),u) = K(x,R(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,11573,a(flip),b,11576,a)].">
      <j1 rule="hyper" parents="63 11573 11576"/>
    </justification>
  </clause>

  <clause id="11580">
    <literal><![CDATA[
      K(x,R(y,z,u)) * (z * u) = (K(x,y) * z) * u
    ]]></literal>
    <justification jstring="[hyper(125,a,11576,a(flip),b,20,a(flip))].">
      <j1 rule="hyper" parents="125 11576 20"/>
    </justification>
  </clause>

  <clause id="11581">
    <literal><![CDATA[
      R(K(x,y),K(y,z),u) = K(x,y)
    ]]></literal>
    <justification jstring="[para(3836(a,1),11576(a,2,2))].">
      <j1 rule="para" parents="3836 11576"/>
    </justification>
  </clause>

  <clause id="11582">
    <literal><![CDATA[
      (K(x,y) * K(y,z)) * (K(y,z) \ u) = K(x,y) * u
    ]]></literal>
    <justification jstring="[hyper(125,a,11581,a(flip),b,106,a),flip(a)].">
      <j1 rule="hyper" parents="125 11581 106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11583">
    <literal><![CDATA[
      (K(x,y) * K(y,z)) * u = K(x,y) * (K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(125,a,11581,a(flip),b,20,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="125 11581 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11585">
    <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(11581(a,1),4039(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11581 4039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11586">
    <literal><![CDATA[
      R(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,R(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(11578(a,1),134(a,1)),flip(b)].">
      <j1 rule="para" parents="11578 134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11587">
    <literal><![CDATA[
      T(R(x,x \ y,z),u) \ (y * z) = (K(u,x) * (x \ y)) * z
    ]]></literal>
    <justification jstring="[hyper(63,a,4695,a(flip),b,11580,a)].">
      <j1 rule="hyper" parents="63 4695 11580"/>
    </justification>
  </clause>

  <clause id="11588">
    <literal><![CDATA[
      K(x,y) * (K(z,x) * (K(x,y) \ u)) = K(z,x) * u
    ]]></literal>
    <justification jstring="[hyper(63,a,8080,a(flip),b,11582,a)].">
      <j1 rule="hyper" parents="63 8080 11582"/>
    </justification>
  </clause>

  <clause id="11591">
    <literal><![CDATA[
      L(x,K(y,z),K(u,y)) = x
    ]]></literal>
    <justification jstring="[hyper(501,a,11583,a)].">
      <j1 rule="hyper" parents="501 11583"/>
    </justification>
  </clause>

  <clause id="11592">
    <literal><![CDATA[
      K(x,y) * (K(z,x) * u) = K(z,x) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,8080,a(flip),b,11583,a)].">
      <j1 rule="hyper" parents="63 8080 11583"/>
    </justification>
  </clause>

  <clause id="11593">
    <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(123,a,11583,a(flip),b,4291,a)].">
      <j1 rule="hyper" parents="123 11583 4291"/>
    </justification>
  </clause>

  <clause id="11594">
    <literal><![CDATA[
      x \ (K(y,z) * (K(z,u) * x)) != w
    ]]></literal>
    <literal><![CDATA[
      T(K(y,z) * K(z,u),x) = w
    ]]></literal>
    <justification jstring="[para(11583(a,1),347(a,1,2))].">
      <j1 rule="para" parents="11583 347"/>
    </justification>
  </clause>

  <clause id="11595">
    <literal><![CDATA[
      (K(x,y) * K(z,x)) * u = K(z,x) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[para(2005(a,2),11583(a,1,1))].">
      <j1 rule="para" parents="2005 11583"/>
    </justification>
  </clause>

  <clause id="11596">
    <literal><![CDATA[
      K(x,y) * (K(y,x * y) * z) = (y \ L(y,x,y)) * z
    ]]></literal>
    <justification jstring="[para(4924(a,1),11583(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4924 11583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11598">
    <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(11591(a,1),9152(a,2,1))].">
      <j1 rule="para" parents="11591 9152"/>
    </justification>
  </clause>

  <clause id="11599">
    <literal><![CDATA[
      T(T(K(x,y) * z,K(u,w)),K(u,w)) = K(y,v5) * (K(x,y) * (K(y,v5) \ z))
    ]]></literal>
    <justification jstring="[hyper(333,a,6848,a,b,11588,a)].">
      <j1 rule="hyper" parents="333 6848 11588"/>
    </justification>
  </clause>

  <clause id="11600">
    <literal><![CDATA[
      T(x,y) \ (x * (K(x,z) * u)) = K(x,z) * (K(y,x) * u)
    ]]></literal>
    <justification jstring="[hyper(333,a,4550,a,b,11592,a)].">
      <j1 rule="hyper" parents="333 4550 11592"/>
    </justification>
  </clause>

  <clause id="11601">
    <literal><![CDATA[
      K(x,y) * (K(y,z) * (K(y,x) * u)) = K(y,z) * u
    ]]></literal>
    <justification jstring="[para(4558(a,1),11592(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4558 11592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11603">
    <literal><![CDATA[
      K(x,y) * (K(x,z) * u) = K(x,z) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[hyper(4577,a,11601,a)].">
      <j1 rule="hyper" parents="4577 11601"/>
    </justification>
  </clause>

  <clause id="11604">
    <literal><![CDATA[
      a(x,y,x) * (K(x,x * y) * z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(126,a,11601,a(flip),b,8372,a(flip))].">
      <j1 rule="hyper" parents="126 11601 8372"/>
    </justification>
  </clause>

  <clause id="11605">
    <literal><![CDATA[
      (K(x,y) * z) / (K(x,u) * z) = K(u,x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(123,a,11601,a(flip),b,11583,a)].">
      <j1 rule="hyper" parents="123 11601 11583"/>
    </justification>
  </clause>

  <clause id="11606">
    <literal><![CDATA[
      a(x,y,x) * (K(x,x * y) * ((x * y) \ z)) = (y * x) \ z
    ]]></literal>
    <justification jstring="[hyper(333,a,10014,a(flip),b,11604,a),flip(a)].">
      <j1 rule="hyper" parents="333 10014 11604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11607">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(z,u) * w) = K(z,u) * (K(z,K(x,y)) * w)
    ]]></literal>
    <justification jstring="[para(6788(a,2),11603(a,1,1))].">
      <j1 rule="para" parents="6788 11603"/>
    </justification>
  </clause>

  <clause id="11608">
    <literal><![CDATA[
      x / (K(y \ x,z) * (y * (x / y))) = K(z,y \ x) * K(y \ x,y)
    ]]></literal>
    <justification jstring="[para(4185(a,1),11605(a,1,1))].">
      <j1 rule="para" parents="4185 11605"/>
    </justification>
  </clause>

  <clause id="11609">
    <literal><![CDATA[
      (x \ L(x,y,x)) * z = a(x,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(63,a,8373,a(flip),b,11596,a),flip(a)].">
      <j1 rule="hyper" parents="63 8373 11596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11610">
    <literal><![CDATA[
      (x \ L(x,y,x)) \ z = z * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(121,a,9248,a(flip),b,11609,a)].">
      <j1 rule="hyper" parents="121 9248 11609"/>
    </justification>
  </clause>

  <clause id="11611">
    <literal><![CDATA[
      T(x,y) \ (T(x,z) * u) = K(x,z) * (K(y,x) * u)
    ]]></literal>
    <justification jstring="[para(4241(a,1),11600(a,1,2))].">
      <j1 rule="para" parents="4241 11600"/>
    </justification>
  </clause>

  <clause id="11612">
    <literal><![CDATA[
      T(R(x,x \ y,z),u) \ (y * z) = (T(x,u) \ y) * z
    ]]></literal>
    <justification jstring="[para(4555(a,1),11587(a,2,1))].">
      <j1 rule="para" parents="4555 11587"/>
    </justification>
  </clause>

  <clause id="11613">
    <literal><![CDATA[
      a(x,y,x) * (T(x * y,x) \ z) = (y * x) \ z
    ]]></literal>
    <justification jstring="[para(4555(a,1),11606(a,1,2))].">
      <j1 rule="para" parents="4555 11606"/>
    </justification>
  </clause>

  <clause id="11614">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(z,u) * w) = K(z,u) * (K(x,K(y,z)) * w)
    ]]></literal>
    <justification jstring="[para(6788(a,2),11607(a,2,2,1))].">
      <j1 rule="para" parents="6788 11607"/>
    </justification>
  </clause>

  <clause id="11615">
    <literal><![CDATA[
      K(x,y) * (K(z,K(u,x)) * (K(x,y) \ w)) = K(z,K(u,x)) * w
    ]]></literal>
    <justification jstring="[hyper(343,a,11614,a),flip(a)].">
      <j1 rule="hyper" parents="343 11614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11616">
    <literal><![CDATA[
      K(x,y) * (K(z,K(x,u)) * (K(x,y) \ w)) = K(u,K(z,x)) * w
    ]]></literal>
    <justification jstring="[para(6788(a,2),11615(a,1,2,1))].">
      <j1 rule="para" parents="6788 11615"/>
    </justification>
  </clause>

  <clause id="11617">
    <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(225(a,2),11608(a,1,2,2,2))].">
      <j1 rule="para" parents="225 11608"/>
    </justification>
  </clause>

  <clause id="11618">
    <literal><![CDATA[
      R(T(x,K(y,z) * K(z,u)),K(y,z),K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(T(x,K(z,u)),K(z,y)) = w
    ]]></literal>
    <justification jstring="[para(11598(a,2),6868(a,1))].">
      <j1 rule="para" parents="11598 6868"/>
    </justification>
  </clause>

  <clause id="11620">
    <literal><![CDATA[
      T(K(x,y) * z,K(y,u)) = K(x,y) * T(z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(40,a,8104,a,b,11599,a),flip(a)].">
      <j1 rule="hyper" parents="40 8104 11599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11621">
    <literal><![CDATA[
      K(x,y) * T(z,K(y,u / T(y,w))) = T(K(x,y) * z,K(y,y * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,7440,a(flip),b,11620,a),flip(a)].">
      <j1 rule="hyper" parents="63 7440 11620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11622">
    <literal><![CDATA[
      K(x,y) * T(K(x,y) \ z,K(x,u)) = T(z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(34,a,5355,a,b,11620,a(flip))].">
      <j1 rule="hyper" parents="34 5355 11620"/>
    </justification>
  </clause>

  <clause id="11623">
    <literal><![CDATA[
      T(x * K(y,z),K(y,u)) = T(x,K(y,u)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(34,a,5356,a(flip),b,11620,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="34 5356 11620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11625">
    <literal><![CDATA[
      T(K(x,y) * z,K(x,u)) = K(x,y) * T(z,K(x,u))
    ]]></literal>
    <justification jstring="[para(9(a,1),11622(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 11622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11626">
    <literal><![CDATA[
      T(x * K(y,z),K(z,u)) = T(x,K(z,u)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(11622(a,1),5366(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11622 5366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11627">
    <literal><![CDATA[
      T(x * K(y,z * x),K(y,z)) = K(y,z * x) * x
    ]]></literal>
    <justification jstring="[hyper(333,a,7103,a(flip),b,11623,a),flip(a)].">
      <j1 rule="hyper" parents="333 7103 11623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11628">
    <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(6791(a,1),11625(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6791 11625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11629">
    <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(7822(a,1),11625(a,2,2))].">
      <j1 rule="para" parents="7822 11625"/>
    </justification>
  </clause>

  <clause id="11630">
    <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(333,a,9090,a,b,11626,a)].">
      <j1 rule="hyper" parents="333 9090 11626"/>
    </justification>
  </clause>

  <clause id="11631">
    <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(5372(a,1),11626(a,2,2))].">
      <j1 rule="para" parents="5372 11626"/>
    </justification>
  </clause>

  <clause id="11632">
    <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(11627(a,1),3642(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11627 3642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11633">
    <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(11628(a,1),8438(a,1,1))].">
      <j1 rule="para" parents="11628 8438"/>
    </justification>
  </clause>

  <clause id="11634">
    <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(6788(a,1),11633(a,2,1))].">
      <j1 rule="para" parents="6788 11633"/>
    </justification>
  </clause>

  <clause id="11635">
    <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(6785(a,1),11634(a,2,2))].">
      <j1 rule="para" parents="6785 11634"/>
    </justification>
  </clause>

  <clause id="11636">
    <literal><![CDATA[
      K(x,y) * T(z,K(y,u / T(y,w))) = y * T(y \ (K(x,y) * z),K(y,u))
    ]]></literal>
    <justification jstring="[hyper(333,a,7029,a,b,11621,a),flip(a)].">
      <j1 rule="hyper" parents="333 7029 11621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11637">
    <literal><![CDATA[
      (K(x,y) \ z) * (K(x,y) * K(u,x)) = T(z * K(u,x),K(x,y))
    ]]></literal>
    <justification jstring="[para(2297(a,1),11630(a,1,1,1))].">
      <j1 rule="para" parents="2297 11630"/>
    </justification>
  </clause>

  <clause id="11638">
    <literal><![CDATA[
      (K(x,y) * z) * (K(y,x) * K(u,y)) = T(z * K(u,y),K(y,x))
    ]]></literal>
    <justification jstring="[para(4567(a,1),11637(a,1,1))].">
      <j1 rule="para" parents="4567 11637"/>
    </justification>
  </clause>

  <clause id="11639">
    <literal><![CDATA[
      K(x,y) * T(z,K(y,u / T(y,w))) = y * T(L(T(y,x) \ z,T(v5,v6),K(v7,v5)),K(y,u))
    ]]></literal>
    <justification jstring="[para(5667(a,2),11636(a,2,2,1))].">
      <j1 rule="para" parents="5667 11636"/>
    </justification>
  </clause>

  <clause id="11640">
    <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(63,a,7849,a(flip),b,11593,a)].">
      <j1 rule="hyper" parents="63 7849 11593"/>
    </justification>
  </clause>

  <clause id="11641">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,u)) = T(x,K(u,y) * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(11618,a,7839,a)].">
      <j1 rule="hyper" parents="11618 7839"/>
    </justification>
  </clause>

  <clause id="11642">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,u)) = T(x,K(y,z) * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(6854,a,11641,a)].">
      <j1 rule="hyper" parents="6854 11641"/>
    </justification>
  </clause>

  <clause id="11643">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,u)) = T(x,K(y,z) * K(u,y))
    ]]></literal>
    <justification jstring="[para(2005(a,2),11641(a,2,2))].">
      <j1 rule="para" parents="2005 11641"/>
    </justification>
  </clause>

  <clause id="11644">
    <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(11641(a,1),11635(a,1,1))].">
      <j1 rule="para" parents="11641 11635"/>
    </justification>
  </clause>

  <clause id="11645">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,u)) = T(x,K(z,u) * K(y,z))
    ]]></literal>
    <justification jstring="[para(2005(a,2),11642(a,2,2))].">
      <j1 rule="para" parents="2005 11642"/>
    </justification>
  </clause>

  <clause id="11646">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,u)) = T(x,K(y,u) * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(437,a,11643,a)].">
      <j1 rule="hyper" parents="437 11643"/>
    </justification>
  </clause>

  <clause id="11649">
    <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(11645(a,1),8843(a,2,1))].">
      <j1 rule="para" parents="11645 8843"/>
    </justification>
  </clause>

  <clause id="11650">
    <literal><![CDATA[
      T(x,K(y,z) * K(u,y)) = T(x,K(y,u) * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,11643,a(flip),b,11646,a)].">
      <j1 rule="hyper" parents="63 11643 11646"/>
    </justification>
  </clause>

  <clause id="11651">
    <literal><![CDATA[
      T(x,K(y,z) * K(u,y)) != x * w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u) * K(z,y)) = w
    ]]></literal>
    <justification jstring="[para(11650(a,1),4305(a,1))].">
      <j1 rule="para" parents="11650 4305"/>
    </justification>
  </clause>

  <clause id="11652">
    <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="[para(11573(a,2),11650(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11573 11650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11653">
    <literal><![CDATA[
      T(x,K(y,R(z,u,w)) * K(v5,y)) = T(x,K(y,v5) * K(z,R(y,u,w)))
    ]]></literal>
    <justification jstring="[para(11579(a,1),11650(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11579 11650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11654">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(y,u)) = K(K(z,y) * K(y,u),x)
    ]]></literal>
    <justification jstring="[hyper(4249,a,11644,a),flip(a)].">
      <j1 rule="hyper" parents="4249 11644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11655">
    <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(5648(a,1),11654(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5648 11654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11657">
    <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(333,a,4205,a,b,11649,a),flip(a)].">
      <j1 rule="hyper" parents="333 4205 11649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11658">
    <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(4567(a,1),11657(a,1,2))].">
      <j1 rule="para" parents="4567 11657"/>
    </justification>
  </clause>

  <clause id="11660">
    <literal><![CDATA[
      x * K(x,K(y,z) * K(u,R(y,w,v5))) = T(x,K(y,R(u,w,v5)) * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(333,a,4222,a(flip),b,11653,a)].">
      <j1 rule="hyper" parents="333 4222 11653"/>
    </justification>
  </clause>

  <clause id="11664">
    <literal><![CDATA[
      K(x,K(y,R(z,u,w)) * K(v5,y)) = K(x,K(y,v5) * K(z,R(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(34,a,4222,a(flip),b,11660,a)].">
      <j1 rule="hyper" parents="34 4222 11660"/>
    </justification>
  </clause>

  <clause id="11665">
    <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(5372(a,1),11631(a,1,1,2))].">
      <j1 rule="para" parents="5372 11631"/>
    </justification>
  </clause>

  <clause id="11666">
    <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(35,a,4105,a(flip),b,11665,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="35 4105 11665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11667">
    <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(9408(a,1),11666(a,1,1))].">
      <j1 rule="para" parents="9408 11666"/>
    </justification>
  </clause>

  <clause id="11668">
    <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(333,a,9408,a(flip),b,11667,a),flip(a)].">
      <j1 rule="hyper" parents="333 9408 11667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11669">
    <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(333,a,250,a(flip),b,11668,a),flip(a)].">
      <j1 rule="hyper" parents="333 250 11668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11670">
    <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(63,a,11638,a(flip),b,11640,a)].">
      <j1 rule="hyper" parents="63 11638 11640"/>
    </justification>
  </clause>

  <clause id="11671">
    <literal><![CDATA[
      x * K(K(y,z) * K(z,u),x) = T(T(x,K(z,u)),K(z,y))
    ]]></literal>
    <justification jstring="[para(6844(a,1),11670(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6844 11670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11672">
    <literal><![CDATA[
      x * K(K(y,z) * K(z,u),x) = T(x,K(z,u) * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(333,a,11643,a(flip),b,11671,a),flip(a)].">
      <j1 rule="hyper" parents="333 11643 11671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11673">
    <literal><![CDATA[
      K(K(x,y) * K(y,z),u) = K(u,K(y,x) * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(11651,a,11672,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="11651 11672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11674">
    <literal><![CDATA[
      x * K(K(y,z) * K(u,y),x) = T(x,K(y,z) * K(u,y))
    ]]></literal>
    <justification jstring="[para(2005(a,2),11672(a,1,2,1))].">
      <j1 rule="para" parents="2005 11672"/>
    </justification>
  </clause>

  <clause id="11675">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(y,u)) = K(x,K(y,z) * K(u,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,11654,a,b,11673,a)].">
      <j1 rule="hyper" parents="63 11654 11673"/>
    </justification>
  </clause>

  <clause id="11676">
    <literal><![CDATA[
      K(K(x,y) * K(z,x),u) = K(u,K(x,y) * K(z,x))
    ]]></literal>
    <justification jstring="[hyper(34,a,4222,a(flip),b,11674,a),flip(a)].">
      <j1 rule="hyper" parents="34 4222 11674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11677">
    <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(63,a,11658,a,b,11676,a)].">
      <j1 rule="hyper" parents="63 11658 11676"/>
    </justification>
  </clause>

  <clause id="11678">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(y,u)) = K(K(y,z) * K(u,y),x)
    ]]></literal>
    <justification jstring="[hyper(333,a,11676,a,b,11675,a),flip(a)].">
      <j1 rule="hyper" parents="333 11676 11675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11679">
    <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(63,a,11616,a,b,11675,a)].">
      <j1 rule="hyper" parents="63 11616 11675"/>
    </justification>
  </clause>

  <clause id="11680">
    <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(63,a,11505,a,b,11675,a),flip(a)].">
      <j1 rule="hyper" parents="63 11505 11675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11681">
    <literal><![CDATA[
      K(x,K(y,R(z,u,u \ x)) * K(z,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(333,a,11477,a(flip),b,11680,a),flip(a)].">
      <j1 rule="hyper" parents="333 11477 11680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11682">
    <literal><![CDATA[
      K(x,K(y,z) * K(z,R(y,u,u \ x))) = 1
    ]]></literal>
    <justification jstring="[hyper(63,a,11664,a(flip),b,11681,a)].">
      <j1 rule="hyper" parents="63 11664 11681"/>
    </justification>
  </clause>

  <clause id="11683">
    <literal><![CDATA[
      K(x * y,K(z,u) * K(u,R(z,x,y))) = 1
    ]]></literal>
    <justification jstring="[para(9(a,1),11682(a,1,2,2,2,3))].">
      <j1 rule="para" parents="9 11682"/>
    </justification>
  </clause>

  <clause id="11684">
    <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(6785(a,1),11679(a,1,2,2,2))].">
      <j1 rule="para" parents="6785 11679"/>
    </justification>
  </clause>

  <clause id="11685">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(z,u)) = K(z,K(x,y) * K(u,x))
    ]]></literal>
    <justification jstring="[hyper(4861,a,11684,a)].">
      <j1 rule="hyper" parents="4861 11684"/>
    </justification>
  </clause>

  <clause id="11686">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,K(z,u)) = K(z,K(y,x) * K(u,y))
    ]]></literal>
    <justification jstring="[para(6785(a,1),11685(a,1,1))].">
      <j1 rule="para" parents="6785 11685"/>
    </justification>
  </clause>

  <clause id="11688">
    <literal><![CDATA[
      K(x,y) * T(z,K(y,u / T(y,w))) = y * L(T(T(y,x) \ z,K(y,u)),T(v5,v6),K(v7,v5))
    ]]></literal>
    <justification jstring="[para(25(a,2),11639(a,2,2))].">
      <j1 rule="para" parents="25 11639"/>
    </justification>
  </clause>

  <clause id="11689">
    <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(7815(a,1),11655(a,2,2))].">
      <j1 rule="para" parents="7815 11655"/>
    </justification>
  </clause>

  <clause id="11690">
    <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(111(a,1),11669(a,1,1))].">
      <j1 rule="para" parents="111 11669"/>
    </justification>
  </clause>

  <clause id="11691">
    <literal><![CDATA[
      T(x,K(y,z / T(y,u))) = T(y,w) * T(T(y,w) \ x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(4314,a,11688,a),flip(a)].">
      <j1 rule="hyper" parents="4314 11688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11692">
    <literal><![CDATA[
      T(x,y) \ T(z,K(x,x * u)) = T(T(x,y) \ z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(7504,a,11691,a)].">
      <j1 rule="hyper" parents="7504 11691"/>
    </justification>
  </clause>

  <clause id="11693">
    <literal><![CDATA[
      T(T(x,y) \ z,K(x,u)) = T(x,y) \ T(z,K(x,u))
    ]]></literal>
    <justification jstring="[para(6956(a,1),11692(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6956 11692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11694">
    <literal><![CDATA[
      T(T(K(x,y) * z,K(x,y)) \ u,K(K(x,y) * z,w)) = (z * K(x,y)) \ T(u,K(K(x,y) * z,w))
    ]]></literal>
    <justification jstring="[para(6019(a,1),11693(a,2,1))].">
      <j1 rule="para" parents="6019 11693"/>
    </justification>
  </clause>

  <clause id="11695">
    <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(333,a,11654,a(flip),b,11689,a),flip(a)].">
      <j1 rule="hyper" parents="333 11654 11689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11696">
    <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(5648(a,1),11695(a,1,1,2))].">
      <j1 rule="para" parents="5648 11695"/>
    </justification>
  </clause>

  <clause id="11697">
    <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(11581(a,1),11585(a,2,2,1,1))].">
      <j1 rule="para" parents="11581 11585"/>
    </justification>
  </clause>

  <clause id="11698">
    <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(4367(a,1),11697(a,2,2,1))].">
      <j1 rule="para" parents="4367 11697"/>
    </justification>
  </clause>

  <clause id="11700">
    <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(4367(a,1),11698(a,1,1,2,1))].">
      <j1 rule="para" parents="4367 11698"/>
    </justification>
  </clause>

  <clause id="11701">
    <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(63,a,4595,a(flip),b,11700,a)].">
      <j1 rule="hyper" parents="63 4595 11700"/>
    </justification>
  </clause>

  <clause id="11702">
    <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(11700(a,1),539(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11700 539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11703">
    <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(11700(a,2),5704(a,1,1))].">
      <j1 rule="para" parents="11700 5704"/>
    </justification>
  </clause>

  <clause id="11705">
    <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(6763(a,1),11703(a,1,1,1,2,1))].">
      <j1 rule="para" parents="6763 11703"/>
    </justification>
  </clause>

  <clause id="11706">
    <literal><![CDATA[
      T(T(K(x,y) * z,K(x,y)) \ u,K(K(x,y) * z,w)) = (z * K(x,y)) \ T(u,K(w,K(x,y) * z))
    ]]></literal>
    <justification jstring="[para(6840(a,1),11694(a,2,2))].">
      <j1 rule="para" parents="6840 11694"/>
    </justification>
  </clause>

  <clause id="11708">
    <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(7813(a,1),11705(a,1,1,1,2))].">
      <j1 rule="para" parents="7813 11705"/>
    </justification>
  </clause>

  <clause id="11709">
    <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(11686(a,1),11708(a,1,1,1))].">
      <j1 rule="para" parents="11686 11708"/>
    </justification>
  </clause>

  <clause id="11710">
    <literal><![CDATA[
      L(T((x / y) \ 1,x) \ 1,(x / y) \ 1,T(y * (x / y),(x / y) \ 1)) = (((y \ x) \ 1) * x) \ (y * (x / y))
    ]]></literal>
    <justification jstring="[para(8555(a,1),10122(a,1,1,1))].">
      <j1 rule="para" parents="8555 10122"/>
    </justification>
  </clause>

  <clause id="11711">
    <literal><![CDATA[
      L(T((x / y) \ 1,x) \ 1,(x / y) \ 1,y * (T(x,(x / y) \ 1) / y)) = (((y \ x) \ 1) * x) \ (y * (x / y))
    ]]></literal>
    <justification jstring="[para(4083(a,1),11710(a,1,3))].">
      <j1 rule="para" parents="4083 11710"/>
    </justification>
  </clause>

  <clause id="11712">
    <literal><![CDATA[
      L(T((x / y) \ 1,x) \ 1,(x / y) \ 1,y * (T(x,x \ y) / y)) = (((y \ x) \ 1) * x) \ (y * (x / y))
    ]]></literal>
    <justification jstring="[para(3593(a,1),11711(a,1,3,2,1))].">
      <j1 rule="para" parents="3593 11711"/>
    </justification>
  </clause>

  <clause id="11713">
    <literal><![CDATA[
      L(T((x / y) \ 1,x) \ 1,(x / y) \ 1,(x \ y) \ T(y,y \ x)) = (((y \ x) \ 1) * x) \ (y * (x / y))
    ]]></literal>
    <justification jstring="[para(5264(a,2),11712(a,1,3))].">
      <j1 rule="para" parents="5264 11712"/>
    </justification>
  </clause>

  <clause id="11714">
    <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(6465(a,1),11003(a,1,2,1,1))].">
      <j1 rule="para" parents="6465 11003"/>
    </justification>
  </clause>

  <clause id="11715">
    <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(11700(a,1),11546(a,1,1))].">
      <j1 rule="para" parents="11700 11546"/>
    </justification>
  </clause>

  <clause id="11716">
    <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(63,a,5783,a(flip),b,11715,a)].">
      <j1 rule="hyper" parents="63 5783 11715"/>
    </justification>
  </clause>

  <clause id="11718">
    <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(63,a,11696,a(flip),b,11716,a)].">
      <j1 rule="hyper" parents="63 11696 11716"/>
    </justification>
  </clause>

  <clause id="11719">
    <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(63,a,11677,a(flip),b,11718,a),flip(a)].">
      <j1 rule="hyper" parents="63 11677 11718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11720">
    <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(333,a,11664,a(flip),b,11719,a),flip(a)].">
      <j1 rule="hyper" parents="333 11664 11719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11721">
    <literal><![CDATA[
      K(a(K(x,y),z,u),((z * u) \ K(y,x)) \ 1) = 1
    ]]></literal>
    <justification jstring="[hyper(333,a,11683,a(flip),b,11720,a),flip(a)].">
      <j1 rule="hyper" parents="333 11683 11720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11723">
    <literal><![CDATA[
      K(a(K(x,y),z,u),K(x,y) * (z * u)) = 1
    ]]></literal>
    <justification jstring="[hyper(63,a,5783,a(flip),b,11721,a)].">
      <j1 rule="hyper" parents="63 5783 11721"/>
    </justification>
  </clause>

  <clause id="11724">
    <literal><![CDATA[
      1 * (((K(x,y) * z) * u) / (K(x,y) * (z * u))) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(11723(a,1),4409(a,1,1))].">
      <j1 rule="para" parents="11723 4409"/>
    </justification>
  </clause>

  <clause id="11725">
    <literal><![CDATA[
      1 * (K(x,y) * R(K(y,x),z,u)) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(11701(a,1),11724(a,1,2))].">
      <j1 rule="para" parents="11701 11724"/>
    </justification>
  </clause>

  <clause id="11726">
    <literal><![CDATA[
      K(x,y) * R(K(y,x),z,u) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(127,a,11725,a)].">
      <j1 rule="hyper" parents="127 11725"/>
    </justification>
  </clause>

  <clause id="11727">
    <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(6799(a,1),11725(a,1,2,1))].">
      <j1 rule="para" parents="6799 11725"/>
    </justification>
  </clause>

  <clause id="11728">
    <literal><![CDATA[
      K(x,y) * a(K(x,y),z,u) = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(4577,a,11726,a)].">
      <j1 rule="hyper" parents="4577 11726"/>
    </justification>
  </clause>

  <clause id="11729">
    <literal><![CDATA[
      R(K(x,y),z,u) * K(y,x) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(2014,a,11726,a)].">
      <j1 rule="hyper" parents="2014 11726"/>
    </justification>
  </clause>

  <clause id="11730">
    <literal><![CDATA[
      K(x \ 1,y) * K(y,R(x,z,u) \ 1) = a(K(y,x \ 1),z,u)
    ]]></literal>
    <justification jstring="[para(5629(a,1),11726(a,1,2))].">
      <j1 rule="para" parents="5629 11726"/>
    </justification>
  </clause>

  <clause id="11731">
    <literal><![CDATA[
      K(x,y) * K(y,R(x,z,u)) = a(K(y,x),z * x,u)
    ]]></literal>
    <justification jstring="[para(8062(a,1),11726(a,1,2))].">
      <j1 rule="para" parents="8062 11726"/>
    </justification>
  </clause>

  <clause id="11733">
    <literal><![CDATA[
      (x * a(K(y,z),u,w)) * (K(y,z) * R(K(z,y),u,w)) = x
    ]]></literal>
    <justification jstring="[para(11726(a,1),11419(a,1,1,2))].">
      <j1 rule="para" parents="11726 11419"/>
    </justification>
  </clause>

  <clause id="11734">
    <literal><![CDATA[
      K(x,y) * K(y,R(x,z,u)) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(11576(a,1),11726(a,1,2))].">
      <j1 rule="para" parents="11576 11726"/>
    </justification>
  </clause>

  <clause id="11735">
    <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(11726(a,1),11652(a,2,2))].">
      <j1 rule="para" parents="11726 11652"/>
    </justification>
  </clause>

  <clause id="11737">
    <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(11728(a,1),10554(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11728 10554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11738">
    <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(11729(a,1),8689(a,2,2))].">
      <j1 rule="para" parents="11729 8689"/>
    </justification>
  </clause>

  <clause id="11739">
    <literal><![CDATA[
      K(x,K(y,z) * K(R(z,u,w),y)) = K(a(K(y,z),u,w),x)
    ]]></literal>
    <justification jstring="[para(11734(a,1),11673(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11734 11673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11741">
    <literal><![CDATA[
      a(K(x,y),z * y,u) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,11734,a(flip),b,11731,a),flip(a)].">
      <j1 rule="hyper" parents="63 11734 11731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11742">
    <literal><![CDATA[
      (x * a(K(y,z),u,w)) * a(K(z,y),u,w) = x
    ]]></literal>
    <justification jstring="[para(11726(a,1),11733(a,1,2))].">
      <j1 rule="para" parents="11726 11733"/>
    </justification>
  </clause>

  <clause id="11744">
    <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(121,a,112,a(flip),b,11742,a)].">
      <j1 rule="hyper" parents="121 112 11742"/>
    </justification>
  </clause>

  <clause id="11746">
    <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(11739(a,1),11709(a,1,1,1))].">
      <j1 rule="para" parents="11739 11709"/>
    </justification>
  </clause>

  <clause id="11747">
    <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(7814(a,1),11727(a,1,2,2))].">
      <j1 rule="para" parents="7814 11727"/>
    </justification>
  </clause>

  <clause id="11748">
    <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(11686(a,1),11747(a,1,2))].">
      <j1 rule="para" parents="11686 11747"/>
    </justification>
  </clause>

  <clause id="11749">
    <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(333,a,11738,a(flip),b,11737,a),flip(a)].">
      <j1 rule="hyper" parents="333 11738 11737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11750">
    <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(534(a,1),11746(a,1,1)),flip(a)].">
      <j1 rule="para" parents="534 11746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11751">
    <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(333,a,7917,a(flip),b,11750,a),flip(a)].">
      <j1 rule="hyper" parents="333 7917 11750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11752">
    <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(6763(a,1),11751(a,1,2,1,1))].">
      <j1 rule="para" parents="6763 11751"/>
    </justification>
  </clause>

  <clause id="11753">
    <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(7813(a,1),11752(a,1,2,1))].">
      <j1 rule="para" parents="7813 11752"/>
    </justification>
  </clause>

  <clause id="11754">
    <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(4274(a,2),11753(a,1,2))].">
      <j1 rule="para" parents="4274 11753"/>
    </justification>
  </clause>

  <clause id="11755">
    <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(63,a,11629,a,b,11754,a)].">
      <j1 rule="hyper" parents="63 11629 11754"/>
    </justification>
  </clause>

  <clause id="11756">
    <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(6791(a,1),11755(a,1,1))].">
      <j1 rule="para" parents="6791 11755"/>
    </justification>
  </clause>

  <clause id="11757">
    <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(63,a,11646,a(flip),b,11756,a)].">
      <j1 rule="hyper" parents="63 11646 11756"/>
    </justification>
  </clause>

  <clause id="11758">
    <literal><![CDATA[
      x * K(a(K(x,y),z,u),w) = T(x,a(K(w,y),z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,11735,a(flip),b,11757,a),flip(a)].">
      <j1 rule="hyper" parents="63 11735 11757"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11759">
    <literal><![CDATA[
      K(a(K(x,y),z,u),w) = K(x,a(K(w,y),z,u))
    ]]></literal>
    <justification jstring="[hyper(34,a,4222,a(flip),b,11758,a),flip(a)].">
      <j1 rule="hyper" parents="34 4222 11758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11760">
    <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(63,a,11739,a,b,11759,a)].">
      <j1 rule="hyper" parents="63 11739 11759"/>
    </justification>
  </clause>

  <clause id="11761">
    <literal><![CDATA[
      1 * K(x,a(K(y,z),u,w)) = a(K(z,K(x,y)),u,w)
    ]]></literal>
    <justification jstring="[para(11760(a,1),11748(a,1,2))].">
      <j1 rule="para" parents="11760 11748"/>
    </justification>
  </clause>

  <clause id="11762">
    <literal><![CDATA[
      a(K(x,K(y,z)),u,w) = K(y,a(K(z,x),u,w))
    ]]></literal>
    <justification jstring="[hyper(127,a,11761,a),flip(a)].">
      <j1 rule="hyper" parents="127 11761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11763">
    <literal><![CDATA[
      a(K(x,K(y,z)),u,w) = K(a(K(y,x),u,w),z)
    ]]></literal>
    <justification jstring="[hyper(333,a,11759,a,b,11762,a),flip(a)].">
      <j1 rule="hyper" parents="333 11759 11762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11764">
    <literal><![CDATA[
      a(K(x,K(y,z)),u,w) = K(x,a(K(z,y),u,w))
    ]]></literal>
    <justification jstring="[para(6785(a,1),11762(a,1,1))].">
      <j1 rule="para" parents="6785 11762"/>
    </justification>
  </clause>

  <clause id="11765">
    <literal><![CDATA[
      a(K(x,K(y,z)),u,w) = K(a(K(x,y),u,w),z)
    ]]></literal>
    <justification jstring="[para(6785(a,1),11763(a,1,1))].">
      <j1 rule="para" parents="6785 11763"/>
    </justification>
  </clause>

  <clause id="11766">
    <literal><![CDATA[
      K(a(K(x,y),z * y,u),w) = a(K(y,K(x,w)),z,u)
    ]]></literal>
    <justification jstring="[para(11741(a,2),11763(a,2,1)),flip(a)].">
      <j1 rule="para" parents="11741 11763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11767">
    <literal><![CDATA[
      a(K(x,K(y,z)),u * y,w) = a(K(y,K(x,z)),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,11765,a,b,11766,a)].">
      <j1 rule="hyper" parents="63 11765 11766"/>
    </justification>
  </clause>

  <clause id="11768">
    <literal><![CDATA[
      x * T(((x * L(y,z,u)) / L(y,z,u)) \ (x * y),w) = ((x * L(y,z,u)) * T(y,w)) / L(y,z,u)
    ]]></literal>
    <justification jstring="[para(11(a,1),1826(a,1,1))].">
      <j1 rule="para" parents="11 1826"/>
    </justification>
  </clause>

  <clause id="11769">
    <literal><![CDATA[
      ((x * L(y,z,u)) * T(y,w)) / L(y,z,u) = x * T(x \ (x * y),w)
    ]]></literal>
    <justification jstring="[para(11(a,1),11768(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="11 11768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11770">
    <literal><![CDATA[
      ((x * L(y,z,u)) * T(y,w)) / L(y,z,u) = x * T(y,w)
    ]]></literal>
    <justification jstring="[para(9(a,1),11769(a,2,2,1))].">
      <j1 rule="para" parents="9 11769"/>
    </justification>
  </clause>

  <clause id="11771">
    <literal><![CDATA[
      (x * L(y,z,u)) * T(y,x) = (y * x) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(579,a,11770,a),flip(a)].">
      <j1 rule="hyper" parents="579 11770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11772">
    <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(11771(a,1),8279(a,1,2))].">
      <j1 rule="para" parents="11771 8279"/>
    </justification>
  </clause>

  <clause id="11773">
    <literal><![CDATA[
      x \ R(x,y,L(x,z,u)) = a(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(752,a,11772,a),flip(a)].">
      <j1 rule="hyper" parents="752 11772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11774">
    <literal><![CDATA[
      K(x,y) * K(y * L(x,z,u),x) = a(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(8792,a,11773,a)].">
      <j1 rule="hyper" parents="8792 11773"/>
    </justification>
  </clause>

  <clause id="11775">
    <literal><![CDATA[
      K(x,y) * a(y,x,L(y,z,u)) = K(x * L(y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(4577,a,11774,a)].">
      <j1 rule="hyper" parents="4577 11774"/>
    </justification>
  </clause>

  <clause id="11776">
    <literal><![CDATA[
      K(x * L(y,z,u),y) * K(y,x) = a(y,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(2006,a,11774,a)].">
      <j1 rule="hyper" parents="2006 11774"/>
    </justification>
  </clause>

  <clause id="11777">
    <literal><![CDATA[
      a(x,y,L(x,z,u)) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(34,a,10812,a(flip),b,11775,a),flip(a)].">
      <j1 rule="hyper" parents="34 10812 11775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11779">
    <literal><![CDATA[
      (x / y) * R(y,z,y) = x * a(y,z,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(11777(a,2),9318(a,2,2))].">
      <j1 rule="para" parents="11777 9318"/>
    </justification>
  </clause>

  <clause id="11781">
    <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(11110(a,1),11779(a,1,2))].">
      <j1 rule="para" parents="11110 11779"/>
    </justification>
  </clause>

  <clause id="11782">
    <literal><![CDATA[
      x * (K(y,z) * K(z,y * L(z,u,w))) = x / a(z,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[para(11776(a,1),7850(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11776 7850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11783">
    <literal><![CDATA[
      K(L(x,y,z) * u,x) * K(x,u) = a(x,u,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(9419(a,2),11776(a,1,1))].">
      <j1 rule="para" parents="9419 11776"/>
    </justification>
  </clause>

  <clause id="11784">
    <literal><![CDATA[
      L(x,y,L(x,z,u)) \ x = a(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,8350,a(flip),b,11783,a)].">
      <j1 rule="hyper" parents="63 8350 11783"/>
    </justification>
  </clause>

  <clause id="11785">
    <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(11784(a,1),8171(a,1,1,1))].">
      <j1 rule="para" parents="11784 8171"/>
    </justification>
  </clause>

  <clause id="11786">
    <literal><![CDATA[
      K(x,y) * K(y,x * L(y,z,u)) = a(y,x,L(y,z,u)) \ 1
    ]]></literal>
    <justification jstring="[hyper(121,a,73,a(flip),b,11782,a),flip(a)].">
      <j1 rule="hyper" parents="121 73 11782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11787">
    <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(63,a,11333,a(flip),b,11781,a),flip(a)].">
      <j1 rule="hyper" parents="63 11333 11781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11788">
    <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(371(a,1),11787(a,1,2,3))].">
      <j1 rule="para" parents="371 11787"/>
    </justification>
  </clause>

  <clause id="11789">
    <literal><![CDATA[
      a(R(x,y,z),u,R(x,y,z)) = a(x,u,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(9259,a,11788,a)].">
      <j1 rule="hyper" parents="9259 11788"/>
    </justification>
  </clause>

  <clause id="11790">
    <literal><![CDATA[
      R(a(x,y,x),x * z,u) = a(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(11126,a,11789,a)].">
      <j1 rule="hyper" parents="11126 11789"/>
    </justification>
  </clause>

  <clause id="11791">
    <literal><![CDATA[
      a(x,y,R(x,x \ z,u)) = R(a(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),11790(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 11790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11792">
    <literal><![CDATA[
      R(a(x,y,x),z,u) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,11120,a(flip),b,11791,a),flip(a)].">
      <j1 rule="hyper" parents="63 11120 11791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11796">
    <literal><![CDATA[
      a(x,y * K(z,y),x) = L(a(x,y,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,9363,a(flip),b,11792,a),flip(a)].">
      <j1 rule="hyper" parents="63 9363 11792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11797">
    <literal><![CDATA[
      (a(x,y,x) * z) * u = a(x,y,x) * (z * u)
    ]]></literal>
    <justification jstring="[hyper(125,a,11792,a(flip),b,6117,a),flip(a)].">
      <j1 rule="hyper" parents="125 11792 6117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11798">
    <literal><![CDATA[
      (a(x,y,x) \ z) * (z \ u) = a(x,y,x) \ u
    ]]></literal>
    <justification jstring="[para(11792(a,1),759(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11792 759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11800">
    <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(4941(a,1),11796(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4941 11796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11801">
    <literal><![CDATA[
      L(x,y,a(z,u,z)) = x
    ]]></literal>
    <justification jstring="[hyper(2942,a,11797,a)].">
      <j1 rule="hyper" parents="2942 11797"/>
    </justification>
  </clause>

  <clause id="11802">
    <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(11797(a,1),14(a,2,1)),flip(a)].">
      <j1 rule="para" parents="11797 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11803">
    <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(11797(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="11797 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11804">
    <literal><![CDATA[
      x \ (a(y,z,y) * (u * x)) != w
    ]]></literal>
    <literal><![CDATA[
      T(a(y,z,y) * u,x) = w
    ]]></literal>
    <justification jstring="[para(11797(a,1),347(a,1,2))].">
      <j1 rule="para" parents="11797 347"/>
    </justification>
  </clause>

  <clause id="11805">
    <literal><![CDATA[
      (x * a(y,z,y)) * u = a(y,z,y) * (x * u)
    ]]></literal>
    <justification jstring="[para(9246(a,1),11797(a,1,1))].">
      <j1 rule="para" parents="9246 11797"/>
    </justification>
  </clause>

  <clause id="11806">
    <literal><![CDATA[
      (x * (a(y,z,y) * (u * w))) \ ((x * (u * a(y,z,y))) * w) = a(x,a(y,z,y) * u,w)
    ]]></literal>
    <justification jstring="[para(11797(a,1),9286(a,1,1,2))].">
      <j1 rule="para" parents="11797 9286"/>
    </justification>
  </clause>

  <clause id="11807">
    <literal><![CDATA[
      (a(x,y,x) * z) / u = a(x,y,x) * (z / u)
    ]]></literal>
    <justification jstring="[hyper(197,a,11801,a(flip),b,10409,a(flip))].">
      <j1 rule="hyper" parents="197 11801 10409"/>
    </justification>
  </clause>

  <clause id="11808">
    <literal><![CDATA[
      L(x,y,a(z,u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(11801(a,1),50(a,2))].">
      <j1 rule="para" parents="11801 50"/>
    </justification>
  </clause>

  <clause id="11809">
    <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(11801(a,1),499(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11801 499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11810">
    <literal><![CDATA[
      (a(x,y,x) \ z) / u = a(x,y,x) \ (z / u)
    ]]></literal>
    <justification jstring="[hyper(466,a,11798,a)].">
      <j1 rule="hyper" parents="466 11798"/>
    </justification>
  </clause>

  <clause id="11811">
    <literal><![CDATA[
      a(x,y,x) \ T(z * a(x,y,x),u) = z * K(z * a(x,y,x),u)
    ]]></literal>
    <justification jstring="[hyper(4287,a,11805,a)].">
      <j1 rule="hyper" parents="4287 11805"/>
    </justification>
  </clause>

  <clause id="11812">
    <literal><![CDATA[
      (a(x,y,x) * z) / u = (z / u) * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,9246,a(flip),b,11807,a),flip(a)].">
      <j1 rule="hyper" parents="333 9246 11807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11813">
    <literal><![CDATA[
      a(x,y,x) \ (x / z) = L(x,y,x) / z
    ]]></literal>
    <justification jstring="[para(8239(a,1),11810(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8239 11810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11814">
    <literal><![CDATA[
      (x / y) * a(x,z,x) = R(x,z,x) / y
    ]]></literal>
    <justification jstring="[para(8222(a,1),11812(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8222 11812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11815">
    <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(63,a,9119,a(flip),b,11800,a)].">
      <j1 rule="hyper" parents="63 9119 11800"/>
    </justification>
  </clause>

  <clause id="11816">
    <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(11797(a,1),11803(a,1,2))].">
      <j1 rule="para" parents="11797 11803"/>
    </justification>
  </clause>

  <clause id="11817">
    <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(877,a,11816,a)].">
      <j1 rule="hyper" parents="877 11816"/>
    </justification>
  </clause>

  <clause id="11818">
    <literal><![CDATA[
      L(x,y,a(z,u,z) * w) = L(x,y,w)
    ]]></literal>
    <justification jstring="[hyper(11808,a,11817,a),flip(a)].">
      <j1 rule="hyper" parents="11808 11817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11820">
    <literal><![CDATA[
      L(L(x,y,K(z,u)),K(z,u) * y,a(u,z,u)) = L(x,y,K(u * z,u))
    ]]></literal>
    <justification jstring="[para(8249(a,1),11817(a,2,3))].">
      <j1 rule="para" parents="8249 11817"/>
    </justification>
  </clause>

  <clause id="11822">
    <literal><![CDATA[
      L(x,y,a(z,u,z) \ w) = L(x,y,w)
    ]]></literal>
    <justification jstring="[para(10(a,1),11818(a,1,3)),flip(a)].">
      <j1 rule="para" parents="10 11818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11823">
    <literal><![CDATA[
      L(x,y,K(z,z * u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(8242(a,1),11818(a,1,3)),flip(a)].">
      <j1 rule="para" parents="8242 11818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11824">
    <literal><![CDATA[
      L(x,y,T(z * u,z)) = L(x,y,u * z)
    ]]></literal>
    <justification jstring="[para(8248(a,1),11818(a,1,3))].">
      <j1 rule="para" parents="8248 11818"/>
    </justification>
  </clause>

  <clause id="11825">
    <literal><![CDATA[
      L(x,y,K(z * u,z)) = L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[para(8249(a,1),11818(a,1,3))].">
      <j1 rule="para" parents="8249 11818"/>
    </justification>
  </clause>

  <clause id="11826">
    <literal><![CDATA[
      L(x,y,K(z,z \ u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(8207(a,1),11818(a,1,3))].">
      <j1 rule="para" parents="8207 11818"/>
    </justification>
  </clause>

  <clause id="11827">
    <literal><![CDATA[
      L(x,y,z * a(u,w,u)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(9246(a,1),11818(a,1,3))].">
      <j1 rule="para" parents="9246 11818"/>
    </justification>
  </clause>

  <clause id="11828">
    <literal><![CDATA[
      L(x,y,z * R(u,w,u)) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(9322(a,1),11818(a,1,3))].">
      <j1 rule="para" parents="9322 11818"/>
    </justification>
  </clause>

  <clause id="11829">
    <literal><![CDATA[
      L(x,y,R(z,u,z) \ w) = L(x,y,z \ w)
    ]]></literal>
    <justification jstring="[para(9340(a,1),11818(a,1,3)),flip(a)].">
      <j1 rule="para" parents="9340 11818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11830">
    <literal><![CDATA[
      L(x,y,L(z,u,z)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(8239(a,1),11822(a,1,3))].">
      <j1 rule="para" parents="8239 11822"/>
    </justification>
  </clause>

  <clause id="11831">
    <literal><![CDATA[
      L(x,y,K(z \ u,z)) = L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[para(8206(a,1),11822(a,1,3))].">
      <j1 rule="para" parents="8206 11822"/>
    </justification>
  </clause>

  <clause id="11832">
    <literal><![CDATA[
      L(x,y,z / R(u,w,u)) = L(x,y,z / u)
    ]]></literal>
    <justification jstring="[para(9315(a,1),11822(a,1,3))].">
      <j1 rule="para" parents="9315 11822"/>
    </justification>
  </clause>

  <clause id="11833">
    <literal><![CDATA[
      L(T((1 / x) \ y,z),1 / x,x) = T(1 \ (L(x,x,x) * y),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,8791,a(flip),b,11830,a),flip(a)].">
      <j1 rule="hyper" parents="63 8791 11830"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11834">
    <literal><![CDATA[
      L(x,y,T(z / u,z)) = L(x,y,u \ z)
    ]]></literal>
    <justification jstring="[para(3781(a,1),11830(a,1,3))].">
      <j1 rule="para" parents="3781 11830"/>
    </justification>
  </clause>

  <clause id="11835">
    <literal><![CDATA[
      L(x,y,(z \ u) \ u) = L(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[para(11339(a,1),11830(a,1,3)),flip(a)].">
      <j1 rule="para" parents="11339 11830"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11837">
    <literal><![CDATA[
      L(x,y,K(z,u * z)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(4636(a,2),11823(a,1,3))].">
      <j1 rule="para" parents="4636 11823"/>
    </justification>
  </clause>

  <clause id="11838">
    <literal><![CDATA[
      L(x,y,K(z * u,(z * u) * (u \ 1))) = L(x,y,K(u * z,u \ 1))
    ]]></literal>
    <justification jstring="[para(8582(a,1),11823(a,2,3))].">
      <j1 rule="para" parents="8582 11823"/>
    </justification>
  </clause>

  <clause id="11839">
    <literal><![CDATA[
      L(x,y,(z \ u) * z) = L(x,y,T(u,z))
    ]]></literal>
    <justification jstring="[para(10(a,1),11824(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="10 11824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11840">
    <literal><![CDATA[
      L(x,y,T((z \ u) * z,z \ u)) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),11824(a,2,3))].">
      <j1 rule="para" parents="10 11824"/>
    </justification>
  </clause>

  <clause id="11841">
    <literal><![CDATA[
      L(x,y,T((T(z,z \ u) / u) * u,T(z,z \ u) / u)) = L(x,y,(z \ u) \ T(u,u \ z))
    ]]></literal>
    <justification jstring="[para(5264(a,2),11824(a,2,3))].">
      <j1 rule="para" parents="5264 11824"/>
    </justification>
  </clause>

  <clause id="11843">
    <literal><![CDATA[
      L(x,y,K(z * y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(333,a,3563,a(flip),b,11825,a),flip(a)].">
      <j1 rule="hyper" parents="333 3563 11825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11844">
    <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(63,a,9198,a(flip),b,11825,a),flip(a)].">
      <j1 rule="hyper" parents="63 9198 11825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11845">
    <literal><![CDATA[
      L(x,y / z,K(y,z)) = x
    ]]></literal>
    <justification jstring="[para(4544(a,1),11843(a,1,3))].">
      <j1 rule="para" parents="4544 11843"/>
    </justification>
  </clause>

  <clause id="11846">
    <literal><![CDATA[
      (K(x,y) * (x / y)) \ z = (x / y) \ (K(x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(578,a,11845,a),flip(a)].">
      <j1 rule="hyper" parents="578 11845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11847">
    <literal><![CDATA[
      K(x,y) * ((x / y) * z) = (x / T(y,x)) * z
    ]]></literal>
    <justification jstring="[para(11845(a,1),4822(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11845 4822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11848">
    <literal><![CDATA[
      L(x \ y,z,K(x,y)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(6638,a,11826,a),flip(a)].">
      <j1 rule="hyper" parents="6638 11826"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11849">
    <literal><![CDATA[
      L(x,y \ z,K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(4893,a,11826,a),flip(a)].">
      <j1 rule="hyper" parents="4893 11826"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11850">
    <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(333,a,11801,a,b,11826,a)].">
      <j1 rule="hyper" parents="333 11801 11826"/>
    </justification>
  </clause>

  <clause id="11851">
    <literal><![CDATA[
      (K(x,y) * z) / (x \ y) = K(x,y) * (z / (x \ y))
    ]]></literal>
    <justification jstring="[hyper(197,a,11848,a(flip),b,10409,a(flip))].">
      <j1 rule="hyper" parents="197 11848 10409"/>
    </justification>
  </clause>

  <clause id="11852">
    <literal><![CDATA[
      L(x,y,K(z,u \ z)) = L(x,y,K(u,u \ z))
    ]]></literal>
    <justification jstring="[para(4377(a,1),11831(a,1,3)),flip(a)].">
      <j1 rule="para" parents="4377 11831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11853">
    <literal><![CDATA[
      L(x,y,K(z * u,z \ 1)) = L(x,y,K(u,z \ 1))
    ]]></literal>
    <justification jstring="[para(4867(a,1),11831(a,1,3))].">
      <j1 rule="para" parents="4867 11831"/>
    </justification>
  </clause>

  <clause id="11854">
    <literal><![CDATA[
      L(x,y,y / z) = L(x,y,z \ y)
    ]]></literal>
    <justification jstring="[hyper(10106,a,11834,a)].">
      <j1 rule="hyper" parents="10106 11834"/>
    </justification>
  </clause>

  <clause id="11855">
    <literal><![CDATA[
      L(x,y * z,(y * z) / y) = L(x,y * z,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),11854(a,2,3))].">
      <j1 rule="para" parents="9 11854"/>
    </justification>
  </clause>

  <clause id="11856">
    <literal><![CDATA[
      L(x,y,T(z,z \ u)) = L(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,1645,a,b,11835,a)].">
      <j1 rule="hyper" parents="63 1645 11835"/>
    </justification>
  </clause>

  <clause id="11857">
    <literal><![CDATA[
      L(x,y,T(z * u,u \ 1)) = L(x,y,T(z * u,z))
    ]]></literal>
    <justification jstring="[para(5824(a,2),11835(a,1,3))].">
      <j1 rule="para" parents="5824 11835"/>
    </justification>
  </clause>

  <clause id="11858">
    <literal><![CDATA[
      L(x,y,T(T(z,z \ u),w)) = L(x,y,T(T(z,w),u))
    ]]></literal>
    <justification jstring="[para(6677(a,2),11835(a,1,3))].">
      <j1 rule="para" parents="6677 11835"/>
    </justification>
  </clause>

  <clause id="11859">
    <literal><![CDATA[
      L(x,y,z * T(u,u \ w)) = L(x,y,z * T(u,w))
    ]]></literal>
    <justification jstring="[para(3849(a,1),11828(a,1,3,2))].">
      <j1 rule="para" parents="3849 11828"/>
    </justification>
  </clause>

  <clause id="11860">
    <literal><![CDATA[
      L(x,y,(z \ T(u,z \ u)) \ w) = L(x,y,(u / z) \ w)
    ]]></literal>
    <justification jstring="[para(3794(a,1),11829(a,1,3,1))].">
      <j1 rule="para" parents="3794 11829"/>
    </justification>
  </clause>

  <clause id="11861">
    <literal><![CDATA[
      L(x,y,K(z,u) * (z \ u)) = L(x,y,u / z)
    ]]></literal>
    <justification jstring="[para(8339(a,1),11832(a,1,3))].">
      <j1 rule="para" parents="8339 11832"/>
    </justification>
  </clause>

  <clause id="11862">
    <literal><![CDATA[
      L(x,y,(z \ T(u,z \ u)) * z) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(4105(a,1),11840(a,1,3))].">
      <j1 rule="para" parents="4105 11840"/>
    </justification>
  </clause>

  <clause id="11863">
    <literal><![CDATA[
      K(x,y) * ((y / T(x,y)) * z) = (y / x) * z
    ]]></literal>
    <justification jstring="[hyper(4577,a,11847,a)].">
      <j1 rule="hyper" parents="4577 11847"/>
    </justification>
  </clause>

  <clause id="11864">
    <literal><![CDATA[
      K(x,T(y,y \ x)) * ((y \ x) * z) = (x / T(T(y,y \ x),x)) * z
    ]]></literal>
    <justification jstring="[para(281(a,1),11847(a,1,2,1))].">
      <j1 rule="para" parents="281 11847"/>
    </justification>
  </clause>

  <clause id="11865">
    <literal><![CDATA[
      K(x,y) * ((y \ x) * ((x / y) * z)) = (x / T(y,x)) * ((y \ x) * z)
    ]]></literal>
    <justification jstring="[para(1125(a,1),11847(a,1,2))].">
      <j1 rule="para" parents="1125 11847"/>
    </justification>
  </clause>

  <clause id="11866">
    <literal><![CDATA[
      K(x * K(y,z),z) * (((x * K(y,z)) / z) * u) = ((x * K(y,z)) / T(z,x)) * u
    ]]></literal>
    <justification jstring="[para(7361(a,1),11847(a,2,1,2))].">
      <j1 rule="para" parents="7361 11847"/>
    </justification>
  </clause>

  <clause id="11867">
    <literal><![CDATA[
      L(x,y * z,z * K(y,z)) = L(x,y * z,z)
    ]]></literal>
    <justification jstring="[para(4238(a,1),11855(a,1,3))].">
      <j1 rule="para" parents="4238 11855"/>
    </justification>
  </clause>

  <clause id="11868">
    <literal><![CDATA[
      L(x,y,((z * u) / z) \ z) = L(x,y,z / u)
    ]]></literal>
    <justification jstring="[para(4519(a,2),11861(a,1,3))].">
      <j1 rule="para" parents="4519 11861"/>
    </justification>
  </clause>

  <clause id="11869">
    <literal><![CDATA[
      L(x,y,T(T(z,u \ z),u)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,11839,a(flip),b,11862,a)].">
      <j1 rule="hyper" parents="63 11839 11862"/>
    </justification>
  </clause>

  <clause id="11870">
    <literal><![CDATA[
      L(x,y,T(T(z,u),u \ z)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(23(a,1),11869(a,1,3))].">
      <j1 rule="para" parents="23 11869"/>
    </justification>
  </clause>

  <clause id="11871">
    <literal><![CDATA[
      R(K(x,y),x \ y,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(8099,a,11863,a)].">
      <j1 rule="hyper" parents="8099 11863"/>
    </justification>
  </clause>

  <clause id="11872">
    <literal><![CDATA[
      R(K(x,x * y),y,z) = K(x,x * y)
    ]]></literal>
    <justification jstring="[para(9(a,1),11871(a,1,2))].">
      <j1 rule="para" parents="9 11871"/>
    </justification>
  </clause>

  <clause id="11874">
    <literal><![CDATA[
      T(x,R(y \ 1,y,z) \ x) = x * K(x,x * y)
    ]]></literal>
    <justification jstring="[para(11872(a,1),10296(a,2,2))].">
      <j1 rule="para" parents="11872 10296"/>
    </justification>
  </clause>

  <clause id="11875">
    <literal><![CDATA[
      L(x,y,z / T(u,z)) = L(x,y,u \ z)
    ]]></literal>
    <justification jstring="[para(239(a,1),11868(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="239 11868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11876">
    <literal><![CDATA[
      L(x,T(y,z),T(y,z) \ z) = L(x,T(y,z),y \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,10091,a(flip),b,11875,a)].">
      <j1 rule="hyper" parents="63 10091 11875"/>
    </justification>
  </clause>

  <clause id="11877">
    <literal><![CDATA[
      T(x,R(y \ 1,y,z) \ x) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(333,a,4222,a,b,11874,a),flip(a)].">
      <j1 rule="hyper" parents="333 4222 11874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11879">
    <literal><![CDATA[
      T(x,(y / (z * y)) \ x) = T(x,x * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,3185,a(flip),b,11877,a)].">
      <j1 rule="hyper" parents="63 3185 11877"/>
    </justification>
  </clause>

  <clause id="11880">
    <literal><![CDATA[
      T(x,(y / z) \ x) = T(x,x * (z / y))
    ]]></literal>
    <justification jstring="[para(12(a,1),11879(a,1,2,1,2))].">
      <j1 rule="para" parents="12 11879"/>
    </justification>
  </clause>

  <clause id="11881">
    <literal><![CDATA[
      T(x,(y * x) / z) = T(x,x * (y / z))
    ]]></literal>
    <justification jstring="[hyper(63,a,9623,a,b,11880,a)].">
      <j1 rule="hyper" parents="63 9623 11880"/>
    </justification>
  </clause>

  <clause id="11882">
    <literal><![CDATA[
      x * K(x,x * (y / z)) = T(x,(y * x) / z)
    ]]></literal>
    <justification jstring="[hyper(333,a,4222,a(flip),b,11881,a)].">
      <j1 rule="hyper" parents="333 4222 11881"/>
    </justification>
  </clause>

  <clause id="11883">
    <literal><![CDATA[
      K(x,(y * x) / z) = K(x,x * (y / z))
    ]]></literal>
    <justification jstring="[hyper(34,a,4222,a(flip),b,11882,a)].">
      <j1 rule="hyper" parents="34 4222 11882"/>
    </justification>
  </clause>

  <clause id="11884">
    <literal><![CDATA[
      K(x,(y / z) \ x) = K(x,x * (z / y))
    ]]></literal>
    <justification jstring="[hyper(9645,a,11883,a)].">
      <j1 rule="hyper" parents="9645 11883"/>
    </justification>
  </clause>

  <clause id="11885">
    <literal><![CDATA[
      K(x,x * (y / ((z * x) * u))) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,11231,a(flip),b,11883,a),flip(a)].">
      <j1 rule="hyper" parents="63 11231 11883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11886">
    <literal><![CDATA[
      K(x,(y / z) \ x) \ T(x,z / y) = R(x,z / y,x)
    ]]></literal>
    <justification jstring="[para(11884(a,2),4737(a,1,1))].">
      <j1 rule="para" parents="11884 4737"/>
    </justification>
  </clause>

  <clause id="11887">
    <literal><![CDATA[
      (x / y) \ (K(x,y) \ z) = (T(x,y) / y) \ z
    ]]></literal>
    <justification jstring="[para(4820(a,1),11846(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4820 11846"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11888">
    <literal><![CDATA[
      (x / y) \ (K(y,x) * z) = (T(x,y) / y) \ z
    ]]></literal>
    <justification jstring="[para(4567(a,1),11887(a,1,2))].">
      <j1 rule="para" parents="4567 11887"/>
    </justification>
  </clause>

  <clause id="11889">
    <literal><![CDATA[
      (((x \ y) * T(x,y)) / x) \ (K(x,(x \ y) * T(x,y)) * z) = (((x \ y) * x) / x) \ z
    ]]></literal>
    <justification jstring="[para(3692(a,1),11888(a,2,1,1))].">
      <j1 rule="para" parents="3692 11888"/>
    </justification>
  </clause>

  <clause id="11890">
    <literal><![CDATA[
      L(x,y,T(z * u,u \ 1)) = L(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(333,a,11824,a(flip),b,11857,a),flip(a)].">
      <j1 rule="hyper" parents="333 11824 11857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11891">
    <literal><![CDATA[
      L(x,y,T(T(z,z \ u),w)) = L(x,y,T(T(z,u),w))
    ]]></literal>
    <justification jstring="[para(23(a,1),11858(a,2,3))].">
      <j1 rule="para" parents="23 11858"/>
    </justification>
  </clause>

  <clause id="11892">
    <literal><![CDATA[
      L(x,y,(z / u) * T(u,w)) = L(x,y,z * K(u,u \ w))
    ]]></literal>
    <justification jstring="[para(5974(a,1),11859(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5974 11859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11893">
    <literal><![CDATA[
      L(T(x,y) \ z,T(x,y),x \ y) = y \ ((T(y,x) / x) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,10124,a(flip),b,11876,a),flip(a)].">
      <j1 rule="hyper" parents="63 10124 11876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11894">
    <literal><![CDATA[
      L(x,y,K(z,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(11850(a,1),509(a,1))].">
      <j1 rule="para" parents="11850 509"/>
    </justification>
  </clause>

  <clause id="11895">
    <literal><![CDATA[
      L(x,y,K(z,u \ z)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(11852(a,2),11894(a,1))].">
      <j1 rule="para" parents="11852 11894"/>
    </justification>
  </clause>

  <clause id="11896">
    <literal><![CDATA[
      L(x,y,z * K(u,u \ w)) = L(x,y,z * K(u,w))
    ]]></literal>
    <justification jstring="[para(5974(a,1),11892(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5974 11892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11897">
    <literal><![CDATA[
      L(T((1 / x) \ y,z),x,x) = T(1 \ (L(x,x,x) * y),z)
    ]]></literal>
    <justification jstring="[hyper(2627,a,11833,a)].">
      <j1 rule="hyper" parents="2627 11833"/>
    </justification>
  </clause>

  <clause id="11899">
    <literal><![CDATA[
      L(T((1 / x) \ y,z),x,x) = T(L(x,x,x) * y,z)
    ]]></literal>
    <justification jstring="[para(65(a,1),11897(a,2,1))].">
      <j1 rule="para" parents="65 11897"/>
    </justification>
  </clause>

  <clause id="11900">
    <literal><![CDATA[
      L(x,y,K(z * u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(11820(a,1),11808(a,1))].">
      <j1 rule="para" parents="11820 11808"/>
    </justification>
  </clause>

  <clause id="11901">
    <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(385(a,1),11838(a,1,3,2))].">
      <j1 rule="para" parents="385 11838"/>
    </justification>
  </clause>

  <clause id="11902">
    <literal><![CDATA[
      L(x,y,K(z * u,z \ 1)) = L(x,y,K(u * z,u))
    ]]></literal>
    <justification jstring="[para(5657(a,1),11901(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5657 11901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11903">
    <literal><![CDATA[
      L(x,y,K(z * u,z \ 1)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(333,a,11825,a(flip),b,11902,a),flip(a)].">
      <j1 rule="hyper" parents="333 11825 11902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11905">
    <literal><![CDATA[
      L(x,y,K(z,u \ 1)) = L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,11853,a(flip),b,11903,a)].">
      <j1 rule="hyper" parents="63 11853 11903"/>
    </justification>
  </clause>

  <clause id="11907">
    <literal><![CDATA[
      L(x,y,K(z \ 1,u)) = L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[para(4621(a,1),11905(a,1,3)),flip(a)].">
      <j1 rule="para" parents="4621 11905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11909">
    <literal><![CDATA[
      (x / T(T(y,y \ x),x)) * z = K(x,y) * ((y \ x) * z)
    ]]></literal>
    <justification jstring="[para(4642(a,1),11864(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4642 11864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11910">
    <literal><![CDATA[
      K(x,y) * ((y \ x) * z) = (T(y,x) \ x) * z
    ]]></literal>
    <justification jstring="[para(6669(a,1),11909(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6669 11909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11911">
    <literal><![CDATA[
      (x \ y) \ (K(y,x) \ z) = (T(x,y) \ y) \ z
    ]]></literal>
    <justification jstring="[hyper(629,a,11910,a),flip(a)].">
      <j1 rule="hyper" parents="629 11910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11912">
    <literal><![CDATA[
      (x \ y) \ (K(x,y) * z) = (T(x,y) \ y) \ z
    ]]></literal>
    <justification jstring="[para(4567(a,1),11911(a,1,2))].">
      <j1 rule="para" parents="4567 11911"/>
    </justification>
  </clause>

  <clause id="11913">
    <literal><![CDATA[
      (x / T(y,x)) * ((y \ x) * z) = (T(y,x) \ x) * ((x / y) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,11910,a(flip),b,11865,a),flip(a)].">
      <j1 rule="hyper" parents="63 11910 11865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11916">
    <literal><![CDATA[
      K(x,y) * (((x * K(z,y)) / y) * u) = ((x * K(z,y)) / T(y,x)) * u
    ]]></literal>
    <justification jstring="[para(7391(a,1),11866(a,1,1))].">
      <j1 rule="para" parents="7391 11866"/>
    </justification>
  </clause>

  <clause id="11917">
    <literal><![CDATA[
      ((x * K(y,z)) / T(z,x)) * u = K(x,z) * ((x / T(z,y)) * u)
    ]]></literal>
    <justification jstring="[para(5460(a,1),11916(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5460 11916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11919">
    <literal><![CDATA[
      ((x / T(y,x)) * K(z,y)) * u = K(x,y) * ((x / T(y,z)) * u)
    ]]></literal>
    <justification jstring="[para(8055(a,1),11917(a,1,1))].">
      <j1 rule="para" parents="8055 11917"/>
    </justification>
  </clause>

  <clause id="11920">
    <literal><![CDATA[
      K(x,y) * ((x / T(y,z)) * u) = (T(x,y) / T(y,z)) * u
    ]]></literal>
    <justification jstring="[para(5449(a,1),11919(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5449 11919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11921">
    <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(11797(a,1),11809(a,2,1))].">
      <j1 rule="para" parents="11797 11809"/>
    </justification>
  </clause>

  <clause id="11922">
    <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(333,a,11807,a(flip),b,11921,a),flip(a)].">
      <j1 rule="hyper" parents="333 11807 11921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11923">
    <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(20(a,2),11922(a,2,2))].">
      <j1 rule="para" parents="20 11922"/>
    </justification>
  </clause>

  <clause id="11924">
    <literal><![CDATA[
      R(a(x,y,x) * z,u,w) = a(x,y,x) * R(z,u,w)
    ]]></literal>
    <justification jstring="[para(11801(a,1),11923(a,1,2))].">
      <j1 rule="para" parents="11801 11923"/>
    </justification>
  </clause>

  <clause id="11925">
    <literal><![CDATA[
      R(a(x,y,x) * z,u,w) * v5 = a(x,y,x) * (R(z,u,w) * v5)
    ]]></literal>
    <justification jstring="[para(11924(a,2),11797(a,1,1))].">
      <j1 rule="para" parents="11924 11797"/>
    </justification>
  </clause>

  <clause id="11926">
    <literal><![CDATA[
      R(x * a(y,z,y),u,w) * v5 = a(y,z,y) * (R(x,u,w) * v5)
    ]]></literal>
    <justification jstring="[para(9246(a,1),11925(a,1,1,1))].">
      <j1 rule="para" parents="9246 11925"/>
    </justification>
  </clause>

  <clause id="11927">
    <literal><![CDATA[
      a(x,y,x) * (R(y,z,u) * x) = T(x * R(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,8375,a(flip),b,11926,a),flip(a)].">
      <j1 rule="hyper" parents="63 8375 11926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11928">
    <literal><![CDATA[
      a(x,R(y,z,u),x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,8248,a,b,11927,a)].">
      <j1 rule="hyper" parents="35 8248 11927"/>
    </justification>
  </clause>

  <clause id="11929">
    <literal><![CDATA[
      R(a(x,y,x),z,u) = a(x,R(y,w,v5),x)
    ]]></literal>
    <justification jstring="[hyper(333,a,11792,a,b,11928,a)].">
      <j1 rule="hyper" parents="333 11792 11928"/>
    </justification>
  </clause>

  <clause id="11930">
    <literal><![CDATA[
      R(T(x,y),R(z,u,w),x) = a(x,z,x) * T(x,y)
    ]]></literal>
    <justification jstring="[para(11928(a,1),8267(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11928 8267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11931">
    <literal><![CDATA[
      a(x,R(y,z,u),x) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = w
    ]]></literal>
    <justification jstring="[para(11929(a,1),552(a,1)),flip(b)].">
      <j1 rule="para" parents="11929 552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11932">
    <literal><![CDATA[
      R(T(x,y),R(z,u,w),x) = R(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,8267,a(flip),b,11930,a),flip(a)].">
      <j1 rule="hyper" parents="333 8267 11930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11933">
    <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(11797(a,1),11802(a,1,2,1))].">
      <j1 rule="para" parents="11797 11802"/>
    </justification>
  </clause>

  <clause id="11934">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (y * (T(u * z,u) / u))) = a(u,(x * (y * z)) / (x * y),u)
    ]]></literal>
    <justification jstring="[para(4429(a,1),11815(a,2,2))].">
      <j1 rule="para" parents="4429 11815"/>
    </justification>
  </clause>

  <clause id="11935">
    <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(8256,a,11934,a)].">
      <j1 rule="hyper" parents="8256 11934"/>
    </justification>
  </clause>

  <clause id="11936">
    <literal><![CDATA[
      ((x \ y) * K(x,y)) \ (K(x,(x \ y) * T(x,y)) * z) = (((x \ y) * x) / x) \ z
    ]]></literal>
    <justification jstring="[para(5979(a,1),11889(a,1,1))].">
      <j1 rule="para" parents="5979 11889"/>
    </justification>
  </clause>

  <clause id="11937">
    <literal><![CDATA[
      (K(x,y) * (x \ y)) \ (K(x,(x \ y) * T(x,y)) * z) = (((x \ y) * x) / x) \ z
    ]]></literal>
    <justification jstring="[para(6185(a,2),11936(a,1,1))].">
      <j1 rule="para" parents="6185 11936"/>
    </justification>
  </clause>

  <clause id="11938">
    <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(11797(a,1),11933(a,1,2))].">
      <j1 rule="para" parents="11797 11933"/>
    </justification>
  </clause>

  <clause id="11939">
    <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(878,a,11938,a)].">
      <j1 rule="hyper" parents="878 11938"/>
    </justification>
  </clause>

  <clause id="11940">
    <literal><![CDATA[
      a(a(x,y,x) * z,u,w) = a(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(11808,a,11939,a),flip(a)].">
      <j1 rule="hyper" parents="11808 11939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11942">
    <literal><![CDATA[
      a(a(x,y,x) \ z,u,w) = a(z,u,w)
    ]]></literal>
    <justification jstring="[para(10(a,1),11940(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 11940"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11943">
    <literal><![CDATA[
      a(T(x * y,x),z,u) = a(y * x,z,u)
    ]]></literal>
    <justification jstring="[para(8248(a,1),11940(a,1,1))].">
      <j1 rule="para" parents="8248 11940"/>
    </justification>
  </clause>

  <clause id="11944">
    <literal><![CDATA[
      a(K(x * y,y),z,u) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(8265(a,1),11940(a,1,1))].">
      <j1 rule="para" parents="8265 11940"/>
    </justification>
  </clause>

  <clause id="11945">
    <literal><![CDATA[
      a(K(x,x \ y),z,u) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(8207(a,1),11940(a,1,1))].">
      <j1 rule="para" parents="8207 11940"/>
    </justification>
  </clause>

  <clause id="11946">
    <literal><![CDATA[
      a(x * a(y,z,y),u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[para(9246(a,1),11940(a,1,1))].">
      <j1 rule="para" parents="9246 11940"/>
    </justification>
  </clause>

  <clause id="11947">
    <literal><![CDATA[
      a(R(x,y,x) * z,u,w) = a(x * z,u,w)
    ]]></literal>
    <justification jstring="[para(9334(a,1),11940(a,1,1))].">
      <j1 rule="para" parents="9334 11940"/>
    </justification>
  </clause>

  <clause id="11948">
    <literal><![CDATA[
      a(L(x,y,x),z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[para(8239(a,1),11942(a,1,1))].">
      <j1 rule="para" parents="8239 11942"/>
    </justification>
  </clause>

  <clause id="11949">
    <literal><![CDATA[
      a(K(x \ y,x),z,u) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(8206(a,1),11942(a,1,1))].">
      <j1 rule="para" parents="8206 11942"/>
    </justification>
  </clause>

  <clause id="11950">
    <literal><![CDATA[
      a(K(x \ 1,y),z,u) = a(K(x \ y,y),z,u)
    ]]></literal>
    <justification jstring="[para(8258(a,1),11942(a,1,1))].">
      <j1 rule="para" parents="8258 11942"/>
    </justification>
  </clause>

  <clause id="11951">
    <literal><![CDATA[
      a(x / R(y,z,y),u,w) = a(x / y,u,w)
    ]]></literal>
    <justification jstring="[para(9315(a,1),11942(a,1,1))].">
      <j1 rule="para" parents="9315 11942"/>
    </justification>
  </clause>

  <clause id="11952">
    <literal><![CDATA[
      a(T(x / y,x),z,u) = a(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(3781(a,1),11948(a,1,1))].">
      <j1 rule="para" parents="3781 11948"/>
    </justification>
  </clause>

  <clause id="11953">
    <literal><![CDATA[
      a(T(x,x \ y),z,u) = a((x \ y) \ y,z,u)
    ]]></literal>
    <justification jstring="[para(5426(a,1),11948(a,1,1))].">
      <j1 rule="para" parents="5426 11948"/>
    </justification>
  </clause>

  <clause id="11954">
    <literal><![CDATA[
      a((x \ y) \ y,z,u) = a(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(11339(a,1),11948(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11339 11948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11955">
    <literal><![CDATA[
      a(T(x,y) / y,z,u) = a(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(8251(a,1),11946(a,1,1))].">
      <j1 rule="para" parents="8251 11946"/>
    </justification>
  </clause>

  <clause id="11956">
    <literal><![CDATA[
      a(T(x * (y / x),x),z,u) = a(y,z,u)
    ]]></literal>
    <justification jstring="[para(9241(a,1),11946(a,1,1))].">
      <j1 rule="para" parents="9241 11946"/>
    </justification>
  </clause>

  <clause id="11957">
    <literal><![CDATA[
      a(K(x,y \ x),z,u) = a(K(y,y \ x),z,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),11944(a,1,1,1))].">
      <j1 rule="para" parents="10 11944"/>
    </justification>
  </clause>

  <clause id="11958">
    <literal><![CDATA[
      a(x * (y / x),x,z) = a(y,T(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(5165,a,11956,a)].">
      <j1 rule="hyper" parents="5165 11956"/>
    </justification>
  </clause>

  <clause id="11959">
    <literal><![CDATA[
      a(T(x,x \ y) * z,u,w) = a(T(x,y) * z,u,w)
    ]]></literal>
    <justification jstring="[para(3849(a,1),11947(a,1,1,1))].">
      <j1 rule="para" parents="3849 11947"/>
    </justification>
  </clause>

  <clause id="11960">
    <literal><![CDATA[
      a(K(x,y) * (x \ y),z,u) = a(y / x,z,u)
    ]]></literal>
    <justification jstring="[para(8339(a,1),11951(a,1,1))].">
      <j1 rule="para" parents="8339 11951"/>
    </justification>
  </clause>

  <clause id="11961">
    <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(3094(a,1),11953(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3094 11953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11962">
    <literal><![CDATA[
      a(K(x,y \ x),z,u) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(333,a,11945,a(flip),b,11957,a),flip(a)].">
      <j1 rule="hyper" parents="333 11945 11957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11963">
    <literal><![CDATA[
      a(K(x \ y,y),z,u) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(4643(a,1),11962(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4643 11962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11964">
    <literal><![CDATA[
      a(K(x \ 1,y),z,u) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,11950,a,b,11963,a)].">
      <j1 rule="hyper" parents="63 11950 11963"/>
    </justification>
  </clause>

  <clause id="11965">
    <literal><![CDATA[
      a(K(x,y \ 1),z,u) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(3334(a,1),11964(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3334 11964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11966">
    <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(10544(a,2),11964(a,2,1)),flip(a)].">
      <j1 rule="para" parents="10544 11964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11967">
    <literal><![CDATA[
      K(x \ 1,y) * K(y,R(x,z,u) \ 1) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,11730,a,b,11965,a)].">
      <j1 rule="hyper" parents="63 11730 11965"/>
    </justification>
  </clause>

  <clause id="11968">
    <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(11579(a,1),11965(a,2,1))].">
      <j1 rule="para" parents="11579 11965"/>
    </justification>
  </clause>

  <clause id="11969">
    <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(5658(a,1),11966(a,2,1))].">
      <j1 rule="para" parents="5658 11966"/>
    </justification>
  </clause>

  <clause id="11970">
    <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(333,a,11964,a(flip),b,11969,a),flip(a)].">
      <j1 rule="hyper" parents="333 11964 11969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11971">
    <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(10544(a,1),11970(a,1,1))].">
      <j1 rule="para" parents="10544 11970"/>
    </justification>
  </clause>

  <clause id="11972">
    <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(11579(a,1),11971(a,2,1))].">
      <j1 rule="para" parents="11579 11971"/>
    </justification>
  </clause>

  <clause id="11974">
    <literal><![CDATA[
      L(x,y,T(T(z,z \ u),T(z,z \ u) / u)) = L(x,y,(z \ u) \ T(u,u \ z))
    ]]></literal>
    <justification jstring="[para(12(a,1),11841(a,1,3,1))].">
      <j1 rule="para" parents="12 11841"/>
    </justification>
  </clause>

  <clause id="11976">
    <literal><![CDATA[
      L(x,y,T(T(z,z \ u),u \ T(z,z \ u))) = L(x,y,(z \ u) \ T(u,u \ z))
    ]]></literal>
    <justification jstring="[para(3363(a,1),11974(a,1,3))].">
      <j1 rule="para" parents="3363 11974"/>
    </justification>
  </clause>

  <clause id="11977">
    <literal><![CDATA[
      L(x,y,T(T(z,z \ u),z / u)) = L(x,y,(z \ u) \ T(u,u \ z))
    ]]></literal>
    <justification jstring="[para(7975(a,1),11976(a,1,3))].">
      <j1 rule="para" parents="7975 11976"/>
    </justification>
  </clause>

  <clause id="11978">
    <literal><![CDATA[
      L(x,y,T(T(z,z \ u),u \ z)) = L(x,y,(z \ u) \ T(u,u \ z))
    ]]></literal>
    <justification jstring="[para(7234(a,1),11977(a,1,3))].">
      <j1 rule="para" parents="7234 11977"/>
    </justification>
  </clause>

  <clause id="11979">
    <literal><![CDATA[
      L(x,y,(z \ u) \ T(u,u \ z)) = L(x,y,T(T(z,u \ z),u))
    ]]></literal>
    <justification jstring="[hyper(63,a,11858,a(flip),b,11978,a),flip(a)].">
      <j1 rule="hyper" parents="63 11858 11978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11980">
    <literal><![CDATA[
      L(x,y,(z \ u) \ T(u,u \ z)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,11869,a(flip),b,11979,a),flip(a)].">
      <j1 rule="hyper" parents="333 11869 11979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11982">
    <literal><![CDATA[
      L(T((x / y) \ 1,x) \ 1,(x / y) \ 1,x) = (((y \ x) \ 1) * x) \ (y * (x / y))
    ]]></literal>
    <justification jstring="[hyper(63,a,11713,a(flip),b,11980,a),flip(a)].">
      <j1 rule="hyper" parents="63 11713 11980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11983">
    <literal><![CDATA[
      (((x \ y) \ 1) * y) \ (x * (y / x)) = (((y / x) \ 1) * y) \ y
    ]]></literal>
    <justification jstring="[hyper(5088,a,11982,a),flip(a)].">
      <j1 rule="hyper" parents="5088 11982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11985">
    <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(63,a,5184,a(flip),b,11844,a),flip(a)].">
      <j1 rule="hyper" parents="63 5184 11844"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11986">
    <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(7409(a,1),11985(a,1,1,1))].">
      <j1 rule="para" parents="7409 11985"/>
    </justification>
  </clause>

  <clause id="11987">
    <literal><![CDATA[
      (K(x,x * y) \ z) \ T(x * y,x) = (K(x,y) \ z) \ (y * x)
    ]]></literal>
    <justification jstring="[para(3411(a,1),11986(a,1,2,1))].">
      <j1 rule="para" parents="3411 11986"/>
    </justification>
  </clause>

  <clause id="11989">
    <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(4095(a,1),11961(a,2,1))].">
      <j1 rule="para" parents="4095 11961"/>
    </justification>
  </clause>

  <clause id="11990">
    <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(63,a,11954,a(flip),b,11989,a)].">
      <j1 rule="hyper" parents="63 11954 11989"/>
    </justification>
  </clause>

  <clause id="11992">
    <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(63,a,5176,a(flip),b,4825,a),flip(a)].">
      <j1 rule="hyper" parents="63 5176 4825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11994">
    <literal><![CDATA[
      K((((x \ 1) * (y * z)) / z) \ 1,z / (y * z)) = K(x * (z / (y * z)),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,5281,a(flip),b,11992,a)].">
      <j1 rule="hyper" parents="63 5281 11992"/>
    </justification>
  </clause>

  <clause id="11995">
    <literal><![CDATA[
      K((x \ 1) \ (y / (z * y)),((z * y) / y) \ 1) = K(x * (y / (z * y)),z \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,5722,a(flip),b,11994,a)].">
      <j1 rule="hyper" parents="63 5722 11994"/>
    </justification>
  </clause>

  <clause id="11996">
    <literal><![CDATA[
      K((x \ 1) \ (y / (z * y)),z \ 1) = K(x * (y / (z * y)),z \ 1)
    ]]></literal>
    <justification jstring="[para(11(a,1),11995(a,1,2,1))].">
      <j1 rule="para" parents="11 11995"/>
    </justification>
  </clause>

  <clause id="11997">
    <literal><![CDATA[
      K((x \ 1) \ ((y * z) \ z),y \ 1) = K(x * (z / (y * z)),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,9582,a(flip),b,11996,a)].">
      <j1 rule="hyper" parents="63 9582 11996"/>
    </justification>
  </clause>

  <clause id="11998">
    <literal><![CDATA[
      K((x \ 1) \ ((y * z) \ z),y \ 1) = K(x * ((y * z) \ z),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(333,a,9509,a(flip),b,11997,a),flip(a)].">
      <j1 rule="hyper" parents="333 9509 11997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11999">
    <literal><![CDATA[
      K((x \ 1) \ (y \ 1),y \ 1) = K(x * ((y * z) \ z),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,9963,a(flip),b,11998,a)].">
      <j1 rule="hyper" parents="63 9963 11998"/>
    </justification>
  </clause>

  <clause id="12000">
    <literal><![CDATA[
      K(x * ((y * z) \ z),y \ 1) = K(x * (y \ 1),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(7463,a,11999,a),flip(a)].">
      <j1 rule="hyper" parents="7463 11999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12002">
    <literal><![CDATA[
      K(x * ((y * z) \ z),y \ 1) = K(y \ x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(333,a,6163,a(flip),b,12000,a),flip(a)].">
      <j1 rule="hyper" parents="333 6163 12000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12003">
    <literal><![CDATA[
      K(x * R(y \ 1,y,z),y \ 1) = K(y \ x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,11529,a,b,12002,a)].">
      <j1 rule="hyper" parents="63 11529 12002"/>
    </justification>
  </clause>

  <clause id="12005">
    <literal><![CDATA[
      T(K(x \ y,x \ 1) / x,y) = R(1 / x,y,z / (x * z))
    ]]></literal>
    <justification jstring="[para(12003(a,1),10586(a,1,1,1))].">
      <j1 rule="para" parents="12003 10586"/>
    </justification>
  </clause>

  <clause id="12006">
    <literal><![CDATA[
      R(1 / x,y,z / (x * z)) = R(1 / x,y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,6208,a(flip),b,12005,a),flip(a)].">
      <j1 rule="hyper" parents="63 6208 12005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12008">
    <literal><![CDATA[
      R(1 / (x / y),z,(x / y) \ 1) = R(1 / (x / y),z,y / x)
    ]]></literal>
    <justification jstring="[para(12(a,1),12006(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="12 12006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12009">
    <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(12008(a,1),9275(a,2,2))].">
      <j1 rule="para" parents="12008 9275"/>
    </justification>
  </clause>

  <clause id="12010">
    <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(333,a,1321,a(flip),b,12009,a),flip(a)].">
      <j1 rule="hyper" parents="333 1321 12009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12011">
    <literal><![CDATA[
      T(a(1 / (x / y),z,1 / (x / y)),u) = (x * R(x \ y,z,y / x)) / y
    ]]></literal>
    <justification jstring="[hyper(333,a,1546,a(flip),b,12010,a),flip(a)].">
      <j1 rule="hyper" parents="333 1546 12010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12012">
    <literal><![CDATA[
      T(a(1 / (x / y),z,1 / (x / y)),u) = (x * R(x \ y,z,x \ y)) / y
    ]]></literal>
    <justification jstring="[para(8667(a,1),12011(a,2,1,2))].">
      <j1 rule="para" parents="8667 12011"/>
    </justification>
  </clause>

  <clause id="12013">
    <literal><![CDATA[
      T(a(1 / (x / y),z,1 / (x / y)),u) = a(x \ y,z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(333,a,9332,a(flip),b,12012,a),flip(a)].">
      <j1 rule="hyper" parents="333 9332 12012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12014">
    <literal><![CDATA[
      T(a(1 / (x / y),z,(x / y) \ 1),u) = a(x \ y,z,x \ y)
    ]]></literal>
    <justification jstring="[para(3276(a,1),12013(a,1,1))].">
      <j1 rule="para" parents="3276 12013"/>
    </justification>
  </clause>

  <clause id="12023">
    <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(4482(a,1),5503(a,1,1))].">
      <j1 rule="para" parents="4482 5503"/>
    </justification>
  </clause>

  <clause id="12024">
    <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(4482(a,1),12023(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="4482 12023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12025">
    <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(4367(a,1),12024(a,2,2,1))].">
      <j1 rule="para" parents="4367 12024"/>
    </justification>
  </clause>

  <clause id="12026">
    <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(5629(a,1),12025(a,2,2))].">
      <j1 rule="para" parents="5629 12025"/>
    </justification>
  </clause>

  <clause id="12027">
    <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(4216(a,1),12026(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4216 12026"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12028">
    <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(5629(a,1),12027(a,2,1,2))].">
      <j1 rule="para" parents="5629 12027"/>
    </justification>
  </clause>

  <clause id="12029">
    <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(63,a,11730,a(flip),b,12028,a),flip(a)].">
      <j1 rule="hyper" parents="63 11730 12028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12030">
    <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(333,a,11968,a(flip),b,12029,a),flip(a)].">
      <j1 rule="hyper" parents="333 11968 12029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12031">
    <literal><![CDATA[
      a(K(x,R(y,z,u)),w,v5) = R(a(K(x,y),w,v5),z,u)
    ]]></literal>
    <justification jstring="[para(11967(a,1),12030(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11967 12030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12034">
    <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(6365(a,2),11632(a,2,2))].">
      <j1 rule="para" parents="6365 11632"/>
    </justification>
  </clause>

  <clause id="12035">
    <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(7736(a,1),11785(a,1,1,2))].">
      <j1 rule="para" parents="7736 11785"/>
    </justification>
  </clause>

  <clause id="12037">
    <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(7737(a,1),12035(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7737 12035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12038">
    <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(63,a,2566,a(flip),b,12037,a),flip(a)].">
      <j1 rule="hyper" parents="63 2566 12037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12041">
    <literal><![CDATA[
      L(x,y,L(x,z,u)) = (a(x,y,x) * K(x,w)) \ T(x,w)
    ]]></literal>
    <justification jstring="[para(11777(a,1),12038(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11777 12038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12043">
    <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(7493(a,1),12034(a,2,2))].">
      <j1 rule="para" parents="7493 12034"/>
    </justification>
  </clause>

  <clause id="12044">
    <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(333,a,6424,a(flip),b,12043,a),flip(a)].">
      <j1 rule="hyper" parents="333 6424 12043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12046">
    <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(333,a,9504,a(flip),b,12044,a),flip(a)].">
      <j1 rule="hyper" parents="333 9504 12044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12047">
    <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(333,a,6398,a(flip),b,12046,a),flip(a)].">
      <j1 rule="hyper" parents="333 6398 12046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12048">
    <literal><![CDATA[
      (x * K(y,z * x)) / K(y,z) = K(y,z * x) * (K(z,y) * x)
    ]]></literal>
    <justification jstring="[para(6891(a,1),12047(a,1,2))].">
      <j1 rule="para" parents="6891 12047"/>
    </justification>
  </clause>

  <clause id="12049">
    <literal><![CDATA[
      (x * K(y,z * x)) * K(z,y) = K(y,z * x) * (K(z,y) * x)
    ]]></literal>
    <justification jstring="[hyper(5999,a,12048,a)].">
      <j1 rule="hyper" parents="5999 12048"/>
    </justification>
  </clause>

  <clause id="12051">
    <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(12049(a,1),8163(a,1))].">
      <j1 rule="para" parents="12049 8163"/>
    </justification>
  </clause>

  <clause id="12052">
    <literal><![CDATA[
      R(x,T(K(y,z),x),T(K(z,K(u,w)),K(y,z) * x)) \ ((K(u,K(z,w)) * K(y,z)) * x) = T(K(y,z),x) * T(K(u,K(z,w)),K(y,z) * x)
    ]]></literal>
    <justification jstring="[para(6785(a,1),8190(a,1,1,3,1))].">
      <j1 rule="para" parents="6785 8190"/>
    </justification>
  </clause>

  <clause id="12053">
    <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(10901(a,1),9797(a,1,1))].">
      <j1 rule="para" parents="10901 9797"/>
    </justification>
  </clause>

  <clause id="12054">
    <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(5927(a,1),11617(a,1,2,1))].">
      <j1 rule="para" parents="5927 11617"/>
    </justification>
  </clause>

  <clause id="12055">
    <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(3118(a,1),12054(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3118 12054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12056">
    <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(7724(a,1),12055(a,2,2))].">
      <j1 rule="para" parents="7724 12055"/>
    </justification>
  </clause>

  <clause id="12057">
    <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(9(a,1),12056(a,2,2,1))].">
      <j1 rule="para" parents="9 12056"/>
    </justification>
  </clause>

  <clause id="12058">
    <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(10613(a,1),12057(a,1,1,2))].">
      <j1 rule="para" parents="10613 12057"/>
    </justification>
  </clause>

  <clause id="12059">
    <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(7658(a,1),12058(a,1,1))].">
      <j1 rule="para" parents="7658 12058"/>
    </justification>
  </clause>

  <clause id="12061">
    <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(10613(a,1),12059(a,1,2,1))].">
      <j1 rule="para" parents="10613 12059"/>
    </justification>
  </clause>

  <clause id="12062">
    <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(4790(a,1),12061(a,1,2))].">
      <j1 rule="para" parents="4790 12061"/>
    </justification>
  </clause>

  <clause id="12063">
    <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(6720(a,1),12062(a,1,2))].">
      <j1 rule="para" parents="6720 12062"/>
    </justification>
  </clause>

  <clause id="12064">
    <literal><![CDATA[
      (x * y) / (y * T(x,z)) = T(K(z,x),y) * K(x,y)
    ]]></literal>
    <justification jstring="[para(9488(a,1),12063(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9488 12063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12065">
    <literal><![CDATA[
      (x * y) / (y * T(x,z)) = T(K(z,x) * K(x,y),y)
    ]]></literal>
    <justification jstring="[hyper(333,a,6647,a,b,12064,a),flip(a)].">
      <j1 rule="hyper" parents="333 6647 12064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12067">
    <literal><![CDATA[
      R(x,T(K(y,z),x),T(K(z,K(u,w)),x)) \ ((K(u,K(z,w)) * K(y,z)) * x) = T(K(y,z),x) * T(K(u,K(z,w)),K(y,z) * x)
    ]]></literal>
    <justification jstring="[para(7499(a,1),12052(a,1,1,3))].">
      <j1 rule="para" parents="7499 12052"/>
    </justification>
  </clause>

  <clause id="12068">
    <literal><![CDATA[
      R(x,T(K(y,z),x),K(z,K(u,T(w,x)))) \ ((K(u,K(z,w)) * K(y,z)) * x) = T(K(y,z),x) * T(K(u,K(z,w)),K(y,z) * x)
    ]]></literal>
    <justification jstring="[para(6416(a,2),12067(a,1,1,3))].">
      <j1 rule="para" parents="6416 12067"/>
    </justification>
  </clause>

  <clause id="12070">
    <literal><![CDATA[
      R(x,T(K(y,z),x),K(z,K(u,T(w,x)))) \ ((K(z,K(u,w)) * K(y,z)) * x) = T(K(y,z),x) * T(K(u,K(z,w)),K(y,z) * x)
    ]]></literal>
    <justification jstring="[para(6785(a,1),12068(a,1,2,1,1))].">
      <j1 rule="para" parents="6785 12068"/>
    </justification>
  </clause>

  <clause id="12071">
    <literal><![CDATA[
      R(x,T(K(y,z),x),K(z,K(u,T(w,x)))) \ (K(y,z) * (K(z,K(u,w)) * x)) = T(K(y,z),x) * T(K(u,K(z,w)),K(y,z) * x)
    ]]></literal>
    <justification jstring="[para(11595(a,1),12070(a,1,2))].">
      <j1 rule="para" parents="11595 12070"/>
    </justification>
  </clause>

  <clause id="12072">
    <literal><![CDATA[
      R(x,T(K(y,z),x),K(z,K(u,T(w,x)))) \ (K(y,z) * (K(z,K(u,w)) * x)) = T(K(y,z),x) * T(K(z,K(u,w)),K(y,z) * x)
    ]]></literal>
    <justification jstring="[para(6785(a,1),12071(a,2,2,1))].">
      <j1 rule="para" parents="6785 12071"/>
    </justification>
  </clause>

  <clause id="12073">
    <literal><![CDATA[
      R(x,T(K(y,z),x),K(z,K(u,T(w,x)))) \ (K(y,z) * (K(z,K(u,w)) * x)) = T(K(y,z),x) * T(K(z,K(u,w)),x)
    ]]></literal>
    <justification jstring="[para(7499(a,1),12072(a,2,2))].">
      <j1 rule="para" parents="7499 12072"/>
    </justification>
  </clause>

  <clause id="12074">
    <literal><![CDATA[
      R(x,T(K(y,z),x),K(z,K(u,T(w,x)))) \ (K(y,z) * (K(z,K(u,w)) * x)) = T(K(y,z),x) * K(z,K(u,T(w,x)))
    ]]></literal>
    <justification jstring="[para(6416(a,2),12073(a,2,2))].">
      <j1 rule="para" parents="6416 12073"/>
    </justification>
  </clause>

  <clause id="12076">
    <literal><![CDATA[
      x \ (K(y,z) * (K(z,K(u,w)) * x)) = T(K(y,z),x) * K(z,K(u,T(w,x)))
    ]]></literal>
    <justification jstring="[para(7841(a,1),12074(a,1,1))].">
      <j1 rule="para" parents="7841 12074"/>
    </justification>
  </clause>

  <clause id="12077">
    <literal><![CDATA[
      T(K(x,y),z) * K(y,K(u,T(w,z))) = T(K(x,y) * K(y,K(u,w)),z)
    ]]></literal>
    <justification jstring="[hyper(11594,a,12076,a),flip(a)].">
      <j1 rule="hyper" parents="11594 12076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12078">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) * T(K(w,x),u) = T(K(w,x) * K(x,K(y,z)),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,2007,a(flip),b,12077,a)].">
      <j1 rule="hyper" parents="63 2007 12077"/>
    </justification>
  </clause>

  <clause id="12079">
    <literal><![CDATA[
      T(K(x,y) * K(y,K(z,u)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(y,K(z,T(u,w))) * K(x,T(y,w)) = v5
    ]]></literal>
    <justification jstring="[para(12078(a,1),7329(a,1))].">
      <j1 rule="para" parents="12078 7329"/>
    </justification>
  </clause>

  <clause id="12080">
    <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(9725(a,1),12053(a,1,1,2))].">
      <j1 rule="para" parents="9725 12053"/>
    </justification>
  </clause>

  <clause id="12081">
    <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(6785(a,1),12080(a,1,1))].">
      <j1 rule="para" parents="6785 12080"/>
    </justification>
  </clause>

  <clause id="12083">
    <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(9426(a,1),12081(a,1,1,2))].">
      <j1 rule="para" parents="9426 12081"/>
    </justification>
  </clause>

  <clause id="12084">
    <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(9(a,1),12083(a,1,1,2,1,2))].">
      <j1 rule="para" parents="9 12083"/>
    </justification>
  </clause>

  <clause id="12086">
    <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(6788(a,1),12084(a,1,1))].">
      <j1 rule="para" parents="6788 12084"/>
    </justification>
  </clause>

  <clause id="12087">
    <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(7043(a,1),12086(a,1,1))].">
      <j1 rule="para" parents="7043 12086"/>
    </justification>
  </clause>

  <clause id="12088">
    <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(6870(a,1),12087(a,1,1))].">
      <j1 rule="para" parents="6870 12087"/>
    </justification>
  </clause>

  <clause id="12089">
    <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(6785(a,1),12088(a,1,1))].">
      <j1 rule="para" parents="6785 12088"/>
    </justification>
  </clause>

  <clause id="12090">
    <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(9966(a,1),12089(a,1,2))].">
      <j1 rule="para" parents="9966 12089"/>
    </justification>
  </clause>

  <clause id="12091">
    <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(9449,a,12090,a)].">
      <j1 rule="hyper" parents="9449 12090"/>
    </justification>
  </clause>

  <clause id="12092">
    <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(6370(a,1),12091(a,1,2,1))].">
      <j1 rule="para" parents="6370 12091"/>
    </justification>
  </clause>

  <clause id="12093">
    <literal><![CDATA[
      L(K(x * y,T(y,z)),x,z) = K(y * x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(34,a,10694,a(flip),b,12092,a),flip(a)].">
      <j1 rule="hyper" parents="34 10694 12092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12094">
    <literal><![CDATA[
      K((x / (x * y)) \ z,z) = K(z * y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,9931,a(flip),b,12093,a)].">
      <j1 rule="hyper" parents="63 9931 12093"/>
    </justification>
  </clause>

  <clause id="12096">
    <literal><![CDATA[
      K(x * (y \ z),T(x,y)) = K((y / z) \ x,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),12094(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10 12094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12097">
    <literal><![CDATA[
      K((x \ y) * z,T(z,x)) = K((x / y) \ z,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5207,a,b,12096,a)].">
      <j1 rule="hyper" parents="63 5207 12096"/>
    </justification>
  </clause>

  <clause id="12098">
    <literal><![CDATA[
      K(x / y,z) * a(z,y \ x,z) = K((y / x) \ z,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,8425,a,b,12097,a)].">
      <j1 rule="hyper" parents="63 8425 12097"/>
    </justification>
  </clause>

  <clause id="12099">
    <literal><![CDATA[
      K(x,y / z) * K((z / y) \ x,x) = a(x,z \ y,x)
    ]]></literal>
    <justification jstring="[hyper(4577,a,12098,a)].">
      <j1 rule="hyper" parents="4577 12098"/>
    </justification>
  </clause>

  <clause id="12100">
    <literal><![CDATA[
      T(x,(y / z) \ x) \ T(x,z / y) = a(x,y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,4842,a,b,12099,a)].">
      <j1 rule="hyper" parents="63 4842 12099"/>
    </justification>
  </clause>

  <clause id="12101">
    <literal><![CDATA[
      T(x,(y / z) \ x) \ T(x,(y / z) \ 1) = a(x,y \ z,x)
    ]]></literal>
    <justification jstring="[para(3760(a,2),12100(a,1,2))].">
      <j1 rule="para" parents="3760 12100"/>
    </justification>
  </clause>

  <clause id="12102">
    <literal><![CDATA[
      T(x,(y / z) \ x) \ T(x,x \ ((y / z) \ x)) = a(x,y \ z,x)
    ]]></literal>
    <justification jstring="[para(3591(a,2),12101(a,1,2))].">
      <j1 rule="para" parents="3591 12101"/>
    </justification>
  </clause>

  <clause id="12103">
    <literal><![CDATA[
      T(x,(y / z) \ x) \ ((x \ ((y / z) \ x)) \ ((y / z) \ x)) = a(x,y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,325,a(flip),b,12102,a)].">
      <j1 rule="hyper" parents="63 325 12102"/>
    </justification>
  </clause>

  <clause id="12104">
    <literal><![CDATA[
      a(x,(y / z) \ 1,x) = a(x,y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,8282,a(flip),b,12103,a)].">
      <j1 rule="hyper" parents="63 8282 12103"/>
    </justification>
  </clause>

  <clause id="12105">
    <literal><![CDATA[
      a(x,(y * z) \ z,x) = a(x,y \ 1,x)
    ]]></literal>
    <justification jstring="[para(11(a,1),12104(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11 12104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12107">
    <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(9716(a,1),5346(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9716 5346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12108">
    <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(333,a,6627,a,b,12107,a),flip(a)].">
      <j1 rule="hyper" parents="333 6627 12107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12110">
    <literal><![CDATA[
      R(x,y,z) * T(R(u,R(x,y,z),u),R(u,R(x,y,z),u) * x) = T(T(u,u * x) * R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(4273(a,1),12108(a,2,1))].">
      <j1 rule="para" parents="4273 12108"/>
    </justification>
  </clause>

  <clause id="12111">
    <literal><![CDATA[
      R(x,y,z) * T(R(u,R(x,y,z),u),R(u,R(x,y,z),u) * x) = T(u * R(x,y,z),u * x)
    ]]></literal>
    <justification jstring="[hyper(333,a,8710,a(flip),b,12110,a),flip(a)].">
      <j1 rule="hyper" parents="333 8710 12110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12112">
    <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(3684(a,2),12111(a,1,2))].">
      <j1 rule="para" parents="3684 12111"/>
    </justification>
  </clause>

  <clause id="12113">
    <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(9712(a,1),12112(a,1,2,1))].">
      <j1 rule="para" parents="9712 12112"/>
    </justification>
  </clause>

  <clause id="12114">
    <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(3678(a,2),12113(a,1,2,1))].">
      <j1 rule="para" parents="3678 12113"/>
    </justification>
  </clause>

  <clause id="12116">
    <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(11932(a,1),12114(a,1,2))].">
      <j1 rule="para" parents="11932 12114"/>
    </justification>
  </clause>

  <clause id="12117">
    <literal><![CDATA[
      T(x * R(y,z,u),x * y) = R(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(845(a,1),12116(a,1,2)),flip(a)].">
      <j1 rule="para" parents="845 12116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12119">
    <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="[hyper(197,a,12117,a(flip),b,4233,a(flip))].">
      <j1 rule="hyper" parents="197 12117 4233"/>
    </justification>
  </clause>

  <clause id="12120">
    <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(63,a,12065,a(flip),b,12119,a)].">
      <j1 rule="hyper" parents="63 12065 12119"/>
    </justification>
  </clause>

  <clause id="12121">
    <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(11731(a,1),12120(a,1,1))].">
      <j1 rule="para" parents="11731 12120"/>
    </justification>
  </clause>

  <clause id="12122">
    <literal><![CDATA[
      L(x,y,z) * T(R(u,L(x,y,z),u),R(u,L(x,y,z),u) * x) = K(u,u * x) * T(u * L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(9716(a,1),5397(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9716 5397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12123">
    <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(333,a,6627,a,b,12122,a),flip(a)].">
      <j1 rule="hyper" parents="333 6627 12122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12125">
    <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(4273(a,1),12123(a,2,1))].">
      <j1 rule="para" parents="4273 12123"/>
    </justification>
  </clause>

  <clause id="12126">
    <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(8230(a,1),8284(a,1,2))].">
      <j1 rule="para" parents="8230 8284"/>
    </justification>
  </clause>

  <clause id="12127">
    <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(219(a,1),12126(a,1,3)),flip(a)].">
      <j1 rule="para" parents="219 12126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12128">
    <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(333,a,9362,a(flip),b,12127,a),flip(a)].">
      <j1 rule="hyper" parents="333 9362 12127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12130">
    <literal><![CDATA[
      (K(x,y) * a(x,z,x)) \ u = R(T(x,y),z,x) \ (x * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,4751,a(flip),b,12128,a),flip(a)].">
      <j1 rule="hyper" parents="63 4751 12128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12131">
    <literal><![CDATA[
      (K(x,y) * a(x,z,x)) \ u = x * (R(T(x,y),z,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(333,a,1629,a(flip),b,12130,a),flip(a)].">
      <j1 rule="hyper" parents="333 1629 12130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12132">
    <literal><![CDATA[
      (a(x,y,x) * K(x,z)) \ u = x * (R(T(x,z),y,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,9257,a,b,12131,a)].">
      <j1 rule="hyper" parents="63 9257 12131"/>
    </justification>
  </clause>

  <clause id="12133">
    <literal><![CDATA[
      L(x,y,L(x,z,u)) = x * (R(T(x,w),y,x) \ T(x,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,12041,a,b,12132,a)].">
      <j1 rule="hyper" parents="63 12041 12132"/>
    </justification>
  </clause>

  <clause id="12134">
    <literal><![CDATA[
      L(x,y,L(x,z,u)) = x * (T(x,w) \ L(T(x,w),y,x))
    ]]></literal>
    <justification jstring="[para(10000(a,1),12133(a,2,2))].">
      <j1 rule="para" parents="10000 12133"/>
    </justification>
  </clause>

  <clause id="12135">
    <literal><![CDATA[
      L(x,y,L(x,z,u)) = x * (x \ L(x,y,x))
    ]]></literal>
    <justification jstring="[para(6560(a,1),12134(a,2,2))].">
      <j1 rule="para" parents="6560 12134"/>
    </justification>
  </clause>

  <clause id="12136">
    <literal><![CDATA[
      L(x,y,L(x,z,u)) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,10,a(flip),b,12135,a),flip(a)].">
      <j1 rule="hyper" parents="333 10 12135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12138">
    <literal><![CDATA[
      L(L(x,y,z),u,L(x,w,v5)) = L(L(x,u,x),y,z)
    ]]></literal>
    <justification jstring="[para(12136(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12136 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12139">
    <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(12138(a,1),11610(a,1,1,2))].">
      <j1 rule="para" parents="12138 11610"/>
    </justification>
  </clause>

  <clause id="12140">
    <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(9294(a,1),9296(a,2,2,1,1))].">
      <j1 rule="para" parents="9294 9296"/>
    </justification>
  </clause>

  <clause id="12141">
    <literal><![CDATA[
      T((x \ a(y,x \ 1,y)) * R((x \ a(y,x \ 1,y)) \ 1,z,u),y) = y \ (T(y * (x \ 1),y) * R(T(y * (x \ 1),y) \ y,z,u))
    ]]></literal>
    <justification jstring="[hyper(333,a,1538,a(flip),b,12140,a),flip(a)].">
      <j1 rule="hyper" parents="333 1538 12140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12142">
    <literal><![CDATA[
      T((x \ a(y,x \ 1,y)) * R((x \ a(y,x \ 1,y)) \ 1,z,u),y) = y \ T((y * (x \ 1)) * R((y * (x \ 1)) \ y,z,u),y)
    ]]></literal>
    <justification jstring="[para(1748(a,1),12141(a,2,2))].">
      <j1 rule="para" parents="1748 12141"/>
    </justification>
  </clause>

  <clause id="12143">
    <literal><![CDATA[
      T((x \ a(y,x \ 1,y)) * R((x \ a(y,x \ 1,y)) \ 1,z,u),y) = y \ T(y * ((x \ 1) * R((x \ 1) \ 1,z,u)),y)
    ]]></literal>
    <justification jstring="[para(1026(a,1),12142(a,2,2,1))].">
      <j1 rule="para" parents="1026 12142"/>
    </justification>
  </clause>

  <clause id="12144">
    <literal><![CDATA[
      T((x \ a(y,x \ 1,y)) * R((x \ a(y,x \ 1,y)) \ 1,z,u),y) = y \ T(y * (x \ R(x,z,u)),y)
    ]]></literal>
    <justification jstring="[para(1313(a,1),12143(a,2,2,1,2))].">
      <j1 rule="para" parents="1313 12143"/>
    </justification>
  </clause>

  <clause id="12145">
    <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(1538(a,1),12144(a,1,1))].">
      <j1 rule="para" parents="1538 12144"/>
    </justification>
  </clause>

  <clause id="12146">
    <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(11924(a,2),12145(a,1,1,2))].">
      <j1 rule="para" parents="11924 12145"/>
    </justification>
  </clause>

  <clause id="12147">
    <literal><![CDATA[
      x \ T(x * (y \ R(y,z,u)),x) = T(y \ R(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(10(a,1),12146(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 12146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12148">
    <literal><![CDATA[
      K(a(x,y,z),T((((x * y) * z) \ 1) * ((u \ ((x * y) * z)) * u),x * (y * z))) = K(a(x,y,z),K((x * y) * z,u))
    ]]></literal>
    <justification jstring="[hyper(333,a,8109,a(flip),b,8409,a),flip(a)].">
      <j1 rule="hyper" parents="333 8109 8409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12149">
    <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(333,a,6788,a(flip),b,12148,a),flip(a)].">
      <j1 rule="hyper" parents="333 6788 12148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12151">
    <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(2897(a,1),8357(a,1,1,1,2))].">
      <j1 rule="para" parents="2897 8357"/>
    </justification>
  </clause>

  <clause id="12152">
    <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(10851(a,1),11262(a,1,2,2))].">
      <j1 rule="para" parents="10851 11262"/>
    </justification>
  </clause>

  <clause id="12153">
    <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(333,a,9,a(flip),b,11702,a),flip(a)].">
      <j1 rule="hyper" parents="333 9 11702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12155">
    <literal><![CDATA[
      L(x,K(y,z),K(u,y) * R(K(y,u),w,v5)) = x
    ]]></literal>
    <justification jstring="[para(11700(a,1),12153(a,1,3))].">
      <j1 rule="para" parents="11700 12153"/>
    </justification>
  </clause>

  <clause id="12157">
    <literal><![CDATA[
      L(x,K(y,z),a(K(y,u),w,v5)) = x
    ]]></literal>
    <justification jstring="[para(11726(a,1),12155(a,1,3))].">
      <j1 rule="para" parents="11726 12155"/>
    </justification>
  </clause>

  <clause id="12158">
    <literal><![CDATA[
      (a(K(x,y),z,u) * K(x,w)) * v5 != v6
    ]]></literal>
    <literal><![CDATA[
      a(K(x,y),z,u) * (K(x,w) * v5) = v6
    ]]></literal>
    <justification jstring="[para(12157(a,1),306(a,1,2))].">
      <j1 rule="para" parents="12157 306"/>
    </justification>
  </clause>

  <clause id="12159">
    <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(12158,a,11749,a)].">
      <j1 rule="hyper" parents="12158 11749"/>
    </justification>
  </clause>

  <clause id="12160">
    <literal><![CDATA[
      a(K(x,T(y,z)),u,w) * z = z * a(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(4558(a,1),12159(a,1,2))].">
      <j1 rule="para" parents="4558 12159"/>
    </justification>
  </clause>

  <clause id="12161">
    <literal><![CDATA[
      x * a(K(y,T(z,x)),u,w) = a(K(y,z),u,w) * x
    ]]></literal>
    <justification jstring="[para(6900(a,1),12160(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6900 12160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12162">
    <literal><![CDATA[
      a(K(x,T(y,z)),u,w) = T(a(K(x,y),u,w),z)
    ]]></literal>
    <justification jstring="[hyper(254,a,12161,a),flip(a)].">
      <j1 rule="hyper" parents="254 12161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12163">
    <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(333,a,12121,a(flip),b,12162,a)].">
      <j1 rule="hyper" parents="333 12121 12162"/>
    </justification>
  </clause>

  <clause id="12164">
    <literal><![CDATA[
      K(x * y,x * R(y,z,u)) = a(K(x,y),z * y,u)
    ]]></literal>
    <justification jstring="[para(177(a,1),12163(a,2,1,2))].">
      <j1 rule="para" parents="177 12163"/>
    </justification>
  </clause>

  <clause id="12165">
    <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(4896,a,12164,a)].">
      <j1 rule="hyper" parents="4896 12164"/>
    </justification>
  </clause>

  <clause id="12166">
    <literal><![CDATA[
      K(x,(x / y) * R(y,z,u)) = a(K(x / y,y),z * y,u)
    ]]></literal>
    <justification jstring="[para(12(a,1),12164(a,1,1))].">
      <j1 rule="para" parents="12 12164"/>
    </justification>
  </clause>

  <clause id="12167">
    <literal><![CDATA[
      K(x,(y \ x) * R(y,z,u)) = a(K(x / y,y),z * y,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,9755,a(flip),b,12166,a)].">
      <j1 rule="hyper" parents="63 9755 12166"/>
    </justification>
  </clause>

  <clause id="12168">
    <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(12164(a,1),12165(a,1,1))].">
      <j1 rule="para" parents="12164 12165"/>
    </justification>
  </clause>

  <clause id="12169">
    <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(63,a,12031,a,b,12168,a)].">
      <j1 rule="hyper" parents="63 12031 12168"/>
    </justification>
  </clause>

  <clause id="12170">
    <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(63,a,11972,a(flip),b,12169,a)].">
      <j1 rule="hyper" parents="63 11972 12169"/>
    </justification>
  </clause>

  <clause id="12172">
    <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(3176(a,1),12151(a,1,1,1))].">
      <j1 rule="para" parents="3176 12151"/>
    </justification>
  </clause>

  <clause id="12173">
    <literal><![CDATA[
      K(((x \ (x / (y \ x))) * (y \ x)) \ (x / (((y \ x) \ 1) \ 1)),z) = K(R(y,y \ x,x \ (x / (((y \ x) \ 1) \ 1))),z)
    ]]></literal>
    <justification jstring="[para(110(a,1),12172(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="110 12172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12177">
    <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(2897(a,1),12173(a,2,1,3,2))].">
      <j1 rule="para" parents="2897 12173"/>
    </justification>
  </clause>

  <clause id="12178">
    <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(9(a,1),12177(a,2,1,3))].">
      <j1 rule="para" parents="9 12177"/>
    </justification>
  </clause>

  <clause id="12182">
    <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(1862(a,1),12178(a,2,1))].">
      <j1 rule="para" parents="1862 12178"/>
    </justification>
  </clause>

  <clause id="12183">
    <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(76(a,1),12182(a,1,1,1,1,2))].">
      <j1 rule="para" parents="76 12182"/>
    </justification>
  </clause>

  <clause id="12185">
    <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(2897(a,1),12183(a,1,1,2))].">
      <j1 rule="para" parents="2897 12183"/>
    </justification>
  </clause>

  <clause id="12186">
    <literal><![CDATA[
      K(((x \ y) * (y \ x)) \ y,z) = K(R(y,y \ x,x \ y),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5139,a(flip),b,12185,a)].">
      <j1 rule="hyper" parents="63 5139 12185"/>
    </justification>
  </clause>

  <clause id="12188">
    <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(22(a,2),12186(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="22 12186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12189">
    <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(8402(a,1),12188(a,2,1,1))].">
      <j1 rule="para" parents="8402 12188"/>
    </justification>
  </clause>

  <clause id="12190">
    <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(333,a,6471,a(flip),b,12189,a),flip(a)].">
      <j1 rule="hyper" parents="333 6471 12189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12191">
    <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(22(a,2),12190(a,1,1,3))].">
      <j1 rule="para" parents="22 12190"/>
    </justification>
  </clause>

  <clause id="12192">
    <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(6370(a,1),12191(a,2,1))].">
      <j1 rule="para" parents="6370 12191"/>
    </justification>
  </clause>

  <clause id="12193">
    <literal><![CDATA[
      R(K(x * y,z),y,T(x,y)) = L(K(y * x,T(z,y)),y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,5560,a(flip),b,12192,a)].">
      <j1 rule="hyper" parents="63 5560 12192"/>
    </justification>
  </clause>

  <clause id="12194">
    <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(12193(a,1),6172(a,2,2))].">
      <j1 rule="para" parents="12193 6172"/>
    </justification>
  </clause>

  <clause id="12195">
    <literal><![CDATA[
      K(x,T(y,K(y * T(x,y),z))) * ((K(y * T(x,y),z) * y) * x) = (x * y) * L(K(y * x,T(z,y)),y,x)
    ]]></literal>
    <justification jstring="[para(12193(a,1),7726(a,2,2))].">
      <j1 rule="para" parents="12193 7726"/>
    </justification>
  </clause>

  <clause id="12196">
    <literal><![CDATA[
      (K(x * y,z) * ((x * y) / x)) * x = x * (y * K(y * x,T(z,y)))
    ]]></literal>
    <justification jstring="[hyper(333,a,97,a(flip),b,12194,a),flip(a)].">
      <j1 rule="hyper" parents="333 97 12194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12197">
    <literal><![CDATA[
      (K(x * y,z) * ((x * y) / x)) * x = x * (K(y * x,z) * y)
    ]]></literal>
    <justification jstring="[hyper(333,a,6398,a(flip),b,12196,a),flip(a)].">
      <j1 rule="hyper" parents="333 6398 12196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12198">
    <literal><![CDATA[
      (K(x * y,z) * y) * T(x,y) = x * (K(y * x,z) * y)
    ]]></literal>
    <justification jstring="[hyper(6157,a,12197,a)].">
      <j1 rule="hyper" parents="6157 12197"/>
    </justification>
  </clause>

  <clause id="12199">
    <literal><![CDATA[
      K(x * y,z) * x = x * K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(34,a,11360,a(flip),b,12198,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="34 11360 12198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12201">
    <literal><![CDATA[
      K(x * y,T(z,y)) = K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(6961,a,12199,a),flip(a)].">
      <j1 rule="hyper" parents="6961 12199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12202">
    <literal><![CDATA[
      K(x * y,T(z,x)) = K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(6496,a,12199,a)].">
      <j1 rule="hyper" parents="6496 12199"/>
    </justification>
  </clause>

  <clause id="12204">
    <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(12199(a,1),10001(a,1,2,2))].">
      <j1 rule="para" parents="12199 10001"/>
    </justification>
  </clause>

  <clause id="12205">
    <literal><![CDATA[
      K(x * y,(z * y) \ y) = K(y * x,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,7220,a(flip),b,12201,a)].">
      <j1 rule="hyper" parents="63 7220 12201"/>
    </justification>
  </clause>

  <clause id="12207">
    <literal><![CDATA[
      K((x \ y) * x,z) = K(y,T(z,x \ y))
    ]]></literal>
    <justification jstring="[para(10(a,1),12201(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 12201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12208">
    <literal><![CDATA[
      K(x * (y / x),z) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[para(12(a,1),12201(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12 12201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12209">
    <literal><![CDATA[
      K(x * y,z) * y = y * K(y * x,z)
    ]]></literal>
    <justification jstring="[para(12201(a,1),6390(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12201 6390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12210">
    <literal><![CDATA[
      K(x * y,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y * x,z) = u
    ]]></literal>
    <justification jstring="[para(12201(a,1),7064(a,1))].">
      <j1 rule="para" parents="12201 7064"/>
    </justification>
  </clause>

  <clause id="12211">
    <literal><![CDATA[
      K((x * y) * (z / (y * x)),u) = K(z * K(x,y),T(u,x * y))
    ]]></literal>
    <justification jstring="[para(10358(a,1),12201(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10358 12201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12212">
    <literal><![CDATA[
      K((x \ 1) * y,T(z,x)) = K(y * (x \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(7282,a,12202,a)].">
      <j1 rule="hyper" parents="7282 12202"/>
    </justification>
  </clause>

  <clause id="12213">
    <literal><![CDATA[
      K(x * y,(z * x) \ x) = K(y * x,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,7220,a(flip),b,12202,a)].">
      <j1 rule="hyper" parents="63 7220 12202"/>
    </justification>
  </clause>

  <clause id="12214">
    <literal><![CDATA[
      K((x \ y) * x,z) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[para(10(a,1),12202(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 12202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12215">
    <literal><![CDATA[
      K(x * y,T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y * x,z) = u
    ]]></literal>
    <justification jstring="[para(12202(a,1),7064(a,1))].">
      <j1 rule="para" parents="12202 7064"/>
    </justification>
  </clause>

  <clause id="12216">
    <literal><![CDATA[
      K(x * y,z) * T(x,y) = T(x,y) * K(y * x,z)
    ]]></literal>
    <justification jstring="[para(12202(a,1),7244(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12202 7244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12217">
    <literal><![CDATA[
      K(T(x,y) * y,z) = K(x * y,T(z,x))
    ]]></literal>
    <justification jstring="[para(3311(a,2),12208(a,1,1))].">
      <j1 rule="para" parents="3311 12208"/>
    </justification>
  </clause>

  <clause id="12218">
    <literal><![CDATA[
      K(x * K(y \ x,z),T(u,y)) = K(y * T(x / y,z),u)
    ]]></literal>
    <justification jstring="[para(5914(a,1),12208(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5914 12208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12219">
    <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(12208(a,1),7298(a,1,1,2))].">
      <j1 rule="para" parents="12208 7298"/>
    </justification>
  </clause>

  <clause id="12220">
    <literal><![CDATA[
      T(x,(y \ z) * y) = x / K(z,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(197,a,12214,a(flip),b,4205,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="197 12214 4205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12221">
    <literal><![CDATA[
      K((x \ y) * x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(12207(a,2),7277(a,1))].">
      <j1 rule="para" parents="12207 7277"/>
    </justification>
  </clause>

  <clause id="12222">
    <literal><![CDATA[
      K(T(x,y) * y,z) = K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,12202,a(flip),b,12217,a),flip(a)].">
      <j1 rule="hyper" parents="333 12202 12217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12223">
    <literal><![CDATA[
      ((T(x,y) * y) \ z) * K(y * x,(T(x,y) * y) \ z) = z / (T(x,y) * y)
    ]]></literal>
    <justification jstring="[hyper(126,a,12222,a(flip),b,4445,a)].">
      <j1 rule="hyper" parents="126 12222 4445"/>
    </justification>
  </clause>

  <clause id="12224">
    <literal><![CDATA[
      T(x,(y \ z) * y) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(333,a,6425,a(flip),b,12220,a),flip(a)].">
      <j1 rule="hyper" parents="333 6425 12220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12225">
    <literal><![CDATA[
      T(x,T(y * z,y)) = T(x,z * y)
    ]]></literal>
    <justification jstring="[para(9(a,1),12224(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 12224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12226">
    <literal><![CDATA[
      T(x,T(T(y * z,u),y)) = T(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[para(4104(a,1),12224(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4104 12224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12227">
    <literal><![CDATA[
      T(x,T(y * z,y)) = x * K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(333,a,4222,a(flip),b,12225,a),flip(a)].">
      <j1 rule="hyper" parents="333 4222 12225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12228">
    <literal><![CDATA[
      T(T(x,K(y,z)),z * y) = T(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,7038,a,b,12225,a)].">
      <j1 rule="hyper" parents="63 7038 12225"/>
    </justification>
  </clause>

  <clause id="12229">
    <literal><![CDATA[
      K(x,T(y * z,y)) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(4305,a,12227,a)].">
      <j1 rule="hyper" parents="4305 12227"/>
    </justification>
  </clause>

  <clause id="12230">
    <literal><![CDATA[
      T(K(x,y * z),y) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(34,a,6393,a,b,12227,a(flip))].">
      <j1 rule="hyper" parents="34 6393 12227"/>
    </justification>
  </clause>

  <clause id="12231">
    <literal><![CDATA[
      K(x,T((y \ 1) * z,y)) = K(x,z * (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(34,a,7262,a(flip),b,12227,a(flip))].">
      <j1 rule="hyper" parents="34 7262 12227"/>
    </justification>
  </clause>

  <clause id="12232">
    <literal><![CDATA[
      T(x,T(y * z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(12227(a,2),4285(a,1))].">
      <j1 rule="para" parents="12227 4285"/>
    </justification>
  </clause>

  <clause id="12233">
    <literal><![CDATA[
      K(x,T((1 / y) * z,y)) = K(x,z * (1 / y))
    ]]></literal>
    <justification jstring="[hyper(7284,a,12229,a)].">
      <j1 rule="hyper" parents="7284 12229"/>
    </justification>
  </clause>

  <clause id="12234">
    <literal><![CDATA[
      K(x,T(y * (z \ x),z)) = K(x,(z \ x) * y)
    ]]></literal>
    <justification jstring="[hyper(7283,a,12229,a)].">
      <j1 rule="hyper" parents="7283 12229"/>
    </justification>
  </clause>

  <clause id="12235">
    <literal><![CDATA[
      K(x / y,y * z) = K(y \ x,z * y)
    ]]></literal>
    <justification jstring="[hyper(7072,a,12229,a)].">
      <j1 rule="hyper" parents="7072 12229"/>
    </justification>
  </clause>

  <clause id="12236">
    <literal><![CDATA[
      K(T(x,y),z * y) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(7063,a,12229,a),flip(a)].">
      <j1 rule="hyper" parents="7063 12229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12237">
    <literal><![CDATA[
      K(x / y,z * x) = K(y \ x,x * z)
    ]]></literal>
    <justification jstring="[hyper(6700,a,12229,a),flip(a)].">
      <j1 rule="hyper" parents="6700 12229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12239">
    <literal><![CDATA[
      K(x,T(y * z,z)) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,7267,a,b,12229,a)].">
      <j1 rule="hyper" parents="63 7267 12229"/>
    </justification>
  </clause>

  <clause id="12240">
    <literal><![CDATA[
      K(x * y,z * x) = K(y * x,x * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,12202,a(flip),b,12229,a),flip(a)].">
      <j1 rule="hyper" parents="63 12202 12229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12241">
    <literal><![CDATA[
      K(x,(y \ z) * y) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(10(a,1),12229(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 12229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12242">
    <literal><![CDATA[
      K(x,T(y * z,z)) = K(x,T(y,z) * z)
    ]]></literal>
    <justification jstring="[para(111(a,1),12229(a,1,2,1))].">
      <j1 rule="para" parents="111 12229"/>
    </justification>
  </clause>

  <clause id="12243">
    <literal><![CDATA[
      K(x,y * z) * (z * x) = z * T(x,z * y)
    ]]></literal>
    <justification jstring="[para(12229(a,1),7717(a,1,1))].">
      <j1 rule="para" parents="12229 7717"/>
    </justification>
  </clause>

  <clause id="12244">
    <literal><![CDATA[
      K(x,K(y,(z \ 1) \ u)) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[para(12229(a,1),11482(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12229 11482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12246">
    <literal><![CDATA[
      K(x,K(y,T(x,z) * u)) = K(x,K(y,u * T(x,z)))
    ]]></literal>
    <justification jstring="[para(12230(a,1),4639(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12230 4639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12247">
    <literal><![CDATA[
      T(x,T(y * z,z)) = T(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(124,a,12239,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 12239 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12248">
    <literal><![CDATA[
      K(x,T(y,z \ y)) = K(x,(z \ y) * z)
    ]]></literal>
    <justification jstring="[para(10(a,1),12239(a,1,2,1))].">
      <j1 rule="para" parents="10 12239"/>
    </justification>
  </clause>

  <clause id="12249">
    <literal><![CDATA[
      K(x,y * (z / y)) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(12(a,1),12239(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12 12239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12250">
    <literal><![CDATA[
      T(K(x,y * z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(12239(a,1),6960(a,1,1))].">
      <j1 rule="para" parents="12239 6960"/>
    </justification>
  </clause>

  <clause id="12251">
    <literal><![CDATA[
      K(x / y,y * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z * y) = u
    ]]></literal>
    <justification jstring="[para(12239(a,1),7067(a,1))].">
      <j1 rule="para" parents="12239 7067"/>
    </justification>
  </clause>

  <clause id="12252">
    <literal><![CDATA[
      K(x,T(T(y * z,u),y)) = K(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[para(4104(a,1),12241(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4104 12241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12253">
    <literal><![CDATA[
      T(T(x,y * z),K(y * z,z)) = T(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(6193,a,12247,a)].">
      <j1 rule="hyper" parents="6193 12247"/>
    </justification>
  </clause>

  <clause id="12254">
    <literal><![CDATA[
      T(x,T(y * z,z \ 1)) = T(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,7264,a,b,12247,a)].">
      <j1 rule="hyper" parents="63 7264 12247"/>
    </justification>
  </clause>

  <clause id="12255">
    <literal><![CDATA[
      T(x,((y \ z) \ 1) * z) = T(x,z * ((z / y) \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,6528,a(flip),b,12247,a)].">
      <j1 rule="hyper" parents="63 6528 12247"/>
    </justification>
  </clause>

  <clause id="12256">
    <literal><![CDATA[
      T(x,y * (z / y)) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(12(a,1),12247(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12 12247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12257">
    <literal><![CDATA[
      T(x,T(T(y,z) * (y \ u),T((y \ u) \ u,z))) = T(x,T((y \ u) \ u,z) * (y \ u))
    ]]></literal>
    <justification jstring="[para(473(a,1),12247(a,1,2,1))].">
      <j1 rule="para" parents="473 12247"/>
    </justification>
  </clause>

  <clause id="12258">
    <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(12247(a,1),11714(a,1,2,1,1))].">
      <j1 rule="para" parents="12247 11714"/>
    </justification>
  </clause>

  <clause id="12259">
    <literal><![CDATA[
      K(x,T(y / (z \ 1),z)) = K(x,y / (T(z,y) \ 1))
    ]]></literal>
    <justification jstring="[para(8596(a,2),12249(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8596 12249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12260">
    <literal><![CDATA[
      T(x,T(T(y * z,u),z)) = T(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[para(4092(a,1),12256(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4092 12256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12261">
    <literal><![CDATA[
      T(x / (y * z),z * y) = T((y * z) \ x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(740,a,12228,a),flip(a)].">
      <j1 rule="hyper" parents="740 12228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12262">
    <literal><![CDATA[
      T(K(x,y) * z,x * y) = T(z * K(x,y),y * x)
    ]]></literal>
    <justification jstring="[para(6019(a,1),12228(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6019 12228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12263">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * z) = T(x,z * y)
    ]]></literal>
    <justification jstring="[para(6840(a,1),12228(a,1,1))].">
      <j1 rule="para" parents="6840 12228"/>
    </justification>
  </clause>

  <clause id="12264">
    <literal><![CDATA[
      T(T(x,y * z),K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(12228(a,1),6876(a,1,1))].">
      <j1 rule="para" parents="12228 6876"/>
    </justification>
  </clause>

  <clause id="12265">
    <literal><![CDATA[
      K(1 / x,x * T(y,z)) = K(x \ 1,T(y * x,z))
    ]]></literal>
    <justification jstring="[hyper(333,a,11354,a,b,12235,a),flip(a)].">
      <j1 rule="hyper" parents="333 11354 12235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12266">
    <literal><![CDATA[
      K(1 / x,y * x) = K(1 / x,x * y)
    ]]></literal>
    <justification jstring="[hyper(333,a,3333,a,b,12235,a)].">
      <j1 rule="hyper" parents="333 3333 12235"/>
    </justification>
  </clause>

  <clause id="12267">
    <literal><![CDATA[
      K(x,T(y,z) * z) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,12239,a(flip),b,12242,a),flip(a)].">
      <j1 rule="hyper" parents="63 12239 12242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12268">
    <literal><![CDATA[
      T(x,T(y,z) * z) = T(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(124,a,12267,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 12267 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12269">
    <literal><![CDATA[
      T(x,T(y,z) * z) = x * K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(126,a,12267,a(flip),b,4215,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="126 12267 4215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12270">
    <literal><![CDATA[
      K(x,y * (z * K(y,z))) = K(x,z * y)
    ]]></literal>
    <justification jstring="[para(4239(a,1),12267(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4239 12267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12271">
    <literal><![CDATA[
      T(x,T(y \ z,u) * y) = T(x,y * T(z / y,u))
    ]]></literal>
    <justification jstring="[para(259(a,1),12268(a,1,2,1))].">
      <j1 rule="para" parents="259 12268"/>
    </justification>
  </clause>

  <clause id="12272">
    <literal><![CDATA[
      K(x,(y \ z) * y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y)) = u
    ]]></literal>
    <justification jstring="[para(12248(a,1),7276(a,1))].">
      <j1 rule="para" parents="12248 7276"/>
    </justification>
  </clause>

  <clause id="12273">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * z) = x * K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(333,a,4222,a(flip),b,12263,a),flip(a)].">
      <j1 rule="hyper" parents="333 4222 12263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12274">
    <literal><![CDATA[
      x * K(1 / y,z * y) = x * K(1 / y,y * z)
    ]]></literal>
    <justification jstring="[hyper(126,a,12266,a,b,9,a)].">
      <j1 rule="hyper" parents="126 12266 9"/>
    </justification>
  </clause>

  <clause id="12275">
    <literal><![CDATA[
      T(x,T(y,z) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(12269(a,2),4285(a,1))].">
      <j1 rule="para" parents="12269 4285"/>
    </justification>
  </clause>

  <clause id="12276">
    <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(10107(a,1),12221(a,1,1,1))].">
      <j1 rule="para" parents="10107 12221"/>
    </justification>
  </clause>

  <clause id="12277">
    <literal><![CDATA[
      T(T(x,K(y,z)),z * y) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(7038(a,2),12232(a,1))].">
      <j1 rule="para" parents="7038 12232"/>
    </justification>
  </clause>

  <clause id="12278">
    <literal><![CDATA[
      K(x,T(y * z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(6365(a,2),12250(a,1))].">
      <j1 rule="para" parents="6365 12250"/>
    </justification>
  </clause>

  <clause id="12279">
    <literal><![CDATA[
      T(x,T(y \ z,u) * y) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y * T(z / y,u)) = w
    ]]></literal>
    <justification jstring="[para(259(a,1),12275(a,1,2,1))].">
      <j1 rule="para" parents="259 12275"/>
    </justification>
  </clause>

  <clause id="12280">
    <literal><![CDATA[
      T(x,T(y,((z \ 1) * u) * w) * (((1 / z) * u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,(((1 / z) * u) * w) * y) = v5
    ]]></literal>
    <justification jstring="[para(3182(a,1),12275(a,1,2,1))].">
      <j1 rule="para" parents="3182 12275"/>
    </justification>
  </clause>

  <clause id="12281">
    <literal><![CDATA[
      K(x,T(y * z,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(7267(a,2),12278(a,1))].">
      <j1 rule="para" parents="7267 12278"/>
    </justification>
  </clause>

  <clause id="12282">
    <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(668(a,1),12281(a,1,2,1))].">
      <j1 rule="para" parents="668 12281"/>
    </justification>
  </clause>

  <clause id="12283">
    <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(10085(a,1),12281(a,1,2,1))].">
      <j1 rule="para" parents="10085 12281"/>
    </justification>
  </clause>

  <clause id="12284">
    <literal><![CDATA[
      K(x,T(y,z) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(12242(a,1),12281(a,1))].">
      <j1 rule="para" parents="12242 12281"/>
    </justification>
  </clause>

  <clause id="12285">
    <literal><![CDATA[
      K(x,T(y,z * u) * T(u * z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(u * z,u) * y) = w
    ]]></literal>
    <justification jstring="[para(12225(a,1),12284(a,1,2,1))].">
      <j1 rule="para" parents="12225 12284"/>
    </justification>
  </clause>

  <clause id="12286">
    <literal><![CDATA[
      K(T(x * y,(z * y) \ y) \ ((x * y) * u),w) = K(K(y * x,z \ 1) \ u,w)
    ]]></literal>
    <justification jstring="[para(12205(a,1),4685(a,2,1,1))].">
      <j1 rule="para" parents="12205 4685"/>
    </justification>
  </clause>

  <clause id="12287">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,x / y) = K(z * ((x \ y) \ 1),x / y)
    ]]></literal>
    <justification jstring="[hyper(5851,a,12212,a)].">
      <j1 rule="hyper" parents="5851 12212"/>
    </justification>
  </clause>

  <clause id="12288">
    <literal><![CDATA[
      T(x,y) * K(y * x,y \ 1) = (x * y) * (x / (y * x))
    ]]></literal>
    <justification jstring="[para(12213(a,1),5541(a,1,2))].">
      <j1 rule="para" parents="12213 5541"/>
    </justification>
  </clause>

  <clause id="12289">
    <literal><![CDATA[
      T(x,T(T(y * z,y),u)) = T(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[para(23(a,1),12226(a,1,2))].">
      <j1 rule="para" parents="23 12226"/>
    </justification>
  </clause>

  <clause id="12290">
    <literal><![CDATA[
      K(x,T((y \ 1) * (z * y),y)) = R(K(x,z),y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(333,a,11520,a(flip),b,12231,a),flip(a)].">
      <j1 rule="hyper" parents="333 11520 12231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12291">
    <literal><![CDATA[
      K(x \ y,(1 / (y / x)) * z) = K(x \ y,z * (1 / (y / x)))
    ]]></literal>
    <justification jstring="[hyper(7061,a,12233,a)].">
      <j1 rule="hyper" parents="7061 12233"/>
    </justification>
  </clause>

  <clause id="12292">
    <literal><![CDATA[
      K(x,(y \ x) * R(y,z,u)) = K(x,x * (y \ R(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,10693,a(flip),b,12234,a),flip(a)].">
      <j1 rule="hyper" parents="63 10693 12234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12293">
    <literal><![CDATA[
      K(x,K(y,z \ (u \ 1))) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(7195,a,12244,a)].">
      <j1 rule="hyper" parents="7195 12244"/>
    </justification>
  </clause>

  <clause id="12294">
    <literal><![CDATA[
      x \ T(x * y,K(z,u)) = y * K(z,K(u,x * y))
    ]]></literal>
    <justification jstring="[para(12244(a,1),6808(a,2,2))].">
      <j1 rule="para" parents="12244 6808"/>
    </justification>
  </clause>

  <clause id="12295">
    <literal><![CDATA[
      K(x / y,T(z * y,u)) = K(y \ x,T(y * z,u))
    ]]></literal>
    <justification jstring="[hyper(7067,a,12252,a),flip(a)].">
      <j1 rule="hyper" parents="7067 12252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12296">
    <literal><![CDATA[
      T(x,T(T(y * z,z),u)) = T(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[para(23(a,1),12260(a,1,2))].">
      <j1 rule="para" parents="23 12260"/>
    </justification>
  </clause>

  <clause id="12297">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(12273(a,2),4285(a,1))].">
      <j1 rule="para" parents="12273 4285"/>
    </justification>
  </clause>

  <clause id="12298">
    <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(6998(a,1),12289(a,1,2,1,1))].">
      <j1 rule="para" parents="6998 12289"/>
    </justification>
  </clause>

  <clause id="12299">
    <literal><![CDATA[
      T(x,K(y,z \ (u \ 1))) = T(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(124,a,12293,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 12293 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12300">
    <literal><![CDATA[
      K(x,K(y \ (z * u),z * u)) = K(x,K(z * u,(z \ y) \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,9833,a(flip),b,12293,a),flip(a)].">
      <j1 rule="hyper" parents="63 9833 12293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12301">
    <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(471(a,1),12296(a,1,2,1,1))].">
      <j1 rule="para" parents="471 12296"/>
    </justification>
  </clause>

  <clause id="12302">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),y * (u \ (z \ 1))) = T(x,(u \ (z \ 1)) * y)
    ]]></literal>
    <justification jstring="[para(12299(a,1),12263(a,1,1))].">
      <j1 rule="para" parents="12299 12263"/>
    </justification>
  </clause>

  <clause id="12304">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),y * (u \ (z \ 1))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(u \ (z \ 1)) * y) = w
    ]]></literal>
    <justification jstring="[para(12299(a,1),12297(a,1,1))].">
      <j1 rule="para" parents="12299 12297"/>
    </justification>
  </clause>

  <clause id="12305">
    <literal><![CDATA[
      K(x,K(y,z * T(x,u))) = K(x,K(y,1 / z))
    ]]></literal>
    <justification jstring="[hyper(7525,a,12246,a),flip(a)].">
      <j1 rule="hyper" parents="7525 12246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12306">
    <literal><![CDATA[
      K(x,K(y,1 / (z / T(x,u)))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(12(a,1),12305(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 12305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12307">
    <literal><![CDATA[
      K(x,K(y,T(x,z) / u)) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(5058(a,1),12306(a,1,2))].">
      <j1 rule="para" parents="5058 12306"/>
    </justification>
  </clause>

  <clause id="12308">
    <literal><![CDATA[
      (T(x,y) / z) * K(x,K(u,z)) = T(T(x,y) / z,K(u,x))
    ]]></literal>
    <justification jstring="[para(12307(a,1),6766(a,1,2))].">
      <j1 rule="para" parents="12307 6766"/>
    </justification>
  </clause>

  <clause id="12309">
    <literal><![CDATA[
      K(x,y / (T(z,y) \ 1)) = K(x,(z \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,7269,a(flip),b,12259,a),flip(a)].">
      <j1 rule="hyper" parents="63 7269 12259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12310">
    <literal><![CDATA[
      K(x,(y / z) / (z \ 1)) = K(x,(z \ 1) \ (z \ y))
    ]]></literal>
    <justification jstring="[para(8473(a,1),12309(a,1,2))].">
      <j1 rule="para" parents="8473 12309"/>
    </justification>
  </clause>

  <clause id="12311">
    <literal><![CDATA[
      K(T(K(x,y) * z,x * y),u) = K(z * K(x,y),T(u,y * x))
    ]]></literal>
    <justification jstring="[para(12262(a,2),6370(a,1,1))].">
      <j1 rule="para" parents="12262 6370"/>
    </justification>
  </clause>

  <clause id="12312">
    <literal><![CDATA[
      K(1 / x,T(y * x,z)) = K(1 / x,x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(333,a,3333,a,b,12265,a)].">
      <j1 rule="hyper" parents="333 3333 12265"/>
    </justification>
  </clause>

  <clause id="12313">
    <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(4082(a,1),12271(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="4082 12271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12314">
    <literal><![CDATA[
      x * K(1 / (y / z),(y / z) * u) = x * K(z / y,u * (y / z))
    ]]></literal>
    <justification jstring="[para(4968(a,1),12274(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4968 12274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12316">
    <literal><![CDATA[
      L(K(x,K(y,z * L(u \ 1,u,w))),(w * u) \ w,w * u) = w \ ((w * u) * (z \ T(z * L(u \ 1,u,w),K(x,y))))
    ]]></literal>
    <justification jstring="[para(12294(a,2),755(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12294 755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12317">
    <literal><![CDATA[
      K(x,(y \ 1) \ (y \ K(z,u))) = K(z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,11502,a(flip),b,12310,a),flip(a)].">
      <j1 rule="hyper" parents="63 11502 12310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12318">
    <literal><![CDATA[
      (x \ K(y,z)) \ (x \ K(y,T(z,u))) = K(y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,9182,a,b,12317,a)].">
      <j1 rule="hyper" parents="63 9182 12317"/>
    </justification>
  </clause>

  <clause id="12319">
    <literal><![CDATA[
      (x \ K(y,z)) * K(y,K(z,u)) = x \ K(y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(126,a,12317,a(flip),b,9182,a)].">
      <j1 rule="hyper" parents="126 12317 9182"/>
    </justification>
  </clause>

  <clause id="12320">
    <literal><![CDATA[
      T(1 / x,T(y * x,z)) = T(1 / x,x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(124,a,12312,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 12312 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12321">
    <literal><![CDATA[
      K(1 / x,T(y / (1 / x),z)) = K(1 / x,x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,10499,a,b,12312,a)].">
      <j1 rule="hyper" parents="63 10499 12312"/>
    </justification>
  </clause>

  <clause id="12322">
    <literal><![CDATA[
      K(1 / (x / y),(x / y) * T(z,x)) = K(1 / (y \ x),z * (x / y))
    ]]></literal>
    <justification jstring="[hyper(63,a,8593,a(flip),b,12312,a),flip(a)].">
      <j1 rule="hyper" parents="63 8593 12312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12326">
    <literal><![CDATA[
      (x \ K(y,z)) * K(z,K(y,u)) = x \ K(y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(126,a,6785,a,b,12318,a)].">
      <j1 rule="hyper" parents="126 6785 12318"/>
    </justification>
  </clause>

  <clause id="12327">
    <literal><![CDATA[
      R(K(x,y),z,z \ 1) = K(x,L(y,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,7960,a(flip),b,12290,a),flip(a)].">
      <j1 rule="hyper" parents="63 7960 12290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12328">
    <literal><![CDATA[
      K(x,R(y,z,z \ 1)) = K(x,L(y,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(11586,a,12327,a)].">
      <j1 rule="hyper" parents="11586 12327"/>
    </justification>
  </clause>

  <clause id="12329">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,R(y,z,z \ 1)) = u
    ]]></literal>
    <justification jstring="[para(12327(a,1),11586(a,1))].">
      <j1 rule="para" parents="12327 11586"/>
    </justification>
  </clause>

  <clause id="12330">
    <literal><![CDATA[
      K(x,L(y / z,z,z \ 1)) = K(x,y * (z \ 1))
    ]]></literal>
    <justification jstring="[para(554(a,1),12328(a,1,2)),flip(a)].">
      <j1 rule="para" parents="554 12328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12331">
    <literal><![CDATA[
      K(x,K(y,L(z,u,u \ 1))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(12328(a,1),11432(a,1,2))].">
      <j1 rule="para" parents="12328 11432"/>
    </justification>
  </clause>

  <clause id="12332">
    <literal><![CDATA[
      K(x,K(y,L(z,u \ 1,u))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(3144(a,1),12331(a,1,2,2))].">
      <j1 rule="para" parents="3144 12331"/>
    </justification>
  </clause>

  <clause id="12333">
    <literal><![CDATA[
      (x / y) \ T(x,K(z,u)) = y * K(x,K(z,u))
    ]]></literal>
    <justification jstring="[para(12332(a,1),11493(a,2,2))].">
      <j1 rule="para" parents="12332 11493"/>
    </justification>
  </clause>

  <clause id="12334">
    <literal><![CDATA[
      (x \ y) * K(y,K(z,u)) = x \ T(y,K(z,u))
    ]]></literal>
    <justification jstring="[para(76(a,1),12333(a,1,1)),flip(a)].">
      <j1 rule="para" parents="76 12333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12335">
    <literal><![CDATA[
      (x / y) \ T(x,K(z,u)) = y * K(z,K(u,x))
    ]]></literal>
    <justification jstring="[para(6788(a,2),12333(a,2,2))].">
      <j1 rule="para" parents="6788 12333"/>
    </justification>
  </clause>

  <clause id="12337">
    <literal><![CDATA[
      L(K(x,y / z),z,z \ 1) = K(x,y * (z \ 1))
    ]]></literal>
    <justification jstring="[hyper(10893,a,12330,a)].">
      <j1 rule="hyper" parents="10893 12330"/>
    </justification>
  </clause>

  <clause id="12338">
    <literal><![CDATA[
      K(x,x * (y \ R(y,z,u))) = a(K(x / y,y),z * y,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,12167,a(flip),b,12292,a),flip(a)].">
      <j1 rule="hyper" parents="63 12167 12292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12339">
    <literal><![CDATA[
      T(x,y) / T(z,K(x,u)) = T(T(x,y) / z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(6782,a,12308,a)].">
      <j1 rule="hyper" parents="6782 12308"/>
    </justification>
  </clause>

  <clause id="12340">
    <literal><![CDATA[
      T(x,y) / T(z,K(x,u)) = T(T(x,y) / z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(333,a,6840,a,b,12339,a),flip(a)].">
      <j1 rule="hyper" parents="333 6840 12339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12341">
    <literal><![CDATA[
      T(T(K(x,y) * z,K(x,y)) / u,K(K(x,y) * z,w)) = (z * K(x,y)) / T(u,K(K(x,y) * z,w))
    ]]></literal>
    <justification jstring="[para(6019(a,1),12340(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6019 12340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12342">
    <literal><![CDATA[
      K(x,x * (y \ R(y,z,u))) = a(K(y \ x,y),z * y,u)
    ]]></literal>
    <justification jstring="[para(4375(a,1),12338(a,2,1))].">
      <j1 rule="para" parents="4375 12338"/>
    </justification>
  </clause>

  <clause id="12343">
    <literal><![CDATA[
      K(x,x * (y \ R(y,z,u))) = a(K(x,y),z * y,u)
    ]]></literal>
    <justification jstring="[hyper(333,a,11949,a(flip),b,12342,a),flip(a)].">
      <j1 rule="hyper" parents="333 11949 12342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12344">
    <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(63,a,5051,a,b,12343,a)].">
      <j1 rule="hyper" parents="63 5051 12343"/>
    </justification>
  </clause>

  <clause id="12345">
    <literal><![CDATA[
      (x \ T(x * (y \ R(y,z,u)),x)) \ (x \ (x * (y \ R(y,z,u)))) = a(K(x,y),z * y,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,6004,a(flip),b,12343,a)].">
      <j1 rule="hyper" parents="63 6004 12343"/>
    </justification>
  </clause>

  <clause id="12348">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,x / y) = K((x \ y) \ z,x / y)
    ]]></literal>
    <justification jstring="[hyper(333,a,8849,a(flip),b,12287,a),flip(a)].">
      <j1 rule="hyper" parents="333 8849 12287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12349">
    <literal><![CDATA[
      K((x \ y) \ z,x / y) * K((x \ y) \ 1,T(z,T(x,y))) = a((x \ y) \ 1,z,(x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(12348(a,1),11248(a,1,1))].">
      <j1 rule="para" parents="12348 11248"/>
    </justification>
  </clause>

  <clause id="12350">
    <literal><![CDATA[
      K(x \ y,(1 / (y / x)) * z) = K(x \ y,z / (y / x))
    ]]></literal>
    <justification jstring="[hyper(333,a,8647,a(flip),b,12291,a),flip(a)].">
      <j1 rule="hyper" parents="333 8647 12291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12351">
    <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(3937(a,2),12350(a,1,1))].">
      <j1 rule="para" parents="3937 12350"/>
    </justification>
  </clause>

  <clause id="12352">
    <literal><![CDATA[
      K(x,K(y * z,(y \ u) \ z)) = K(x,K(u,y * z))
    ]]></literal>
    <justification jstring="[hyper(7146,a,12300,a),flip(a)].">
      <j1 rule="hyper" parents="7146 12300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12353">
    <literal><![CDATA[
      K(x,K(y * z,z \ (y \ u))) = K(x,K(u,y * z))
    ]]></literal>
    <justification jstring="[hyper(7195,a,12352,a)].">
      <j1 rule="hyper" parents="7195 12352"/>
    </justification>
  </clause>

  <clause id="12354">
    <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(4638(a,2),12353(a,2,2))].">
      <j1 rule="para" parents="4638 12353"/>
    </justification>
  </clause>

  <clause id="12355">
    <literal><![CDATA[
      T(x,T(T(y \ z,u) * y,w)) = T(x,T(y * T(z / y,u),w))
    ]]></literal>
    <justification jstring="[hyper(63,a,12289,a(flip),b,12301,a)].">
      <j1 rule="hyper" parents="63 12289 12301"/>
    </justification>
  </clause>

  <clause id="12356">
    <literal><![CDATA[
      T(x,T(y * T((y * z) / y,u),w)) = T(x,T(T(z,u) * y,w))
    ]]></literal>
    <justification jstring="[para(9(a,1),12355(a,1,2,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 12355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12357">
    <literal><![CDATA[
      x * K(y / z,(z / y) * u) = x * K(y / z,u * (z / y))
    ]]></literal>
    <justification jstring="[para(4968(a,1),12314(a,1,2))].">
      <j1 rule="para" parents="4968 12314"/>
    </justification>
  </clause>

  <clause id="12358">
    <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(333,a,7289,a(flip),b,12357,a),flip(a)].">
      <j1 rule="hyper" parents="333 7289 12357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12359">
    <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(12357(a,1),44(a,2))].">
      <j1 rule="para" parents="12357 44"/>
    </justification>
  </clause>

  <clause id="12360">
    <literal><![CDATA[
      K(1 / (x \ y),z * (y / x)) = K(x / y,(y / x) * T(z,y))
    ]]></literal>
    <justification jstring="[hyper(5091,a,12322,a),flip(a)].">
      <j1 rule="hyper" parents="5091 12322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12361">
    <literal><![CDATA[
      K(x / y,(y / x) * T(z,y)) = K(y \ x,z * (y / x))
    ]]></literal>
    <justification jstring="[hyper(5960,a,12360,a),flip(a)].">
      <j1 rule="hyper" parents="5960 12360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12362">
    <literal><![CDATA[
      ((x * y) * ((T(y,x) * x) \ z)) / (x * y) = z / (T(y,x) * x)
    ]]></literal>
    <justification jstring="[hyper(4446,a,12223,a)].">
      <j1 rule="hyper" parents="4446 12223"/>
    </justification>
  </clause>

  <clause id="12363">
    <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(471(a,1),12313(a,2,2))].">
      <j1 rule="para" parents="471 12313"/>
    </justification>
  </clause>

  <clause id="12366">
    <literal><![CDATA[
      T(x \ R(x,y,z),u) \ (u \ (u * (x \ R(x,y,z)))) = a(K(u,x),y * x,z)
    ]]></literal>
    <justification jstring="[para(12147(a,1),12345(a,1,1))].">
      <j1 rule="para" parents="12147 12345"/>
    </justification>
  </clause>

  <clause id="12367">
    <literal><![CDATA[
      T(x \ R(x,y,z),u) \ (x \ R(x,y,z)) = a(K(u,x),y * x,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),12366(a,1,2))].">
      <j1 rule="para" parents="9 12366"/>
    </justification>
  </clause>

  <clause id="12368">
    <literal><![CDATA[
      a(K(x,y),z * y,u) = K(x,y \ R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(4249,a,12367,a),flip(a)].">
      <j1 rule="hyper" parents="4249 12367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12370">
    <literal><![CDATA[
      a(K(x,y),z * y,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ R(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(12367(a,1),4249(a,1))].">
      <j1 rule="para" parents="12367 4249"/>
    </justification>
  </clause>

  <clause id="12371">
    <literal><![CDATA[
      a(K(x,K(y,z)),u * y,w) = K(x,K(z,y \ R(y,u,w)))
    ]]></literal>
    <justification jstring="[para(12368(a,1),11764(a,2,2))].">
      <j1 rule="para" parents="12368 11764"/>
    </justification>
  </clause>

  <clause id="12372">
    <literal><![CDATA[
      K(x,K(y,z \ R(z,u,w))) = a(K(z,K(x,y)),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,11767,a(flip),b,12371,a),flip(a)].">
      <j1 rule="hyper" parents="63 11767 12371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12373">
    <literal><![CDATA[
      K(x,K(y,R(z,u,w) * (z \ y))) = a(K(z,K(x,y)),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,10392,a,b,12372,a)].">
      <j1 rule="hyper" parents="63 10392 12372"/>
    </justification>
  </clause>

  <clause id="12374">
    <literal><![CDATA[
      K(x,K(y,R(z,u,w) * (z \ y))) = a(K(x,K(y,z)),u,w)
    ]]></literal>
    <justification jstring="[para(6788(a,2),12373(a,2,1))].">
      <j1 rule="para" parents="6788 12373"/>
    </justification>
  </clause>

  <clause id="12375">
    <literal><![CDATA[
      K(x,K(y,R(z,u,w) \ z)) = a(K(x,K(y,z)),u,w)
    ]]></literal>
    <justification jstring="[hyper(10469,a,12374,a)].">
      <j1 rule="hyper" parents="10469 12374"/>
    </justification>
  </clause>

  <clause id="12376">
    <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(63,a,8749,a(flip),b,12375,a)].">
      <j1 rule="hyper" parents="63 8749 12375"/>
    </justification>
  </clause>

  <clause id="12377">
    <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(6800(a,1),12376(a,2,1))].">
      <j1 rule="para" parents="6800 12376"/>
    </justification>
  </clause>

  <clause id="12378">
    <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(7819(a,1),12377(a,2,1))].">
      <j1 rule="para" parents="7819 12377"/>
    </justification>
  </clause>

  <clause id="12379">
    <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(8765,a,12378,a)].">
      <j1 rule="hyper" parents="8765 12378"/>
    </justification>
  </clause>

  <clause id="12382">
    <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(63,a,8965,a(flip),b,12379,a)].">
      <j1 rule="hyper" parents="63 8965 12379"/>
    </justification>
  </clause>

  <clause id="12384">
    <literal><![CDATA[
      T(x,T(y,((z \ 1) * u) * w) * (((z \ 1) * u) * w)) = T(x,(((1 / z) * u) * w) * y)
    ]]></literal>
    <justification jstring="[hyper(12280,a,5593,a),flip(a)].">
      <j1 rule="hyper" parents="12280 5593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12385">
    <literal><![CDATA[
      T(x,(((1 / y) * z) * u) * w) = T(x,(((y \ 1) * z) * u) * w)
    ]]></literal>
    <justification jstring="[hyper(12275,a,12384,a),flip(a)].">
      <j1 rule="hyper" parents="12275 12384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12386">
    <literal><![CDATA[
      K((x \ y) \ z,x / y) * K(y \ x,T(z,T(x,y))) = a((x \ y) \ 1,z,(x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(5852(a,1),12349(a,1,2))].">
      <j1 rule="para" parents="5852 12349"/>
    </justification>
  </clause>

  <clause id="12387">
    <literal><![CDATA[
      T(T(K(x,y) * z,K(x,y)) / u,K(K(x,y) * z,w)) = (z * K(x,y)) / T(u,K(w,K(x,y) * z))
    ]]></literal>
    <justification jstring="[para(6840(a,1),12341(a,2,2))].">
      <j1 rule="para" parents="6840 12341"/>
    </justification>
  </clause>

  <clause id="12388">
    <literal><![CDATA[
      K(x,T(y,K(y * T(x,y),z))) * ((K(y * T(x,y),z) * y) * x) = x * (y * K(y * x,T(z,y)))
    ]]></literal>
    <justification jstring="[hyper(333,a,97,a(flip),b,12195,a),flip(a)].">
      <j1 rule="hyper" parents="333 97 12195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12389">
    <literal><![CDATA[
      K(x,T(y,K(y * T(x,y),z))) * ((K(y * T(x,y),z) * y) * x) = x * (K(y * x,z) * y)
    ]]></literal>
    <justification jstring="[hyper(333,a,6398,a(flip),b,12388,a),flip(a)].">
      <j1 rule="hyper" parents="333 6398 12388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12390">
    <literal><![CDATA[
      K(x,T(y,K(x * y,z))) * ((K(y * T(x,y),z) * y) * x) = x * (K(y * x,z) * y)
    ]]></literal>
    <justification jstring="[para(111(a,1),12389(a,1,1,2,2,1))].">
      <j1 rule="para" parents="111 12389"/>
    </justification>
  </clause>

  <clause id="12391">
    <literal><![CDATA[
      K(x,T(y,K(x,z))) * ((K(y * T(x,y),z) * y) * x) = x * (K(y * x,z) * y)
    ]]></literal>
    <justification jstring="[para(7039(a,1),12390(a,1,1,2))].">
      <j1 rule="para" parents="7039 12390"/>
    </justification>
  </clause>

  <clause id="12392">
    <literal><![CDATA[
      K(x,y) * ((K(y * T(x,y),z) * y) * x) = x * (K(y * x,z) * y)
    ]]></literal>
    <justification jstring="[para(6384(a,1),12391(a,1,1))].">
      <j1 rule="para" parents="6384 12391"/>
    </justification>
  </clause>

  <clause id="12393">
    <literal><![CDATA[
      K(x,y) * ((K(x * y,z) * y) * x) = x * (K(y * x,z) * y)
    ]]></literal>
    <justification jstring="[para(111(a,1),12392(a,1,2,1,1,1))].">
      <j1 rule="para" parents="111 12392"/>
    </justification>
  </clause>

  <clause id="12395">
    <literal><![CDATA[
      L(T(K(x * y,z) * y,x),x,K(x,y)) = T(x,y) \ (x * (K(y * x,z) * y))
    ]]></literal>
    <justification jstring="[para(12393(a,1),4347(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12393 4347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12396">
    <literal><![CDATA[
      L(T(K(x * y,z) * y,x),x,K(x,y)) = K(y,x) * (K(y * x,z) * y)
    ]]></literal>
    <justification jstring="[hyper(333,a,4550,a(flip),b,12395,a),flip(a)].">
      <j1 rule="hyper" parents="333 4550 12395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12397">
    <literal><![CDATA[
      K(x,y) * (K(x * y,z) * x) = T(K(y * x,z) * x,y)
    ]]></literal>
    <justification jstring="[hyper(3567,a,12396,a),flip(a)].">
      <j1 rule="hyper" parents="3567 12396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12398">
    <literal><![CDATA[
      T(K(x * y,z) * y,x) = K(y * x,z) * T(y,x)
    ]]></literal>
    <justification jstring="[hyper(8311,a,12397,a),flip(a)].">
      <j1 rule="hyper" parents="8311 12397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12400">
    <literal><![CDATA[
      T(x * K(x * y,z),y) = K(x * y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(12209(a,1),12398(a,1,1))].">
      <j1 rule="para" parents="12209 12398"/>
    </justification>
  </clause>

  <clause id="12401">
    <literal><![CDATA[
      T(x * K(x * y,z),y) = T(x,y) * K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,12216,a(flip),b,12400,a),flip(a)].">
      <j1 rule="hyper" parents="333 12216 12400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12402">
    <literal><![CDATA[
      T(x * K(x * y,y \ 1),y) = (x * y) * (x / (y * x))
    ]]></literal>
    <justification jstring="[hyper(333,a,12288,a(flip),b,12401,a),flip(a)].">
      <j1 rule="hyper" parents="333 12288 12401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12403">
    <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(18(a,2),12354(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="18 12354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12404">
    <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(333,a,11545,a(flip),b,12403,a),flip(a)].">
      <j1 rule="hyper" parents="333 11545 12403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12405">
    <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(333,a,11253,a(flip),b,12404,a),flip(a)].">
      <j1 rule="hyper" parents="333 11253 12404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12406">
    <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(7051,a,12405,a)].">
      <j1 rule="hyper" parents="7051 12405"/>
    </justification>
  </clause>

  <clause id="12407">
    <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(12405(a,1),7051(a,1))].">
      <j1 rule="para" parents="12405 7051"/>
    </justification>
  </clause>

  <clause id="12408">
    <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(63,a,6873,a,b,12406,a)].">
      <j1 rule="hyper" parents="63 6873 12406"/>
    </justification>
  </clause>

  <clause id="12409">
    <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(63,a,12149,a,b,12408,a)].">
      <j1 rule="hyper" parents="63 12149 12408"/>
    </justification>
  </clause>

  <clause id="12410">
    <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(8021,a,12409,a)].">
      <j1 rule="hyper" parents="8021 12409"/>
    </justification>
  </clause>

  <clause id="12411">
    <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(63,a,12382,a(flip),b,12410,a)].">
      <j1 rule="hyper" parents="63 12382 12410"/>
    </justification>
  </clause>

  <clause id="12412">
    <literal><![CDATA[
      K(x,K(y * z,a(y,z,u))) = a(K(y,K(x,z * u)),z,u)
    ]]></literal>
    <justification jstring="[para(7954(a,1),12411(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7954 12411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12413">
    <literal><![CDATA[
      K(x,K(y * z,a(y,z,u))) = 1
    ]]></literal>
    <justification jstring="[hyper(333,a,11477,a(flip),b,12412,a),flip(a)].">
      <j1 rule="hyper" parents="333 11477 12412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12414">
    <literal><![CDATA[
      K(x,K(a(y,z,u),y * (z * u))) = 1
    ]]></literal>
    <justification jstring="[hyper(12407,a,12413,a)].">
      <j1 rule="hyper" parents="12407 12413"/>
    </justification>
  </clause>

  <clause id="12417">
    <literal><![CDATA[
      K(x,((y * z) * u) / (y * (z * u))) = K(x,a(y,z,u)) * 1
    ]]></literal>
    <justification jstring="[para(12414(a,1),8509(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12414 8509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12418">
    <literal><![CDATA[
      K(x,((y * z) * u) / (y * (z * u))) = K(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(333,a,8,a(flip),b,12417,a),flip(a)].">
      <j1 rule="hyper" parents="333 8 12417"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12420">
    <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(63,a,8068,a,b,12418,a)].">
      <j1 rule="hyper" parents="63 8068 12418"/>
    </justification>
  </clause>

  <clause id="12421">
    <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(12368(a,2),12420(a,1,1))].">
      <j1 rule="para" parents="12368 12420"/>
    </justification>
  </clause>

  <clause id="12422">
    <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(63,a,12031,a,b,12421,a)].">
      <j1 rule="hyper" parents="63 12031 12421"/>
    </justification>
  </clause>

  <clause id="12423">
    <literal><![CDATA[
      a(K(x,y),z * y,u) = K(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,12170,a(flip),b,12422,a)].">
      <j1 rule="hyper" parents="63 12170 12422"/>
    </justification>
  </clause>

  <clause id="12424">
    <literal><![CDATA[
      K(x,y \ R(y,z,u)) = K(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(12370,a,12423,a)].">
      <j1 rule="hyper" parents="12370 12423"/>
    </justification>
  </clause>

  <clause id="12426">
    <literal><![CDATA[
      a(K(x,y),z,u) = K(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,11741,a(flip),b,12423,a)].">
      <j1 rule="hyper" parents="63 11741 12423"/>
    </justification>
  </clause>

  <clause id="12428">
    <literal><![CDATA[
      T(x,y \ R(y,z,u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(124,a,12424,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 12424 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12429">
    <literal><![CDATA[
      T(x,a(x,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,3021,a(flip),b,12428,a),flip(a)].">
      <j1 rule="hyper" parents="63 3021 12428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12430">
    <literal><![CDATA[
      T(x \ 1,a(x,y,z)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,1353,a(flip),b,12428,a),flip(a)].">
      <j1 rule="hyper" parents="63 1353 12428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12431">
    <literal><![CDATA[
      T(a(x,y,z),x) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(54,a,12429,a)].">
      <j1 rule="hyper" parents="54 12429"/>
    </justification>
  </clause>

  <clause id="12432">
    <literal><![CDATA[
      a(x,y,z) * x = x * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(126,a,12429,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="126 12429 22"/>
    </justification>
  </clause>

  <clause id="12434">
    <literal><![CDATA[
      a(x,y,z) = (((x * (y * z)) \ ((x * y) * z)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,11318,a,b,12431,a),flip(a)].">
      <j1 rule="hyper" parents="63 11318 12431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12435">
    <literal><![CDATA[
      T(a(1 / x,y,z),x \ 1) = a(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(3201(a,2),12431(a,1,1))].">
      <j1 rule="para" parents="3201 12431"/>
    </justification>
  </clause>

  <clause id="12437">
    <literal><![CDATA[
      a(x,y,z) * (x \ 1) = (x \ 1) * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(126,a,12430,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="126 12430 22"/>
    </justification>
  </clause>

  <clause id="12438">
    <literal><![CDATA[
      (K(x,y) / z) * a(K(x,y) / z,z,K(y,x)) = 1 / (z * K(y,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,9897,a(flip),b,12432,a),flip(a)].">
      <j1 rule="hyper" parents="63 9897 12432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12440">
    <literal><![CDATA[
      a((x / y) \ 1,z,(x / y) \ 1) = a(x \ y,z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,12014,a(flip),b,12435,a),flip(a)].">
      <j1 rule="hyper" parents="63 12014 12435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12441">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ 1 = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(14(a,2),12434(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="14 12434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12442">
    <literal><![CDATA[
      1 / a(x,y,z) = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(198,a,12441,a)].">
      <j1 rule="hyper" parents="198 12441"/>
    </justification>
  </clause>

  <clause id="12443">
    <literal><![CDATA[
      L(R(x,a(y,z,u) \ 1,a(y,z,u) \ 1),a(y,z,u) \ 1,x) = T(((a(y,z,u) \ 1) * x) * a(y,z,u),(a(y,z,u) \ 1) * x)
    ]]></literal>
    <justification jstring="[para(12441(a,1),3841(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="12441 3841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12445">
    <literal><![CDATA[
      (a(x,y,z) * a(x,y,z)) * (u * (a(x,y,z) \ (1 / a(x,y,z)))) = T(u,a(x,y,z) \ (a(x,y,z) \ 1))
    ]]></literal>
    <justification jstring="[para(12442(a,2),729(a,1,2,2,2))].">
      <j1 rule="para" parents="12442 729"/>
    </justification>
  </clause>

  <clause id="12446">
    <literal><![CDATA[
      a(x,y,z) \ R(u,a(x,y,z),a(x,y,z)) = T(u * (a(x,y,z) \ 1),a(x,y,z))
    ]]></literal>
    <justification jstring="[para(12442(a,1),1190(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="12442 1190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12449">
    <literal><![CDATA[
      K((x \ y) \ z,x / y) * K(x / y,z) = a(y \ x,z,y \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,10786,a,b,12440,a)].">
      <j1 rule="hyper" parents="63 10786 12440"/>
    </justification>
  </clause>

  <clause id="12450">
    <literal><![CDATA[
      K(x,y * (1 / (z * K(x,u)))) = K(x,y * (K(u,x) / z))
    ]]></literal>
    <justification jstring="[para(12438(a,1),9908(a,1,2,2))].">
      <j1 rule="para" parents="12438 9908"/>
    </justification>
  </clause>

  <clause id="12451">
    <literal><![CDATA[
      K(x,y * ((z * K(x,u)) \ 1)) = K(x,y * (K(u,x) / z))
    ]]></literal>
    <justification jstring="[hyper(63,a,4785,a(flip),b,12450,a)].">
      <j1 rule="hyper" parents="63 4785 12450"/>
    </justification>
  </clause>

  <clause id="12452">
    <literal><![CDATA[
      K(x,y * ((K(x,z) * u) \ 1)) = K(x,y * (K(z,x) / u))
    ]]></literal>
    <justification jstring="[hyper(63,a,9442,a,b,12451,a)].">
      <j1 rule="hyper" parents="63 9442 12451"/>
    </justification>
  </clause>

  <clause id="12453">
    <literal><![CDATA[
      K(x,y * ((K(x,z) * u) \ 1)) = K(x,y * (u \ 1))
    ]]></literal>
    <justification jstring="[hyper(333,a,10732,a(flip),b,12452,a),flip(a)].">
      <j1 rule="hyper" parents="333 10732 12452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12455">
    <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(63,a,8903,a,b,12453,a)].">
      <j1 rule="hyper" parents="63 8903 12453"/>
    </justification>
  </clause>

  <clause id="12457">
    <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(385(a,1),12455(a,2,2))].">
      <j1 rule="para" parents="385 12455"/>
    </justification>
  </clause>

  <clause id="12458">
    <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(333,a,8189,a(flip),b,12457,a),flip(a)].">
      <j1 rule="hyper" parents="333 8189 12457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12460">
    <literal><![CDATA[
      K(x,R(y,z,(K(x,u) * z) \ 1)) = K(x,R(y,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,7936,a(flip),b,12458,a)].">
      <j1 rule="hyper" parents="63 7936 12458"/>
    </justification>
  </clause>

  <clause id="12461">
    <literal><![CDATA[
      K(x,R(y,z,(K(x,u) * z) \ 1)) = K(x,L(y,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(333,a,12328,a(flip),b,12460,a),flip(a)].">
      <j1 rule="hyper" parents="333 12328 12460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12463">
    <literal><![CDATA[
      R(K(x,y),z,(K(x,u) * z) \ 1) = K(x,L(y,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(11577,a,12461,a)].">
      <j1 rule="hyper" parents="11577 12461"/>
    </justification>
  </clause>

  <clause id="12464">
    <literal><![CDATA[
      x / (K(y,L(z,u,u \ 1)) * x) = u * ((K(y,z) * u) \ 1)
    ]]></literal>
    <justification jstring="[para(12463(a,1),5676(a,1,2,1))].">
      <j1 rule="para" parents="12463 5676"/>
    </justification>
  </clause>

  <clause id="12465">
    <literal><![CDATA[
      x * ((K(y,z) * x) \ 1) = K(L(z,x,x \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(4579,a,12464,a),flip(a)].">
      <j1 rule="hyper" parents="4579 12464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12467">
    <literal><![CDATA[
      x \ K(y,L(z,x,x \ 1)) = (K(z,y) * x) \ 1
    ]]></literal>
    <justification jstring="[hyper(121,a,10898,a(flip),b,12465,a)].">
      <j1 rule="hyper" parents="121 10898 12465"/>
    </justification>
  </clause>

  <clause id="12468">
    <literal><![CDATA[
      K(x,((K(y,x) * (z \ 1)) \ 1) \ u) = K(x,z \ u)
    ]]></literal>
    <justification jstring="[para(12467(a,1),8031(a,1,2,1))].">
      <j1 rule="para" parents="12467 8031"/>
    </justification>
  </clause>

  <clause id="12469">
    <literal><![CDATA[
      K(x,(((y \ 1) * K(z,x)) \ 1) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(6888(a,1),12468(a,1,2,1,1))].">
      <j1 rule="para" parents="6888 12468"/>
    </justification>
  </clause>

  <clause id="12470">
    <literal><![CDATA[
      K(x,((y * K(z,x)) \ 1) \ u) = K(x,(y \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,5077,a(flip),b,12469,a)].">
      <j1 rule="hyper" parents="63 5077 12469"/>
    </justification>
  </clause>

  <clause id="12471">
    <literal><![CDATA[
      K(x,((T(y,x) / z) \ 1) \ u) = K(x,((y / z) \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(2170(a,1),12470(a,1,2,1,1))].">
      <j1 rule="para" parents="2170 12470"/>
    </justification>
  </clause>

  <clause id="12472">
    <literal><![CDATA[
      (T(x,y) / z) \ x = z * K(y,((x / z) \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(126,a,12471,a(flip),b,9619,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="126 12471 9619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12473">
    <literal><![CDATA[
      (T(x,y) / z) \ x = (1 / z) \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,11188,a(flip),b,12472,a),flip(a)].">
      <j1 rule="hyper" parents="333 11188 12472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12474">
    <literal><![CDATA[
      T(x,y) / (1 / y) = x / (K(y,x) / y)
    ]]></literal>
    <justification jstring="[hyper(197,a,4988,a(flip),b,12473,a),flip(a)].">
      <j1 rule="hyper" parents="197 4988 12473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12475">
    <literal><![CDATA[
      (1 / (x \ T(y,z))) \ K(z,y) = x \ y
    ]]></literal>
    <justification jstring="[para(76(a,1),12473(a,1,1)),flip(a)].">
      <j1 rule="para" parents="76 12473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12477">
    <literal><![CDATA[
      1 / ((1 / x) \ K(y,z)) = K(z,y) / x
    ]]></literal>
    <justification jstring="[para(12473(a,1),11176(a,1,2))].">
      <j1 rule="para" parents="12473 11176"/>
    </justification>
  </clause>

  <clause id="12478">
    <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(12475(a,2),6474(a,2,2)),flip(a)].">
      <j1 rule="para" parents="12475 6474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12479">
    <literal><![CDATA[
      (K(x,y) / z) \ 1 = (1 / z) \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(192,a,12477,a)].">
      <j1 rule="hyper" parents="192 12477"/>
    </justification>
  </clause>

  <clause id="12481">
    <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(333,a,6474,a(flip),b,12478,a),flip(a)].">
      <j1 rule="hyper" parents="333 6474 12478"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12482">
    <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(25(a,2),12481(a,1,2,1,2,2))].">
      <j1 rule="para" parents="25 12481"/>
    </justification>
  </clause>

  <clause id="12483">
    <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(25(a,2),12482(a,1,2,1,2,2,1))].">
      <j1 rule="para" parents="25 12482"/>
    </justification>
  </clause>

  <clause id="12484">
    <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(63,a,10220,a(flip),b,12483,a)].">
      <j1 rule="hyper" parents="63 10220 12483"/>
    </justification>
  </clause>

  <clause id="12486">
    <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(79(a,1),12484(a,1,2))].">
      <j1 rule="para" parents="79 12484"/>
    </justification>
  </clause>

  <clause id="12487">
    <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(63,a,11411,a,b,12486,a)].">
      <j1 rule="hyper" parents="63 11411 12486"/>
    </justification>
  </clause>

  <clause id="12490">
    <literal><![CDATA[
      K(x,y \ L(L(x,z,x),u,w)) = K(x,y \ L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,11218,a(flip),b,12487,a),flip(a)].">
      <j1 rule="hyper" parents="63 11218 12487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12492">
    <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(12490(a,1),9106(a,1,1))].">
      <j1 rule="para" parents="12490 9106"/>
    </justification>
  </clause>

  <clause id="12493">
    <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(10197(a,1),12492(a,1,1))].">
      <j1 rule="para" parents="10197 12492"/>
    </justification>
  </clause>

  <clause id="12495">
    <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(65(a,1),12493(a,1,1,2))].">
      <j1 rule="para" parents="65 12493"/>
    </justification>
  </clause>

  <clause id="12496">
    <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(4515(a,1),12495(a,1,2))].">
      <j1 rule="para" parents="4515 12495"/>
    </justification>
  </clause>

  <clause id="12497">
    <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(12051,a,12496,a)].">
      <j1 rule="hyper" parents="12051 12496"/>
    </justification>
  </clause>

  <clause id="12498">
    <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(2005(a,1),12497(a,1,2))].">
      <j1 rule="para" parents="2005 12497"/>
    </justification>
  </clause>

  <clause id="12499">
    <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(11786(a,1),12498(a,1,2))].">
      <j1 rule="para" parents="11786 12498"/>
    </justification>
  </clause>

  <clause id="12500">
    <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(129,a,12499,a)].">
      <j1 rule="hyper" parents="129 12499"/>
    </justification>
  </clause>

  <clause id="12501">
    <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(12500(a,1),12139(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12500 12139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12502">
    <literal><![CDATA[
      a(L(x,y,z),u,L(x,y,z)) = a(x,u,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,12501,a,b,12441,a(flip))].">
      <j1 rule="hyper" parents="119 12501 12441"/>
    </justification>
  </clause>

  <clause id="12503">
    <literal><![CDATA[
      a(L(x,y,z),u,L(x,y,z)) = a(x,u,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,11777,a(flip),b,12502,a),flip(a)].">
      <j1 rule="hyper" parents="333 11777 12502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12505">
    <literal><![CDATA[
      L(a(x,y,x),z,u) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,11064,a(flip),b,12503,a)].">
      <j1 rule="hyper" parents="63 11064 12503"/>
    </justification>
  </clause>

  <clause id="12506">
    <literal><![CDATA[
      L(a(x,y,x),z,u) = L(a(x,y,x),w,v5)
    ]]></literal>
    <justification jstring="[hyper(333,a,12505,a,b,12505,a)].">
      <j1 rule="hyper" parents="333 12505 12505"/>
    </justification>
  </clause>

  <clause id="12508">
    <literal><![CDATA[
      R(a(x,y,x),z,u) = L(a(x,y,x),w,v5)
    ]]></literal>
    <justification jstring="[hyper(333,a,11792,a,b,12505,a)].">
      <j1 rule="hyper" parents="333 11792 12505"/>
    </justification>
  </clause>

  <clause id="12514">
    <literal><![CDATA[
      (x * y) * a(z,u,z) = x * (y * a(z,u,z))
    ]]></literal>
    <justification jstring="[hyper(126,a,12505,a(flip),b,5100,a)].">
      <j1 rule="hyper" parents="126 12505 5100"/>
    </justification>
  </clause>

  <clause id="12516">
    <literal><![CDATA[
      x \ (y * a(z,u,z)) = (x \ y) * a(z,u,z)
    ]]></literal>
    <justification jstring="[para(12505(a,1),495(a,1,2,2))].">
      <j1 rule="para" parents="12505 495"/>
    </justification>
  </clause>

  <clause id="12518">
    <literal><![CDATA[
      L(a(x,y,x),z * y,u) = a(x,(u * (z * y)) / (u * z),x)
    ]]></literal>
    <justification jstring="[para(12505(a,1),11935(a,1,1))].">
      <j1 rule="para" parents="12505 11935"/>
    </justification>
  </clause>

  <clause id="12541">
    <literal><![CDATA[
      L(a(x,y,x),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = w
    ]]></literal>
    <justification jstring="[para(12506(a,1),372(a,1)),flip(b)].">
      <j1 rule="para" parents="12506 372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12544">
    <literal><![CDATA[
      a(x,T(y,z),x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(42,a,9306,a(flip),b,12508,a),flip(a)].">
      <j1 rule="hyper" parents="42 9306 12508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12545">
    <literal><![CDATA[
      a(x,T(y,z),x) = a(x,T(y,u),x)
    ]]></literal>
    <justification jstring="[hyper(333,a,12544,a,b,12544,a)].">
      <j1 rule="hyper" parents="333 12544 12544"/>
    </justification>
  </clause>

  <clause id="12546">
    <literal><![CDATA[
      a(x,T(y,z),x) = K(x * y,T(T(x,u),w)) * K(x,T(T(y,u),w))
    ]]></literal>
    <justification jstring="[hyper(333,a,10778,a,b,12544,a),flip(a)].">
      <j1 rule="hyper" parents="333 10778 12544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12547">
    <literal><![CDATA[
      a(x,T(y,z),x) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,8210,a,b,12544,a),flip(a)].">
      <j1 rule="hyper" parents="333 8210 12544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12549">
    <literal><![CDATA[
      a(x,y / z,x) = a(x,z \ y,x)
    ]]></literal>
    <justification jstring="[para(113(a,1),12544(a,1,2)),flip(a)].">
      <j1 rule="para" parents="113 12544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12550">
    <literal><![CDATA[
      L(x,T(y,z),x) = a(x,y,x) \ x
    ]]></literal>
    <justification jstring="[para(12544(a,1),8239(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12544 8239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12551">
    <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(12544(a,1),8266(a,1,1))].">
      <j1 rule="para" parents="12544 8266"/>
    </justification>
  </clause>

  <clause id="12554">
    <literal><![CDATA[
      a(x,T(y / z,u),x) = a(x,z \ y,x)
    ]]></literal>
    <justification jstring="[para(113(a,1),12545(a,1,2)),flip(a)].">
      <j1 rule="para" parents="113 12545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12561">
    <literal><![CDATA[
      R(x,T(y,z),x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(8223,a,12547,a)].">
      <j1 rule="hyper" parents="8223 12547"/>
    </justification>
  </clause>

  <clause id="12564">
    <literal><![CDATA[
      R(x,y / z,x) = R(x,z \ y,x)
    ]]></literal>
    <justification jstring="[para(113(a,1),12561(a,1,2)),flip(a)].">
      <j1 rule="para" parents="113 12561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12566">
    <literal><![CDATA[
      R(x,y \ (y \ (T(y,z) * u)),x) = R(x,y \ ((y \ u) * T(y,z)),x)
    ]]></literal>
    <justification jstring="[para(8694(a,1),12561(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8694 12561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12569">
    <literal><![CDATA[
      a(x,y / (z * y),x) = a(x,z \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,12105,a(flip),b,12549,a),flip(a)].">
      <j1 rule="hyper" parents="333 12105 12549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12571">
    <literal><![CDATA[
      L(x,T(y,z),x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,8239,a(flip),b,12550,a),flip(a)].">
      <j1 rule="hyper" parents="333 8239 12550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12572">
    <literal><![CDATA[
      L(x,T(y,z),x) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,x) = u
    ]]></literal>
    <justification jstring="[para(12550(a,2),9283(a,1))].">
      <j1 rule="para" parents="12550 9283"/>
    </justification>
  </clause>

  <clause id="12573">
    <literal><![CDATA[
      L(x,T(y,z),x) = T(x,T(x * y,u)) * K(y,T(x,u))
    ]]></literal>
    <justification jstring="[hyper(333,a,8429,a,b,12571,a),flip(a)].">
      <j1 rule="hyper" parents="333 8429 12571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12576">
    <literal><![CDATA[
      L(x,y * K(z,y),x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,4562,a,b,12571,a)].">
      <j1 rule="hyper" parents="63 4562 12571"/>
    </justification>
  </clause>

  <clause id="12577">
    <literal><![CDATA[
      L(x,y / z,x) = L(x,z \ y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,4845,a(flip),b,12571,a)].">
      <j1 rule="hyper" parents="63 4845 12571"/>
    </justification>
  </clause>

  <clause id="12582">
    <literal><![CDATA[
      R(x,T(x,y) \ z,x) = R(x,z / x,x)
    ]]></literal>
    <justification jstring="[hyper(8835,a,12564,a),flip(a)].">
      <j1 rule="hyper" parents="8835 12564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12583">
    <literal><![CDATA[
      K(x,(y / z) \ x) \ T(x,z / y) = R(x,y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,11886,a,b,12564,a)].">
      <j1 rule="hyper" parents="63 11886 12564"/>
    </justification>
  </clause>

  <clause id="12584">
    <literal><![CDATA[
      L(x,R(y * K(z,y),u,w),x) = L(x,R(y,u,w),x)
    ]]></literal>
    <justification jstring="[para(4949(a,1),12576(a,1,2))].">
      <j1 rule="para" parents="4949 12576"/>
    </justification>
  </clause>

  <clause id="12585">
    <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(3033(a,2),12577(a,1,2))].">
      <j1 rule="para" parents="3033 12577"/>
    </justification>
  </clause>

  <clause id="12586">
    <literal><![CDATA[
      L(x,R(y * K(z,y),z,u),x) = L(x,(z * u) \ ((z * y) * u),x)
    ]]></literal>
    <justification jstring="[para(4419(a,2),12577(a,1,2))].">
      <j1 rule="para" parents="4419 12577"/>
    </justification>
  </clause>

  <clause id="12587">
    <literal><![CDATA[
      a(x,y * K(z,y),x) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = u
    ]]></literal>
    <justification jstring="[para(11796(a,2),12541(a,1))].">
      <j1 rule="para" parents="11796 12541"/>
    </justification>
  </clause>

  <clause id="12588">
    <literal><![CDATA[
      a(x,R(y \ z,y,u),x) = a(x,(y * u) \ (z * u),x)
    ]]></literal>
    <justification jstring="[para(688(a,1),12554(a,1,2))].">
      <j1 rule="para" parents="688 12554"/>
    </justification>
  </clause>

  <clause id="12589">
    <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(3286(a,1),12569(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3286 12569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12590">
    <literal><![CDATA[
      R(x,T(x,y) \ z,x) = R(x,x \ z,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,12564,a(flip),b,12582,a),flip(a)].">
      <j1 rule="hyper" parents="333 12564 12582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12591">
    <literal><![CDATA[
      a(x,y / z,x) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,z \ y,x) = u
    ]]></literal>
    <justification jstring="[para(4292(a,1),12587(a,1,2))].">
      <j1 rule="para" parents="4292 12587"/>
    </justification>
  </clause>

  <clause id="12592">
    <literal><![CDATA[
      R(x,y,a(z,u,z)) = x
    ]]></literal>
    <justification jstring="[hyper(543,a,12514,a)].">
      <j1 rule="hyper" parents="543 12514"/>
    </justification>
  </clause>

  <clause id="12593">
    <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(12514(a,1),541(a,1,1))].">
      <j1 rule="para" parents="12514 541"/>
    </justification>
  </clause>

  <clause id="12595">
    <literal><![CDATA[
      (x \ K(y,z)) * a(y,y \ z,y) = x \ K(y,y \ z)
    ]]></literal>
    <justification jstring="[para(8263(a,1),12516(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8263 12516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12596">
    <literal><![CDATA[
      x \ (a(y,z,y) * u) = (x \ u) * a(y,z,y)
    ]]></literal>
    <justification jstring="[para(9246(a,2),12516(a,1,2))].">
      <j1 rule="para" parents="9246 12516"/>
    </justification>
  </clause>

  <clause id="12597">
    <literal><![CDATA[
      x \ (y * (z * a(u,w,u))) = (x \ (y * z)) * a(u,w,u)
    ]]></literal>
    <justification jstring="[para(12514(a,1),12516(a,1,2))].">
      <j1 rule="para" parents="12514 12516"/>
    </justification>
  </clause>

  <clause id="12598">
    <literal><![CDATA[
      (x \ (y * x)) * a(z,u,z) = T(a(z,u,z) * y,x)
    ]]></literal>
    <justification jstring="[hyper(11804,a,12596,a),flip(a)].">
      <j1 rule="hyper" parents="11804 12596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12599">
    <literal><![CDATA[
      T(a(x,y,x) * z,u) = T(z,u) * a(x,y,x)
    ]]></literal>
    <justification jstring="[para(22(a,2),12598(a,1,1)),flip(a)].">
      <j1 rule="para" parents="22 12598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12600">
    <literal><![CDATA[
      (x \ (y * x)) * a(z,u,z) = T(y * a(z,u,z),x)
    ]]></literal>
    <justification jstring="[para(9246(a,1),12598(a,2,1))].">
      <j1 rule="para" parents="9246 12598"/>
    </justification>
  </clause>

  <clause id="12601">
    <literal><![CDATA[
      T(a(x,y,x) * z,u) = a(x,y,x) * T(z,u)
    ]]></literal>
    <justification jstring="[hyper(333,a,9246,a,b,12599,a),flip(a)].">
      <j1 rule="hyper" parents="333 9246 12599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12602">
    <literal><![CDATA[
      T(a(x,y,x) \ z,u) = a(x,y,x) \ T(z,u)
    ]]></literal>
    <justification jstring="[hyper(121,a,679,a(flip),b,12601,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="121 679 12601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12603">
    <literal><![CDATA[
      a(x,y,x) \ T(z * a(x,y,x),u) = T(z,u)
    ]]></literal>
    <justification jstring="[para(9248(a,1),12602(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9248 12602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12604">
    <literal><![CDATA[
      T(a(x,y,x) \ z,u) / w = a(x,y,x) \ (T(z,u) / w)
    ]]></literal>
    <justification jstring="[para(12602(a,2),11810(a,1,1))].">
      <j1 rule="para" parents="12602 11810"/>
    </justification>
  </clause>

  <clause id="12605">
    <literal><![CDATA[
      a(x,y,x) \ T(z * a(x,y,x),u) = z * K(z,u)
    ]]></literal>
    <justification jstring="[hyper(333,a,4222,a(flip),b,12603,a),flip(a)].">
      <j1 rule="hyper" parents="333 4222 12603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12606">
    <literal><![CDATA[
      K(x * a(y,z,y),u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(34,a,11811,a(flip),b,12605,a(flip))].">
      <j1 rule="hyper" parents="34 11811 12605"/>
    </justification>
  </clause>

  <clause id="12607">
    <literal><![CDATA[
      K(x * a(y,z,y),u) = u / T(u,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,4212,a(flip),b,12606,a),flip(a)].">
      <j1 rule="hyper" parents="333 4212 12606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12609">
    <literal><![CDATA[
      K(T(x,y) / y,z) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[para(8251(a,1),12606(a,1,1))].">
      <j1 rule="para" parents="8251 12606"/>
    </justification>
  </clause>

  <clause id="12610">
    <literal><![CDATA[
      K(a(x,y,x) * z,u) = K(z,u)
    ]]></literal>
    <justification jstring="[para(9246(a,2),12606(a,1,1))].">
      <j1 rule="para" parents="9246 12606"/>
    </justification>
  </clause>

  <clause id="12612">
    <literal><![CDATA[
      K(x \ (a(y,z,y) * u),w) = K(x \ u,w)
    ]]></literal>
    <justification jstring="[para(12596(a,2),12606(a,1,1))].">
      <j1 rule="para" parents="12596 12606"/>
    </justification>
  </clause>

  <clause id="12615">
    <literal><![CDATA[
      K(L(x,y,x) * z,u) = K(x * z,u)
    ]]></literal>
    <justification jstring="[para(9281(a,1),12610(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9281 12610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12616">
    <literal><![CDATA[
      K(K(x,x * y) * z,u) = K(K(x,y) * z,u)
    ]]></literal>
    <justification jstring="[para(11604(a,1),12610(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11604 12610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12617">
    <literal><![CDATA[
      K(T(x * y,x) \ z,u) = K((y * x) \ z,u)
    ]]></literal>
    <justification jstring="[para(11613(a,1),12610(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11613 12610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12620">
    <literal><![CDATA[
      K(x / T(y,x),z) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,8420,a(flip),b,12609,a)].">
      <j1 rule="hyper" parents="63 8420 12609"/>
    </justification>
  </clause>

  <clause id="12621">
    <literal><![CDATA[
      T(x * K(x / y,z),x) = x * K(y \ x,z)
    ]]></literal>
    <justification jstring="[para(12609(a,1),8727(a,2,2))].">
      <j1 rule="para" parents="12609 8727"/>
    </justification>
  </clause>

  <clause id="12622">
    <literal><![CDATA[
      T(x,y * a(z,u,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(4253,a,12607,a)].">
      <j1 rule="hyper" parents="4253 12607"/>
    </justification>
  </clause>

  <clause id="12623">
    <literal><![CDATA[
      K(x * a(y,z,y),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u) = w
    ]]></literal>
    <justification jstring="[para(12607(a,2),4313(a,1))].">
      <j1 rule="para" parents="12607 4313"/>
    </justification>
  </clause>

  <clause id="12624">
    <literal><![CDATA[
      K(x,y * a(z,u,z)) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(121,a,12622,a(flip),b,4222,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="121 12622 4222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12625">
    <literal><![CDATA[
      T(x,T(y,z) / z) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[para(8251(a,1),12622(a,1,2))].">
      <j1 rule="para" parents="8251 12622"/>
    </justification>
  </clause>

  <clause id="12626">
    <literal><![CDATA[
      T(x,a(y,z,y) \ u) = T(x,u)
    ]]></literal>
    <justification jstring="[para(9247(a,1),12622(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9247 12622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12627">
    <literal><![CDATA[
      T(x,y / R(z,u,z)) = T(x,y / z)
    ]]></literal>
    <justification jstring="[para(9316(a,1),12622(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9316 12622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12628">
    <literal><![CDATA[
      T(x,L(y,z,y) * u) = T(x,y * u)
    ]]></literal>
    <justification jstring="[para(9280(a,1),12626(a,1,2))].">
      <j1 rule="para" parents="9280 12626"/>
    </justification>
  </clause>

  <clause id="12629">
    <literal><![CDATA[
      T(x,(y \ z) * T(y,z)) = T(x,z)
    ]]></literal>
    <justification jstring="[para(9279(a,1),12626(a,1,2))].">
      <j1 rule="para" parents="9279 12626"/>
    </justification>
  </clause>

  <clause id="12630">
    <literal><![CDATA[
      T(x,T(y,z) / z) = x * K(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(333,a,4222,a(flip),b,12625,a),flip(a)].">
      <j1 rule="hyper" parents="333 4222 12625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12631">
    <literal><![CDATA[
      T(x,y / T(z,y)) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,7243,a(flip),b,12625,a)].">
      <j1 rule="hyper" parents="63 7243 12625"/>
    </justification>
  </clause>

  <clause id="12633">
    <literal><![CDATA[
      T(x,y / T(T(z,y),u)) = T(x,T(z,u) \ y)
    ]]></literal>
    <justification jstring="[para(23(a,1),12631(a,1,2,2))].">
      <j1 rule="para" parents="23 12631"/>
    </justification>
  </clause>

  <clause id="12634">
    <literal><![CDATA[
      K(T(x / y,x) * z,u) = K((y \ x) * z,u)
    ]]></literal>
    <justification jstring="[para(3781(a,1),12615(a,1,1,1))].">
      <j1 rule="para" parents="3781 12615"/>
    </justification>
  </clause>

  <clause id="12635">
    <literal><![CDATA[
      K(x,y * a(z,u,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,4215,a,b,12624,a),flip(a)].">
      <j1 rule="hyper" parents="333 4215 12624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12636">
    <literal><![CDATA[
      K(x,y * a(z,u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = w
    ]]></literal>
    <justification jstring="[para(12624(a,2),4306(a,1))].">
      <j1 rule="para" parents="12624 4306"/>
    </justification>
  </clause>

  <clause id="12637">
    <literal><![CDATA[
      K(x,y * L(z,u,z)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(8274(a,1),12635(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8274 12635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12638">
    <literal><![CDATA[
      K(x,T(y,z) / z) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[para(8251(a,1),12635(a,1,2))].">
      <j1 rule="para" parents="8251 12635"/>
    </justification>
  </clause>

  <clause id="12639">
    <literal><![CDATA[
      K(x,L(y,z,y) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(9233(a,1),12635(a,1,2))].">
      <j1 rule="para" parents="9233 12635"/>
    </justification>
  </clause>

  <clause id="12640">
    <literal><![CDATA[
      K(x,a(y,z,y) * u) = K(x,u)
    ]]></literal>
    <justification jstring="[para(9246(a,2),12635(a,1,2))].">
      <j1 rule="para" parents="9246 12635"/>
    </justification>
  </clause>

  <clause id="12641">
    <literal><![CDATA[
      K(x,a(y,z,y) \ u) = K(x,u)
    ]]></literal>
    <justification jstring="[para(9247(a,1),12635(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9247 12635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12642">
    <literal><![CDATA[
      K(x,y * R(z,u,z)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(9319(a,1),12635(a,1,2))].">
      <j1 rule="para" parents="9319 12635"/>
    </justification>
  </clause>

  <clause id="12644">
    <literal><![CDATA[
      K(x,(a(y,z,y) * u) / w) = K(x,u / w)
    ]]></literal>
    <justification jstring="[para(11812(a,2),12635(a,1,2))].">
      <j1 rule="para" parents="11812 12635"/>
    </justification>
  </clause>

  <clause id="12645">
    <literal><![CDATA[
      K(x,y * (z * a(u,w,u))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(12514(a,1),12635(a,1,2))].">
      <j1 rule="para" parents="12514 12635"/>
    </justification>
  </clause>

  <clause id="12646">
    <literal><![CDATA[
      K(x,y \ (a(z,u,z) * w)) = K(x,y \ w)
    ]]></literal>
    <justification jstring="[para(12596(a,2),12635(a,1,2))].">
      <j1 rule="para" parents="12596 12635"/>
    </justification>
  </clause>

  <clause id="12647">
    <literal><![CDATA[
      K(x,R(y,z,y) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(9340(a,1),12640(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9340 12640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12648">
    <literal><![CDATA[
      K(x,T(y * z,y) \ u) = K(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[para(11613(a,1),12640(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11613 12640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12649">
    <literal><![CDATA[
      K(x,(y \ z) * T(y,z)) = K(x,z)
    ]]></literal>
    <justification jstring="[para(9279(a,1),12641(a,1,2))].">
      <j1 rule="para" parents="9279 12641"/>
    </justification>
  </clause>

  <clause id="12650">
    <literal><![CDATA[
      K(x,L(y,z,y) / u) = K(x,y / u)
    ]]></literal>
    <justification jstring="[para(11813(a,1),12641(a,1,2))].">
      <j1 rule="para" parents="11813 12641"/>
    </justification>
  </clause>

  <clause id="12651">
    <literal><![CDATA[
      K(x,L(T(y,z),u,w) / z) = K(x,z \ L(y,u,w))
    ]]></literal>
    <justification jstring="[para(25(a,2),12638(a,1,2,1))].">
      <j1 rule="para" parents="25 12638"/>
    </justification>
  </clause>

  <clause id="12652">
    <literal><![CDATA[
      K(x,y / T(z,y)) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[para(3625(a,1),12638(a,1,2))].">
      <j1 rule="para" parents="3625 12638"/>
    </justification>
  </clause>

  <clause id="12653">
    <literal><![CDATA[
      (K(x,y) * (x \ y)) \ (K(x,y) * z) = (((x \ y) * x) / x) \ z
    ]]></literal>
    <justification jstring="[para(12649(a,1),11937(a,1,2,1))].">
      <j1 rule="para" parents="12649 11937"/>
    </justification>
  </clause>

  <clause id="12654">
    <literal><![CDATA[
      K(x,y / T(z,y)) = K(x,T(y / z,y))
    ]]></literal>
    <justification jstring="[hyper(333,a,6368,a,b,12652,a),flip(a)].">
      <j1 rule="hyper" parents="333 6368 12652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12655">
    <literal><![CDATA[
      T(x,y / ((z \ u) \ u)) = T(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(8668(a,1),12627(a,1,2,2))].">
      <j1 rule="para" parents="8668 12627"/>
    </justification>
  </clause>

  <clause id="12656">
    <literal><![CDATA[
      T(x,((y \ z) \ z) * u) = T(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[para(11339(a,1),12628(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11339 12628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12657">
    <literal><![CDATA[
      K(x,y * T(z,z * u)) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(3742(a,1),12637(a,1,2,2))].">
      <j1 rule="para" parents="3742 12637"/>
    </justification>
  </clause>

  <clause id="12658">
    <literal><![CDATA[
      K(x,y * ((z \ u) \ u)) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(11339(a,1),12637(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11339 12637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12659">
    <literal><![CDATA[
      K(x,T(y / z,y) \ u) = K(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[para(3781(a,1),12639(a,1,2,1))].">
      <j1 rule="para" parents="3781 12639"/>
    </justification>
  </clause>

  <clause id="12660">
    <literal><![CDATA[
      K(x,((y \ z) \ z) \ u) = K(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(11339(a,1),12639(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11339 12639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12662">
    <literal><![CDATA[
      L(K(x,y \ (z \ u)),z \ u,z) = K(x,T(y * z,y) \ u)
    ]]></literal>
    <justification jstring="[para(12647(a,1),9698(a,1,1))].">
      <j1 rule="para" parents="12647 9698"/>
    </justification>
  </clause>

  <clause id="12663">
    <literal><![CDATA[
      K(x,T(y / z,y) / u) = K(x,(z \ y) / u)
    ]]></literal>
    <justification jstring="[para(3781(a,1),12650(a,1,2,1))].">
      <j1 rule="para" parents="3781 12650"/>
    </justification>
  </clause>

  <clause id="12664">
    <literal><![CDATA[
      K(x,((y \ z) \ z) / u) = K(x,T(y,z) / u)
    ]]></literal>
    <justification jstring="[para(11339(a,1),12650(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11339 12650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12665">
    <literal><![CDATA[
      K(a(x,y,x) * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(z,u) = w
    ]]></literal>
    <justification jstring="[para(9246(a,2),12623(a,1,1))].">
      <j1 rule="para" parents="9246 12623"/>
    </justification>
  </clause>

  <clause id="12666">
    <literal><![CDATA[
      T(x,T(y,z) / z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(12630(a,2),4285(a,1))].">
      <j1 rule="para" parents="12630 4285"/>
    </justification>
  </clause>

  <clause id="12667">
    <literal><![CDATA[
      K(x,T(y,z) / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(8251(a,1),12636(a,1,2))].">
      <j1 rule="para" parents="8251 12636"/>
    </justification>
  </clause>

  <clause id="12668">
    <literal><![CDATA[
      K(x,R(y,z,y) / u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / u) = w
    ]]></literal>
    <justification jstring="[para(11814(a,1),12636(a,1,2))].">
      <j1 rule="para" parents="11814 12636"/>
    </justification>
  </clause>

  <clause id="12669">
    <literal><![CDATA[
      K(x,y * (z * a(u,w,u))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = v5
    ]]></literal>
    <justification jstring="[para(12514(a,1),12636(a,1,2))].">
      <j1 rule="para" parents="12514 12636"/>
    </justification>
  </clause>

  <clause id="12670">
    <literal><![CDATA[
      K(x,y / T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(12654(a,2),6413(a,1))].">
      <j1 rule="para" parents="12654 6413"/>
    </justification>
  </clause>

  <clause id="12671">
    <literal><![CDATA[
      K(K(x \ 1,x) * y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) = u
    ]]></literal>
    <justification jstring="[para(2446(a,1),12665(a,1,1,1))].">
      <j1 rule="para" parents="2446 12665"/>
    </justification>
  </clause>

  <clause id="12672">
    <literal><![CDATA[
      K(x \ T(y * z,y),u) = K(x \ (z * y),u)
    ]]></literal>
    <justification jstring="[para(8248(a,1),12612(a,1,1,2))].">
      <j1 rule="para" parents="8248 12612"/>
    </justification>
  </clause>

  <clause id="12673">
    <literal><![CDATA[
      K(x \ K(y,y \ z),u) = K(x \ K(y,z),u)
    ]]></literal>
    <justification jstring="[para(8207(a,1),12612(a,1,1,2))].">
      <j1 rule="para" parents="8207 12612"/>
    </justification>
  </clause>

  <clause id="12674">
    <literal><![CDATA[
      K(x,T(y * z,y) / u) = K(x,(z * y) / u)
    ]]></literal>
    <justification jstring="[para(8248(a,1),12644(a,1,2,1))].">
      <j1 rule="para" parents="8248 12644"/>
    </justification>
  </clause>

  <clause id="12675">
    <literal><![CDATA[
      K(x,y * (T(z,u) / u)) = K(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[para(8251(a,1),12645(a,1,2,2))].">
      <j1 rule="para" parents="8251 12645"/>
    </justification>
  </clause>

  <clause id="12676">
    <literal><![CDATA[
      K(x,y * K(z,z \ u)) = K(x,y * K(z,u))
    ]]></literal>
    <justification jstring="[para(8263(a,1),12645(a,1,2,2))].">
      <j1 rule="para" parents="8263 12645"/>
    </justification>
  </clause>

  <clause id="12677">
    <literal><![CDATA[
      K(x,y * (a(z,u,z) \ w)) = K(x,y * w)
    ]]></literal>
    <justification jstring="[para(9247(a,1),12645(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9247 12645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12678">
    <literal><![CDATA[
      K(x,y * T(z * u,z)) = K(x,y * (u * z))
    ]]></literal>
    <justification jstring="[para(9256(a,1),12645(a,1,2,2))].">
      <j1 rule="para" parents="9256 12645"/>
    </justification>
  </clause>

  <clause id="12679">
    <literal><![CDATA[
      K(x,y * (R(z,u,z) * w)) = K(x,y * (z * w))
    ]]></literal>
    <justification jstring="[para(9328(a,1),12645(a,1,2,2))].">
      <j1 rule="para" parents="9328 12645"/>
    </justification>
  </clause>

  <clause id="12680">
    <literal><![CDATA[
      K(x,y * (z * (u * a(w,v5,w)))) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(12514(a,1),12645(a,1,2,2))].">
      <j1 rule="para" parents="12514 12645"/>
    </justification>
  </clause>

  <clause id="12681">
    <literal><![CDATA[
      K(x,y \ (a(z,u,z) \ w)) = K(x,y \ w)
    ]]></literal>
    <justification jstring="[para(10(a,1),12646(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 12646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12682">
    <literal><![CDATA[
      K(x,y \ T(z * u,z)) = K(x,y \ (u * z))
    ]]></literal>
    <justification jstring="[para(8248(a,1),12646(a,1,2,2))].">
      <j1 rule="para" parents="8248 12646"/>
    </justification>
  </clause>

  <clause id="12683">
    <literal><![CDATA[
      K(x,y \ (z * R(u,w,u))) = K(x,y \ (z * u))
    ]]></literal>
    <justification jstring="[para(9322(a,1),12646(a,1,2,2))].">
      <j1 rule="para" parents="9322 12646"/>
    </justification>
  </clause>

  <clause id="12684">
    <literal><![CDATA[
      K(x,y \ (R(z,u,z) * w)) = K(x,y \ (z * w))
    ]]></literal>
    <justification jstring="[para(9334(a,1),12646(a,1,2,2))].">
      <j1 rule="para" parents="9334 12646"/>
    </justification>
  </clause>

  <clause id="12685">
    <literal><![CDATA[
      T(x,y / T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(3625(a,1),12666(a,1,2))].">
      <j1 rule="para" parents="3625 12666"/>
    </justification>
  </clause>

  <clause id="12686">
    <literal><![CDATA[
      K(((x \ 1) \ 1) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,z) = u
    ]]></literal>
    <justification jstring="[para(2687(a,1),12671(a,1,1))].">
      <j1 rule="para" parents="2687 12671"/>
    </justification>
  </clause>

  <clause id="12687">
    <literal><![CDATA[
      T(x,y * (a(z,u,z) \ w)) = T(x,y * w)
    ]]></literal>
    <justification jstring="[hyper(124,a,12677,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 12677 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12689">
    <literal><![CDATA[
      K(x,y \ K(z \ u,z)) = K(x,y \ K(u,z))
    ]]></literal>
    <justification jstring="[para(8206(a,1),12681(a,1,2,2))].">
      <j1 rule="para" parents="8206 12681"/>
    </justification>
  </clause>

  <clause id="12690">
    <literal><![CDATA[
      K(x,y \ K(z \ 1,u)) = K(x,y \ K(z \ u,u))
    ]]></literal>
    <justification jstring="[para(8258(a,1),12681(a,1,2,2))].">
      <j1 rule="para" parents="8258 12681"/>
    </justification>
  </clause>

  <clause id="12691">
    <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(12631(a,1),12685(a,1,2,2))].">
      <j1 rule="para" parents="12631 12685"/>
    </justification>
  </clause>

  <clause id="12692">
    <literal><![CDATA[
      T(x,y * (R(z,u,z) \ w)) = T(x,y * (z \ w))
    ]]></literal>
    <justification jstring="[para(9339(a,1),12687(a,1,2,2))].">
      <j1 rule="para" parents="9339 12687"/>
    </justification>
  </clause>

  <clause id="12693">
    <literal><![CDATA[
      K(K(x,x \ y) * z,u) = K(K(x,y) * z,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),12616(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10 12616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12694">
    <literal><![CDATA[
      T(x,T(y * z,y) \ u) = (w * K((z * y) \ u,x)) \ (w * x)
    ]]></literal>
    <justification jstring="[para(12617(a,1),5447(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="12617 5447"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12696">
    <literal><![CDATA[
      (x \ (x * K(y \ x,z))) \ (x * K(x / y,z)) = L(x,K(y \ x,z),x)
    ]]></literal>
    <justification jstring="[para(12621(a,1),8766(a,1,1,2))].">
      <j1 rule="para" parents="12621 8766"/>
    </justification>
  </clause>

  <clause id="12697">
    <literal><![CDATA[
      K((x \ y) * z,T(u,T(y / x,y))) = K(z * T(y / x,y),u)
    ]]></literal>
    <justification jstring="[hyper(12210,a,12634,a),flip(a)].">
      <j1 rule="hyper" parents="12210 12634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12698">
    <literal><![CDATA[
      K(x,L(T(y * z,y) \ u,w,v5)) = K(L(x,w,v5),(z * y) \ u)
    ]]></literal>
    <justification jstring="[hyper(10963,a,12648,a)].">
      <j1 rule="hyper" parents="10963 12648"/>
    </justification>
  </clause>

  <clause id="12699">
    <literal><![CDATA[
      T(x,T(y * z,y) \ u) = T(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[hyper(124,a,12648,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 12648 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12700">
    <literal><![CDATA[
      K(x,((y \ z) * y) \ u) = K(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(10(a,1),12648(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="10 12648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12701">
    <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(12648(a,1),7620(a,1,1,2))].">
      <j1 rule="para" parents="12648 7620"/>
    </justification>
  </clause>

  <clause id="12703">
    <literal><![CDATA[
      T(x,y / T((z \ u) \ u,w)) = T(x,y / T(T(z,w),u))
    ]]></literal>
    <justification jstring="[para(6668(a,2),12655(a,1,2,2))].">
      <j1 rule="para" parents="6668 12655"/>
    </justification>
  </clause>

  <clause id="12704">
    <literal><![CDATA[
      K(x,((y \ z) \ z) * u) = x \ T(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(121,a,12656,a(flip),b,4222,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="121 12656 4222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12705">
    <literal><![CDATA[
      T(x,T(y,y \ z) * u) = T(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[para(112(a,2),12656(a,1,2,1))].">
      <j1 rule="para" parents="112 12656"/>
    </justification>
  </clause>

  <clause id="12706">
    <literal><![CDATA[
      K(x,y * T(z,z * u)) = x \ T(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(333,a,4215,a(flip),b,12657,a),flip(a)].">
      <j1 rule="hyper" parents="333 4215 12657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12707">
    <literal><![CDATA[
      K(x,y * T(z,u * z)) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(3678(a,2),12657(a,1,2,2))].">
      <j1 rule="para" parents="3678 12657"/>
    </justification>
  </clause>

  <clause id="12708">
    <literal><![CDATA[
      K(T(x / y,x) \ z,u) = (w * K(u,(y \ x) \ z)) \ w
    ]]></literal>
    <justification jstring="[para(12659(a,1),5990(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="12659 5990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12709">
    <literal><![CDATA[
      K(x,L(((y \ z) \ z) \ u,w,v5)) = K(L(x,w,v5),T(y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(10963,a,12660,a)].">
      <j1 rule="hyper" parents="10963 12660"/>
    </justification>
  </clause>

  <clause id="12710">
    <literal><![CDATA[
      K(x,((y \ z) \ z) \ u) = (w * K(T(y,z) \ u,x)) \ w
    ]]></literal>
    <justification jstring="[hyper(333,a,5990,a,b,12660,a),flip(a)].">
      <j1 rule="hyper" parents="333 5990 12660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12711">
    <literal><![CDATA[
      T(x,((y \ z) \ z) \ u) = T(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(124,a,12660,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 12660 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12712">
    <literal><![CDATA[
      K(x,T(((y / z) \ 1) * y,y) \ u) = K(x,(((z \ y) \ 1) * y) \ u)
    ]]></literal>
    <justification jstring="[para(5743(a,1),12660(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5743 12660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12713">
    <literal><![CDATA[
      T(x,((y \ z) \ z) / u) = T(x,T(y,z) / u)
    ]]></literal>
    <justification jstring="[hyper(124,a,12664,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 12664 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12714">
    <literal><![CDATA[
      K(x,T(y,y \ z) / u) = K(x,T(y,z) / u)
    ]]></literal>
    <justification jstring="[para(112(a,2),12664(a,1,2,1))].">
      <j1 rule="para" parents="112 12664"/>
    </justification>
  </clause>

  <clause id="12715">
    <literal><![CDATA[
      K(x,T(y * (1 / z),z) / u) = K(x,T(y * (1 / z),y) / u)
    ]]></literal>
    <justification jstring="[para(5900(a,2),12664(a,1,2,1))].">
      <j1 rule="para" parents="5900 12664"/>
    </justification>
  </clause>

  <clause id="12716">
    <literal><![CDATA[
      K((x \ y) \ (z * u),L(w,x \ y,x)) = K(y \ (x * T(u * z,u)),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,10909,a(flip),b,12672,a),flip(a)].">
      <j1 rule="hyper" parents="63 10909 12672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12717">
    <literal><![CDATA[
      K(x \ ((y \ z) * y),u) = K(x \ T(z,y),u)
    ]]></literal>
    <justification jstring="[para(10(a,1),12672(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 12672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12718">
    <literal><![CDATA[
      K(x \ K(y,(z * y) * u),w) = K(x \ K(y,z * u),w)
    ]]></literal>
    <justification jstring="[para(11401(a,1),12673(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="11401 12673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12719">
    <literal><![CDATA[
      K(x,((y \ z) * y) / u) = K(x,T(z,y) / u)
    ]]></literal>
    <justification jstring="[para(10(a,1),12674(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="10 12674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12720">
    <literal><![CDATA[
      K(x,T(L(y,z,y) * u,y) / w) = K(x,(u * L(y,z,y)) / w)
    ]]></literal>
    <justification jstring="[para(9483(a,1),12674(a,1,2,1))].">
      <j1 rule="para" parents="9483 12674"/>
    </justification>
  </clause>

  <clause id="12721">
    <literal><![CDATA[
      K(x,y * ((z \ u) / z)) = K(x,y * (z \ (u / z)))
    ]]></literal>
    <justification jstring="[para(113(a,1),12675(a,1,2,2,1))].">
      <j1 rule="para" parents="113 12675"/>
    </justification>
  </clause>

  <clause id="12722">
    <literal><![CDATA[
      K(x,y * ((T(z,u / (u / w)) / w) * K(w,w \ u))) = K(x,y * ((u / (u / w)) \ z))
    ]]></literal>
    <justification jstring="[para(7672(a,1),12675(a,1,2,2))].">
      <j1 rule="para" parents="7672 12675"/>
    </justification>
  </clause>

  <clause id="12723">
    <literal><![CDATA[
      K(x,T(y,z * u) * (z * u)) = K(x,T(u * z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(12285,a,12678,a),flip(a)].">
      <j1 rule="hyper" parents="12285 12678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12724">
    <literal><![CDATA[
      T(x,y * T(z * u,z)) = T(x,y * (u * z))
    ]]></literal>
    <justification jstring="[hyper(124,a,12678,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 12678 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12725">
    <literal><![CDATA[
      K(x,y * ((z \ u) * z)) = K(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[para(10(a,1),12678(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10 12678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12726">
    <literal><![CDATA[
      K(x,y \ ((z \ u) * z)) = K(x,y \ T(u,z))
    ]]></literal>
    <justification jstring="[para(10(a,1),12682(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10 12682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12727">
    <literal><![CDATA[
      K(x,y \ (z * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (x * z)) = u
    ]]></literal>
    <justification jstring="[para(12682(a,1),7528(a,1))].">
      <j1 rule="para" parents="12682 7528"/>
    </justification>
  </clause>

  <clause id="12728">
    <literal><![CDATA[
      K(K(x,x \ y) * z,u) = T(u,K(x,y) * z) \ u
    ]]></literal>
    <justification jstring="[hyper(333,a,4205,a(flip),b,12693,a),flip(a)].">
      <j1 rule="hyper" parents="333 4205 12693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12729">
    <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(126,a,12699,a(flip),b,8027,a),flip(a)].">
      <j1 rule="hyper" parents="126 12699 8027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12730">
    <literal><![CDATA[
      T(x,((y \ z) * y) \ u) = T(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(10(a,1),12699(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="10 12699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12731">
    <literal><![CDATA[
      (((x \ y) * x) \ z) * K(y,T(y,x) \ z) = (K(x,x \ y) * z) / y
    ]]></literal>
    <justification jstring="[para(12700(a,1),10157(a,1,2))].">
      <j1 rule="para" parents="12700 10157"/>
    </justification>
  </clause>

  <clause id="12732">
    <literal><![CDATA[
      T(x,T(y,z) \ z) = T(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(63,a,7014,a(flip),b,12711,a),flip(a)].">
      <j1 rule="hyper" parents="63 7014 12711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12733">
    <literal><![CDATA[
      T(x,y \ T(z,y)) = T(x,z / y)
    ]]></literal>
    <justification jstring="[para(3628(a,1),12732(a,1,2))].">
      <j1 rule="para" parents="3628 12732"/>
    </justification>
  </clause>

  <clause id="12734">
    <literal><![CDATA[
      T(x,T(y \ T(z,y),u)) = K(x,u) * T(x * K(u,x),z / y)
    ]]></literal>
    <justification jstring="[hyper(126,a,12733,a(flip),b,8027,a),flip(a)].">
      <j1 rule="hyper" parents="126 12733 8027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12735">
    <literal><![CDATA[
      T(x,y / z) \ (T(z \ T(y,z),x) \ u) = x \ ((z \ T(y,z)) \ u)
    ]]></literal>
    <justification jstring="[para(12733(a,1),4696(a,1,1))].">
      <j1 rule="para" parents="12733 4696"/>
    </justification>
  </clause>

  <clause id="12736">
    <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(12713(a,1),12284(a,1,2,1))].">
      <j1 rule="para" parents="12713 12284"/>
    </justification>
  </clause>

  <clause id="12737">
    <literal><![CDATA[
      K(x,T(y,y \ z) / z) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(333,a,12638,a(flip),b,12714,a),flip(a)].">
      <j1 rule="hyper" parents="333 12638 12714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12738">
    <literal><![CDATA[
      K(x,y \ z) / (T(z,z \ y) / y) != u
    ]]></literal>
    <literal><![CDATA[
      1 / T(T(z,z \ y) / y,x) = u
    ]]></literal>
    <justification jstring="[para(12737(a,1),4360(a,1,1))].">
      <j1 rule="para" parents="12737 4360"/>
    </justification>
  </clause>

  <clause id="12739">
    <literal><![CDATA[
      K(x \ T(y,z),T(u,(z \ y) * z)) = K(((z \ y) * z) / x,u)
    ]]></literal>
    <justification jstring="[hyper(7062,a,12717,a),flip(a)].">
      <j1 rule="hyper" parents="7062 12717"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12740">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),(z * u) * y) = T(x,y * T(u * z,u))
    ]]></literal>
    <justification jstring="[hyper(333,a,12228,a,b,12724,a)].">
      <j1 rule="hyper" parents="333 12228 12724"/>
    </justification>
  </clause>

  <clause id="12741">
    <literal><![CDATA[
      T(x,y * ((z \ u) * z)) = T(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[para(10(a,1),12724(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10 12724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12742">
    <literal><![CDATA[
      T(x,y * T(L(z,u,u \ 1),1 / u)) = T(x,y * ((u * z) * (1 / u)))
    ]]></literal>
    <justification jstring="[para(2652(a,1),12724(a,1,2,2,1))].">
      <j1 rule="para" parents="2652 12724"/>
    </justification>
  </clause>

  <clause id="12743">
    <literal><![CDATA[
      K(x,y * T((z \ 1) \ u,z)) = K(x,y * ((z \ K(z,u)) \ u))
    ]]></literal>
    <justification jstring="[para(8519(a,2),12725(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8519 12725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12744">
    <literal><![CDATA[
      (x * ((x \ y) * x)) * K(x,x * T(y,x)) = T(x,x * y) * ((x \ y) * x)
    ]]></literal>
    <justification jstring="[para(12725(a,1),7794(a,1,2))].">
      <j1 rule="para" parents="12725 7794"/>
    </justification>
  </clause>

  <clause id="12745">
    <literal><![CDATA[
      T(x,T(y,z) \ (z \ y)) = T(x,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,5801,a(flip),b,12730,a),flip(a)].">
      <j1 rule="hyper" parents="63 5801 12730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12746">
    <literal><![CDATA[
      L(x,y,T(T(z,u),u \ 1)) = L(x,y,T(T(z,u),u \ z))
    ]]></literal>
    <justification jstring="[para(12745(a,1),11856(a,1,3))].">
      <j1 rule="para" parents="12745 11856"/>
    </justification>
  </clause>

  <clause id="12747">
    <literal><![CDATA[
      T(x,y * T(z * T(u,u \ w),(u \ w) \ w)) = T(x,y * (T(z,T(u,w)) * ((u \ w) \ w)))
    ]]></literal>
    <justification jstring="[para(6461(a,1),12741(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="6461 12741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12748">
    <literal><![CDATA[
      K(x,y * (((z \ u) \ u) * w)) = K(x,y * (T(z,u) * w))
    ]]></literal>
    <justification jstring="[para(8668(a,1),12679(a,1,2,2,1))].">
      <j1 rule="para" parents="8668 12679"/>
    </justification>
  </clause>

  <clause id="12749">
    <literal><![CDATA[
      K(x,y \ (z * ((u \ w) \ w))) = K(x,y \ (z * T(u,w)))
    ]]></literal>
    <justification jstring="[para(8668(a,1),12683(a,1,2,2,2))].">
      <j1 rule="para" parents="8668 12683"/>
    </justification>
  </clause>

  <clause id="12750">
    <literal><![CDATA[
      K(x,y \ ((z * u) * z)) = K(x,y \ (z * (u * z)))
    ]]></literal>
    <justification jstring="[para(107(a,1),12684(a,1,2,2))].">
      <j1 rule="para" parents="107 12684"/>
    </justification>
  </clause>

  <clause id="12751">
    <literal><![CDATA[
      K(x,y \ (((z \ u) \ u) * w)) = K(x,y \ (T(z,u) * w))
    ]]></literal>
    <justification jstring="[para(8668(a,1),12684(a,1,2,2,1))].">
      <j1 rule="para" parents="8668 12684"/>
    </justification>
  </clause>

  <clause id="12752">
    <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(3764(a,1),12651(a,1,2,1,1))].">
      <j1 rule="para" parents="3764 12651"/>
    </justification>
  </clause>

  <clause id="12753">
    <literal><![CDATA[
      K(x,y * ((z * u) * z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z * (u * z))) = w
    ]]></literal>
    <justification jstring="[para(84(a,1),12669(a,1,2,2))].">
      <j1 rule="para" parents="84 12669"/>
    </justification>
  </clause>

  <clause id="12754">
    <literal><![CDATA[
      K(x,y * K(z * u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(8243(a,1),12669(a,1,2,2))].">
      <j1 rule="para" parents="8243 12669"/>
    </justification>
  </clause>

  <clause id="12755">
    <literal><![CDATA[
      K(x,y * (T(z,u) / u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (u \ z)) = w
    ]]></literal>
    <justification jstring="[para(8251(a,1),12669(a,1,2,2))].">
      <j1 rule="para" parents="8251 12669"/>
    </justification>
  </clause>

  <clause id="12756">
    <literal><![CDATA[
      K(x,y * T(z * u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (u * z)) = w
    ]]></literal>
    <justification jstring="[para(9256(a,1),12669(a,1,2,2))].">
      <j1 rule="para" parents="9256 12669"/>
    </justification>
  </clause>

  <clause id="12757">
    <literal><![CDATA[
      K(x,((y \ z) \ z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(12704(a,2),4306(a,1))].">
      <j1 rule="para" parents="12704 4306"/>
    </justification>
  </clause>

  <clause id="12758">
    <literal><![CDATA[
      K(x,y * T(z,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(12706(a,2),4306(a,1))].">
      <j1 rule="para" parents="12706 4306"/>
    </justification>
  </clause>

  <clause id="12759">
    <literal><![CDATA[
      T(x,y * ((z \ u) / z)) = T(x,y * (z \ (u / z)))
    ]]></literal>
    <justification jstring="[hyper(124,a,12721,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 12721 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12760">
    <literal><![CDATA[
      T(x,K(y,y \ z) * u) = T(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(4209,a,12728,a)].">
      <j1 rule="hyper" parents="4209 12728"/>
    </justification>
  </clause>

  <clause id="12761">
    <literal><![CDATA[
      a(x,(y * z) \ (u * z),x) = a(x,y \ u,x)
    ]]></literal>
    <justification jstring="[hyper(11931,a,12588,a),flip(a)].">
      <j1 rule="hyper" parents="11931 12588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12762">
    <literal><![CDATA[
      a(x,(y * z) \ (u * z),x) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y \ u,x) = w
    ]]></literal>
    <justification jstring="[para(12588(a,1),11931(a,1))].">
      <j1 rule="para" parents="12588 11931"/>
    </justification>
  </clause>

  <clause id="12764">
    <literal><![CDATA[
      L(x,(y * z) \ (u * z),x) = (w / x) \ (a(x,y \ u,x) \ w)
    ]]></literal>
    <justification jstring="[para(12761(a,1),9282(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12761 9282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12765">
    <literal><![CDATA[
      L(x,y,z \ K(u,u \ w)) = L(x,y,z \ K(u,w))
    ]]></literal>
    <justification jstring="[para(12595(a,1),11827(a,1,3))].">
      <j1 rule="para" parents="12595 11827"/>
    </justification>
  </clause>

  <clause id="12766">
    <literal><![CDATA[
      K(x \ K(y,y \ z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x \ K(y,z),u) = w
    ]]></literal>
    <justification jstring="[para(12595(a,1),12623(a,1,1))].">
      <j1 rule="para" parents="12595 12623"/>
    </justification>
  </clause>

  <clause id="12767">
    <literal><![CDATA[
      K(x,y \ K(z,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(12595(a,1),12636(a,1,2))].">
      <j1 rule="para" parents="12595 12636"/>
    </justification>
  </clause>

  <clause id="12768">
    <literal><![CDATA[
      K(x,y * (K(z,z * u) * w)) = K(x,y * (K(z,u) * w))
    ]]></literal>
    <justification jstring="[para(9245(a,1),12680(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9245 12680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12769">
    <literal><![CDATA[
      K(x,y * (z * (u \ K(w,w \ v5)))) = K(x,y * (z * (u \ K(w,v5))))
    ]]></literal>
    <justification jstring="[para(12595(a,1),12680(a,1,2,2,2))].">
      <j1 rule="para" parents="12595 12680"/>
    </justification>
  </clause>

  <clause id="12770">
    <literal><![CDATA[
      K(x,y * (z / T(u,z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (u \ z)) = w
    ]]></literal>
    <justification jstring="[para(3625(a,1),12755(a,1,2,2))].">
      <j1 rule="para" parents="3625 12755"/>
    </justification>
  </clause>

  <clause id="12771">
    <literal><![CDATA[
      K(x,T(y,y \ z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(112(a,2),12757(a,1,2,1))].">
      <j1 rule="para" parents="112 12757"/>
    </justification>
  </clause>

  <clause id="12772">
    <literal><![CDATA[
      a(x,y \ (z * T(y,u)),x) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,K(u,y) \ z,x) = w
    ]]></literal>
    <justification jstring="[para(4224(a,1),12762(a,1,2,1))].">
      <j1 rule="para" parents="4224 12762"/>
    </justification>
  </clause>

  <clause id="12773">
    <literal><![CDATA[
      K(x,T(y,y \ z) * u) = K(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(12771,a,xx),flip(a)].">
      <j1 rule="hyper" parents="12771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12774">
    <literal><![CDATA[
      K(x,T(y,y * z) * u) = K(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[para(9(a,1),12773(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="9 12773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12775">
    <literal><![CDATA[
      K(x,T(y / z,y) * u) = K(x,(z \ y) * u)
    ]]></literal>
    <justification jstring="[para(332(a,1),12773(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="332 12773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12776">
    <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(10963,a,12774,a)].">
      <j1 rule="hyper" parents="10963 12774"/>
    </justification>
  </clause>

  <clause id="12777">
    <literal><![CDATA[
      (x * y) \ (x * ((y * z) * a(u,w,u))) = L(z,y,x) * a(u,w,u)
    ]]></literal>
    <justification jstring="[para(18(a,2),12597(a,2,1))].">
      <j1 rule="para" parents="18 12597"/>
    </justification>
  </clause>

  <clause id="12778">
    <literal><![CDATA[
      x \ (y * (a(z,u,z) * w)) = (x \ (y * w)) * a(z,u,z)
    ]]></literal>
    <justification jstring="[para(9246(a,2),12597(a,1,2,2))].">
      <j1 rule="para" parents="9246 12597"/>
    </justification>
  </clause>

  <clause id="12780">
    <literal><![CDATA[
      K(T(x / y,x) \ z,u) = K((y \ x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(333,a,5990,a(flip),b,12708,a),flip(a)].">
      <j1 rule="hyper" parents="333 5990 12708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12781">
    <literal><![CDATA[
      K(((x \ y) \ y) \ z,u) = K(T(x,y) \ z,u)
    ]]></literal>
    <justification jstring="[para(76(a,1),12780(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="76 12780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12782">
    <literal><![CDATA[
      K(T(x,y) \ z,T(u,z)) = K(z / ((x \ y) \ y),u)
    ]]></literal>
    <justification jstring="[hyper(7062,a,12781,a),flip(a)].">
      <j1 rule="hyper" parents="7062 12781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12783">
    <literal><![CDATA[
      K(T(x,x \ y) \ z,u) = K(T(x,y) \ z,u)
    ]]></literal>
    <justification jstring="[para(112(a,2),12781(a,1,1,1))].">
      <j1 rule="para" parents="112 12781"/>
    </justification>
  </clause>

  <clause id="12784">
    <literal><![CDATA[
      K(T(x \ y,y) \ z,u) = K(T(x \ y,x) \ z,u)
    ]]></literal>
    <justification jstring="[para(3674(a,2),12781(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="3674 12781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12785">
    <literal><![CDATA[
      K(T(x * y,y) \ ((x * y) * z),u) = K(K(y * x,x \ 1) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,12286,a(flip),b,12783,a),flip(a)].">
      <j1 rule="hyper" parents="63 12286 12783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12786">
    <literal><![CDATA[
      K(x / ((y \ z) \ z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x / T(y,z),u) = w
    ]]></literal>
    <justification jstring="[para(12782(a,1),7062(a,1))].">
      <j1 rule="para" parents="12782 7062"/>
    </justification>
  </clause>

  <clause id="12787">
    <literal><![CDATA[
      K(x,((y \ z) \ z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z) \ u) = w
    ]]></literal>
    <justification jstring="[para(12710(a,2),6024(a,1))].">
      <j1 rule="para" parents="12710 6024"/>
    </justification>
  </clause>

  <clause id="12788">
    <literal><![CDATA[
      K(x,T(y,y \ z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z) \ u) = w
    ]]></literal>
    <justification jstring="[para(112(a,2),12787(a,1,2,1))].">
      <j1 rule="para" parents="112 12787"/>
    </justification>
  </clause>

  <clause id="12789">
    <literal><![CDATA[
      K(x,T(y * z,y) * u) = K(x,(z * y) * u)
    ]]></literal>
    <justification jstring="[hyper(12284,a,12723,a),flip(a)].">
      <j1 rule="hyper" parents="12284 12723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12790">
    <literal><![CDATA[
      K(x,T(y * z,y) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z * y) * u) = w
    ]]></literal>
    <justification jstring="[para(12723(a,1),12284(a,1))].">
      <j1 rule="para" parents="12723 12284"/>
    </justification>
  </clause>

  <clause id="12791">
    <literal><![CDATA[
      T(x,T(y * z,y) * u) = x * K(x,(z * y) * u)
    ]]></literal>
    <justification jstring="[hyper(126,a,12789,a(flip),b,4215,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="126 12789 4215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12792">
    <literal><![CDATA[
      K(x,((y \ z) * y) * u) = K(x,T(z,y) * u)
    ]]></literal>
    <justification jstring="[para(10(a,1),12789(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="10 12789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12793">
    <literal><![CDATA[
      T(x,((y \ z) * y) * u) = T(x,T(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(124,a,12792,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 12792 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12794">
    <literal><![CDATA[
      T(x,T(y * z,y) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(z * y) * u) = w
    ]]></literal>
    <justification jstring="[para(12791(a,2),4285(a,1))].">
      <j1 rule="para" parents="12791 4285"/>
    </justification>
  </clause>

  <clause id="12795">
    <literal><![CDATA[
      L(x,y,T(T(z,u),u \ 1)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,11870,a(flip),b,12746,a),flip(a)].">
      <j1 rule="hyper" parents="333 11870 12746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12797">
    <literal><![CDATA[
      K(x,y \ (T(z / u,z) * w)) = K(x,y \ ((u \ z) * w))
    ]]></literal>
    <justification jstring="[para(79(a,1),12751(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="79 12751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12798">
    <literal><![CDATA[
      K(x,y * (K(z,z \ u) * w)) = K(x,y * (K(z,u) * w))
    ]]></literal>
    <justification jstring="[para(10(a,1),12768(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="10 12768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12799">
    <literal><![CDATA[
      a(x,y,x) \ (z * (a(x,y,x) * u)) = z * u
    ]]></literal>
    <justification jstring="[hyper(333,a,9247,a(flip),b,12778,a),flip(a)].">
      <j1 rule="hyper" parents="333 9247 12778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12800">
    <literal><![CDATA[
      a(x,y,x) \ (z * u) = z * (a(x,y,x) \ u)
    ]]></literal>
    <justification jstring="[para(10(a,1),12799(a,1,2,2))].">
      <j1 rule="para" parents="10 12799"/>
    </justification>
  </clause>

  <clause id="12801">
    <literal><![CDATA[
      a(x,y,x) * (z * u) != w
    ]]></literal>
    <literal><![CDATA[
      z * (a(x,y,x) * u) = w
    ]]></literal>
    <justification jstring="[para(12799(a,1),273(a,1,2)),flip(b)].">
      <j1 rule="para" parents="12799 273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12802">
    <literal><![CDATA[
      x * (a(x,y,x) \ L(x \ a(x,y,x),z,u)) = L(x \ L(x,z,u),y,x)
    ]]></literal>
    <justification jstring="[hyper(8908,a,12800,a),flip(a)].">
      <j1 rule="hyper" parents="8908 12800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12803">
    <literal><![CDATA[
      a(x,y,x) \ (z \ a(x,y,x)) = z \ 1
    ]]></literal>
    <justification jstring="[hyper(585,a,12800,a),flip(a)].">
      <j1 rule="hyper" parents="585 12800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12804">
    <literal><![CDATA[
      x \ ((a(y,z,y) \ x) * u) = a(y,z,y) \ u
    ]]></literal>
    <justification jstring="[hyper(34,a,11798,a,b,12800,a(flip))].">
      <j1 rule="hyper" parents="34 11798 12800"/>
    </justification>
  </clause>

  <clause id="12805">
    <literal><![CDATA[
      (a(x,y,x) \ z) * u = z * (a(x,y,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(142,a,12804,a),flip(a)].">
      <j1 rule="hyper" parents="142 12804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12806">
    <literal><![CDATA[
      a(x,y,x) \ (z \ u) = z \ (a(x,y,x) \ u)
    ]]></literal>
    <justification jstring="[para(11798(a,1),12804(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11798 12804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12807">
    <literal><![CDATA[
      (a(x,y,x) \ z) \ u = a(x,y,x) * (z \ u)
    ]]></literal>
    <justification jstring="[hyper(121,a,71,a(flip),b,12805,a)].">
      <j1 rule="hyper" parents="121 71 12805"/>
    </justification>
  </clause>

  <clause id="12808">
    <literal><![CDATA[
      ((x * (a(y,z,y) \ u)) * w) / (u * (a(y,z,y) \ w)) = R(x,a(y,z,y) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(197,a,12805,a(flip),b,187,a)].">
      <j1 rule="hyper" parents="197 12805 187"/>
    </justification>
  </clause>

  <clause id="12809">
    <literal><![CDATA[
      K(x,(a(y,z,y) \ u) * w) = K(x,u * w)
    ]]></literal>
    <justification jstring="[para(12805(a,2),12677(a,1,2))].">
      <j1 rule="para" parents="12805 12677"/>
    </justification>
  </clause>

  <clause id="12810">
    <literal><![CDATA[
      (x * (a(y,z,y) \ u)) * w = (x * u) * (a(y,z,y) \ w)
    ]]></literal>
    <justification jstring="[para(12800(a,1),12805(a,1,1))].">
      <j1 rule="para" parents="12800 12805"/>
    </justification>
  </clause>

  <clause id="12811">
    <literal><![CDATA[
      K(x,K(y \ z,y) * u) = K(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(8206(a,1),12809(a,1,2,1))].">
      <j1 rule="para" parents="8206 12809"/>
    </justification>
  </clause>

  <clause id="12812">
    <literal><![CDATA[
      K(x,(L(y,z,y) * u) * w) = K(x,(y * u) * w)
    ]]></literal>
    <justification jstring="[para(9280(a,1),12809(a,1,2,1))].">
      <j1 rule="para" parents="9280 12809"/>
    </justification>
  </clause>

  <clause id="12813">
    <literal><![CDATA[
      a(x,y,x) \ (z \ x) = z \ L(x,y,x)
    ]]></literal>
    <justification jstring="[para(8239(a,1),12806(a,2,2))].">
      <j1 rule="para" parents="8239 12806"/>
    </justification>
  </clause>

  <clause id="12814">
    <literal><![CDATA[
      a(x,y,x) \ (z \ (x * u)) = z \ (L(x,y,x) * u)
    ]]></literal>
    <justification jstring="[para(9280(a,1),12806(a,2,2))].">
      <j1 rule="para" parents="9280 12806"/>
    </justification>
  </clause>

  <clause id="12815">
    <literal><![CDATA[
      L(x,y,x) \ (z \ L(x,y,x)) = x \ (z \ x)
    ]]></literal>
    <justification jstring="[hyper(121,a,12813,a(flip),b,9273,a)].">
      <j1 rule="hyper" parents="121 12813 9273"/>
    </justification>
  </clause>

  <clause id="12816">
    <literal><![CDATA[
      K(x,y * (z \ L(u,w,u))) = K(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[para(12813(a,1),12677(a,1,2,2))].">
      <j1 rule="para" parents="12813 12677"/>
    </justification>
  </clause>

  <clause id="12817">
    <literal><![CDATA[
      (x \ y) \ ((x \ L(y,z,y)) * u) = a(y,z,y) \ u
    ]]></literal>
    <justification jstring="[para(12813(a,1),12804(a,1,2,1))].">
      <j1 rule="para" parents="12813 12804"/>
    </justification>
  </clause>

  <clause id="12818">
    <literal><![CDATA[
      (a(x,y,x) \ z) \ u = (z \ u) * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,9246,a(flip),b,12807,a),flip(a)].">
      <j1 rule="hyper" parents="333 9246 12807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12819">
    <literal><![CDATA[
      K((a(x,y,x) \ z) \ u,w) = K(z \ u,w)
    ]]></literal>
    <justification jstring="[para(12807(a,2),12610(a,1,1))].">
      <j1 rule="para" parents="12807 12610"/>
    </justification>
  </clause>

  <clause id="12820">
    <literal><![CDATA[
      K(K(x * y,x) \ z,u) = K(K(y,x) \ z,u)
    ]]></literal>
    <justification jstring="[para(8226(a,1),12819(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="8226 12819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12821">
    <literal><![CDATA[
      K((L(x,y,x) * z) \ u,w) = K((x * z) \ u,w)
    ]]></literal>
    <justification jstring="[para(9280(a,1),12819(a,1,1,1))].">
      <j1 rule="para" parents="9280 12819"/>
    </justification>
  </clause>

  <clause id="12822">
    <literal><![CDATA[
      K(x,K(y \ z,y) * u) = x \ T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(333,a,4215,a(flip),b,12811,a),flip(a)].">
      <j1 rule="hyper" parents="333 4215 12811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12823">
    <literal><![CDATA[
      T(x,K(y \ z,y) * u) = T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(124,a,12811,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 12811 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12824">
    <literal><![CDATA[
      K(x,K(y,z) * ((z \ y) \ u)) = K(x,(y / z) \ u)
    ]]></literal>
    <justification jstring="[para(4830(a,1),12811(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4830 12811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12825">
    <literal><![CDATA[
      (x * y) \ L(y,x,y) = T(y * x,y) \ y
    ]]></literal>
    <justification jstring="[hyper(38,a,10070,a,b,12815,a),flip(a)].">
      <j1 rule="hyper" parents="38 10070 12815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12826">
    <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(4154(a,1),12825(a,1,1))].">
      <j1 rule="para" parents="4154 12825"/>
    </justification>
  </clause>

  <clause id="12827">
    <literal><![CDATA[
      x / (y * a(z,u,z)) = a(z,u,z) \ (x / y)
    ]]></literal>
    <justification jstring="[hyper(197,a,195,a(flip),b,12818,a)].">
      <j1 rule="hyper" parents="197 195 12818"/>
    </justification>
  </clause>

  <clause id="12828">
    <literal><![CDATA[
      K(K(x * T(y,K(x,z)),x) \ u,w) = K(K(y,x) \ u,w)
    ]]></literal>
    <justification jstring="[para(6354(a,1),12820(a,2,1,1))].">
      <j1 rule="para" parents="6354 12820"/>
    </justification>
  </clause>

  <clause id="12829">
    <literal><![CDATA[
      K(K(x \ y,x) * z,u) = u / T(u,K(y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(197,a,12823,a(flip),b,4233,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="197 12823 4233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12831">
    <literal><![CDATA[
      L(x,y,z / (u * a(w,v5,w))) = L(x,y,z / u)
    ]]></literal>
    <justification jstring="[para(12827(a,2),11822(a,1,3))].">
      <j1 rule="para" parents="12827 11822"/>
    </justification>
  </clause>

  <clause id="12832">
    <literal><![CDATA[
      K(x,y * (z \ T(u,u * w))) = K(x,y * (z \ T(u,w)))
    ]]></literal>
    <justification jstring="[para(3742(a,1),12816(a,1,2,2,2))].">
      <j1 rule="para" parents="3742 12816"/>
    </justification>
  </clause>

  <clause id="12833">
    <literal><![CDATA[
      K(x,y * (z \ T(u / w,u))) = K(x,y * (z \ (w \ u)))
    ]]></literal>
    <justification jstring="[para(3781(a,1),12816(a,1,2,2,2))].">
      <j1 rule="para" parents="3781 12816"/>
    </justification>
  </clause>

  <clause id="12834">
    <literal><![CDATA[
      K((x * y) \ z,y * x) * (z * u) = (((y * x) \ z) * (y * x)) * u
    ]]></literal>
    <justification jstring="[para(12821(a,1),10177(a,1,1))].">
      <j1 rule="para" parents="12821 10177"/>
    </justification>
  </clause>

  <clause id="12835">
    <literal><![CDATA[
      L(x,y,z / T(u * (w / u),u)) = L(x,y,z / w)
    ]]></literal>
    <justification jstring="[para(9241(a,1),12831(a,1,3,2))].">
      <j1 rule="para" parents="9241 12831"/>
    </justification>
  </clause>

  <clause id="12836">
    <literal><![CDATA[
      K(x,y * (z \ (L(u,w,u) * v5))) = K(x,y * (z \ (u * v5)))
    ]]></literal>
    <justification jstring="[para(12814(a,1),12677(a,1,2,2))].">
      <j1 rule="para" parents="12814 12677"/>
    </justification>
  </clause>

  <clause id="12837">
    <literal><![CDATA[
      (a(x,y,x) \ z) * L(((u \ x) \ ((u \ L(x,y,x)) * z)) \ ((u \ L(x,y,x)) * z),w,v5) = L(u \ x,w,v5) * ((u \ x) \ ((u \ L(x,y,x)) * z))
    ]]></literal>
    <justification jstring="[para(12817(a,1),670(a,1,1))].">
      <j1 rule="para" parents="12817 670"/>
    </justification>
  </clause>

  <clause id="12838">
    <literal><![CDATA[
      K(x,K(y \ z,y) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y) * u) = w
    ]]></literal>
    <justification jstring="[para(12822(a,2),4306(a,1))].">
      <j1 rule="para" parents="12822 4306"/>
    </justification>
  </clause>

  <clause id="12839">
    <literal><![CDATA[
      K(K(x \ y,x) * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(y,x) * z,u) = w
    ]]></literal>
    <justification jstring="[para(12829(a,2),4313(a,1))].">
      <j1 rule="para" parents="12829 4313"/>
    </justification>
  </clause>

  <clause id="12840">
    <literal><![CDATA[
      L(x,y,(z * (u / z)) \ z) = L(x,y,z / u)
    ]]></literal>
    <justification jstring="[hyper(63,a,11875,a(flip),b,12835,a)].">
      <j1 rule="hyper" parents="63 11875 12835"/>
    </justification>
  </clause>

  <clause id="12841">
    <literal><![CDATA[
      L(x,y,z / (u * z)) = L(x,y,(z * u) \ z)
    ]]></literal>
    <justification jstring="[para(11(a,1),12840(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="11 12840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12842">
    <literal><![CDATA[
      L(x,y,z \ (z / (z / u))) = L(x,y,u / z)
    ]]></literal>
    <justification jstring="[para(4508(a,1),12840(a,1,3))].">
      <j1 rule="para" parents="4508 12840"/>
    </justification>
  </clause>

  <clause id="12843">
    <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(4773(a,2),12840(a,2,3))].">
      <j1 rule="para" parents="4773 12840"/>
    </justification>
  </clause>

  <clause id="12844">
    <literal><![CDATA[
      L(x,y,(z \ u) / u) = L(x,y,u \ (u / z))
    ]]></literal>
    <justification jstring="[para(76(a,1),12842(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="76 12842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12845">
    <literal><![CDATA[
      L(x,y,y \ (y / z)) = L(x,y,y \ (z \ y))
    ]]></literal>
    <justification jstring="[hyper(63,a,10091,a(flip),b,12844,a),flip(a)].">
      <j1 rule="hyper" parents="63 10091 12844"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12846">
    <literal><![CDATA[
      (x * a(y,z,y)) * u = x * (a(y,z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(12801,a,11805,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="12801 11805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12849">
    <literal><![CDATA[
      L(x,a(y,z,y),u) = x
    ]]></literal>
    <justification jstring="[hyper(501,a,12846,a)].">
      <j1 rule="hyper" parents="501 12846"/>
    </justification>
  </clause>

  <clause id="12850">
    <literal><![CDATA[
      (x * a(y,z,y)) \ u = a(y,z,y) \ (x \ u)
    ]]></literal>
    <justification jstring="[hyper(121,a,72,a(flip),b,12846,a)].">
      <j1 rule="hyper" parents="121 72 12846"/>
    </justification>
  </clause>

  <clause id="12851">
    <literal><![CDATA[
      (x * (y * a(z,u,z))) * w = (x * y) * (a(z,u,z) * w)
    ]]></literal>
    <justification jstring="[para(12514(a,1),12846(a,1,1))].">
      <j1 rule="para" parents="12514 12846"/>
    </justification>
  </clause>

  <clause id="12852">
    <literal><![CDATA[
      L(x,K(y,z),z \ y) = x
    ]]></literal>
    <justification jstring="[hyper(9374,a,12849,a)].">
      <j1 rule="hyper" parents="9374 12849"/>
    </justification>
  </clause>

  <clause id="12854">
    <literal><![CDATA[
      x / (a(y,z,y) \ u) = (x / u) * a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(197,a,12849,a(flip),b,518,a(flip))].">
      <j1 rule="hyper" parents="197 12849 518"/>
    </justification>
  </clause>

  <clause id="12855">
    <literal><![CDATA[
      L(x,K(y,z),y \ z) = x
    ]]></literal>
    <justification jstring="[hyper(4391,a,12852,a)].">
      <j1 rule="hyper" parents="4391 12852"/>
    </justification>
  </clause>

  <clause id="12856">
    <literal><![CDATA[
      ((x \ y) * K(x,y)) \ z = K(x,y) \ ((x \ y) \ z)
    ]]></literal>
    <justification jstring="[hyper(578,a,12855,a),flip(a)].">
      <j1 rule="hyper" parents="578 12855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12857">
    <literal><![CDATA[
      (a(x,y,x) * z) \ u = a(x,y,x) \ (z \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,9257,a,b,12850,a)].">
      <j1 rule="hyper" parents="63 9257 12850"/>
    </justification>
  </clause>

  <clause id="12858">
    <literal><![CDATA[
      (x * (y * a(z,u,z))) \ w = a(z,u,z) \ ((x * y) \ w)
    ]]></literal>
    <justification jstring="[para(12514(a,1),12850(a,1,1))].">
      <j1 rule="para" parents="12514 12850"/>
    </justification>
  </clause>

  <clause id="12859">
    <literal><![CDATA[
      K(x,(a(y,z,y) * u) \ w) = K(x,u \ w)
    ]]></literal>
    <justification jstring="[para(12857(a,2),12641(a,1,2))].">
      <j1 rule="para" parents="12857 12641"/>
    </justification>
  </clause>

  <clause id="12860">
    <literal><![CDATA[
      K(x,K(y * z,y) \ u) = K(x,K(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(8249(a,1),12859(a,1,2,1))].">
      <j1 rule="para" parents="8249 12859"/>
    </justification>
  </clause>

  <clause id="12861">
    <literal><![CDATA[
      K(x,K(y * z,z) \ u) = K(x,K(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(8265(a,1),12859(a,1,2,1))].">
      <j1 rule="para" parents="8265 12859"/>
    </justification>
  </clause>

  <clause id="12862">
    <literal><![CDATA[
      K(x,(L(y,z,y) * u) \ w) = K(x,(y * u) \ w)
    ]]></literal>
    <justification jstring="[para(9281(a,1),12859(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9281 12859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12863">
    <literal><![CDATA[
      K(x,(T(y * z,y) \ u) \ w) = K(x,((z * y) \ u) \ w)
    ]]></literal>
    <justification jstring="[para(11613(a,1),12859(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11613 12859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12864">
    <literal><![CDATA[
      K(x,K(y \ z,y) \ u) = K(x,K(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(10(a,1),12860(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="10 12860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12865">
    <literal><![CDATA[
      K(x,K(y,z \ y) \ u) = K(x,K(z,z \ y) \ u)
    ]]></literal>
    <justification jstring="[para(10(a,1),12861(a,1,2,1,1))].">
      <j1 rule="para" parents="10 12861"/>
    </justification>
  </clause>

  <clause id="12866">
    <literal><![CDATA[
      (K(x,y) * (x \ y)) \ z = K(x,y) \ ((x \ y) \ z)
    ]]></literal>
    <justification jstring="[para(6185(a,2),12856(a,1,1))].">
      <j1 rule="para" parents="6185 12856"/>
    </justification>
  </clause>

  <clause id="12867">
    <literal><![CDATA[
      (K(x,y) * (x \ y)) \ z != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * ((x \ y) \ z) = u
    ]]></literal>
    <justification jstring="[para(12866(a,2),4580(a,1))].">
      <j1 rule="para" parents="12866 4580"/>
    </justification>
  </clause>

  <clause id="12868">
    <literal><![CDATA[
      (x * (a(y,z,y) * (u * w))) \ ((x * u) * (a(y,z,y) * w)) = a(x,a(y,z,y) * u,w)
    ]]></literal>
    <justification jstring="[para(12851(a,1),11806(a,1,2))].">
      <j1 rule="para" parents="12851 11806"/>
    </justification>
  </clause>

  <clause id="12869">
    <literal><![CDATA[
      a(x,y,x) \ ((z * u) \ (z * (u * (w * a(x,y,x))))) = L(L(w,a(x,y,x),u),u * a(x,y,x),z)
    ]]></literal>
    <justification jstring="[hyper(9263,a,12858,a),flip(a)].">
      <j1 rule="hyper" parents="9263 12858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12870">
    <literal><![CDATA[
      (x * (a(y,z,y) * u)) \ w = a(y,z,y) \ ((x * u) \ w)
    ]]></literal>
    <justification jstring="[para(9246(a,2),12858(a,1,1,2))].">
      <j1 rule="para" parents="9246 12858"/>
    </justification>
  </clause>

  <clause id="12871">
    <literal><![CDATA[
      L(a(x,y,x),z * y,u) = a(x,(u * z) \ (u * (z * y)),x)
    ]]></literal>
    <justification jstring="[hyper(333,a,12549,a(flip),b,12518,a),flip(a)].">
      <j1 rule="hyper" parents="333 12549 12518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12873">
    <literal><![CDATA[
      K(x,T(y * z,y) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z * y) \ u) = w
    ]]></literal>
    <justification jstring="[para(12662(a,1),9697(a,1))].">
      <j1 rule="para" parents="12662 9697"/>
    </justification>
  </clause>

  <clause id="12875">
    <literal><![CDATA[
      K(x,T((1 / y) * z,y \ 1) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z * (1 / y)) \ u) = w
    ]]></literal>
    <justification jstring="[para(2986(a,1),12873(a,1,2,1))].">
      <j1 rule="para" parents="2986 12873"/>
    </justification>
  </clause>

  <clause id="12877">
    <literal><![CDATA[
      L(a(x,y,x),z * y,u) = a(x,L(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(18(a,2),12871(a,2,2))].">
      <j1 rule="para" parents="18 12871"/>
    </justification>
  </clause>

  <clause id="12878">
    <literal><![CDATA[
      a(x,L(y,z,u),x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(12541,a,12877,a),flip(a)].">
      <j1 rule="hyper" parents="12541 12877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12881">
    <literal><![CDATA[
      R(x,L(y,z,u),x) = x * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(126,a,12878,a(flip),b,8210,a),flip(a)].">
      <j1 rule="hyper" parents="126 12878 8210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12882">
    <literal><![CDATA[
      a(x,(y * z) \ u,x) = a(x,z \ (y \ u),x)
    ]]></literal>
    <justification jstring="[para(311(a,1),12878(a,1,2))].">
      <j1 rule="para" parents="311 12878"/>
    </justification>
  </clause>

  <clause id="12883">
    <literal><![CDATA[
      a(x,(y \ z) \ u,x) = a(x,z \ (y * u),x)
    ]]></literal>
    <justification jstring="[para(515(a,1),12878(a,1,2)),flip(a)].">
      <j1 rule="para" parents="515 12878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12884">
    <literal><![CDATA[
      a(x,(y * z) \ (z * u),x) = a(x,T(y,z) \ u,x)
    ]]></literal>
    <justification jstring="[para(520(a,1),12878(a,1,2))].">
      <j1 rule="para" parents="520 12878"/>
    </justification>
  </clause>

  <clause id="12885">
    <literal><![CDATA[
      L(x,L(y,z,u),x) = a(x,y,x) \ x
    ]]></literal>
    <justification jstring="[para(12878(a,1),8239(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12878 8239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12886">
    <literal><![CDATA[
      R(x,L(y,z,u),x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,8214,a(flip),b,12881,a),flip(a)].">
      <j1 rule="hyper" parents="333 8214 12881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12887">
    <literal><![CDATA[
      R(x,(y * z) \ u,x) = R(x,z \ (y \ u),x)
    ]]></literal>
    <justification jstring="[para(311(a,1),12886(a,1,2))].">
      <j1 rule="para" parents="311 12886"/>
    </justification>
  </clause>

  <clause id="12888">
    <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(12886(a,1),12125(a,1,2,1))].">
      <j1 rule="para" parents="12886 12125"/>
    </justification>
  </clause>

  <clause id="12889">
    <literal><![CDATA[
      L(x,L(y,z,u),x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,8239,a(flip),b,12885,a),flip(a)].">
      <j1 rule="hyper" parents="333 8239 12885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12890">
    <literal><![CDATA[
      L(x,L(y,z,u) \ y,x) = L(x,a(u,z,y),x)
    ]]></literal>
    <justification jstring="[para(1638(a,2),12889(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1638 12889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12891">
    <literal><![CDATA[
      a(x,y \ (z \ (u * y)),x) = a(x,z \ u,x)
    ]]></literal>
    <justification jstring="[hyper(12762,a,12882,a),flip(a)].">
      <j1 rule="hyper" parents="12762 12882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12892">
    <literal><![CDATA[
      a(x,y \ (z \ u),x) = a(x,z \ (u / y),x)
    ]]></literal>
    <justification jstring="[para(12(a,1),12891(a,1,2,2,2))].">
      <j1 rule="para" parents="12 12891"/>
    </justification>
  </clause>

  <clause id="12893">
    <literal><![CDATA[
      K(x \ (y / z),u) \ K((x \ (y / z)) * u,u) = a(u,z \ (x \ y),u)
    ]]></literal>
    <justification jstring="[hyper(333,a,8250,a,b,12892,a)].">
      <j1 rule="hyper" parents="333 8250 12892"/>
    </justification>
  </clause>

  <clause id="12894">
    <literal><![CDATA[
      a(x,y \ (z \ (y * u)),x) = a(x,T(z,y) \ u,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,12882,a(flip),b,12884,a)].">
      <j1 rule="hyper" parents="63 12882 12884"/>
    </justification>
  </clause>

  <clause id="12895">
    <literal><![CDATA[
      a(x,T(y,z) \ (z \ u),x) = a(x,z \ (y \ u),x)
    ]]></literal>
    <justification jstring="[para(10(a,1),12894(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="10 12894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12896">
    <literal><![CDATA[
      K(x,y) * ((y \ x) \ (K(y,x) * z)) = (((y \ x) * y) / y) \ z
    ]]></literal>
    <justification jstring="[hyper(12867,a,12653,a)].">
      <j1 rule="hyper" parents="12867 12653"/>
    </justification>
  </clause>

  <clause id="12898">
    <literal><![CDATA[
      T(x,T(y * z,y) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(z * y) \ u) = w
    ]]></literal>
    <justification jstring="[para(12694(a,2),5458(a,1))].">
      <j1 rule="para" parents="12694 5458"/>
    </justification>
  </clause>

  <clause id="12899">
    <literal><![CDATA[
      K((x \ y) * z,T(u,x \ y)) = K(z * T(y / x,y),u)
    ]]></literal>
    <justification jstring="[para(6466(a,1),12697(a,1,2))].">
      <j1 rule="para" parents="6466 12697"/>
    </justification>
  </clause>

  <clause id="12900">
    <literal><![CDATA[
      K(x * T(y / z,y),u) = K(x * (z \ y),u)
    ]]></literal>
    <justification jstring="[hyper(12210,a,12899,a),flip(a)].">
      <j1 rule="hyper" parents="12210 12899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12901">
    <literal><![CDATA[
      K(x * (y / z),y) = K(x * (z \ y),y)
    ]]></literal>
    <justification jstring="[hyper(7449,a,12900,a)].">
      <j1 rule="hyper" parents="7449 12900"/>
    </justification>
  </clause>

  <clause id="12902">
    <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(12698(a,2),10963(a,1))].">
      <j1 rule="para" parents="12698 10963"/>
    </justification>
  </clause>

  <clause id="12903">
    <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(12709(a,2),10963(a,1))].">
      <j1 rule="para" parents="12709 10963"/>
    </justification>
  </clause>

  <clause id="12904">
    <literal><![CDATA[
      K(x,T(y * (1 / z),z) / u) = K(x,((1 / z) * y) / u)
    ]]></literal>
    <justification jstring="[hyper(333,a,12674,a(flip),b,12715,a),flip(a)].">
      <j1 rule="hyper" parents="333 12674 12715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12905">
    <literal><![CDATA[
      T(x,T(y \ T(z,y),u)) = T(x,T(z / y,u))
    ]]></literal>
    <justification jstring="[hyper(333,a,8025,a(flip),b,12734,a),flip(a)].">
      <j1 rule="hyper" parents="333 8025 12734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12906">
    <literal><![CDATA[
      K(x \ T(y,z),T(u,T(y,z))) = K(((z \ y) * z) / x,u)
    ]]></literal>
    <justification jstring="[para(12224(a,1),12739(a,1,2))].">
      <j1 rule="para" parents="12224 12739"/>
    </justification>
  </clause>

  <clause id="12907">
    <literal><![CDATA[
      K(((x \ y) * x) / z,u) = K(T(y,x) / z,u)
    ]]></literal>
    <justification jstring="[hyper(7062,a,12906,a),flip(a)].">
      <j1 rule="hyper" parents="7062 12906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12908">
    <literal><![CDATA[
      T(x,y * T(z * u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y * (u * z)) = w
    ]]></literal>
    <justification jstring="[para(12740(a,1),12277(a,1))].">
      <j1 rule="para" parents="12740 12277"/>
    </justification>
  </clause>

  <clause id="12909">
    <literal><![CDATA[
      L(x,(y * z) \ (u * z),x) = L(x,y \ u,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,9282,a(flip),b,12764,a),flip(a)].">
      <j1 rule="hyper" parents="333 9282 12764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12910">
    <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(12776(a,2),10963(a,1))].">
      <j1 rule="para" parents="12776 10963"/>
    </justification>
  </clause>

  <clause id="12911">
    <literal><![CDATA[
      (((x \ y) * x) / x) \ z = K(y,x) * ((T(x,y) \ y) \ z)
    ]]></literal>
    <justification jstring="[para(11912(a,1),12896(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11912 12896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12912">
    <literal><![CDATA[
      K(x,y) * ((T(y,x) \ x) \ z) = (y \ x) \ z
    ]]></literal>
    <justification jstring="[para(11(a,1),12911(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 12911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12914">
    <literal><![CDATA[
      K(x * T(y,z),T(x,u)) = K(x * y,T(T(x,u),z))
    ]]></literal>
    <justification jstring="[hyper(9900,a,12546,a)].">
      <j1 rule="hyper" parents="9900 12546"/>
    </justification>
  </clause>

  <clause id="12915">
    <literal><![CDATA[
      K(x * T(y,z),T(x,u)) = T(K(x * y,T(x,u)),z)
    ]]></literal>
    <justification jstring="[hyper(333,a,6365,a(flip),b,12914,a),flip(a)].">
      <j1 rule="hyper" parents="333 6365 12914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12916">
    <literal><![CDATA[
      T(K(x * y,x) * K(x,K(y,z)),u) = K(x * T(y,u),T(x,z))
    ]]></literal>
    <justification jstring="[para(7092(a,2),12915(a,2,1)),flip(a)].">
      <j1 rule="para" parents="7092 12915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12917">
    <literal><![CDATA[
      T(K(x * y,y) * K(y,K(x,z)),u) = K(y * T(x,u),T(y,z))
    ]]></literal>
    <justification jstring="[para(4543(a,2),12916(a,1,1,1))].">
      <j1 rule="para" parents="4543 12916"/>
    </justification>
  </clause>

  <clause id="12918">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) * K(y * x,T(x,u)) = K(x * T(y,u),T(x,z))
    ]]></literal>
    <justification jstring="[hyper(12079,a,12917,a)].">
      <j1 rule="hyper" parents="12079 12917"/>
    </justification>
  </clause>

  <clause id="12919">
    <literal><![CDATA[
      L(x,(y * z) \ ((y * u) * z),x) = L(x,R(u,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,12584,a(flip),b,12586,a),flip(a)].">
      <j1 rule="hyper" parents="63 12584 12586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12921">
    <literal><![CDATA[
      L(x,R(y,z,u),x) = L(x,z \ (z * y),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,12909,a(flip),b,12919,a),flip(a)].">
      <j1 rule="hyper" parents="63 12909 12919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12923">
    <literal><![CDATA[
      L(x,R(y,z,u),x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),12921(a,2,2))].">
      <j1 rule="para" parents="9 12921"/>
    </justification>
  </clause>

  <clause id="12924">
    <literal><![CDATA[
      (x * y) \ (x * (y * (z * a(u,w,u)))) = L(z,y,x) * a(u,w,u)
    ]]></literal>
    <justification jstring="[para(12514(a,1),12777(a,1,2,2))].">
      <j1 rule="para" parents="12514 12777"/>
    </justification>
  </clause>

  <clause id="12925">
    <literal><![CDATA[
      L(x * a(y,z,y),u,w) = L(x,u,w) * a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(504,a,12924,a)].">
      <j1 rule="hyper" parents="504 12924"/>
    </justification>
  </clause>

  <clause id="12926">
    <literal><![CDATA[
      a(x,y,x) \ L(z * a(x,y,x),u,w) = L(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(121,a,12925,a,b,9246,a)].">
      <j1 rule="hyper" parents="121 12925 9246"/>
    </justification>
  </clause>

  <clause id="12927">
    <literal><![CDATA[
      a(x,y,x) \ L(a(x,y,x) * z,u,w) = L(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(35,a,2547,a,b,12925,a(flip))].">
      <j1 rule="hyper" parents="35 2547 12925"/>
    </justification>
  </clause>

  <clause id="12928">
    <literal><![CDATA[
      L(a(x,y,x) \ z,u,w) = a(x,y,x) \ L(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(35,a,2549,a(flip),b,12925,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="35 2549 12925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12929">
    <literal><![CDATA[
      L(x,y,z) * a(x,u,x) = L(R(x,u,x),y,z)
    ]]></literal>
    <justification jstring="[para(8214(a,1),12925(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8214 12925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12930">
    <literal><![CDATA[
      (x \ L(y,z,u)) * a(y,w,y) = x \ L(R(y,w,y),z,u)
    ]]></literal>
    <justification jstring="[para(12929(a,1),12516(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12929 12516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12931">
    <literal><![CDATA[
      L(x,y,z) \ L(a(u,w,u) * x,y,z) = a(u,w,u)
    ]]></literal>
    <justification jstring="[para(12927(a,1),9249(a,1,1))].">
      <j1 rule="para" parents="12927 9249"/>
    </justification>
  </clause>

  <clause id="12932">
    <literal><![CDATA[
      L(K(x,y),z,u) \ L(K(x,x \ y),z,u) = a(x,x \ y,x)
    ]]></literal>
    <justification jstring="[para(8261(a,1),12931(a,1,2,1))].">
      <j1 rule="para" parents="8261 12931"/>
    </justification>
  </clause>

  <clause id="12933">
    <literal><![CDATA[
      L(x,y,z) \ L(u * (T(x,u) / u),y,z) = a(u,u \ x,u)
    ]]></literal>
    <justification jstring="[para(9251(a,1),12931(a,1,2,1))].">
      <j1 rule="para" parents="9251 12931"/>
    </justification>
  </clause>

  <clause id="12934">
    <literal><![CDATA[
      L(K(x,y / ((x \ z) * u)),w,v5) \ L(K(x,x \ (y / ((z / x) * u))),w,v5) = a(x,x \ (y / ((z / x) * u)),x)
    ]]></literal>
    <justification jstring="[para(7928(a,1),12932(a,1,1,1))].">
      <j1 rule="para" parents="7928 12932"/>
    </justification>
  </clause>

  <clause id="12935">
    <literal><![CDATA[
      a(x,x \ L(y,z,u),x) = a(x,x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,9309,a(flip),b,12933,a)].">
      <j1 rule="hyper" parents="63 9309 12933"/>
    </justification>
  </clause>

  <clause id="12937">
    <literal><![CDATA[
      a(x,x \ ((y * z) \ u),x) = a(x,x \ (z \ (y \ u)),x)
    ]]></literal>
    <justification jstring="[para(311(a,1),12935(a,1,2,2))].">
      <j1 rule="para" parents="311 12935"/>
    </justification>
  </clause>

  <clause id="12938">
    <literal><![CDATA[
      a(x,x \ ((y \ z) \ u),x) = a(x,x \ (z \ (y * u)),x)
    ]]></literal>
    <justification jstring="[para(515(a,1),12935(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="515 12935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12939">
    <literal><![CDATA[
      (((x \ y) * x) \ z) * K(y,y \ z) = (K(x,x \ y) * z) / y
    ]]></literal>
    <justification jstring="[para(7410(a,1),12731(a,1,2))].">
      <j1 rule="para" parents="7410 12731"/>
    </justification>
  </clause>

  <clause id="12941">
    <literal><![CDATA[
      T(x,y / z) \ (T(z \ T(y,z),x) \ u) = x \ ((T(z,y) \ y) \ u)
    ]]></literal>
    <justification jstring="[para(3628(a,2),12735(a,2,2,1))].">
      <j1 rule="para" parents="3628 12735"/>
    </justification>
  </clause>

  <clause id="12942">
    <literal><![CDATA[
      K(K(x * y,y \ 1) \ z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(y * x,x) \ z,u) = w
    ]]></literal>
    <justification jstring="[para(12785(a,1),4740(a,1))].">
      <j1 rule="para" parents="12785 4740"/>
    </justification>
  </clause>

  <clause id="12944">
    <literal><![CDATA[
      K(x * T(y,z),x) = K(y * x,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(34,a,7553,a,b,12918,a)].">
      <j1 rule="hyper" parents="34 7553 12918"/>
    </justification>
  </clause>

  <clause id="12945">
    <literal><![CDATA[
      1 / (x \ K(y * x,T(x,z))) = T(x,x * T(y,z))
    ]]></literal>
    <justification jstring="[para(12944(a,1),4403(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="12944 4403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12946">
    <literal><![CDATA[
      T(x,T(y * x,z)) = T(x,x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(6446,a,12945,a)].">
      <j1 rule="hyper" parents="6446 12945"/>
    </justification>
  </clause>

  <clause id="12947">
    <literal><![CDATA[
      T(x,T(x * y,z)) = T(x,x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,4120,a(flip),b,12946,a)].">
      <j1 rule="hyper" parents="63 4120 12946"/>
    </justification>
  </clause>

  <clause id="12948">
    <literal><![CDATA[
      T(x,T(x * (x \ y),z)) = T(x,y * K(x \ y,z))
    ]]></literal>
    <justification jstring="[para(5860(a,1),12947(a,2,2))].">
      <j1 rule="para" parents="5860 12947"/>
    </justification>
  </clause>

  <clause id="12949">
    <literal><![CDATA[
      T(x,y * K(x \ y,z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(10(a,1),12948(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 12948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12951">
    <literal><![CDATA[
      T(x \ y,y * K(x,T(z,y))) = T(x \ y,T(y,z))
    ]]></literal>
    <justification jstring="[para(6373(a,1),12949(a,1,2,2))].">
      <j1 rule="para" parents="6373 12949"/>
    </justification>
  </clause>

  <clause id="12952">
    <literal><![CDATA[
      T(x \ y,K(x,z) * y) = T(x \ y,T(y,z))
    ]]></literal>
    <justification jstring="[para(6390(a,1),12951(a,1,2))].">
      <j1 rule="para" parents="6390 12951"/>
    </justification>
  </clause>

  <clause id="12953">
    <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(12952(a,1),12633(a,1,2,2,1))].">
      <j1 rule="para" parents="12952 12633"/>
    </justification>
  </clause>

  <clause id="12954">
    <literal><![CDATA[
      x \ ((T(y,z) \ z) \ u) = x \ ((y \ T(z,y)) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,12735,a(flip),b,12941,a),flip(a)].">
      <j1 rule="hyper" parents="63 12735 12941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12955">
    <literal><![CDATA[
      K(x \ y,z) \ (y * K(y / x,z)) = L(y,K(x \ y,z),y)
    ]]></literal>
    <justification jstring="[para(9(a,1),12696(a,1,1))].">
      <j1 rule="para" parents="9 12696"/>
    </justification>
  </clause>

  <clause id="12956">
    <literal><![CDATA[
      L(x,K(y \ x,z),x) = x
    ]]></literal>
    <justification jstring="[hyper(7105,a,12955,a)].">
      <j1 rule="hyper" parents="7105 12955"/>
    </justification>
  </clause>

  <clause id="12958">
    <literal><![CDATA[
      L(x,K(y,z),x) = x
    ]]></literal>
    <justification jstring="[para(79(a,1),12956(a,1,2,1))].">
      <j1 rule="para" parents="79 12956"/>
    </justification>
  </clause>

  <clause id="12959">
    <literal><![CDATA[
      T(K(x,y) * z,z) = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,8846,a(flip),b,12958,a)].">
      <j1 rule="hyper" parents="63 8846 12958"/>
    </justification>
  </clause>

  <clause id="12960">
    <literal><![CDATA[
      T(x,x * K(y,z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,3742,a(flip),b,12958,a)].">
      <j1 rule="hyper" parents="63 3742 12958"/>
    </justification>
  </clause>

  <clause id="12963">
    <literal><![CDATA[
      T(K(x,y) \ z,z) = z * K(y,x)
    ]]></literal>
    <justification jstring="[para(4567(a,2),12959(a,1,1))].">
      <j1 rule="para" parents="4567 12959"/>
    </justification>
  </clause>

  <clause id="12964">
    <literal><![CDATA[
      T(x * T(x \ y,z),y) = y * K((x / y) \ 1,z)
    ]]></literal>
    <justification jstring="[para(4487(a,1),12959(a,1,1))].">
      <j1 rule="para" parents="4487 12959"/>
    </justification>
  </clause>

  <clause id="12965">
    <literal><![CDATA[
      K(x * K(y,z),x) = T(x,K(y,z)) \ x
    ]]></literal>
    <justification jstring="[para(12960(a,1),4205(a,2,1))].">
      <j1 rule="para" parents="12960 4205"/>
    </justification>
  </clause>

  <clause id="12966">
    <literal><![CDATA[
      T(T(K(x,y) \ z,u),z) = T(z * K(y,x),u)
    ]]></literal>
    <justification jstring="[para(12963(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12963 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12967">
    <literal><![CDATA[
      K(x * K(y,z),x) = K(K(y,z),x)
    ]]></literal>
    <justification jstring="[hyper(333,a,4205,a,b,12965,a),flip(a)].">
      <j1 rule="hyper" parents="333 4205 12965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12968">
    <literal><![CDATA[
      K(x * K(y,z),x) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(333,a,6799,a(flip),b,12967,a),flip(a)].">
      <j1 rule="hyper" parents="333 6799 12967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12969">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x * K(y,z),L(x,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(12968(a,1),10960(a,1,1))].">
      <j1 rule="para" parents="12968 10960"/>
    </justification>
  </clause>

  <clause id="12970">
    <literal><![CDATA[
      T(T(x,T(K(y,z) \ x,u)),x \ T(K(y,z) \ x,u)) = (x \ T(x * K(z,y),u)) \ T(K(y,z) \ x,u)
    ]]></literal>
    <justification jstring="[para(12966(a,1),6685(a,2,1,2))].">
      <j1 rule="para" parents="12966 6685"/>
    </justification>
  </clause>

  <clause id="12971">
    <literal><![CDATA[
      (x \ T(K(y,z) \ x,u)) * ((x \ T(x * K(z,y),u)) \ T(K(y,z) \ x,u)) = (x * T(K(y,z) \ x,u)) / x
    ]]></literal>
    <justification jstring="[para(12966(a,1),8918(a,1,2,1,2))].">
      <j1 rule="para" parents="12966 8918"/>
    </justification>
  </clause>

  <clause id="12972">
    <literal><![CDATA[
      K((T(x,y) \ y) \ 1,z) = K((y / x) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(5322,a,12964,a)].">
      <j1 rule="hyper" parents="5322 12964"/>
    </justification>
  </clause>

  <clause id="12973">
    <literal><![CDATA[
      K(x \ (y * T(z * u,z)),w) = K(x \ (y * (u * z)),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,10909,a(flip),b,12716,a),flip(a)].">
      <j1 rule="hyper" parents="63 10909 12716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12974">
    <literal><![CDATA[
      T(x,y * T(L(z,u,u \ 1),1 / u)) = T(x,y * ((u * z) * (u \ 1)))
    ]]></literal>
    <justification jstring="[hyper(333,a,3180,a(flip),b,12742,a),flip(a)].">
      <j1 rule="hyper" parents="333 3180 12742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12975">
    <literal><![CDATA[
      x * L(a(x,y,x) \ (x \ a(x,y,x)),z,u) = L(x \ L(x,z,u),y,x)
    ]]></literal>
    <justification jstring="[para(12928(a,2),12802(a,1,2))].">
      <j1 rule="para" parents="12928 12802"/>
    </justification>
  </clause>

  <clause id="12976">
    <literal><![CDATA[
      T(x,y * T(L(z,u,u \ 1),u \ 1)) = T(x,y * ((u * z) * (u \ 1)))
    ]]></literal>
    <justification jstring="[para(2986(a,1),12974(a,1,2,2))].">
      <j1 rule="para" parents="2986 12974"/>
    </justification>
  </clause>

  <clause id="12977">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,x) = x * L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(12803(a,1),12975(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12803 12975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12978">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,x) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,2582,a(flip),b,12977,a),flip(a)].">
      <j1 rule="hyper" parents="333 2582 12977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12980">
    <literal><![CDATA[
      L((x \ L(x,y,z)) \ 1,u,x) = ((x \ L(x,y,z)) \ 1) * ((x \ L(x,y,z)) \ (x \ L(x,y,z)))
    ]]></literal>
    <justification jstring="[para(12978(a,1),2588(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12978 2588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12981">
    <literal><![CDATA[
      T(x,y * L(T(z,u \ 1),u,u \ 1)) = T(x,y * ((u * z) * (u \ 1)))
    ]]></literal>
    <justification jstring="[para(25(a,2),12976(a,1,2,2))].">
      <j1 rule="para" parents="25 12976"/>
    </justification>
  </clause>

  <clause id="12982">
    <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(12729(a,2),8028(a,1))].">
      <j1 rule="para" parents="12729 8028"/>
    </justification>
  </clause>

  <clause id="12983">
    <literal><![CDATA[
      (x * ((x \ y) * x)) * K(x,x * y) = T(x,x * y) * ((x \ y) * x)
    ]]></literal>
    <justification jstring="[para(7419(a,1),12744(a,1,2))].">
      <j1 rule="para" parents="7419 12744"/>
    </justification>
  </clause>

  <clause id="12984">
    <literal><![CDATA[
      x * (((x \ y) * x) * K(x,x * y)) = T(x,x * y) * ((x \ y) * x)
    ]]></literal>
    <justification jstring="[hyper(6153,a,12983,a)].">
      <j1 rule="hyper" parents="6153 12983"/>
    </justification>
  </clause>

  <clause id="12985">
    <literal><![CDATA[
      T(x,x * y) * ((x \ y) * x) = x * ((x \ y) * T(x,x * y))
    ]]></literal>
    <justification jstring="[para(5984(a,1),12984(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5984 12984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12986">
    <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(14(a,2),12585(a,2,2))].">
      <j1 rule="para" parents="14 12585"/>
    </justification>
  </clause>

  <clause id="12987">
    <literal><![CDATA[
      L(x,y \ R(y,z,u),x) = L(x,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,12923,a(flip),b,12986,a)].">
      <j1 rule="hyper" parents="63 12923 12986"/>
    </justification>
  </clause>

  <clause id="12989">
    <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(12987(a,1),12344(a,1,2))].">
      <j1 rule="para" parents="12987 12344"/>
    </justification>
  </clause>

  <clause id="12990">
    <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(5161,a,12989,a)].">
      <j1 rule="hyper" parents="5161 12989"/>
    </justification>
  </clause>

  <clause id="12991">
    <literal><![CDATA[
      a(K(x,y),z * y,u) * (x \ L(x,a(y,z,u),x)) = a(K(x,y),z * y,u)
    ]]></literal>
    <justification jstring="[para(12368(a,2),12990(a,1,1))].">
      <j1 rule="para" parents="12368 12990"/>
    </justification>
  </clause>

  <clause id="12992">
    <literal><![CDATA[
      a(x,a(y,z,u),x) \ a(K(x,y),z * y,u) = a(K(x,y),z * y,u)
    ]]></literal>
    <justification jstring="[hyper(9341,a,12991,a)].">
      <j1 rule="hyper" parents="9341 12991"/>
    </justification>
  </clause>

  <clause id="12993">
    <literal><![CDATA[
      a(x,a(y,z,u),x) = 1
    ]]></literal>
    <justification jstring="[hyper(170,a,12992,a),flip(a)].">
      <j1 rule="hyper" parents="170 12992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12994">
    <literal><![CDATA[
      a(x,a(y,z,u),x) \ K(x,a(y,z,u)) = a(K(x,y),z * y,u)
    ]]></literal>
    <justification jstring="[para(12423(a,1),12992(a,1,2))].">
      <j1 rule="para" parents="12423 12992"/>
    </justification>
  </clause>

  <clause id="12995">
    <literal><![CDATA[
      a(x,a(y,z,u),x) = a(w,a(v5,v6,v7),w)
    ]]></literal>
    <justification jstring="[hyper(333,a,12993,a,b,12993,a)].">
      <j1 rule="hyper" parents="333 12993 12993"/>
    </justification>
  </clause>

  <clause id="12996">
    <literal><![CDATA[
      L(x,a(y,z,u),x) = x
    ]]></literal>
    <justification jstring="[hyper(52,a,12993,a)].">
      <j1 rule="hyper" parents="52 12993"/>
    </justification>
  </clause>

  <clause id="12998">
    <literal><![CDATA[
      (x * a(y,z,u)) * x = x * (a(y,z,u) * x)
    ]]></literal>
    <justification jstring="[hyper(126,a,12996,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="126 12996 18"/>
    </justification>
  </clause>

  <clause id="12999">
    <literal><![CDATA[
      L(R(x,y,z),a(u,w,v5),x) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(12996(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12996 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13000">
    <literal><![CDATA[
      T(x * a(y,z,u),x) = a(y,z,u) * x
    ]]></literal>
    <justification jstring="[para(12996(a,1),3725(a,1,1,1))].">
      <j1 rule="para" parents="12996 3725"/>
    </justification>
  </clause>

  <clause id="13001">
    <literal><![CDATA[
      a(x,a(y,z,u),x) != w
    ]]></literal>
    <literal><![CDATA[
      1 = w
    ]]></literal>
    <justification jstring="[para(12995(a,1),4898(a,1))].">
      <j1 rule="para" parents="12995 4898"/>
    </justification>
  </clause>

  <clause id="13002">
    <literal><![CDATA[
      x \ T((x / a(y,z,u)) * a(y,z,u),x / a(y,z,u)) = K(a(y,z,u),a(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(121,a,13000,a,b,4461,a)].">
      <j1 rule="hyper" parents="121 13000 4461"/>
    </justification>
  </clause>

  <clause id="13003">
    <literal><![CDATA[
      T((x * x) \ (x * (a(y,z,u) * x)),x) = R(T(a(y,z,u),x * x),x,x)
    ]]></literal>
    <justification jstring="[para(12998(a,1),1044(a,1,1,2))].">
      <j1 rule="para" parents="12998 1044"/>
    </justification>
  </clause>

  <clause id="13004">
    <literal><![CDATA[
      K(x,x * a(y,z,u)) = a(K(x,y),z * y,u)
    ]]></literal>
    <justification jstring="[hyper(8246,a,12994,a)].">
      <j1 rule="hyper" parents="8246 12994"/>
    </justification>
  </clause>

  <clause id="13006">
    <literal><![CDATA[
      K(x,x * a(y,z,u)) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(333,a,11741,a(flip),b,13004,a),flip(a)].">
      <j1 rule="hyper" parents="333 11741 13004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13007">
    <literal><![CDATA[
      R(T(a(x,y,z),u * u),u,u) = T(L(T(a(x,y,z),u),u,u),u)
    ]]></literal>
    <justification jstring="[para(246(a,1),13003(a,1,1)),flip(a)].">
      <j1 rule="para" parents="246 13003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13008">
    <literal><![CDATA[
      R(T(a(x,y,z),u * u),u,u) = L(T(T(a(x,y,z),u),u),u,u)
    ]]></literal>
    <justification jstring="[hyper(333,a,25,a,b,13007,a),flip(a)].">
      <j1 rule="hyper" parents="333 25 13007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13009">
    <literal><![CDATA[
      ((x * y) * (a(z,u,z) \ w)) / (y * (a(z,u,z) \ w)) = R(x,a(z,u,z) \ y,w)
    ]]></literal>
    <justification jstring="[para(12810(a,1),12808(a,1,1))].">
      <j1 rule="para" parents="12810 12808"/>
    </justification>
  </clause>

  <clause id="13010">
    <literal><![CDATA[
      R(x,a(y,z,y) \ u,w) = R(x,u,a(y,z,y) \ w)
    ]]></literal>
    <justification jstring="[hyper(544,a,13009,a),flip(a)].">
      <j1 rule="hyper" parents="544 13009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13011">
    <literal><![CDATA[
      K(x,y * ((T(z,T(u,w)) / u) * K(u,u \ w))) = K(x,y * ((w / (w / u)) \ z))
    ]]></literal>
    <justification jstring="[para(7030(a,1),12722(a,1,2,2,1,1))].">
      <j1 rule="para" parents="7030 12722"/>
    </justification>
  </clause>

  <clause id="13012">
    <literal><![CDATA[
      ((x * (a(y,z,y) * (u * w))) \ ((x * u) * w)) * a(y,z,y) = a(x,a(y,z,y) * u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,12778,a(flip),b,12868,a)].">
      <j1 rule="hyper" parents="63 12778 12868"/>
    </justification>
  </clause>

  <clause id="13013">
    <literal><![CDATA[
      (a(x,y,x) \ ((z * (u * w)) \ ((z * u) * w))) * a(x,y,x) = a(z,a(x,y,x) * u,w)
    ]]></literal>
    <justification jstring="[para(12870(a,1),13012(a,1,1))].">
      <j1 rule="para" parents="12870 13012"/>
    </justification>
  </clause>

  <clause id="13014">
    <literal><![CDATA[
      (a(x,y,x) \ a(z,u,w)) * a(x,y,x) = a(z,a(x,y,x) * u,w)
    ]]></literal>
    <justification jstring="[para(14(a,2),13013(a,1,1,2))].">
      <j1 rule="para" parents="14 13013"/>
    </justification>
  </clause>

  <clause id="13015">
    <literal><![CDATA[
      a(x,a(y,z,y) * u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(9261,a,13014,a),flip(a)].">
      <j1 rule="hyper" parents="9261 13014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13017">
    <literal><![CDATA[
      a(x,a(y,z,y) \ u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[para(10(a,1),13015(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 13015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13018">
    <literal><![CDATA[
      a(x,T(y * z,y),u) = a(x,z * y,u)
    ]]></literal>
    <justification jstring="[para(8248(a,1),13015(a,1,2))].">
      <j1 rule="para" parents="8248 13015"/>
    </justification>
  </clause>

  <clause id="13019">
    <literal><![CDATA[
      a(x,y * a(z,u,z),w) = a(x,y,w)
    ]]></literal>
    <justification jstring="[para(9246(a,1),13015(a,1,2))].">
      <j1 rule="para" parents="9246 13015"/>
    </justification>
  </clause>

  <clause id="13020">
    <literal><![CDATA[
      a(x,y * (T(z,y) / y),u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[para(9251(a,1),13015(a,1,2))].">
      <j1 rule="para" parents="9251 13015"/>
    </justification>
  </clause>

  <clause id="13021">
    <literal><![CDATA[
      a(x,((y \ 1) * y) \ z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[para(2445(a,1),13017(a,1,2,1))].">
      <j1 rule="para" parents="2445 13017"/>
    </justification>
  </clause>

  <clause id="13022">
    <literal><![CDATA[
      a(x,L(y,z,y),u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[para(8239(a,1),13017(a,1,2))].">
      <j1 rule="para" parents="8239 13017"/>
    </justification>
  </clause>

  <clause id="13023">
    <literal><![CDATA[
      a(x,y / (T(y,z) / z),u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[para(3882(a,1),13022(a,1,2))].">
      <j1 rule="para" parents="3882 13022"/>
    </justification>
  </clause>

  <clause id="13024">
    <literal><![CDATA[
      a(x,y \ (z * a(u,w,u)),v5) = a(x,y \ z,v5)
    ]]></literal>
    <justification jstring="[para(12516(a,2),13019(a,1,2))].">
      <j1 rule="para" parents="12516 13019"/>
    </justification>
  </clause>

  <clause id="13025">
    <literal><![CDATA[
      a(x,y * z,x) = a(x,z * y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,12544,a(flip),b,13018,a)].">
      <j1 rule="hyper" parents="63 12544 13018"/>
    </justification>
  </clause>

  <clause id="13026">
    <literal><![CDATA[
      a(x,(y \ z) * y,u) = a(x,T(z,y),u)
    ]]></literal>
    <justification jstring="[para(10(a,1),13018(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 13018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13027">
    <literal><![CDATA[
      K(x,y * z) * K(x * (y * z),x) = a(x,z * y,x)
    ]]></literal>
    <justification jstring="[hyper(8224,a,13025,a)].">
      <j1 rule="hyper" parents="8224 13025"/>
    </justification>
  </clause>

  <clause id="13028">
    <literal><![CDATA[
      a(x,y * (z / y),x) = a(x,z,x)
    ]]></literal>
    <justification jstring="[para(12(a,1),13025(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12 13025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13029">
    <literal><![CDATA[
      a(x,y \ T(z,y \ 1),x) = a(x,y \ z,x)
    ]]></literal>
    <justification jstring="[para(3107(a,2),13028(a,1,2))].">
      <j1 rule="para" parents="3107 13028"/>
    </justification>
  </clause>

  <clause id="13030">
    <literal><![CDATA[
      a(x,y * (((y \ T(z,y)) * T(y,u)) / y),w) = a(x,(y \ z) * T(y,u),w)
    ]]></literal>
    <justification jstring="[para(7544(a,1),13020(a,1,2,2,1))].">
      <j1 rule="para" parents="7544 13020"/>
    </justification>
  </clause>

  <clause id="13031">
    <literal><![CDATA[
      a(x,y \ ((z * (1 / z)) \ u),w) = a(x,y \ u,w)
    ]]></literal>
    <justification jstring="[para(10136(a,1),13021(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10136 13021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13032">
    <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(13026(a,1),3783(a,1,2))].">
      <j1 rule="para" parents="13026 3783"/>
    </justification>
  </clause>

  <clause id="13033">
    <literal><![CDATA[
      a(x,T(y \ z,u) \ T(w,T(z \ y,u)),x) = a(x,T(y \ z,u) \ w,x)
    ]]></literal>
    <justification jstring="[para(7973(a,1),13029(a,1,2,2))].">
      <j1 rule="para" parents="7973 13029"/>
    </justification>
  </clause>

  <clause id="13034">
    <literal><![CDATA[
      a(x,y \ (T(z * u,z) / z),w) = a(x,y \ u,w)
    ]]></literal>
    <justification jstring="[para(8225(a,2),13024(a,1,2,2))].">
      <j1 rule="para" parents="8225 13024"/>
    </justification>
  </clause>

  <clause id="13035">
    <literal><![CDATA[
      a(x,y \ (z * (T(u,z) / z)),w) = a(x,y \ u,w)
    ]]></literal>
    <justification jstring="[para(9239(a,1),13024(a,1,2,2))].">
      <j1 rule="para" parents="9239 13024"/>
    </justification>
  </clause>

  <clause id="13036">
    <literal><![CDATA[
      a(x,y \ T(z * u,z),w) = a(x,y \ (u * z),w)
    ]]></literal>
    <justification jstring="[para(9256(a,1),13024(a,1,2,2))].">
      <j1 rule="para" parents="9256 13024"/>
    </justification>
  </clause>

  <clause id="13037">
    <literal><![CDATA[
      a(x,y \ (z * ((1 / z) * u)),w) = a(x,y \ L(u,1 / z,z),w)
    ]]></literal>
    <justification jstring="[para(18(a,2),13031(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="18 13031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13038">
    <literal><![CDATA[
      a(x,y \ (z \ T(y * u,y)),x) = a(x,z \ u,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,12892,a,b,13034,a)].">
      <j1 rule="hyper" parents="63 12892 13034"/>
    </justification>
  </clause>

  <clause id="13039">
    <literal><![CDATA[
      a(x,T(y,z) \ T(y * u,y),x) = a(x,K(y,z) \ u,x)
    ]]></literal>
    <justification jstring="[para(4531(a,1),13038(a,1,2))].">
      <j1 rule="para" parents="4531 13038"/>
    </justification>
  </clause>

  <clause id="13040">
    <literal><![CDATA[
      K(x,y * z) * K(x * (y * z),x) = x \ R(x,z * y,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,8210,a,b,13027,a),flip(a)].">
      <j1 rule="hyper" parents="333 8210 13027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13041">
    <literal><![CDATA[
      R(x,y * z,x) = R(x,z * y,x)
    ]]></literal>
    <justification jstring="[hyper(4921,a,13040,a(flip))].">
      <j1 rule="hyper" parents="4921 13040"/>
    </justification>
  </clause>

  <clause id="13042">
    <literal><![CDATA[
      R(x,y \ (T(y,z) * u),x) = R(x,(y \ u) * T(y,z),x)
    ]]></literal>
    <justification jstring="[para(1053(a,2),13041(a,1,2))].">
      <j1 rule="para" parents="1053 13041"/>
    </justification>
  </clause>

  <clause id="13043">
    <literal><![CDATA[
      R(x,K(y,z) \ ((y \ u) * y),x) = R(x,y * (y \ (K(y,z) \ u)),x)
    ]]></literal>
    <justification jstring="[para(7221(a,2),13041(a,1,2))].">
      <j1 rule="para" parents="7221 13041"/>
    </justification>
  </clause>

  <clause id="13044">
    <literal><![CDATA[
      a(x,y \ (z * ((1 / z) * u)),w) = a(x,y \ L(u,z \ 1,z),w)
    ]]></literal>
    <justification jstring="[para(2604(a,1),13037(a,2,2,2))].">
      <j1 rule="para" parents="2604 13037"/>
    </justification>
  </clause>

  <clause id="13045">
    <literal><![CDATA[
      a(x,y * ((y \ T(z,y)) * K(y,u)),w) = a(x,(y \ z) * T(y,u),w)
    ]]></literal>
    <justification jstring="[para(5979(a,1),13030(a,1,2,2))].">
      <j1 rule="para" parents="5979 13030"/>
    </justification>
  </clause>

  <clause id="13046">
    <literal><![CDATA[
      a(x,y * (y \ (T(z,y) * K(y,u))),w) = a(x,(y \ z) * T(y,u),w)
    ]]></literal>
    <justification jstring="[para(6121(a,2),13045(a,1,2,2))].">
      <j1 rule="para" parents="6121 13045"/>
    </justification>
  </clause>

  <clause id="13047">
    <literal><![CDATA[
      a(x,y * (y \ (y \ (z * T(y,u)))),w) = a(x,(y \ z) * T(y,u),w)
    ]]></literal>
    <justification jstring="[para(6663(a,2),13046(a,1,2,2,2))].">
      <j1 rule="para" parents="6663 13046"/>
    </justification>
  </clause>

  <clause id="13048">
    <literal><![CDATA[
      a(x,y \ (z * T(y,u)),w) = a(x,(y \ z) * T(y,u),w)
    ]]></literal>
    <justification jstring="[para(10(a,1),13047(a,1,2))].">
      <j1 rule="para" parents="10 13047"/>
    </justification>
  </clause>

  <clause id="13050">
    <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(12514(a,1),12593(a,1,2))].">
      <j1 rule="para" parents="12514 12593"/>
    </justification>
  </clause>

  <clause id="13051">
    <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(12886(a,1),12888(a,1,2,2,1))].">
      <j1 rule="para" parents="12886 12888"/>
    </justification>
  </clause>

  <clause id="13053">
    <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(3678(a,2),13051(a,1,2))].">
      <j1 rule="para" parents="3678 13051"/>
    </justification>
  </clause>

  <clause id="13055">
    <literal><![CDATA[
      L(x,y,z) * T(R(u,x,u),T(u * x,u)) = T(T(u,u * x) * L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(3744(a,1),13053(a,1,2,2))].">
      <j1 rule="para" parents="3744 13053"/>
    </justification>
  </clause>

  <clause id="13056">
    <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(12225(a,1),13055(a,1,2))].">
      <j1 rule="para" parents="12225 13055"/>
    </justification>
  </clause>

  <clause id="13057">
    <literal><![CDATA[
      T(T(x,x * y) * L(y,z,u),x) = L(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(844(a,1),13056(a,1,2)),flip(a)].">
      <j1 rule="para" parents="844 13056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13058">
    <literal><![CDATA[
      T(x * L(y,z,u),x * y) = L(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,8711,a(flip),b,13057,a)].">
      <j1 rule="hyper" parents="63 8711 13057"/>
    </justification>
  </clause>

  <clause id="13059">
    <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(121,a,13058,a(flip),b,4222,a(flip))].">
      <j1 rule="hyper" parents="121 13058 4222"/>
    </justification>
  </clause>

  <clause id="13060">
    <literal><![CDATA[
      K(x * L(y,z,u),x * y) = K(x,y) * K(L(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(8203,a,13059,a),flip(a)].">
      <j1 rule="hyper" parents="8203 13059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13061">
    <literal><![CDATA[
      K(x * L(y,z,u),x * y) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(333,a,10904,a(flip),b,13060,a),flip(a)].">
      <j1 rule="hyper" parents="333 10904 13060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13062">
    <literal><![CDATA[
      K(x,(x / L(y,z,u)) * y) = a(u,z,K(x / L(y,z,u),y))
    ]]></literal>
    <justification jstring="[para(12(a,1),13061(a,1,1))].">
      <j1 rule="para" parents="12 13061"/>
    </justification>
  </clause>

  <clause id="13063">
    <literal><![CDATA[
      K(x,y * (L(y,z,u) \ x)) = a(u,z,K(x / L(y,z,u),y))
    ]]></literal>
    <justification jstring="[hyper(63,a,9763,a(flip),b,13062,a)].">
      <j1 rule="hyper" parents="63 9763 13062"/>
    </justification>
  </clause>

  <clause id="13064">
    <literal><![CDATA[
      K(x,y * (L(y,z,u) \ x)) = a(u,z,K(y \ x,y))
    ]]></literal>
    <justification jstring="[para(10830(a,1),13063(a,2,3))].">
      <j1 rule="para" parents="10830 13063"/>
    </justification>
  </clause>

  <clause id="13065">
    <literal><![CDATA[
      K(x,y * (L(y,z,u) \ x)) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(333,a,11149,a(flip),b,13064,a),flip(a)].">
      <j1 rule="hyper" parents="333 11149 13064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13067">
    <literal><![CDATA[
      K(x,x * (L(y,z,u) \ y)) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,10652,a(flip),b,13065,a)].">
      <j1 rule="hyper" parents="63 10652 13065"/>
    </justification>
  </clause>

  <clause id="13068">
    <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(63,a,5051,a,b,13067,a)].">
      <j1 rule="hyper" parents="63 5051 13067"/>
    </justification>
  </clause>

  <clause id="13069">
    <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(12(a,1),13067(a,1,2))].">
      <j1 rule="para" parents="12 13067"/>
    </justification>
  </clause>

  <clause id="13070">
    <literal><![CDATA[
      K(x * (L(y,z,u) \ y),x) = w / (a(u,z,K(x,y)) * w)
    ]]></literal>
    <justification jstring="[para(13067(a,1),4569(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13067 4569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13071">
    <literal><![CDATA[
      K(x * (L(y,z,u) \ y),x) = a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(333,a,9792,a(flip),b,13070,a),flip(a)].">
      <j1 rule="hyper" parents="333 9792 13070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13072">
    <literal><![CDATA[
      L(x,y,a(z,u,K(w,y))) = x
    ]]></literal>
    <justification jstring="[para(13071(a,1),4890(a,1,3))].">
      <j1 rule="para" parents="13071 4890"/>
    </justification>
  </clause>

  <clause id="13073">
    <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(13071(a,1),11152(a,1,3)),flip(a)].">
      <j1 rule="para" parents="13071 11152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13074">
    <literal><![CDATA[
      (a(x,y,K(z,u)) * u) * w = a(x,y,K(z,u)) * (u * w)
    ]]></literal>
    <justification jstring="[hyper(1170,a,13072,a),flip(a)].">
      <j1 rule="hyper" parents="1170 13072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13075">
    <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(63,a,11163,a(flip),b,13073,a)].">
      <j1 rule="hyper" parents="63 11163 13073"/>
    </justification>
  </clause>

  <clause id="13076">
    <literal><![CDATA[
      K(a(x,y,z),u) * a(x * y,z,a(x,y,K(z,u))) = K(L(z,y,x) \ z,u)
    ]]></literal>
    <justification jstring="[para(13073(a,1),9746(a,1,2))].">
      <j1 rule="para" parents="13073 9746"/>
    </justification>
  </clause>

  <clause id="13077">
    <literal><![CDATA[
      a(x,T(y,z),a(u,w,K(y,v5))) * K(v5,L(y \ L(y,w,u),y,x)) = K(v5,y \ L(y,w,u))
    ]]></literal>
    <justification jstring="[para(13075(a,1),10957(a,1,1))].">
      <j1 rule="para" parents="13075 10957"/>
    </justification>
  </clause>

  <clause id="13078">
    <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(63,a,5921,a(flip),b,13069,a)].">
      <j1 rule="hyper" parents="63 5921 13069"/>
    </justification>
  </clause>

  <clause id="13079">
    <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(63,a,10673,a(flip),b,13078,a)].">
      <j1 rule="hyper" parents="63 10673 13078"/>
    </justification>
  </clause>

  <clause id="13080">
    <literal><![CDATA[
      K(x * (y \ L(y,z,u)),x) = a(u,z,K((y / x) \ y,y))
    ]]></literal>
    <justification jstring="[para(10822(a,1),13079(a,2,3))].">
      <j1 rule="para" parents="10822 13079"/>
    </justification>
  </clause>

  <clause id="13081">
    <literal><![CDATA[
      K(x * (y \ L(y,z,u)),x) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(79(a,1),13080(a,2,3,1))].">
      <j1 rule="para" parents="79 13080"/>
    </justification>
  </clause>

  <clause id="13084">
    <literal><![CDATA[
      K(x,x * (y \ L(y,z,u))) = w / (a(u,z,K(x,y)) * w)
    ]]></literal>
    <justification jstring="[para(13081(a,1),4569(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13081 4569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13085">
    <literal><![CDATA[
      K(x,x * (y \ L(y,z,u))) = a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(333,a,9792,a(flip),b,13084,a),flip(a)].">
      <j1 rule="hyper" parents="333 9792 13084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13086">
    <literal><![CDATA[
      T(x,x * (y \ L(y,z,u))) = x * a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(126,a,13085,a(flip),b,4215,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="126 13085 4215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13087">
    <literal><![CDATA[
      L(x,a(y,z,K(u,w)),L(w,v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      x = v7
    ]]></literal>
    <justification jstring="[para(13085(a,1),3866(a,1,2))].">
      <j1 rule="para" parents="13085 3866"/>
    </justification>
  </clause>

  <clause id="13088">
    <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(12890(a,1),13068(a,1,2))].">
      <j1 rule="para" parents="12890 13068"/>
    </justification>
  </clause>

  <clause id="13089">
    <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(5161,a,13088,a)].">
      <j1 rule="hyper" parents="5161 13088"/>
    </justification>
  </clause>

  <clause id="13090">
    <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(6733,a,13089,a)].">
      <j1 rule="hyper" parents="6733 13089"/>
    </justification>
  </clause>

  <clause id="13091">
    <literal><![CDATA[
      K(L(x,y,z) \ x,u) = K(a(z,y,x),u) * 1
    ]]></literal>
    <justification jstring="[para(9858(a,1),13076(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9858 13076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13092">
    <literal><![CDATA[
      K(L(x,y,z) \ x,u) = K(a(z,y,x),u)
    ]]></literal>
    <justification jstring="[hyper(333,a,8,a(flip),b,13091,a),flip(a)].">
      <j1 rule="hyper" parents="333 8 13091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13094">
    <literal><![CDATA[
      K(x,L(y,z,u) \ y) = w / (K(a(u,z,y),x) * w)
    ]]></literal>
    <justification jstring="[para(13092(a,1),4569(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13092 4569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13095">
    <literal><![CDATA[
      K(x,L(y,z,u) \ y) = K(x,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(333,a,4569,a(flip),b,13094,a),flip(a)].">
      <j1 rule="hyper" parents="333 4569 13094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13096">
    <literal><![CDATA[
      T(x,L(y,z,u) \ y) = T(x,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(124,a,13095,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 13095 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13098">
    <literal><![CDATA[
      T(x,a(y,z,x)) = x
    ]]></literal>
    <justification jstring="[hyper(10564,a,13096,a),flip(a)].">
      <j1 rule="hyper" parents="10564 13096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13100">
    <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(13096(a,1),13090(a,1,2,1))].">
      <j1 rule="para" parents="13096 13090"/>
    </justification>
  </clause>

  <clause id="13101">
    <literal><![CDATA[
      a(x,y,z) * z = z * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(126,a,13098,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="126 13098 22"/>
    </justification>
  </clause>

  <clause id="13102">
    <literal><![CDATA[
      K(x,x * a(y,z,u)) = a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(4473,a,13100,a)].">
      <j1 rule="hyper" parents="4473 13100"/>
    </justification>
  </clause>

  <clause id="13103">
    <literal><![CDATA[
      a(K(x,y),z,u) = a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,13006,a(flip),b,13102,a)].">
      <j1 rule="hyper" parents="63 13006 13102"/>
    </justification>
  </clause>

  <clause id="13104">
    <literal><![CDATA[
      a(x,x,K(y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(4898,a,13103,a),flip(a)].">
      <j1 rule="hyper" parents="4898 13103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13105">
    <literal><![CDATA[
      a(K(x,y),z,z \ x) = 1
    ]]></literal>
    <justification jstring="[hyper(333,a,10666,a(flip),b,13103,a),flip(a)].">
      <j1 rule="hyper" parents="333 10666 13103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13106">
    <literal><![CDATA[
      a(K(x * y,z),x,y) = 1
    ]]></literal>
    <justification jstring="[hyper(333,a,10665,a(flip),b,13103,a),flip(a)].">
      <j1 rule="hyper" parents="333 10665 13103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13107">
    <literal><![CDATA[
      a(x,y,K(z,u)) = K(z,a(x,y,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,12426,a(flip),b,13103,a),flip(a)].">
      <j1 rule="hyper" parents="63 12426 13103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13108">
    <literal><![CDATA[
      a(x,x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      1 = u
    ]]></literal>
    <justification jstring="[para(13103(a,1),4898(a,1))].">
      <j1 rule="para" parents="13103 4898"/>
    </justification>
  </clause>

  <clause id="13109">
    <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(13103(a,1),11744(a,1,1,2))].">
      <j1 rule="para" parents="13103 11744"/>
    </justification>
  </clause>

  <clause id="13110">
    <literal><![CDATA[
      a(x * y,x,K(y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(11004,a,13104,a)].">
      <j1 rule="hyper" parents="11004 13104"/>
    </justification>
  </clause>

  <clause id="13111">
    <literal><![CDATA[
      L(K(x,y),z,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(52,a,13104,a)].">
      <j1 rule="hyper" parents="52 13104"/>
    </justification>
  </clause>

  <clause id="13113">
    <literal><![CDATA[
      a(K(x,y),z,z \ y) = 1
    ]]></literal>
    <justification jstring="[hyper(63,a,11965,a(flip),b,13105,a)].">
      <j1 rule="hyper" parents="63 11965 13105"/>
    </justification>
  </clause>

  <clause id="13114">
    <literal><![CDATA[
      a(x,y,K(z,x * y)) = 1
    ]]></literal>
    <justification jstring="[hyper(63,a,11357,a(flip),b,13105,a)].">
      <j1 rule="hyper" parents="63 11357 13105"/>
    </justification>
  </clause>

  <clause id="13115">
    <literal><![CDATA[
      a(x / y,y,K(z,x)) = 1
    ]]></literal>
    <justification jstring="[hyper(63,a,11356,a(flip),b,13105,a)].">
      <j1 rule="hyper" parents="63 11356 13105"/>
    </justification>
  </clause>

  <clause id="13116">
    <literal><![CDATA[
      L(x \ y,x,K(y,z)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(52,a,13105,a)].">
      <j1 rule="hyper" parents="52 13105"/>
    </justification>
  </clause>

  <clause id="13117">
    <literal><![CDATA[
      a(K(x,y * z),y,z) = 1
    ]]></literal>
    <justification jstring="[hyper(63,a,11965,a(flip),b,13106,a)].">
      <j1 rule="hyper" parents="63 11965 13106"/>
    </justification>
  </clause>

  <clause id="13118">
    <literal><![CDATA[
      L(x,y,K(y * x,z)) = x
    ]]></literal>
    <justification jstring="[hyper(52,a,13106,a)].">
      <j1 rule="hyper" parents="52 13106"/>
    </justification>
  </clause>

  <clause id="13119">
    <literal><![CDATA[
      K(x,L(y,z,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(10960,a,13111,a)].">
      <j1 rule="hyper" parents="10960 13111"/>
    </justification>
  </clause>

  <clause id="13120">
    <literal><![CDATA[
      L(K(x,y),z,z \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(3149,a,13111,a)].">
      <j1 rule="hyper" parents="3149 13111"/>
    </justification>
  </clause>

  <clause id="13122">
    <literal><![CDATA[
      L(K(x,y),z \ 1,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(2626,a,13111,a)].">
      <j1 rule="hyper" parents="2626 13111"/>
    </justification>
  </clause>

  <clause id="13123">
    <literal><![CDATA[
      K(L(x,y,y),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,10894,a(flip),b,13111,a)].">
      <j1 rule="hyper" parents="63 10894 13111"/>
    </justification>
  </clause>

  <clause id="13124">
    <literal><![CDATA[
      K(x,(y * y) \ z) = K(x,y \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(63,a,10875,a(flip),b,13111,a)].">
      <j1 rule="hyper" parents="63 10875 13111"/>
    </justification>
  </clause>

  <clause id="13125">
    <literal><![CDATA[
      K(x,(y \ z) \ y) = K(x,z \ (y * y))
    ]]></literal>
    <justification jstring="[hyper(63,a,9513,a(flip),b,13111,a),flip(a)].">
      <j1 rule="hyper" parents="63 9513 13111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13126">
    <literal><![CDATA[
      (x \ 1) * K(y,z) = x \ K(y,z)
    ]]></literal>
    <justification jstring="[hyper(121,a,13111,a(flip),b,2599,a),flip(a)].">
      <j1 rule="hyper" parents="121 13111 2599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13128">
    <literal><![CDATA[
      T(x,L(y,z,z)) = x * K(x,y)
    ]]></literal>
    <justification jstring="[para(13111(a,1),10858(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13111 10858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13130">
    <literal><![CDATA[
      L(x \ y,x,K(z,y)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(52,a,13113,a)].">
      <j1 rule="hyper" parents="52 13113"/>
    </justification>
  </clause>

  <clause id="13131">
    <literal><![CDATA[
      a(x,y,K(z,x * (y * z))) = 1
    ]]></literal>
    <justification jstring="[hyper(11004,a,13114,a)].">
      <j1 rule="hyper" parents="11004 13114"/>
    </justification>
  </clause>

  <clause id="13133">
    <literal><![CDATA[
      L(K(x,y * z),z,y) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(52,a,13114,a)].">
      <j1 rule="hyper" parents="52 13114"/>
    </justification>
  </clause>

  <clause id="13135">
    <literal><![CDATA[
      L(K(x,y),z,y / z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(52,a,13115,a)].">
      <j1 rule="hyper" parents="52 13115"/>
    </justification>
  </clause>

  <clause id="13136">
    <literal><![CDATA[
      L(x,y,K(z,y * x)) = x
    ]]></literal>
    <justification jstring="[hyper(52,a,13117,a)].">
      <j1 rule="hyper" parents="52 13117"/>
    </justification>
  </clause>

  <clause id="13137">
    <literal><![CDATA[
      L(x,y,K(x * y,z)) = x
    ]]></literal>
    <justification jstring="[para(12201(a,1),13118(a,1,3))].">
      <j1 rule="para" parents="12201 13118"/>
    </justification>
  </clause>

  <clause id="13138">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(2596(a,1),13119(a,1,2))].">
      <j1 rule="para" parents="2596 13119"/>
    </justification>
  </clause>

  <clause id="13139">
    <literal><![CDATA[
      K(x,L(y,z \ 1,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(2596(a,2),13119(a,1,2))].">
      <j1 rule="para" parents="2596 13119"/>
    </justification>
  </clause>

  <clause id="13140">
    <literal><![CDATA[
      K(x,y * ((y \ 1) * z)) = K(x,z)
    ]]></literal>
    <justification jstring="[para(2599(a,2),13119(a,1,2))].">
      <j1 rule="para" parents="2599 13119"/>
    </justification>
  </clause>

  <clause id="13141">
    <literal><![CDATA[
      K(x,(y \ 1) \ z) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(2601(a,1),13119(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2601 13119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13142">
    <literal><![CDATA[
      K((x \ 1) \ y,z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(2601(a,1),13123(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2601 13123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13143">
    <literal><![CDATA[
      L(x,y,K(z,x * y)) = x
    ]]></literal>
    <justification jstring="[para(12236(a,1),13136(a,1,3))].">
      <j1 rule="para" parents="12236 13136"/>
    </justification>
  </clause>

  <clause id="13144">
    <literal><![CDATA[
      L(x / y,y,K(x,z)) = x / y
    ]]></literal>
    <justification jstring="[para(12(a,1),13137(a,1,3,1))].">
      <j1 rule="para" parents="12 13137"/>
    </justification>
  </clause>

  <clause id="13145">
    <literal><![CDATA[
      L(x,x \ y,K(z,y)) = x
    ]]></literal>
    <justification jstring="[para(10(a,1),13143(a,1,3,2))].">
      <j1 rule="para" parents="10 13143"/>
    </justification>
  </clause>

  <clause id="13146">
    <literal><![CDATA[
      (K(x,y) * z) \ T(x,y) = z \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,4346,a(flip),b,13116,a)].">
      <j1 rule="hyper" parents="63 4346 13116"/>
    </justification>
  </clause>

  <clause id="13147">
    <literal><![CDATA[
      T(x,y) / (z \ x) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(197,a,13116,a(flip),b,4346,a(flip))].">
      <j1 rule="hyper" parents="197 13116 4346"/>
    </justification>
  </clause>

  <clause id="13148">
    <literal><![CDATA[
      (K(x,y) * z) * (z \ x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(126,a,13116,a(flip),b,4346,a(flip))].">
      <j1 rule="hyper" parents="126 13116 4346"/>
    </justification>
  </clause>

  <clause id="13150">
    <literal><![CDATA[
      K(x,y * (z \ 1)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(63,a,12337,a(flip),b,13120,a)].">
      <j1 rule="hyper" parents="63 12337 13120"/>
    </justification>
  </clause>

  <clause id="13152">
    <literal><![CDATA[
      (1 / x) \ K(y,z) = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(121,a,13120,a(flip),b,2652,a)].">
      <j1 rule="hyper" parents="121 13120 2652"/>
    </justification>
  </clause>

  <clause id="13153">
    <literal><![CDATA[
      K(x,(y * z) \ 1) = K(x,z \ (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(9697,a,13122,a)].">
      <j1 rule="hyper" parents="9697 13122"/>
    </justification>
  </clause>

  <clause id="13155">
    <literal><![CDATA[
      T(x,L(y,z,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = u
    ]]></literal>
    <justification jstring="[para(13128(a,2),4285(a,1))].">
      <j1 rule="para" parents="13128 4285"/>
    </justification>
  </clause>

  <clause id="13156">
    <literal><![CDATA[
      L(x \ (y \ z),x,K(y,z)) = x \ (y \ z)
    ]]></literal>
    <justification jstring="[hyper(11895,a,13130,a)].">
      <j1 rule="hyper" parents="11895 13130"/>
    </justification>
  </clause>

  <clause id="13157">
    <literal><![CDATA[
      (K(x,y) * z) * (z \ y) = y * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(126,a,13130,a(flip),b,2731,a(flip))].">
      <j1 rule="hyper" parents="126 13130 2731"/>
    </justification>
  </clause>

  <clause id="13158">
    <literal><![CDATA[
      x * ((x \ y) * K(z,y)) = y * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(126,a,13135,a(flip),b,5589,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="126 13135 5589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13159">
    <literal><![CDATA[
      K(x,R(y,z,z \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(12329,a,13138,a)].">
      <j1 rule="hyper" parents="12329 13138"/>
    </justification>
  </clause>

  <clause id="13160">
    <literal><![CDATA[
      K(x,L(y,z \ x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,10958,a(flip),b,13138,a)].">
      <j1 rule="hyper" parents="63 10958 13138"/>
    </justification>
  </clause>

  <clause id="13161">
    <literal><![CDATA[
      K(x,(1 / y) * z) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(2655(a,1),13138(a,1,2))].">
      <j1 rule="para" parents="2655 13138"/>
    </justification>
  </clause>

  <clause id="13162">
    <literal><![CDATA[
      (K(x,y) * z) \ 1 = z \ K(y,x)
    ]]></literal>
    <justification jstring="[para(13138(a,1),12467(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13138 12467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13163">
    <literal><![CDATA[
      K(x,T((y \ 1) \ z,u)) = K(x,T(y * z,u))
    ]]></literal>
    <justification jstring="[para(643(a,1),13139(a,1,2)),flip(a)].">
      <j1 rule="para" parents="643 13139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13164">
    <literal><![CDATA[
      L((x * y) / z,z,K(y,x)) = (x * y) / z
    ]]></literal>
    <justification jstring="[hyper(11900,a,13144,a)].">
      <j1 rule="hyper" parents="11900 13144"/>
    </justification>
  </clause>

  <clause id="13165">
    <literal><![CDATA[
      K(x,R(y,z,z \ 1)) = K(x,L(y,u,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(333,a,13138,a,b,13159,a),flip(a)].">
      <j1 rule="hyper" parents="333 13138 13159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13167">
    <literal><![CDATA[
      K(R(x,y,y \ 1),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,11579,a,b,13159,a)].">
      <j1 rule="hyper" parents="63 11579 13159"/>
    </justification>
  </clause>

  <clause id="13169">
    <literal><![CDATA[
      K(x,(y * z) \ x) = K(x,z \ (y \ x))
    ]]></literal>
    <justification jstring="[hyper(10886,a,13160,a)].">
      <j1 rule="hyper" parents="10886 13160"/>
    </justification>
  </clause>

  <clause id="13171">
    <literal><![CDATA[
      T(x,L(y,z \ x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(124,a,13160,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 13160 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13172">
    <literal><![CDATA[
      K(x * y,L(z,y,x)) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),13160(a,1,2,2))].">
      <j1 rule="para" parents="9 13160"/>
    </justification>
  </clause>

  <clause id="13173">
    <literal><![CDATA[
      K(x * (y \ 1),z) = K(x / y,z)
    ]]></literal>
    <justification jstring="[para(554(a,1),13167(a,1,1))].">
      <j1 rule="para" parents="554 13167"/>
    </justification>
  </clause>

  <clause id="13175">
    <literal><![CDATA[
      T(x * y,L(z,y,x)) = T(x * y,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),13171(a,1,2,2))].">
      <j1 rule="para" parents="9 13171"/>
    </justification>
  </clause>

  <clause id="13176">
    <literal><![CDATA[
      T(x,(y \ x) \ z) = T(x,x \ (y * z))
    ]]></literal>
    <justification jstring="[para(515(a,1),13171(a,1,2)),flip(a)].">
      <j1 rule="para" parents="515 13171"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13177">
    <literal><![CDATA[
      K(x,T(y,z) * L(z,u \ y,u)) = K(x,L(z,u \ y,u) * y)
    ]]></literal>
    <justification jstring="[para(13171(a,1),12267(a,1,2,1))].">
      <j1 rule="para" parents="13171 12267"/>
    </justification>
  </clause>

  <clause id="13178">
    <literal><![CDATA[
      x \ T(x,a(y,z,u)) = a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(333,a,4215,a(flip),b,13107,a)].">
      <j1 rule="hyper" parents="333 4215 13107"/>
    </justification>
  </clause>

  <clause id="13179">
    <literal><![CDATA[
      (x * y) * a(z,u,K(y,w)) = x * T(y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(126,a,13107,a,b,6005,a)].">
      <j1 rule="hyper" parents="126 13107 6005"/>
    </justification>
  </clause>

  <clause id="13180">
    <literal><![CDATA[
      x * a(y,z,K(x,u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(126,a,13107,a,b,4215,a(flip))].">
      <j1 rule="hyper" parents="126 13107 4215"/>
    </justification>
  </clause>

  <clause id="13181">
    <literal><![CDATA[
      x * a(y,z,K(x,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,a(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(13107(a,2),4285(a,1,2))].">
      <j1 rule="para" parents="13107 4285"/>
    </justification>
  </clause>

  <clause id="13182">
    <literal><![CDATA[
      a(x,y,K(z,u)) \ w = K(u,a(x,y,z)) * w
    ]]></literal>
    <justification jstring="[para(13107(a,1),9791(a,2,1))].">
      <j1 rule="para" parents="13107 9791"/>
    </justification>
  </clause>

  <clause id="13183">
    <literal><![CDATA[
      (x \ K(y,z)) * K(z,y) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(5997,a,13126,a)].">
      <j1 rule="hyper" parents="5997 13126"/>
    </justification>
  </clause>

  <clause id="13184">
    <literal><![CDATA[
      K(x,K(y,z)) * (x \ K(u,w)) = (T(x,K(y,z)) \ 1) * K(u,w)
    ]]></literal>
    <justification jstring="[hyper(333,a,6830,a,b,13126,a)].">
      <j1 rule="hyper" parents="333 6830 13126"/>
    </justification>
  </clause>

  <clause id="13187">
    <literal><![CDATA[
      (x \ K(y,z)) * y = (x \ 1) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(125,a,13126,a(flip),b,5979,a)].">
      <j1 rule="hyper" parents="125 13126 5979"/>
    </justification>
  </clause>

  <clause id="13188">
    <literal><![CDATA[
      (x \ K(y,z)) / (x \ 1) = K(y,z) * K(y,K(z,x \ 1))
    ]]></literal>
    <justification jstring="[hyper(123,a,13126,a(flip),b,6812,a)].">
      <j1 rule="hyper" parents="123 13126 6812"/>
    </justification>
  </clause>

  <clause id="13189">
    <literal><![CDATA[
      R(x,x \ 1,K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(39,a,430,a,b,13126,a(flip))].">
      <j1 rule="hyper" parents="39 430 13126"/>
    </justification>
  </clause>

  <clause id="13191">
    <literal><![CDATA[
      (1 / x) \ K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x * K(y,z) = u
    ]]></literal>
    <justification jstring="[para(13126(a,1),654(a,1))].">
      <j1 rule="para" parents="13126 654"/>
    </justification>
  </clause>

  <clause id="13192">
    <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(13126(a,1),748(a,2,2))].">
      <j1 rule="para" parents="13126 748"/>
    </justification>
  </clause>

  <clause id="13193">
    <literal><![CDATA[
      K(x,y) * L(K(x,y) \ (z \ 1),u,w) = L(z \ K(x,y),u,w) / K(x,y)
    ]]></literal>
    <justification jstring="[para(13126(a,1),2574(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="13126 2574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13194">
    <literal><![CDATA[
      T(x,y * ((1 / z) * K(u,w))) = T(x,y * (z \ K(u,w)))
    ]]></literal>
    <justification jstring="[para(13126(a,1),3187(a,2,2,2))].">
      <j1 rule="para" parents="13126 3187"/>
    </justification>
  </clause>

  <clause id="13196">
    <literal><![CDATA[
      (x \ 1) * (y * K(z,y)) = (x \ K(z,y)) * y
    ]]></literal>
    <justification jstring="[para(13126(a,1),5417(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13126 5417"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13197">
    <literal><![CDATA[
      (x \ K(y,z)) \ (x \ 1) = K(z,y)
    ]]></literal>
    <justification jstring="[para(13126(a,1),5990(a,1,1))].">
      <j1 rule="para" parents="13126 5990"/>
    </justification>
  </clause>

  <clause id="13198">
    <literal><![CDATA[
      (x \ K(y,z)) \ (x \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) = u
    ]]></literal>
    <justification jstring="[para(13126(a,1),6024(a,1,1))].">
      <j1 rule="para" parents="13126 6024"/>
    </justification>
  </clause>

  <clause id="13199">
    <literal><![CDATA[
      T(x \ K(y,z),K(z,y)) = K(y,z) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(13126(a,1),6035(a,1,1))].">
      <j1 rule="para" parents="13126 6035"/>
    </justification>
  </clause>

  <clause id="13201">
    <literal><![CDATA[
      T(x \ K(y,z),K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) * (x \ 1) = u
    ]]></literal>
    <justification jstring="[para(13126(a,1),6106(a,1,1))].">
      <j1 rule="para" parents="13126 6106"/>
    </justification>
  </clause>

  <clause id="13202">
    <literal><![CDATA[
      R(1 / x,x,K(y,z)) = 1 / x
    ]]></literal>
    <justification jstring="[para(79(a,1),13189(a,1,2))].">
      <j1 rule="para" parents="79 13189"/>
    </justification>
  </clause>

  <clause id="13203">
    <literal><![CDATA[
      1 / x != y
    ]]></literal>
    <literal><![CDATA[
      K(z,u) / (x * K(z,u)) = y
    ]]></literal>
    <justification jstring="[para(13202(a,1),560(a,1))].">
      <j1 rule="para" parents="13202 560"/>
    </justification>
  </clause>

  <clause id="13204">
    <literal><![CDATA[
      K(x * x,x \ y) = K(x * x,x * y)
    ]]></literal>
    <justification jstring="[hyper(5627,a,13141,a)].">
      <j1 rule="hyper" parents="5627 13141"/>
    </justification>
  </clause>

  <clause id="13205">
    <literal><![CDATA[
      K(x,T(y * z,y)) = K(x,(z \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(333,a,12229,a,b,13141,a)].">
      <j1 rule="hyper" parents="333 12229 13141"/>
    </justification>
  </clause>

  <clause id="13206">
    <literal><![CDATA[
      T(x,(y \ 1) \ z) = T(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(124,a,13141,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 13141 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13207">
    <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(63,a,12752,a,b,13141,a)].">
      <j1 rule="hyper" parents="63 12752 13141"/>
    </justification>
  </clause>

  <clause id="13208">
    <literal><![CDATA[
      K(x,(y \ x) \ (x * z)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,9667,a,b,13141,a)].">
      <j1 rule="hyper" parents="63 9667 13141"/>
    </justification>
  </clause>

  <clause id="13209">
    <literal><![CDATA[
      (x \ T(x * y,z)) \ y = K(z,x * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,5500,a,b,13141,a)].">
      <j1 rule="hyper" parents="63 5500 13141"/>
    </justification>
  </clause>

  <clause id="13210">
    <literal><![CDATA[
      K(x,(1 / y) \ z) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,4792,a,b,13141,a)].">
      <j1 rule="hyper" parents="63 4792 13141"/>
    </justification>
  </clause>

  <clause id="13211">
    <literal><![CDATA[
      K(x,(y \ 1) \ (z * T(u,w))) = K(x,y * (z * ((u \ w) \ w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,12749,a(flip),b,13141,a)].">
      <j1 rule="hyper" parents="63 12749 13141"/>
    </justification>
  </clause>

  <clause id="13212">
    <literal><![CDATA[
      K(x,(y \ 1) * z) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,4795,a(flip),b,13141,a),flip(a)].">
      <j1 rule="hyper" parents="63 4795 13141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13213">
    <literal><![CDATA[
      T(x,(y \ 1) \ z) = x * K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(126,a,13141,a(flip),b,4215,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="126 13141 4215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13214">
    <literal><![CDATA[
      K(x,L((y \ 1) \ z,u,w)) = L(K(x,y * z),u,w)
    ]]></literal>
    <justification jstring="[para(13141(a,1),10851(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13141 10851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13215">
    <literal><![CDATA[
      K((x \ 1) * y,z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(12686,a,13142,a),flip(a)].">
      <j1 rule="hyper" parents="12686 13142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13216">
    <literal><![CDATA[
      K(x / (y \ 1),z) = K(y * x,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(7062,a,13142,a)].">
      <j1 rule="hyper" parents="7062 13142"/>
    </justification>
  </clause>

  <clause id="13219">
    <literal><![CDATA[
      K((x \ 1) \ y,z) = z / T(z,x * y)
    ]]></literal>
    <justification jstring="[hyper(333,a,4212,a(flip),b,13142,a),flip(a)].">
      <j1 rule="hyper" parents="333 4212 13142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13220">
    <literal><![CDATA[
      K((1 / x) \ y,z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,4763,a,b,13142,a)].">
      <j1 rule="hyper" parents="63 4763 13142"/>
    </justification>
  </clause>

  <clause id="13221">
    <literal><![CDATA[
      x \ T(x * y,z) = y * K(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(126,a,13142,a(flip),b,5904,a),flip(a)].">
      <j1 rule="hyper" parents="126 13142 5904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13223">
    <literal><![CDATA[
      K((x \ 1) \ (y \ (1 / y)),z) = K((x * (y \ 1)) / y,z)
    ]]></literal>
    <justification jstring="[para(1180(a,2),13142(a,2,1))].">
      <j1 rule="para" parents="1180 13142"/>
    </justification>
  </clause>

  <clause id="13224">
    <literal><![CDATA[
      (x * K(y * x,z)) / (y \ 1) = T(x / (y \ 1),z)
    ]]></literal>
    <justification jstring="[para(13142(a,1),5914(a,1,1,2))].">
      <j1 rule="para" parents="13142 5914"/>
    </justification>
  </clause>

  <clause id="13225">
    <literal><![CDATA[
      (x * K(y * x,z)) * y = T(x * y,z)
    ]]></literal>
    <justification jstring="[para(13142(a,1),5913(a,1,1,2))].">
      <j1 rule="para" parents="13142 5913"/>
    </justification>
  </clause>

  <clause id="13226">
    <literal><![CDATA[
      T(x * K(y * x,z),y) = y \ T(x * y,z)
    ]]></literal>
    <justification jstring="[para(13142(a,1),5972(a,1,1,2))].">
      <j1 rule="para" parents="13142 5972"/>
    </justification>
  </clause>

  <clause id="13227">
    <literal><![CDATA[
      K((x \ 1) * y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,z) = u
    ]]></literal>
    <justification jstring="[para(13142(a,1),12686(a,1))].">
      <j1 rule="para" parents="13142 12686"/>
    </justification>
  </clause>

  <clause id="13229">
    <literal><![CDATA[
      K(x,y) * (x / z) = T(x,y) / z
    ]]></literal>
    <justification jstring="[hyper(197,a,79,a(flip),b,13146,a),flip(a)].">
      <j1 rule="hyper" parents="197 79 13146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13230">
    <literal><![CDATA[
      K(x,y) * (1 / z) = K(x,y) / z
    ]]></literal>
    <justification jstring="[hyper(39,a,11181,a,b,13146,a),flip(a)].">
      <j1 rule="hyper" parents="39 11181 13146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13231">
    <literal><![CDATA[
      (K(x,y) * z) \ y = z \ T(y,x)
    ]]></literal>
    <justification jstring="[para(4558(a,1),13146(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4558 13146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13232">
    <literal><![CDATA[
      (K(x,y) \ z) \ T(y,x) = z \ y
    ]]></literal>
    <justification jstring="[para(4567(a,2),13146(a,1,1))].">
      <j1 rule="para" parents="4567 13146"/>
    </justification>
  </clause>

  <clause id="13233">
    <literal><![CDATA[
      (T(x,y) * z) \ T(x,y) = (x * z) \ x
    ]]></literal>
    <justification jstring="[para(4273(a,1),13146(a,1,1))].">
      <j1 rule="para" parents="4273 13146"/>
    </justification>
  </clause>

  <clause id="13234">
    <literal><![CDATA[
      (T(x,y) * z) \ y = (x * z) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(4557(a,1),13146(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4557 13146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13235">
    <literal><![CDATA[
      ((x / T(y,x)) * z) \ T(x,y) = ((x / y) * z) \ x
    ]]></literal>
    <justification jstring="[para(11847(a,1),13146(a,1,1))].">
      <j1 rule="para" parents="11847 13146"/>
    </justification>
  </clause>

  <clause id="13236">
    <literal><![CDATA[
      (T(x,y) \ z) * ((x \ z) \ y) = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(5096,a,13147,a)].">
      <j1 rule="hyper" parents="5096 13147"/>
    </justification>
  </clause>

  <clause id="13237">
    <literal><![CDATA[
      T(x,y) / ((y \ z) \ x) = T(y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(333,a,4555,a(flip),b,13147,a),flip(a)].">
      <j1 rule="hyper" parents="333 4555 13147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13238">
    <literal><![CDATA[
      K(x,y) \ (K(x,y) / z) = 1 / z
    ]]></literal>
    <justification jstring="[hyper(121,a,11179,a(flip),b,13147,a(flip))].">
      <j1 rule="hyper" parents="121 11179 13147"/>
    </justification>
  </clause>

  <clause id="13240">
    <literal><![CDATA[
      (x / y) \ T(x,z) = y * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(121,a,13148,a(flip),b,11351,a(flip))].">
      <j1 rule="hyper" parents="121 13148 11351"/>
    </justification>
  </clause>

  <clause id="13241">
    <literal><![CDATA[
      x \ T(x,y * (z \ 1)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(4240,a,13150,a)].">
      <j1 rule="hyper" parents="4240 13150"/>
    </justification>
  </clause>

  <clause id="13244">
    <literal><![CDATA[
      T(x,y * (z \ 1)) = T(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(124,a,13150,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 13150 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13245">
    <literal><![CDATA[
      K(x,(y \ 1) \ (z \ 1)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(63,a,13141,a,b,13150,a)].">
      <j1 rule="hyper" parents="63 13141 13150"/>
    </justification>
  </clause>

  <clause id="13246">
    <literal><![CDATA[
      K(x,y * (1 / z)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(63,a,4785,a,b,13150,a)].">
      <j1 rule="hyper" parents="63 4785 13150"/>
    </justification>
  </clause>

  <clause id="13247">
    <literal><![CDATA[
      K(x,y / (z \ 1)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,4786,a(flip),b,13150,a),flip(a)].">
      <j1 rule="hyper" parents="63 4786 13150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13249">
    <literal><![CDATA[
      T(x,y * (1 / z)) = x * K(x,y / z)
    ]]></literal>
    <justification jstring="[para(13150(a,1),4304(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13150 4304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13250">
    <literal><![CDATA[
      1 / (x * K(y,z)) = K(z,y) / x
    ]]></literal>
    <justification jstring="[hyper(6000,a,13152,a),flip(a)].">
      <j1 rule="hyper" parents="6000 13152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13252">
    <literal><![CDATA[
      (K(x,y) / z) \ 1 = z * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,12479,a,b,13152,a)].">
      <j1 rule="hyper" parents="63 12479 13152"/>
    </justification>
  </clause>

  <clause id="13253">
    <literal><![CDATA[
      (T(x,y) / z) \ x = z * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,12473,a,b,13152,a)].">
      <j1 rule="hyper" parents="63 12473 13152"/>
    </justification>
  </clause>

  <clause id="13254">
    <literal><![CDATA[
      (x \ T(y,z)) * K(z,y) = x \ y
    ]]></literal>
    <justification jstring="[hyper(63,a,12475,a(flip),b,13152,a),flip(a)].">
      <j1 rule="hyper" parents="63 12475 13152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13255">
    <literal><![CDATA[
      (x \ y) * K(y,z) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,11175,a(flip),b,13152,a),flip(a)].">
      <j1 rule="hyper" parents="63 11175 13152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13256">
    <literal><![CDATA[
      x / (y * K(z,x)) = T(x,z) / y
    ]]></literal>
    <justification jstring="[hyper(197,a,13152,a(flip),b,12473,a)].">
      <j1 rule="hyper" parents="197 13152 12473"/>
    </justification>
  </clause>

  <clause id="13257">
    <literal><![CDATA[
      (x \ T(y,z)) \ (x \ y) = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(121,a,12475,a(flip),b,13152,a(flip))].">
      <j1 rule="hyper" parents="121 12475 13152"/>
    </justification>
  </clause>

  <clause id="13259">
    <literal><![CDATA[
      T(x,(y * y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ (y \ z)) = u
    ]]></literal>
    <justification jstring="[para(311(a,1),13155(a,1,2))].">
      <j1 rule="para" parents="311 13155"/>
    </justification>
  </clause>

  <clause id="13260">
    <literal><![CDATA[
      T(x,(1 / y) * z) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(124,a,13161,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 13161 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13261">
    <literal><![CDATA[
      1 / (x \ K(y,z)) = K(z,y) * x
    ]]></literal>
    <justification jstring="[hyper(198,a,13162,a)].">
      <j1 rule="hyper" parents="198 13162"/>
    </justification>
  </clause>

  <clause id="13262">
    <literal><![CDATA[
      K(x,y) * (K(y,x) / z) = 1 / z
    ]]></literal>
    <justification jstring="[hyper(197,a,79,a(flip),b,13162,a),flip(a)].">
      <j1 rule="hyper" parents="197 79 13162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13263">
    <literal><![CDATA[
      T(x,K(y,z)) \ K(z,y) = (x * K(y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(111(a,1),13162(a,1,1)),flip(a)].">
      <j1 rule="para" parents="111 13162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13264">
    <literal><![CDATA[
      L(x,y,z / (1 / (K(u,w) * v5))) = L(x,y,z / (v5 \ K(w,u)))
    ]]></literal>
    <justification jstring="[para(13162(a,1),3145(a,2,3,2))].">
      <j1 rule="para" parents="13162 3145"/>
    </justification>
  </clause>

  <clause id="13265">
    <literal><![CDATA[
      L(x,y,(1 / (K(z,u) * w)) \ v5) = L(x,y,(w \ K(u,z)) \ v5)
    ]]></literal>
    <justification jstring="[para(13162(a,1),3147(a,2,3,1))].">
      <j1 rule="para" parents="13162 3147"/>
    </justification>
  </clause>

  <clause id="13266">
    <literal><![CDATA[
      (K(x,y) * z) \ K(x,y) = z \ 1
    ]]></literal>
    <justification jstring="[para(4558(a,1),13162(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4558 13162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13267">
    <literal><![CDATA[
      (T(x,y) \ z) \ 1 = (x \ z) \ K(x,y)
    ]]></literal>
    <justification jstring="[para(4555(a,1),13162(a,1,1))].">
      <j1 rule="para" parents="4555 13162"/>
    </justification>
  </clause>

  <clause id="13268">
    <literal><![CDATA[
      (T(x,y) * z) \ K(x,y) = (x * z) \ 1
    ]]></literal>
    <justification jstring="[para(4557(a,1),13162(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4557 13162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13269">
    <literal><![CDATA[
      K(x,y / (((z \ K(u,w)) \ 1) * v5)) = K(x,y / ((K(w,u) * z) * v5))
    ]]></literal>
    <justification jstring="[para(13162(a,1),5027(a,1,2,2,1,1))].">
      <j1 rule="para" parents="13162 5027"/>
    </justification>
  </clause>

  <clause id="13270">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) \ 1 = u \ K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(6799(a,1),13162(a,1,1,1))].">
      <j1 rule="para" parents="6799 13162"/>
    </justification>
  </clause>

  <clause id="13271">
    <literal><![CDATA[
      (x * y) \ K(z,T(y,x)) = (x * T(y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(7722(a,1),13162(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7722 13162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13273">
    <literal><![CDATA[
      K(L(x / y,z,z),u) = K(x * (y \ 1),u)
    ]]></literal>
    <justification jstring="[hyper(333,a,13123,a,b,13173,a)].">
      <j1 rule="hyper" parents="333 13123 13173"/>
    </justification>
  </clause>

  <clause id="13274">
    <literal><![CDATA[
      K(x * (1 / y),z) = K(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,4757,a,b,13173,a)].">
      <j1 rule="hyper" parents="63 4757 13173"/>
    </justification>
  </clause>

  <clause id="13275">
    <literal><![CDATA[
      K(x / (y \ 1),z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,4758,a(flip),b,13173,a),flip(a)].">
      <j1 rule="hyper" parents="63 4758 13173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13276">
    <literal><![CDATA[
      K(x / (1 / y),z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(79(a,1),13173(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="79 13173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13277">
    <literal><![CDATA[
      T(T(x,y * (z \ 1)),K(y / z,u)) = T(x,T(y * (z \ 1),u))
    ]]></literal>
    <justification jstring="[para(13173(a,1),6191(a,1,2))].">
      <j1 rule="para" parents="13173 6191"/>
    </justification>
  </clause>

  <clause id="13279">
    <literal><![CDATA[
      (x \ 1) * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x \ K(y,z) = u
    ]]></literal>
    <justification jstring="[para(13183(a,1),5998(a,1,1))].">
      <j1 rule="para" parents="13183 5998"/>
    </justification>
  </clause>

  <clause id="13281">
    <literal><![CDATA[
      (x \ K(y,z * (y \ u))) \ (x \ 1) = K((y \ z) * u,y)
    ]]></literal>
    <justification jstring="[para(10667(a,1),13197(a,1,1,2))].">
      <j1 rule="para" parents="10667 13197"/>
    </justification>
  </clause>

  <clause id="13282">
    <literal><![CDATA[
      T(x,(1 / y) \ z) = T(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,3170,a,b,13206,a)].">
      <j1 rule="hyper" parents="63 3170 13206"/>
    </justification>
  </clause>

  <clause id="13283">
    <literal><![CDATA[
      T(x * (y * (z \ 1)),z * ((z \ 1) \ 1)) = (z * z) \ (x * (y * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,4010,a(flip),b,13206,a),flip(a)].">
      <j1 rule="hyper" parents="63 4010 13206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13284">
    <literal><![CDATA[
      T(x,(y \ 1) * z) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,3173,a(flip),b,13206,a),flip(a)].">
      <j1 rule="hyper" parents="63 3173 13206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13285">
    <literal><![CDATA[
      T(x,(y * y) * z) = T(x,y * (y * z))
    ]]></literal>
    <justification jstring="[para(709(a,1),13206(a,1,2))].">
      <j1 rule="para" parents="709 13206"/>
    </justification>
  </clause>

  <clause id="13286">
    <literal><![CDATA[
      K(x,L((1 / y) \ z,u,w)) = L(K(x,y * z),u,w)
    ]]></literal>
    <justification jstring="[para(13210(a,1),10851(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13210 10851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13287">
    <literal><![CDATA[
      K(x,y \ L(x,z,u)) = K(x,x * (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,10937,a(flip),b,13212,a),flip(a)].">
      <j1 rule="hyper" parents="63 10937 13212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13292">
    <literal><![CDATA[
      K((x \ 1) / y,z) = K(x \ (y \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,13173,a(flip),b,13215,a)].">
      <j1 rule="hyper" parents="63 13173 13215"/>
    </justification>
  </clause>

  <clause id="13293">
    <literal><![CDATA[
      K(x \ T(y / z,y),u) = K((x \ 1) * (z \ y),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,12900,a(flip),b,13215,a),flip(a)].">
      <j1 rule="hyper" parents="63 12900 13215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13294">
    <literal><![CDATA[
      K(x \ (y / (x \ 1)),z) = K(y,T(z,x \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,12208,a(flip),b,13215,a),flip(a)].">
      <j1 rule="hyper" parents="63 12208 13215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13295">
    <literal><![CDATA[
      K(x \ ((x \ 1) \ y),z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),13215(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 13215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13296">
    <literal><![CDATA[
      K((x * (1 / y)) \ z,y) = K(y * (x \ z),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,10376,a,b,13220,a)].">
      <j1 rule="hyper" parents="63 10376 13220"/>
    </justification>
  </clause>

  <clause id="13297">
    <literal><![CDATA[
      T(x,((y * K(z * y,u)) / (z \ 1)) * w) = T(x,T(y / (1 / z),u) * w)
    ]]></literal>
    <justification jstring="[para(13220(a,1),5936(a,1,2,1,1,2))].">
      <j1 rule="para" parents="13220 5936"/>
    </justification>
  </clause>

  <clause id="13298">
    <literal><![CDATA[
      K((x \ K(y,z)) * y,u) = K(x \ T(y,z),u)
    ]]></literal>
    <justification jstring="[para(11182(a,1),13220(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11182 13220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13299">
    <literal><![CDATA[
      K(x,y) \ (y / z) = T(y,x) / z
    ]]></literal>
    <justification jstring="[hyper(4585,a,13229,a)].">
      <j1 rule="hyper" parents="4585 13229"/>
    </justification>
  </clause>

  <clause id="13300">
    <literal><![CDATA[
      K(x,y) * (T(y,x) / z) = y / z
    ]]></literal>
    <justification jstring="[hyper(4577,a,13229,a)].">
      <j1 rule="hyper" parents="4577 13229"/>
    </justification>
  </clause>

  <clause id="13301">
    <literal><![CDATA[
      T(x,y) * (T(y,x) / z) = x * (y / z)
    ]]></literal>
    <justification jstring="[hyper(126,a,13229,a(flip),b,4550,a)].">
      <j1 rule="hyper" parents="126 13229 4550"/>
    </justification>
  </clause>

  <clause id="13302">
    <literal><![CDATA[
      (T(x,y) / z) \ K(K(x,y),x / z) = ((x / z) * K(x,y)) \ 1
    ]]></literal>
    <justification jstring="[para(13229(a,1),4998(a,1,1))].">
      <j1 rule="para" parents="13229 4998"/>
    </justification>
  </clause>

  <clause id="13303">
    <literal><![CDATA[
      T(T(x,y) / z,K(x,y)) = (x / z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(13229(a,1),6019(a,1,1))].">
      <j1 rule="para" parents="13229 6019"/>
    </justification>
  </clause>

  <clause id="13304">
    <literal><![CDATA[
      K(x,y) * (K(z,u) / u) = K(x,y) / T(u,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,4402,a,b,13230,a)].">
      <j1 rule="hyper" parents="63 4402 13230"/>
    </justification>
  </clause>

  <clause id="13305">
    <literal><![CDATA[
      L(x,x,K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(2616,a,13230,a(flip))].">
      <j1 rule="hyper" parents="2616 13230"/>
    </justification>
  </clause>

  <clause id="13306">
    <literal><![CDATA[
      (x * y) * (K(y,x) / z) = (y * x) * (1 / z)
    ]]></literal>
    <justification jstring="[hyper(126,a,13230,a(flip),b,10008,a)].">
      <j1 rule="hyper" parents="126 13230 10008"/>
    </justification>
  </clause>

  <clause id="13307">
    <literal><![CDATA[
      K(x,y) / (z \ 1) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(76(a,1),13230(a,1,2)),flip(a)].">
      <j1 rule="para" parents="76 13230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13308">
    <literal><![CDATA[
      L(x,K(y,z) / u,w) = L(x,K(y,z) * u,w)
    ]]></literal>
    <justification jstring="[para(13230(a,1),2636(a,1,2))].">
      <j1 rule="para" parents="13230 2636"/>
    </justification>
  </clause>

  <clause id="13309">
    <literal><![CDATA[
      T(K(x,y) / z,K(x,y)) = (1 / z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(13230(a,1),6019(a,1,1))].">
      <j1 rule="para" parents="13230 6019"/>
    </justification>
  </clause>

  <clause id="13310">
    <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(13230(a,1),5200(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="13230 5200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13311">
    <literal><![CDATA[
      T(x \ T(y,z),(K(z,y) * x) \ y) = (K(z,y) * x) \ y
    ]]></literal>
    <justification jstring="[hyper(451,a,xx,b,13231,a)].">
      <j1 rule="hyper" parents="451 13231"/>
    </justification>
  </clause>

  <clause id="13312">
    <literal><![CDATA[
      ((K(x,y) * z) / K(x,y)) \ T(y,x) = (T(K(x,y),z) * z) \ y
    ]]></literal>
    <justification jstring="[para(3311(a,2),13231(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3311 13231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13314">
    <literal><![CDATA[
      T((x \ T(y,z)) \ T(y,x),y) = ((K(z,y) * x) \ y) \ y
    ]]></literal>
    <justification jstring="[para(13231(a,1),7353(a,1,1,1))].">
      <j1 rule="para" parents="13231 7353"/>
    </justification>
  </clause>

  <clause id="13315">
    <literal><![CDATA[
      (((x * y) \ y) * z) \ T(y,x) = (((y * x) \ y) * z) \ y
    ]]></literal>
    <justification jstring="[para(10170(a,1),13231(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10170 13231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13316">
    <literal><![CDATA[
      (x * K(y * x,z)) \ z = x \ T(z,x * y)
    ]]></literal>
    <justification jstring="[para(12199(a,1),13231(a,1,1))].">
      <j1 rule="para" parents="12199 13231"/>
    </justification>
  </clause>

  <clause id="13317">
    <literal><![CDATA[
      (x * y) / (z \ (y * x)) = K(y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(197,a,13232,a(flip),b,11987,a(flip))].">
      <j1 rule="hyper" parents="197 13232 11987"/>
    </justification>
  </clause>

  <clause id="13318">
    <literal><![CDATA[
      T(x,y) / (z * T(x,y)) = x / (z * x)
    ]]></literal>
    <justification jstring="[hyper(6090,a,13240,a)].">
      <j1 rule="hyper" parents="6090 13240"/>
    </justification>
  </clause>

  <clause id="13319">
    <literal><![CDATA[
      (x / (y / z)) * (y / T(z,x)) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(5467,a,13240,a)].">
      <j1 rule="hyper" parents="5467 13240"/>
    </justification>
  </clause>

  <clause id="13322">
    <literal><![CDATA[
      x / (y * K(x,z)) = K(z,x) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(197,a,13240,a(flip),b,13231,a)].">
      <j1 rule="hyper" parents="197 13240 13231"/>
    </justification>
  </clause>

  <clause id="13323">
    <literal><![CDATA[
      T(x,y) * K(x * y,z) = y \ T(x * y,z)
    ]]></literal>
    <justification jstring="[para(191(a,1),13240(a,1,1)),flip(a)].">
      <j1 rule="para" parents="191 13240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13324">
    <literal><![CDATA[
      T(x,y * (1 / z)) = T(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(63,a,3165,a,b,13244,a)].">
      <j1 rule="hyper" parents="63 3165 13244"/>
    </justification>
  </clause>

  <clause id="13325">
    <literal><![CDATA[
      T(x,y / (z \ 1)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,3166,a(flip),b,13244,a),flip(a)].">
      <j1 rule="hyper" parents="63 3166 13244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13326">
    <literal><![CDATA[
      T(x,y / (1 / z)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(79(a,1),13244(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="79 13244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13327">
    <literal><![CDATA[
      L(x,y \ 1,z) * (z * (y \ 1)) = z * ((y \ 1) * T(x,z / y))
    ]]></literal>
    <justification jstring="[para(13244(a,1),664(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13244 664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13328">
    <literal><![CDATA[
      T(x,y / (K(z,u) * w)) = T(x,y * (w \ K(u,z)))
    ]]></literal>
    <justification jstring="[para(13162(a,1),13244(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13162 13244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13329">
    <literal><![CDATA[
      K(x / (x / y),z / u) = K(y,T(z * (1 / u),x))
    ]]></literal>
    <justification jstring="[hyper(6983,a,13246,a),flip(a)].">
      <j1 rule="hyper" parents="6983 13246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13331">
    <literal><![CDATA[
      K(x,y / T((z \ 1) \ 1,u)) = K(x,y * (T(z,u) \ 1))
    ]]></literal>
    <justification jstring="[para(2379(a,1),13246(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2379 13246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13332">
    <literal><![CDATA[
      K(x,y * ((z \ (z / u)) \ 1)) = K(x,y / ((z * u) \ z))
    ]]></literal>
    <justification jstring="[para(2890(a,1),13246(a,1,2,2))].">
      <j1 rule="para" parents="2890 13246"/>
    </justification>
  </clause>

  <clause id="13333">
    <literal><![CDATA[
      K(x,(y * (1 / z)) * K(u,y / z)) = K(x,T(y * (1 / z),u))
    ]]></literal>
    <justification jstring="[para(13246(a,1),6925(a,1,2,2))].">
      <j1 rule="para" parents="13246 6925"/>
    </justification>
  </clause>

  <clause id="13334">
    <literal><![CDATA[
      K(x,y / (z \ 1)) = x \ T(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(333,a,4215,a(flip),b,13247,a),flip(a)].">
      <j1 rule="hyper" parents="333 4215 13247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13335">
    <literal><![CDATA[
      K(x,y * z) * (z \ T(z * y,x)) = y
    ]]></literal>
    <justification jstring="[para(13247(a,1),4839(a,1,1))].">
      <j1 rule="para" parents="13247 4839"/>
    </justification>
  </clause>

  <clause id="13336">
    <literal><![CDATA[
      K(x,(y * K(z,u \ 1)) * u) = K(x,y / T(u \ 1,z))
    ]]></literal>
    <justification jstring="[para(5460(a,1),13247(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5460 13247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13337">
    <literal><![CDATA[
      K(x,L(y / (z \ 1),u,w)) = L(K(x,y * z),u,w)
    ]]></literal>
    <justification jstring="[para(13247(a,1),10851(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13247 10851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13338">
    <literal><![CDATA[
      T(K(x,y) / z,z * K(y,x)) = (z * K(y,x)) \ 1
    ]]></literal>
    <justification jstring="[para(13250(a,1),113(a,1,1))].">
      <j1 rule="para" parents="13250 113"/>
    </justification>
  </clause>

  <clause id="13339">
    <literal><![CDATA[
      R(x,K(y,z) / u,w) = R(x,u * K(z,y),w)
    ]]></literal>
    <justification jstring="[para(13250(a,1),1933(a,1,2))].">
      <j1 rule="para" parents="13250 1933"/>
    </justification>
  </clause>

  <clause id="13340">
    <literal><![CDATA[
      (x * K(y,z)) \ L(x * K(y,z),u,w) = (K(z,y) / x) * L(x * K(y,z),u,w)
    ]]></literal>
    <justification jstring="[para(13250(a,1),2521(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13250 2521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13343">
    <literal><![CDATA[
      K(x,y * (z / ((u * K(w,v5)) \ 1))) = K(x,y * (z / (K(v5,w) / u)))
    ]]></literal>
    <justification jstring="[para(13250(a,1),4804(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="13250 4804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13344">
    <literal><![CDATA[
      K(x,(y / (1 / (K(z,u) / w))) * v5) = K(x,(y / (w * K(u,z))) * v5)
    ]]></literal>
    <justification jstring="[para(13250(a,1),5204(a,1,2,1,2,2))].">
      <j1 rule="para" parents="13250 5204"/>
    </justification>
  </clause>

  <clause id="13345">
    <literal><![CDATA[
      1 / T(x * K(y,z),y) = K(z,y) / T(x,y)
    ]]></literal>
    <justification jstring="[para(6650(a,2),13250(a,1,2))].">
      <j1 rule="para" parents="6650 13250"/>
    </justification>
  </clause>

  <clause id="13347">
    <literal><![CDATA[
      ((x * ((x \ y) * K(x / y,y))) / x) \ 1 = x / (x * ((((x / (1 / (x \ y))) / x) \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(13252(a,1),10474(a,1,1,1,2))].">
      <j1 rule="para" parents="13252 10474"/>
    </justification>
  </clause>

  <clause id="13348">
    <literal><![CDATA[
      K(x,y / (K(z,u) / w)) = K(x,y * (w * K(u,z)))
    ]]></literal>
    <justification jstring="[para(13252(a,1),13150(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13252 13150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13349">
    <literal><![CDATA[
      T(x,y) / (z / (y \ 1)) = x / (z / (T(y,x) \ 1))
    ]]></literal>
    <justification jstring="[hyper(197,a,6170,a(flip),b,13253,a),flip(a)].">
      <j1 rule="hyper" parents="197 6170 13253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13350">
    <literal><![CDATA[
      T(x \ T(y,z),K(z,y)) = K(y,z) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(253,a,13254,a,b,4558,a)].">
      <j1 rule="hyper" parents="253 13254 4558"/>
    </justification>
  </clause>

  <clause id="13353">
    <literal><![CDATA[
      (x \ T(y,z)) / T(y,z) = (x \ y) / y
    ]]></literal>
    <justification jstring="[hyper(123,a,13254,a(flip),b,5444,a),flip(a)].">
      <j1 rule="hyper" parents="123 13254 5444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13355">
    <literal><![CDATA[
      (x \ T(y,z)) \ (x \ y) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) = u
    ]]></literal>
    <justification jstring="[para(13254(a,1),342(a,1,2))].">
      <j1 rule="para" parents="13254 342"/>
    </justification>
  </clause>

  <clause id="13356">
    <literal><![CDATA[
      (x \ y) * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x \ T(y,z) = u
    ]]></literal>
    <justification jstring="[para(13254(a,1),5998(a,1,1))].">
      <j1 rule="para" parents="13254 5998"/>
    </justification>
  </clause>

  <clause id="13357">
    <literal><![CDATA[
      K(x * (y \ T(z,u)),z) = K(x * (y \ z),z)
    ]]></literal>
    <justification jstring="[para(13254(a,1),9425(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="13254 9425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13360">
    <literal><![CDATA[
      K(x,T(y,z)) * (z \ x) = z \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,7272,a,b,13255,a)].">
      <j1 rule="hyper" parents="63 7272 13255"/>
    </justification>
  </clause>

  <clause id="13362">
    <literal><![CDATA[
      (x \ y) / (x \ T(y,z)) = K(z,T(y,x \ y))
    ]]></literal>
    <justification jstring="[hyper(197,a,13255,a(flip),b,6916,a)].">
      <j1 rule="hyper" parents="197 13255 6916"/>
    </justification>
  </clause>

  <clause id="13363">
    <literal><![CDATA[
      (x \ T(y,z)) / (x \ y) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(123,a,13255,a(flip),b,7272,a)].">
      <j1 rule="hyper" parents="123 13255 7272"/>
    </justification>
  </clause>

  <clause id="13365">
    <literal><![CDATA[
      (x \ L(y,z,u)) * K(L(y,z,u),w) = x \ L(T(y,w),z,u)
    ]]></literal>
    <justification jstring="[para(25(a,2),13255(a,2,2))].">
      <j1 rule="para" parents="25 13255"/>
    </justification>
  </clause>

  <clause id="13367">
    <literal><![CDATA[
      T(x,x \ y) \ T(y,z) = T(x \ y,x) * K(y,z)
    ]]></literal>
    <justification jstring="[para(3648(a,1),13255(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3648 13255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13368">
    <literal><![CDATA[
      (x \ (y * (z / y))) * K(y * (z / y),u) = x \ (y * (T(z,u) / y))
    ]]></literal>
    <justification jstring="[para(4083(a,1),13255(a,2,2))].">
      <j1 rule="para" parents="4083 13255"/>
    </justification>
  </clause>

  <clause id="13369">
    <literal><![CDATA[
      (K(x,y) * (z \ x)) \ K(K(x,y),z \ x) = (z \ T(x,y)) \ 1
    ]]></literal>
    <justification jstring="[para(13255(a,1),4998(a,2,1))].">
      <j1 rule="para" parents="13255 4998"/>
    </justification>
  </clause>

  <clause id="13371">
    <literal><![CDATA[
      x \ (T(y,z) * L(T(y,z) \ (x * (x \ y)),u,w)) = (x \ T(y,z)) * L(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[para(13257(a,1),1165(a,2,2,1))].">
      <j1 rule="para" parents="13257 1165"/>
    </justification>
  </clause>

  <clause id="13372">
    <literal><![CDATA[
      (((x \ T(y,z)) / (x \ y)) \ L((x \ T(y,z)) / (x \ y),u,w)) * (x \ y) = (x \ T(y,z)) * L(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[para(13257(a,1),2589(a,2,2,1))].">
      <j1 rule="para" parents="13257 2589"/>
    </justification>
  </clause>

  <clause id="13373">
    <literal><![CDATA[
      K(K(x,y) * z,(K(x,y) * z) \ K(x,y)) = (z \ 1) \ (K(x,y) / (K(x,y) * z))
    ]]></literal>
    <justification jstring="[para(13266(a,1),4445(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13266 4445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13375">
    <literal><![CDATA[
      K(x / (y \ K(z,u)),w) = K(x * (K(u,z) * y),w)
    ]]></literal>
    <justification jstring="[para(13261(a,1),13274(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="13261 13274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13376">
    <literal><![CDATA[
      K((x * (y \ 1)) * y,z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),13275(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 13275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13379">
    <literal><![CDATA[
      T(x,(y \ 1) / z) = T(x,y \ (z \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,13244,a(flip),b,13284,a)].">
      <j1 rule="hyper" parents="63 13244 13284"/>
    </justification>
  </clause>

  <clause id="13380">
    <literal><![CDATA[
      T(((x \ 1) * y) * a(z,u,w),x \ y) = a(z,u,w) * ((x \ 1) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,13000,a(flip),b,13284,a),flip(a)].">
      <j1 rule="hyper" parents="63 13000 13284"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13381">
    <literal><![CDATA[
      ((x \ 1) * y) * T(z,x \ y) = z * ((x \ 1) * y)
    ]]></literal>
    <justification jstring="[hyper(126,a,13284,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="126 13284 22"/>
    </justification>
  </clause>

  <clause id="13382">
    <literal><![CDATA[
      T(x,(y * (L(y,z,u) \ y)) \ w) = T(x,L(y \ 1,z,u) * w)
    ]]></literal>
    <justification jstring="[para(2579(a,1),13284(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2579 13284"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13383">
    <literal><![CDATA[
      T(x,y \ ((z * (y \ 1)) \ u)) = T(x,y * ((z * y) \ u))
    ]]></literal>
    <justification jstring="[para(2964(a,1),13284(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2964 13284"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13385">
    <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(13284(a,1),7076(a,1,2))].">
      <j1 rule="para" parents="13284 7076"/>
    </justification>
  </clause>

  <clause id="13386">
    <literal><![CDATA[
      K(x \ ((x \ 1) \ y),z) = K(K(u,u \ 1) * y,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,4760,a,b,13295,a),flip(a)].">
      <j1 rule="hyper" parents="333 4760 13295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13387">
    <literal><![CDATA[
      K(x,T(y,z)) \ ((z * (y / z)) / u) = T(z * (y / z),x) / u
    ]]></literal>
    <justification jstring="[para(12249(a,1),13299(a,1,1))].">
      <j1 rule="para" parents="12249 13299"/>
    </justification>
  </clause>

  <clause id="13388">
    <literal><![CDATA[
      K(x \ y,x) * (((x \ y) \ y) / z) = x / z
    ]]></literal>
    <justification jstring="[para(112(a,1),13300(a,1,2,1))].">
      <j1 rule="para" parents="112 13300"/>
    </justification>
  </clause>

  <clause id="13389">
    <literal><![CDATA[
      K(x,y) * (x / z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) / z = u
    ]]></literal>
    <justification jstring="[para(13300(a,1),4590(a,1,2))].">
      <j1 rule="para" parents="13300 4590"/>
    </justification>
  </clause>

  <clause id="13390">
    <literal><![CDATA[
      (((x \ y) * x) \ z) * ((y \ z) \ 1) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(10152,a,13307,a)].">
      <j1 rule="hyper" parents="10152 13307"/>
    </justification>
  </clause>

  <clause id="13391">
    <literal><![CDATA[
      (T(x,y) \ z) * ((x \ z) \ 1) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(5096,a,13307,a)].">
      <j1 rule="hyper" parents="5096 13307"/>
    </justification>
  </clause>

  <clause id="13392">
    <literal><![CDATA[
      T(x,T(y \ z,y)) = T(x,z * (1 / y))
    ]]></literal>
    <justification jstring="[hyper(333,a,6946,a,b,13324,a)].">
      <j1 rule="hyper" parents="333 6946 13324"/>
    </justification>
  </clause>

  <clause id="13395">
    <literal><![CDATA[
      T(x,y / (z \ K(u,w))) = T(x,y * (K(w,u) * z))
    ]]></literal>
    <justification jstring="[para(13261(a,1),13324(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13261 13324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13396">
    <literal><![CDATA[
      K(x,T(y,(z \ 1) / u)) = K(x,T(y,u * z))
    ]]></literal>
    <justification jstring="[para(13325(a,1),7270(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13325 7270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13399">
    <literal><![CDATA[
      (x * (y \ 1)) * K(y * (x * (y \ 1)),z) = K(x,z) * (x * (y \ 1))
    ]]></literal>
    <justification jstring="[para(13376(a,1),12199(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13376 12199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13400">
    <literal><![CDATA[
      K(L(x,y,z),z * y) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,10894,a(flip),b,13133,a)].">
      <j1 rule="hyper" parents="63 10894 13133"/>
    </justification>
  </clause>

  <clause id="13402">
    <literal><![CDATA[
      K(x * y,(x * y) \ z) = K(x * y,y \ (x \ z))
    ]]></literal>
    <justification jstring="[para(311(a,1),13172(a,1,2))].">
      <j1 rule="para" parents="311 13172"/>
    </justification>
  </clause>

  <clause id="13403">
    <literal><![CDATA[
      L(x,y,z) = (z * (y * x)) / T(z * y,x)
    ]]></literal>
    <justification jstring="[hyper(197,a,13175,a(flip),b,486,a),flip(a)].">
      <j1 rule="hyper" parents="197 13175 486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13404">
    <literal><![CDATA[
      L(x,y,z) * T(z * y,x) = z * (y * x)
    ]]></literal>
    <justification jstring="[hyper(126,a,13175,a(flip),b,486,a)].">
      <j1 rule="hyper" parents="126 13175 486"/>
    </justification>
  </clause>

  <clause id="13405">
    <literal><![CDATA[
      K((x * y) \ z,x * y) = K(y \ (x \ z),x * y)
    ]]></literal>
    <justification jstring="[para(311(a,1),13400(a,1,1))].">
      <j1 rule="para" parents="311 13400"/>
    </justification>
  </clause>

  <clause id="13406">
    <literal><![CDATA[
      (x * (y * z)) * K(z,x * y) = L(z,y,x) * (x * y)
    ]]></literal>
    <justification jstring="[para(13400(a,1),493(a,1,2))].">
      <j1 rule="para" parents="13400 493"/>
    </justification>
  </clause>

  <clause id="13408">
    <literal><![CDATA[
      T(x,(y \ z) \ y) = T(x,z \ (y * y))
    ]]></literal>
    <justification jstring="[hyper(124,a,13125,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 13125 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13409">
    <literal><![CDATA[
      T(x,(y * z) \ 1) = T(x,z \ (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(124,a,13153,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 13153 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13410">
    <literal><![CDATA[
      (x * K(y,x)) / z = K(y,x) * (x / z)
    ]]></literal>
    <justification jstring="[hyper(466,a,13157,a)].">
      <j1 rule="hyper" parents="466 13157"/>
    </justification>
  </clause>

  <clause id="13411">
    <literal><![CDATA[
      (1 / x) * ((K(y,z) / x) \ y) = y * K(z,y)
    ]]></literal>
    <justification jstring="[para(13262(a,1),13157(a,1,1))].">
      <j1 rule="para" parents="13262 13157"/>
    </justification>
  </clause>

  <clause id="13412">
    <literal><![CDATA[
      x \ (y * K(z,y)) = (x \ y) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(129,a,13158,a)].">
      <j1 rule="hyper" parents="129 13158"/>
    </justification>
  </clause>

  <clause id="13413">
    <literal><![CDATA[
      x \ ((y * z) / y) = (x \ z) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(121,a,4238,a,b,13158,a)].">
      <j1 rule="hyper" parents="121 4238 13158"/>
    </justification>
  </clause>

  <clause id="13414">
    <literal><![CDATA[
      (x \ (y \ z)) * K(y,y \ z) = x \ (z / y)
    ]]></literal>
    <justification jstring="[hyper(121,a,4292,a(flip),b,13158,a),flip(a)].">
      <j1 rule="hyper" parents="121 4292 13158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13415">
    <literal><![CDATA[
      x \ (y * K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      (x \ y) * K(z,y) = u
    ]]></literal>
    <justification jstring="[para(13158(a,1),342(a,1,2))].">
      <j1 rule="para" parents="13158 342"/>
    </justification>
  </clause>

  <clause id="13416">
    <literal><![CDATA[
      T(x,(y * z) \ x) = T(x,z \ (y \ x))
    ]]></literal>
    <justification jstring="[hyper(124,a,13169,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 13169 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13417">
    <literal><![CDATA[
      T(x,x \ ((y \ x) \ z)) = T(x,x \ (y * (x \ z)))
    ]]></literal>
    <justification jstring="[hyper(10414,a,13176,a)].">
      <j1 rule="hyper" parents="10414 13176"/>
    </justification>
  </clause>

  <clause id="13418">
    <literal><![CDATA[
      T(T(x,x \ (y * z)),u) \ T(x,u) = K((y \ x) \ z,T(x,u))
    ]]></literal>
    <justification jstring="[para(13176(a,1),4228(a,1,1,1))].">
      <j1 rule="para" parents="13176 4228"/>
    </justification>
  </clause>

  <clause id="13419">
    <literal><![CDATA[
      K(x,T(y,y \ ((z \ y) \ u)) * w) = K(x,T(y,y \ (z * u)) * w)
    ]]></literal>
    <justification jstring="[para(13176(a,1),12773(a,2,2,1))].">
      <j1 rule="para" parents="13176 12773"/>
    </justification>
  </clause>

  <clause id="13420">
    <literal><![CDATA[
      T(x,a(y,z,L(u,w,x))) = x * a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[para(9466(a,1),13180(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="9466 13180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13421">
    <literal><![CDATA[
      K(x,(y \ 1) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(13205(a,1),12278(a,1))].">
      <j1 rule="para" parents="13205 12278"/>
    </justification>
  </clause>

  <clause id="13422">
    <literal><![CDATA[
      K(x,x * ((y \ x) \ z)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,10651,a(flip),b,13208,a)].">
      <j1 rule="hyper" parents="63 10651 13208"/>
    </justification>
  </clause>

  <clause id="13423">
    <literal><![CDATA[
      T(x,(y \ 1) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(13213(a,2),4285(a,1))].">
      <j1 rule="para" parents="13213 4285"/>
    </justification>
  </clause>

  <clause id="13424">
    <literal><![CDATA[
      K(x / (y \ 1),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(13216(a,2),12215(a,1))].">
      <j1 rule="para" parents="13216 12215"/>
    </justification>
  </clause>

  <clause id="13425">
    <literal><![CDATA[
      K((x \ 1) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(13219(a,2),4313(a,1))].">
      <j1 rule="para" parents="13219 4313"/>
    </justification>
  </clause>

  <clause id="13426">
    <literal><![CDATA[
      x * (y * K(x * y,z)) = T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(142,a,13221,a)].">
      <j1 rule="hyper" parents="142 13221"/>
    </justification>
  </clause>

  <clause id="13427">
    <literal><![CDATA[
      L(x * K(y * x,z),y,z) = (z * y) \ ((y * x) * z)
    ]]></literal>
    <justification jstring="[para(13221(a,1),468(a,1,1))].">
      <j1 rule="para" parents="13221 468"/>
    </justification>
  </clause>

  <clause id="13429">
    <literal><![CDATA[
      (x \ T(x * y,z)) \ y != u
    ]]></literal>
    <literal><![CDATA[
      K(z,x * y) = u
    ]]></literal>
    <justification jstring="[para(13221(a,2),6024(a,1,1))].">
      <j1 rule="para" parents="13221 6024"/>
    </justification>
  </clause>

  <clause id="13431">
    <literal><![CDATA[
      K(x * K(y * x,z),T(u,y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(y \ T(x * y,z),u) = w
    ]]></literal>
    <justification jstring="[para(13221(a,1),7206(a,1,1))].">
      <j1 rule="para" parents="13221 7206"/>
    </justification>
  </clause>

  <clause id="13434">
    <literal><![CDATA[
      x \ T(x * y,T(z,y)) = y * K(y * x,z)
    ]]></literal>
    <justification jstring="[para(12201(a,1),13221(a,2,2))].">
      <j1 rule="para" parents="12201 13221"/>
    </justification>
  </clause>

  <clause id="13435">
    <literal><![CDATA[
      (x * K(y,z)) * (y / x) = T(x * (y / x),z)
    ]]></literal>
    <justification jstring="[para(12(a,1),13225(a,1,1,2,1))].">
      <j1 rule="para" parents="12 13225"/>
    </justification>
  </clause>

  <clause id="13436">
    <literal><![CDATA[
      K(x,(((y * z) \ y) \ T(y,u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(T(y,u) * z,T(y,u)) * w) = v5
    ]]></literal>
    <justification jstring="[para(13233(a,1),12757(a,1,2,1,1))].">
      <j1 rule="para" parents="13233 12757"/>
    </justification>
  </clause>

  <clause id="13437">
    <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(6845(a,1),13234(a,2,2))].">
      <j1 rule="para" parents="6845 13234"/>
    </justification>
  </clause>

  <clause id="13438">
    <literal><![CDATA[
      (T(x,K(y,z)) \ u) \ K(y,T(z,x)) = (x \ u) \ K(y,z)
    ]]></literal>
    <justification jstring="[hyper(121,a,6365,a,b,13236,a)].">
      <j1 rule="hyper" parents="121 6365 13236"/>
    </justification>
  </clause>

  <clause id="13439">
    <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(2559(a,1),13236(a,1,2,1))].">
      <j1 rule="para" parents="2559 13236"/>
    </justification>
  </clause>

  <clause id="13441">
    <literal><![CDATA[
      T(x,y) \ K(x * y,x \ 1) = T(y,x) / (y / (x \ 1))
    ]]></literal>
    <justification jstring="[para(8677(a,1),13237(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8677 13237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13442">
    <literal><![CDATA[
      K(x,y / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z \ 1)) = u
    ]]></literal>
    <justification jstring="[para(13241(a,1),4306(a,1))].">
      <j1 rule="para" parents="13241 4306"/>
    </justification>
  </clause>

  <clause id="13443">
    <literal><![CDATA[
      T(x,y * (1 / z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y / z) = u
    ]]></literal>
    <justification jstring="[para(13249(a,2),4285(a,1))].">
      <j1 rule="para" parents="13249 4285"/>
    </justification>
  </clause>

  <clause id="13444">
    <literal><![CDATA[
      K(x,y * ((z \ u) \ K(z,w))) = K(x,y / (T(z,w) \ u))
    ]]></literal>
    <justification jstring="[para(13267(a,1),13150(a,1,2,2))].">
      <j1 rule="para" parents="13267 13150"/>
    </justification>
  </clause>

  <clause id="13445">
    <literal><![CDATA[
      T((x / y) \ 1,x) \ K((x / y) \ 1,x / y) = T(x,(x / y) \ 1) / y
    ]]></literal>
    <justification jstring="[hyper(121,a,276,a,b,13301,a)].">
      <j1 rule="hyper" parents="121 276 13301"/>
    </justification>
  </clause>

  <clause id="13446">
    <literal><![CDATA[
      (x * y) / (z \ (y * x)) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(333,a,4567,a(flip),b,13317,a),flip(a)].">
      <j1 rule="hyper" parents="333 4567 13317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13447">
    <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(444,a,6035,a(flip),b,13319,a)].">
      <j1 rule="hyper" parents="444 6035 13319"/>
    </justification>
  </clause>

  <clause id="13449">
    <literal><![CDATA[
      K(x,y) * (y / (z / x)) = y / (z / T(x,y))
    ]]></literal>
    <justification jstring="[para(5450(a,1),13322(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5450 13322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13450">
    <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(13322(a,1),8702(a,1,2,1,1))].">
      <j1 rule="para" parents="13322 8702"/>
    </justification>
  </clause>

  <clause id="13451">
    <literal><![CDATA[
      K(x,y) * (y / (z \ 1)) = y / (z \ K(y,x))
    ]]></literal>
    <justification jstring="[para(13126(a,1),13322(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13126 13322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13452">
    <literal><![CDATA[
      K(x,y / (z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(13334(a,2),4306(a,1))].">
      <j1 rule="para" parents="13334 4306"/>
    </justification>
  </clause>

  <clause id="13453">
    <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(444,a,6165,a,b,13335,a)].">
      <j1 rule="hyper" parents="444 6165 13335"/>
    </justification>
  </clause>

  <clause id="13454">
    <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(444,a,5981,a,b,13335,a)].">
      <j1 rule="hyper" parents="444 5981 13335"/>
    </justification>
  </clause>

  <clause id="13455">
    <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(444,a,5003,a,b,13335,a)].">
      <j1 rule="hyper" parents="444 5003 13335"/>
    </justification>
  </clause>

  <clause id="13456">
    <literal><![CDATA[
      (x \ y) / (x \ T(y,z)) = K(z,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(197,a,13360,a(flip),b,6427,a)].">
      <j1 rule="hyper" parents="197 13360 6427"/>
    </justification>
  </clause>

  <clause id="13457">
    <literal><![CDATA[
      x \ T(y,T(z,x)) = K(y,z) * (x \ y)
    ]]></literal>
    <justification jstring="[para(6900(a,1),13360(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6900 13360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13458">
    <literal><![CDATA[
      (x \ T(y * x,z)) / (x \ (y * x)) = K(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,12201,a(flip),b,13363,a),flip(a)].">
      <j1 rule="hyper" parents="333 12201 13363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13460">
    <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(11071(a,2),13391(a,1,2))].">
      <j1 rule="para" parents="11071 13391"/>
    </justification>
  </clause>

  <clause id="13461">
    <literal><![CDATA[
      K(x \ ((y \ z) \ 1),((y \ z) \ 1) * (T(y,u) \ z)) = K(((y \ z) \ 1) / x,K(u,y))
    ]]></literal>
    <justification jstring="[para(13391(a,1),12237(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13391 12237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13462">
    <literal><![CDATA[
      L(x * K(y,x),z,u) \ (x * K(y,x)) = K(y,x) * (x / L((y * x) / y,z,u))
    ]]></literal>
    <justification jstring="[hyper(5054,a,13410,a)].">
      <j1 rule="hyper" parents="5054 13410"/>
    </justification>
  </clause>

  <clause id="13463">
    <literal><![CDATA[
      K(x,x \ y) * ((x \ y) / z) = (y / x) / z
    ]]></literal>
    <justification jstring="[para(4292(a,1),13410(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4292 13410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13465">
    <literal><![CDATA[
      ((x * y) / x) / (z * K(x,y)) = y / z
    ]]></literal>
    <justification jstring="[hyper(197,a,195,a(flip),b,13413,a)].">
      <j1 rule="hyper" parents="197 195 13413"/>
    </justification>
  </clause>

  <clause id="13467">
    <literal><![CDATA[
      T(x * x,y) * (y / T(x * x,y)) = T(y,x \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(63,a,5709,a,b,13416,a)].">
      <j1 rule="hyper" parents="63 5709 13416"/>
    </justification>
  </clause>

  <clause id="13468">
    <literal><![CDATA[
      K(x,(x / y) * z) = K(x,x * (y \ z))
    ]]></literal>
    <justification jstring="[para(79(a,1),13422(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="79 13422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13469">
    <literal><![CDATA[
      (x \ 1) * (y * K(x \ y,z)) = T((x \ 1) * y,z)
    ]]></literal>
    <justification jstring="[para(13215(a,1),13426(a,1,2,2))].">
      <j1 rule="para" parents="13215 13426"/>
    </justification>
  </clause>

  <clause id="13470">
    <literal><![CDATA[
      (K(x,y) * z) \ (x * y) = z \ (y * x)
    ]]></literal>
    <justification jstring="[hyper(192,a,13446,a)].">
      <j1 rule="hyper" parents="192 13446"/>
    </justification>
  </clause>

  <clause id="13471">
    <literal><![CDATA[
      K(x,y) * ((y * x) / z) = (x * y) / z
    ]]></literal>
    <justification jstring="[para(79(a,1),13446(a,1,2)),flip(a)].">
      <j1 rule="para" parents="79 13446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13472">
    <literal><![CDATA[
      K(x,y) * ((y / z) * (z * x)) = (x * y) / a(y / z,z,x)
    ]]></literal>
    <justification jstring="[para(87(a,1),13446(a,1,2)),flip(a)].">
      <j1 rule="para" parents="87 13446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13473">
    <literal><![CDATA[
      K(x,y) * (z \ T(y,T(x,z))) = z \ y
    ]]></literal>
    <justification jstring="[hyper(125,a,6901,a(flip),b,13456,a)].">
      <j1 rule="hyper" parents="125 6901 13456"/>
    </justification>
  </clause>

  <clause id="13474">
    <literal><![CDATA[
      T(x,T(K(y,z) * (u \ y),w) * u) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,u * T(T(y,T(z,u)) / u,w)) = v5
    ]]></literal>
    <justification jstring="[para(13457(a,1),12279(a,1,2,1,1))].">
      <j1 rule="para" parents="13457 12279"/>
    </justification>
  </clause>

  <clause id="13475">
    <literal><![CDATA[
      ((x * y) / x) / (y / x) = y / (T(y,x) / x)
    ]]></literal>
    <justification jstring="[para(6014(a,1),13465(a,1,2))].">
      <j1 rule="para" parents="6014 13465"/>
    </justification>
  </clause>

  <clause id="13478">
    <literal><![CDATA[
      K(x,(y \ x) * z) = K(x,x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(63,a,9755,a(flip),b,13468,a)].">
      <j1 rule="hyper" parents="63 9755 13468"/>
    </justification>
  </clause>

  <clause id="13479">
    <literal><![CDATA[
      K(x,y) * ((1 / x) * (y * x)) = L(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(39,a,3991,a(flip),b,13470,a),flip(a)].">
      <j1 rule="hyper" parents="39 3991 13470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13480">
    <literal><![CDATA[
      (T(x,y) / z) \ (x * y) = (x / z) \ (y * x)
    ]]></literal>
    <justification jstring="[para(13229(a,1),13470(a,1,1))].">
      <j1 rule="para" parents="13229 13470"/>
    </justification>
  </clause>

  <clause id="13481">
    <literal><![CDATA[
      ((x * y) / z) \ T(x,y) = ((y * x) / z) \ x
    ]]></literal>
    <justification jstring="[para(13471(a,1),13146(a,1,1))].">
      <j1 rule="para" parents="13471 13146"/>
    </justification>
  </clause>

  <clause id="13482">
    <literal><![CDATA[
      ((x * y) / z) \ K(x,y) = ((y * x) / z) \ 1
    ]]></literal>
    <justification jstring="[para(13471(a,1),13162(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13471 13162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13483">
    <literal><![CDATA[
      K(x,R(y,z,u)) * (y \ T(R(y,z,u),T(x,y))) = R(y,z,u) * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(333,a,1314,a,b,13473,a),flip(a)].">
      <j1 rule="hyper" parents="333 1314 13473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13484">
    <literal><![CDATA[
      T(x,(y \ x) * z) = T(x,x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(124,a,13478,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 13478 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13486">
    <literal><![CDATA[
      K(x,K(y,(z \ y) * u)) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[para(13478(a,2),6874(a,1,2))].">
      <j1 rule="para" parents="13478 6874"/>
    </justification>
  </clause>

  <clause id="13487">
    <literal><![CDATA[
      (K(x,y) * z) \ (x \ ((x * y) / x)) = z \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,4829,a(flip),b,13156,a)].">
      <j1 rule="hyper" parents="63 4829 13156"/>
    </justification>
  </clause>

  <clause id="13488">
    <literal><![CDATA[
      L(x \ (T(y,z) \ z),x,K(T(y,z),z)) = x \ (y \ T(z,y))
    ]]></literal>
    <justification jstring="[para(3628(a,1),13156(a,2,2))].">
      <j1 rule="para" parents="3628 13156"/>
    </justification>
  </clause>

  <clause id="13489">
    <literal><![CDATA[
      (K(x,y) * z) \ K(u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      (z \ K(y,x)) * K(u,w) = v5
    ]]></literal>
    <justification jstring="[para(13261(a,1),13191(a,1,1))].">
      <j1 rule="para" parents="13261 13191"/>
    </justification>
  </clause>

  <clause id="13490">
    <literal><![CDATA[
      K(x,y) / ((L(z,u,w) \ z) * K(x,y)) = (L(z,u,w) \ z) \ 1
    ]]></literal>
    <justification jstring="[hyper(13203,a,3263,a)].">
      <j1 rule="hyper" parents="13203 3263"/>
    </justification>
  </clause>

  <clause id="13491">
    <literal><![CDATA[
      K((1 / x) * y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,z) = u
    ]]></literal>
    <justification jstring="[para(4762(a,2),13227(a,1))].">
      <j1 rule="para" parents="4762 13227"/>
    </justification>
  </clause>

  <clause id="13492">
    <literal><![CDATA[
      K((x \ K(y,z)) * y,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x \ T(y,z),u) = w
    ]]></literal>
    <justification jstring="[para(13187(a,2),13227(a,1,1))].">
      <j1 rule="para" parents="13187 13227"/>
    </justification>
  </clause>

  <clause id="13493">
    <literal><![CDATA[
      K(x * (y \ 1),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x / y,z) = u
    ]]></literal>
    <justification jstring="[para(13273(a,1),6478(a,1))].">
      <j1 rule="para" parents="13273 6478"/>
    </justification>
  </clause>

  <clause id="13494">
    <literal><![CDATA[
      K(x,y \ L(x,z,u)) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(333,a,4781,a(flip),b,13287,a),flip(a)].">
      <j1 rule="hyper" parents="333 4781 13287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13495">
    <literal><![CDATA[
      T(x,y) * K(x * y,z) != u
    ]]></literal>
    <literal><![CDATA[
      y \ T(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(22(a,2),13356(a,1,1))].">
      <j1 rule="para" parents="22 13356"/>
    </justification>
  </clause>

  <clause id="13496">
    <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(3623(a,1),13389(a,1,2))].">
      <j1 rule="para" parents="3623 13389"/>
    </justification>
  </clause>

  <clause id="13498">
    <literal><![CDATA[
      L(x,y,z) \ (z * (y * x)) != u
    ]]></literal>
    <literal><![CDATA[
      T(z * y,x) = u
    ]]></literal>
    <justification jstring="[para(13403(a,2),345(a,1,1))].">
      <j1 rule="para" parents="13403 345"/>
    </justification>
  </clause>

  <clause id="13500">
    <literal><![CDATA[
      L(x,y,z) * (x \ (z * y)) = (z * (y * x)) / x
    ]]></literal>
    <justification jstring="[hyper(123,a,13404,a(flip),b,11067,a),flip(a)].">
      <j1 rule="hyper" parents="123 13404 11067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13502">
    <literal><![CDATA[
      (x * (y * z)) / T(x * y,z) != u
    ]]></literal>
    <literal><![CDATA[
      L(z,y,x) = u
    ]]></literal>
    <justification jstring="[para(13404(a,1),268(a,1,1)),flip(b)].">
      <j1 rule="para" parents="13404 268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13503">
    <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(5450(a,1),13404(a,2,2))].">
      <j1 rule="para" parents="5450 13404"/>
    </justification>
  </clause>

  <clause id="13504">
    <literal><![CDATA[
      K(x,(L(y,z,u) \ y) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(y \ L(y,z,u)) * w) = v5
    ]]></literal>
    <justification jstring="[para(3257(a,1),13421(a,1,2,1))].">
      <j1 rule="para" parents="3257 13421"/>
    </justification>
  </clause>

  <clause id="13505">
    <literal><![CDATA[
      K(x,(1 / y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(4792(a,2),13421(a,1))].">
      <j1 rule="para" parents="4792 13421"/>
    </justification>
  </clause>

  <clause id="13506">
    <literal><![CDATA[
      K(x,y / T(z \ 1,z * (x * y))) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(10546(a,2),13421(a,1))].">
      <j1 rule="para" parents="10546 13421"/>
    </justification>
  </clause>

  <clause id="13507">
    <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(12954(a,2),13421(a,1,2))].">
      <j1 rule="para" parents="12954 13421"/>
    </justification>
  </clause>

  <clause id="13508">
    <literal><![CDATA[
      T(x,((y \ 1) \ 1) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(13284(a,2),13423(a,1))].">
      <j1 rule="para" parents="13284 13423"/>
    </justification>
  </clause>

  <clause id="13509">
    <literal><![CDATA[
      K(x / (1 / y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(4765(a,2),13424(a,1))].">
      <j1 rule="para" parents="4765 13424"/>
    </justification>
  </clause>

  <clause id="13510">
    <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(13162(a,1),13424(a,1,1,2))].">
      <j1 rule="para" parents="13162 13424"/>
    </justification>
  </clause>

  <clause id="13511">
    <literal><![CDATA[
      K((1 / x) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(4763(a,2),13425(a,1))].">
      <j1 rule="para" parents="4763 13425"/>
    </justification>
  </clause>

  <clause id="13512">
    <literal><![CDATA[
      K(((x \ 1) \ 1) * y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(13215(a,2),13425(a,1))].">
      <j1 rule="para" parents="13215 13425"/>
    </justification>
  </clause>

  <clause id="13513">
    <literal><![CDATA[
      T(x,T(y \ z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(13392(a,2),13443(a,1))].">
      <j1 rule="para" parents="13392 13443"/>
    </justification>
  </clause>

  <clause id="13514">
    <literal><![CDATA[
      K(x,y / (1 / z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(4799(a,2),13452(a,1))].">
      <j1 rule="para" parents="4799 13452"/>
    </justification>
  </clause>

  <clause id="13515">
    <literal><![CDATA[
      K((K(x,y) / z) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K((z * K(y,x)) \ u,w) = v5
    ]]></literal>
    <justification jstring="[para(13250(a,1),13491(a,1,1,1))].">
      <j1 rule="para" parents="13250 13491"/>
    </justification>
  </clause>

  <clause id="13516">
    <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(1695(a,1),13505(a,1,2))].">
      <j1 rule="para" parents="1695 13505"/>
    </justification>
  </clause>

  <clause id="13517">
    <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(13261(a,1),13505(a,1,2,1))].">
      <j1 rule="para" parents="13261 13505"/>
    </justification>
  </clause>

  <clause id="13518">
    <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(13250(a,1),13514(a,1,2,2))].">
      <j1 rule="para" parents="13250 13514"/>
    </justification>
  </clause>

  <clause id="13519">
    <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(13261(a,1),13514(a,1,2,2))].">
      <j1 rule="para" parents="13261 13514"/>
    </justification>
  </clause>

  <clause id="13520">
    <literal><![CDATA[
      T(x,T((y \ 1) \ z,u)) = T(x,T(y * z,u))
    ]]></literal>
    <justification jstring="[hyper(124,a,13163,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 13163 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13521">
    <literal><![CDATA[
      R(K(x,y),z,z \ 1) = K(x,L(y,u,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(11577,a,13165,a)].">
      <j1 rule="hyper" parents="11577 13165"/>
    </justification>
  </clause>

  <clause id="13526">
    <literal><![CDATA[
      K(x,R(y,z,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(13165(a,2),9476(a,1))].">
      <j1 rule="para" parents="13165 9476"/>
    </justification>
  </clause>

  <clause id="13527">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(13165(a,1),10507(a,1))].">
      <j1 rule="para" parents="13165 10507"/>
    </justification>
  </clause>

  <clause id="13528">
    <literal><![CDATA[
      K(x,y * (z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / z) = u
    ]]></literal>
    <justification jstring="[para(554(a,1),13526(a,1,2))].">
      <j1 rule="para" parents="554 13526"/>
    </justification>
  </clause>

  <clause id="13529">
    <literal><![CDATA[
      K(x,T(y * (z \ 1),u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y / z,u)) = w
    ]]></literal>
    <justification jstring="[para(646(a,1),13526(a,1,2))].">
      <j1 rule="para" parents="646 13526"/>
    </justification>
  </clause>

  <clause id="13530">
    <literal><![CDATA[
      K(x,(1 / y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(2655(a,1),13527(a,1,2))].">
      <j1 rule="para" parents="2655 13527"/>
    </justification>
  </clause>

  <clause id="13531">
    <literal><![CDATA[
      K(x,K(y,z * (u \ 1))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z / u)) = w
    ]]></literal>
    <justification jstring="[para(12337(a,1),13527(a,1,2))].">
      <j1 rule="para" parents="12337 13527"/>
    </justification>
  </clause>

  <clause id="13532">
    <literal><![CDATA[
      K(x,y * (z \ K(u,z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(4226(a,1),13528(a,1,2,2))].">
      <j1 rule="para" parents="4226 13528"/>
    </justification>
  </clause>

  <clause id="13533">
    <literal><![CDATA[
      K(x,y * (1 / z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / z) = u
    ]]></literal>
    <justification jstring="[para(4785(a,2),13528(a,1))].">
      <j1 rule="para" parents="4785 13528"/>
    </justification>
  </clause>

  <clause id="13534">
    <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(13267(a,1),13528(a,1,2,2))].">
      <j1 rule="para" parents="13267 13528"/>
    </justification>
  </clause>

  <clause id="13535">
    <literal><![CDATA[
      K(x,(y \ 1) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(4791(a,1),13530(a,1))].">
      <j1 rule="para" parents="4791 13530"/>
    </justification>
  </clause>

  <clause id="13536">
    <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(13261(a,1),13530(a,1,2,1))].">
      <j1 rule="para" parents="13261 13530"/>
    </justification>
  </clause>

  <clause id="13537">
    <literal><![CDATA[
      K(x,((y \ 1) \ 1) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(13141(a,2),13535(a,1))].">
      <j1 rule="para" parents="13141 13535"/>
    </justification>
  </clause>

  <clause id="13538">
    <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(13252(a,1),13535(a,1,2,1))].">
      <j1 rule="para" parents="13252 13535"/>
    </justification>
  </clause>

  <clause id="13539">
    <literal><![CDATA[
      a(x,y,K(z,u)) = K(a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(5320,a,13182,a),flip(a)].">
      <j1 rule="hyper" parents="5320 13182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13540">
    <literal><![CDATA[
      a(x,y,K(z,u)) * a(x,y,z) = T(a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(4255,a,13182,a)].">
      <j1 rule="hyper" parents="4255 13182"/>
    </justification>
  </clause>

  <clause id="13541">
    <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="[hyper(4193,a,13182,a)].">
      <j1 rule="hyper" parents="4193 13182"/>
    </justification>
  </clause>

  <clause id="13542">
    <literal><![CDATA[
      K(L(x,y,z) \ x,u) = a(z,y,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(333,a,13092,a,b,13539,a)].">
      <j1 rule="hyper" parents="333 13092 13539"/>
    </justification>
  </clause>

  <clause id="13543">
    <literal><![CDATA[
      a(x,y,K(z,L(u,w,v5))) = L(K(a(x,y,z),u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(333,a,10851,a,b,13539,a),flip(a)].">
      <j1 rule="hyper" parents="333 10851 13539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13544">
    <literal><![CDATA[
      K(a(x,y,z),x * (y * z)) = 1
    ]]></literal>
    <justification jstring="[hyper(63,a,13131,a(flip),b,13539,a),flip(a)].">
      <j1 rule="hyper" parents="63 13131 13539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13545">
    <literal><![CDATA[
      T(x * a(y,z,K(u,x)),a(y,z,u)) = x
    ]]></literal>
    <justification jstring="[para(13539(a,2),4239(a,1,1,2))].">
      <j1 rule="para" parents="13539 4239"/>
    </justification>
  </clause>

  <clause id="13546">
    <literal><![CDATA[
      K(x * (y * z),a(x,y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(122,a,13544,a,b,4373,a),flip(a)].">
      <j1 rule="hyper" parents="122 13544 4373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13547">
    <literal><![CDATA[
      ((x * y) * z) / (x * (y * z)) = a(x,y,z) * 1
    ]]></literal>
    <justification jstring="[para(13546(a,1),4423(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13546 4423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13548">
    <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(3686(a,1),13226(a,1,1,2,1))].">
      <j1 rule="para" parents="3686 13226"/>
    </justification>
  </clause>

  <clause id="13549">
    <literal><![CDATA[
      T(x * K(x * y,z),y) = y \ T(x * y,T(z,x))
    ]]></literal>
    <justification jstring="[para(12201(a,1),13226(a,1,1,2))].">
      <j1 rule="para" parents="12201 13226"/>
    </justification>
  </clause>

  <clause id="13550">
    <literal><![CDATA[
      K(x \ (y / (x \ 1)),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(13294(a,2),7282(a,1))].">
      <j1 rule="para" parents="13294 7282"/>
    </justification>
  </clause>

  <clause id="13551">
    <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(13296(a,2),12676(a,2,2,2))].">
      <j1 rule="para" parents="13296 12676"/>
    </justification>
  </clause>

  <clause id="13552">
    <literal><![CDATA[
      K(x,T(y,z)) / z = (1 / z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,9853,a(flip),b,13309,a)].">
      <j1 rule="hyper" parents="63 9853 13309"/>
    </justification>
  </clause>

  <clause id="13553">
    <literal><![CDATA[
      ((1 / x) * K(y,z)) * K(u,x) = K(y,T(z,x)) / T(x,u)
    ]]></literal>
    <justification jstring="[para(13309(a,1),9854(a,1,1))].">
      <j1 rule="para" parents="13309 9854"/>
    </justification>
  </clause>

  <clause id="13554">
    <literal><![CDATA[
      T(1 / (x * K(y,z)),K(z,y)) = (1 / x) * K(z,y)
    ]]></literal>
    <justification jstring="[para(13250(a,2),13309(a,1,1))].">
      <j1 rule="para" parents="13250 13309"/>
    </justification>
  </clause>

  <clause id="13555">
    <literal><![CDATA[
      (1 / x) * K(y,z / x) = K(y,x \ z) / x
    ]]></literal>
    <justification jstring="[para(113(a,1),13552(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="113 13552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13556">
    <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(13552(a,2),748(a,2,2))].">
      <j1 rule="para" parents="13552 748"/>
    </justification>
  </clause>

  <clause id="13557">
    <literal><![CDATA[
      T(x,y) * (z * K(x * y,z)) = (y \ T(x * y,z)) * z
    ]]></literal>
    <justification jstring="[para(13323(a,1),5417(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13323 5417"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13558">
    <literal><![CDATA[
      (x \ y) / (x \ T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,T(y,x)) = u
    ]]></literal>
    <justification jstring="[para(13362(a,2),7276(a,1))].">
      <j1 rule="para" parents="13362 7276"/>
    </justification>
  </clause>

  <clause id="13559">
    <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(13411(a,1),10931(a,2,2,1))].">
      <j1 rule="para" parents="13411 10931"/>
    </justification>
  </clause>

  <clause id="13561">
    <literal><![CDATA[
      ((x \ y) / z) \ (y / x) = z * K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(654,a,13414,a),flip(a)].">
      <j1 rule="hyper" parents="654 13414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13563">
    <literal><![CDATA[
      (x \ (y \ z)) * ((y \ z) \ z) = (x \ (z / y)) * y
    ]]></literal>
    <justification jstring="[hyper(125,a,13414,a(flip),b,6056,a),flip(a)].">
      <j1 rule="hyper" parents="125 13414 6056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13564">
    <literal><![CDATA[
      K(x,y / (T(z \ (u \ w),x) * K(u,u \ w))) = K(x,y / (z \ (w / u)))
    ]]></literal>
    <justification jstring="[para(13414(a,1),7924(a,2,2,2))].">
      <j1 rule="para" parents="13414 7924"/>
    </justification>
  </clause>

  <clause id="13565">
    <literal><![CDATA[
      K(x,y) * (y / L((x * z) / x,u,w)) = y / ((x * L(z,u,w)) / T(x,y))
    ]]></literal>
    <justification jstring="[para(891(a,2),13449(a,1,2,2))].">
      <j1 rule="para" parents="891 13449"/>
    </justification>
  </clause>

  <clause id="13567">
    <literal><![CDATA[
      a(x / y,x / (T(x,y) / y),z) = a(y \ x,T(y,x),z)
    ]]></literal>
    <justification jstring="[para(13475(a,1),9057(a,1,2))].">
      <j1 rule="para" parents="13475 9057"/>
    </justification>
  </clause>

  <clause id="13568">
    <literal><![CDATA[
      ((x * T(y,x)) / z) \ T(x,T(y,x)) = ((y * ((y * x) / y)) / z) \ x
    ]]></literal>
    <justification jstring="[para(3311(a,1),13481(a,2,1,1))].">
      <j1 rule="para" parents="3311 13481"/>
    </justification>
  </clause>

  <clause id="13569">
    <literal><![CDATA[
      K(x,((y \ z) * u) \ z) * K(x,K(z,y \ u)) = K(x,z / ((y \ z) * u))
    ]]></literal>
    <justification jstring="[para(13486(a,1),7565(a,1,2))].">
      <j1 rule="para" parents="13486 7565"/>
    </justification>
  </clause>

  <clause id="13570">
    <literal><![CDATA[
      K(x,K(y,z \ u)) * K(x,y \ ((z \ y) * u)) = K(x,((z \ y) * u) / y)
    ]]></literal>
    <justification jstring="[para(13486(a,1),7621(a,1,1))].">
      <j1 rule="para" parents="13486 7621"/>
    </justification>
  </clause>

  <clause id="13571">
    <literal><![CDATA[
      T(x,T((y \ 1) * z,u)) = T(x,T(y \ z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,4158,a(flip),b,13520,a),flip(a)].">
      <j1 rule="hyper" parents="63 4158 13520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13578">
    <literal><![CDATA[
      T(x,T((y \ 1) * z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(13571(a,2),3706(a,1))].">
      <j1 rule="para" parents="13571 3706"/>
    </justification>
  </clause>

  <clause id="13579">
    <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(11162(a,1),13181(a,1,2))].">
      <j1 rule="para" parents="11162 13181"/>
    </justification>
  </clause>

  <clause id="13580">
    <literal><![CDATA[
      T(x,T((y \ 1) / z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ (y \ (z \ y))) = u
    ]]></literal>
    <justification jstring="[para(7343(a,2),13259(a,1))].">
      <j1 rule="para" parents="7343 13259"/>
    </justification>
  </clause>

  <clause id="13582">
    <literal><![CDATA[
      T(x,a(y,z,L(u,w,x))) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(333,a,13180,a(flip),b,13420,a),flip(a)].">
      <j1 rule="hyper" parents="333 13180 13420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13583">
    <literal><![CDATA[
      (K(x,y) / x) * (y * x) = L(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,5334,a(flip),b,13479,a)].">
      <j1 rule="hyper" parents="63 5334 13479"/>
    </justification>
  </clause>

  <clause id="13585">
    <literal><![CDATA[
      T(x,L((y \ 1) \ 1,z,u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,L(y,z,u) * w) = v5
    ]]></literal>
    <justification jstring="[para(11071(a,2),13508(a,1,2,1))].">
      <j1 rule="para" parents="11071 13508"/>
    </justification>
  </clause>

  <clause id="13586">
    <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(2383(a,1),13537(a,1,2,1))].">
      <j1 rule="para" parents="2383 13537"/>
    </justification>
  </clause>

  <clause id="13587">
    <literal><![CDATA[
      a(x,y,K(z,u)) * a(x,y,z) = T(a(x,y,z),z \ u)
    ]]></literal>
    <justification jstring="[para(11158(a,1),13540(a,1,1))].">
      <j1 rule="para" parents="11158 13540"/>
    </justification>
  </clause>

  <clause id="13588">
    <literal><![CDATA[
      a(x,y,z) = ((x * y) * z) / (x * (y * z))
    ]]></literal>
    <justification jstring="[hyper(333,a,8,a(flip),b,13547,a)].">
      <j1 rule="hyper" parents="333 8 13547"/>
    </justification>
  </clause>

  <clause id="13589">
    <literal><![CDATA[
      a(x,y,z) * (x * (y * z)) = (x * y) * z
    ]]></literal>
    <justification jstring="[hyper(267,a,13547,a)].">
      <j1 rule="hyper" parents="267 13547"/>
    </justification>
  </clause>

  <clause id="13592">
    <literal><![CDATA[
      a(x,y,z) = R(x \ R(x,y,z),x,y * z)
    ]]></literal>
    <justification jstring="[hyper(333,a,3033,a,b,13588,a),flip(a)].">
      <j1 rule="hyper" parents="333 3033 13588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13593">
    <literal><![CDATA[
      a(x,y,z) = R(R(x,y,z) / x,x,y * z)
    ]]></literal>
    <justification jstring="[hyper(333,a,561,a,b,13588,a),flip(a)].">
      <j1 rule="hyper" parents="333 561 13588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13594">
    <literal><![CDATA[
      ((x * y) * z) / ((x * (y * (z * (u * u)))) / (u * u)) = a(x,y,z * (u * u))
    ]]></literal>
    <justification jstring="[hyper(987,a,13588,a(flip))].">
      <j1 rule="hyper" parents="987 13588"/>
    </justification>
  </clause>

  <clause id="13595">
    <literal><![CDATA[
      a(x * (y / x),x,z) * (y * (T(x,y) * z)) = (y * T(x,y)) * z
    ]]></literal>
    <justification jstring="[hyper(125,a,11958,a,b,13588,a(flip))].">
      <j1 rule="hyper" parents="125 11958 13588"/>
    </justification>
  </clause>

  <clause id="13596">
    <literal><![CDATA[
      (x * (y * z)) / (y * (z * T(x,y * z))) = a(y,z,T(x,y * z))
    ]]></literal>
    <justification jstring="[para(111(a,1),13588(a,2,1)),flip(a)].">
      <j1 rule="para" parents="111 13588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13599">
    <literal><![CDATA[
      ((x * y) * z) / L(y * z,x,a(x,y,z)) = a(x,y,z) * x
    ]]></literal>
    <justification jstring="[hyper(123,a,13589,a(flip),b,97,a)].">
      <j1 rule="hyper" parents="123 13589 97"/>
    </justification>
  </clause>

  <clause id="13601">
    <literal><![CDATA[
      x \ R(x,y,y) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,534,a(flip),b,13592,a)].">
      <j1 rule="hyper" parents="333 534 13592"/>
    </justification>
  </clause>

  <clause id="13602">
    <literal><![CDATA[
      x \ R(x * R(x \ 1,y,z),x \ 1,y * z) = (x \ 1) * a(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(13592(a,2),1312(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13592 1312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13603">
    <literal><![CDATA[
      a(x,y \ R(y,z,u),x) = a(x,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(13592(a,2),11928(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13592 11928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13604">
    <literal><![CDATA[
      (1 / x) * R(x,y,y) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3023,a,b,13601,a)].">
      <j1 rule="hyper" parents="63 3023 13601"/>
    </justification>
  </clause>

  <clause id="13605">
    <literal><![CDATA[
      R(R(x \ 1,y,z) / (x \ 1),x,y * z) = a(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,1927,a(flip),b,13593,a)].">
      <j1 rule="hyper" parents="333 1927 13593"/>
    </justification>
  </clause>

  <clause id="13607">
    <literal><![CDATA[
      a(x,y \ R(y,z,u),x) != w
    ]]></literal>
    <literal><![CDATA[
      1 = w
    ]]></literal>
    <justification jstring="[para(13603(a,2),13001(a,1))].">
      <j1 rule="para" parents="13603 13001"/>
    </justification>
  </clause>

  <clause id="13608">
    <literal><![CDATA[
      T(x,(y \ 1) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(3613(a,1),13578(a,1))].">
      <j1 rule="para" parents="3613 13578"/>
    </justification>
  </clause>

  <clause id="13609">
    <literal><![CDATA[
      T(x,(1 / y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(3169(a,2),13608(a,1))].">
      <j1 rule="para" parents="3169 13608"/>
    </justification>
  </clause>

  <clause id="13610">
    <literal><![CDATA[
      T(x,((y \ 1) \ 1) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(13206(a,2),13608(a,1))].">
      <j1 rule="para" parents="13206 13608"/>
    </justification>
  </clause>

  <clause id="13611">
    <literal><![CDATA[
      T(x,(y \ 1) / z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ (z \ 1)) = u
    ]]></literal>
    <justification jstring="[para(13244(a,1),13608(a,1))].">
      <j1 rule="para" parents="13244 13608"/>
    </justification>
  </clause>

  <clause id="13612">
    <literal><![CDATA[
      T(x,T((y \ 1) \ 1,z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z) \ u) = w
    ]]></literal>
    <justification jstring="[para(2382(a,2),13610(a,1,2,1))].">
      <j1 rule="para" parents="2382 13610"/>
    </justification>
  </clause>

  <clause id="13613">
    <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(2779(a,2),13610(a,1,2,1))].">
      <j1 rule="para" parents="2779 13610"/>
    </justification>
  </clause>

  <clause id="13614">
    <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(2892(a,1),13610(a,1,2,1))].">
      <j1 rule="para" parents="2892 13610"/>
    </justification>
  </clause>

  <clause id="13615">
    <literal><![CDATA[
      K(x,L((y \ 1) \ z,u,w)) = K(x,L(y * z,u,w))
    ]]></literal>
    <justification jstring="[hyper(333,a,10851,a(flip),b,13214,a),flip(a)].">
      <j1 rule="hyper" parents="333 10851 13214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13616">
    <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(13214(a,2),10960(a,1))].">
      <j1 rule="para" parents="13214 10960"/>
    </justification>
  </clause>

  <clause id="13617">
    <literal><![CDATA[
      L(x \ y,x,z / T(y,z)) = ((z / y) * x) \ z
    ]]></literal>
    <justification jstring="[hyper(3645,a,13235,a)].">
      <j1 rule="hyper" parents="3645 13235"/>
    </justification>
  </clause>

  <clause id="13618">
    <literal><![CDATA[
      L(x \ y,x,y \ z) = ((z / y) * x) \ z
    ]]></literal>
    <justification jstring="[hyper(63,a,11875,a(flip),b,13617,a)].">
      <j1 rule="hyper" parents="63 11875 13617"/>
    </justification>
  </clause>

  <clause id="13619">
    <literal><![CDATA[
      x / L(y \ z,y,z \ x) = (x / z) * y
    ]]></literal>
    <justification jstring="[hyper(197,a,11875,a(flip),b,13617,a(flip))].">
      <j1 rule="hyper" parents="197 11875 13617"/>
    </justification>
  </clause>

  <clause id="13620">
    <literal><![CDATA[
      ((x \ y) * z) \ ((x \ y) * x) = ((y / x) * z) \ y
    ]]></literal>
    <justification jstring="[hyper(63,a,99,a(flip),b,13618,a)].">
      <j1 rule="hyper" parents="63 99 13618"/>
    </justification>
  </clause>

  <clause id="13622">
    <literal><![CDATA[
      x / L(y,z,(z * y) \ x) = (x / (z * y)) * z
    ]]></literal>
    <justification jstring="[para(9(a,1),13619(a,1,2,1))].">
      <j1 rule="para" parents="9 13619"/>
    </justification>
  </clause>

  <clause id="13623">
    <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(13286(a,2),10960(a,1))].">
      <j1 rule="para" parents="13286 10960"/>
    </justification>
  </clause>

  <clause id="13624">
    <literal><![CDATA[
      K(x \ T(y / z,y),u) = K(x \ (z \ y),u)
    ]]></literal>
    <justification jstring="[hyper(333,a,13215,a(flip),b,13293,a),flip(a)].">
      <j1 rule="hyper" parents="333 13215 13293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13625">
    <literal><![CDATA[
      K(x \ T(y,y * z),u) = K(x \ (z \ (y * z)),u)
    ]]></literal>
    <justification jstring="[para(11(a,1),13624(a,1,1,2,1))].">
      <j1 rule="para" parents="11 13624"/>
    </justification>
  </clause>

  <clause id="13626">
    <literal><![CDATA[
      K(x \ ((y \ z) \ z),u) = K(x \ T(y,z),u)
    ]]></literal>
    <justification jstring="[para(76(a,1),13624(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="76 13624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13627">
    <literal><![CDATA[
      K(x \ T(y * z,z \ 1),u) = K(x \ T(y * z,y),u)
    ]]></literal>
    <justification jstring="[para(5824(a,2),13626(a,1,1,2))].">
      <j1 rule="para" parents="5824 13626"/>
    </justification>
  </clause>

  <clause id="13628">
    <literal><![CDATA[
      K(x,T(y * (1 / z),u)) = K(x,T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(6983,a,13329,a),flip(a)].">
      <j1 rule="hyper" parents="6983 13329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13629">
    <literal><![CDATA[
      K(x,T(y * (1 / z),u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y / z,u)) = w
    ]]></literal>
    <justification jstring="[para(13329(a,1),6983(a,1))].">
      <j1 rule="para" parents="13329 6983"/>
    </justification>
  </clause>

  <clause id="13630">
    <literal><![CDATA[
      K(x,T(y / (z \ 1),u)) = K(x,T(y * z,u))
    ]]></literal>
    <justification jstring="[para(76(a,1),13628(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="76 13628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13631">
    <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(13337(a,2),10960(a,1))].">
      <j1 rule="para" parents="13337 10960"/>
    </justification>
  </clause>

  <clause id="13632">
    <literal><![CDATA[
      K(x / ((y * a(z,u,z)) \ K(z * u,z)),w) = K(x * (K(z,u) * y),w)
    ]]></literal>
    <justification jstring="[para(9245(a,1),13375(a,2,1,2))].">
      <j1 rule="para" parents="9245 13375"/>
    </justification>
  </clause>

  <clause id="13633">
    <literal><![CDATA[
      K(x \ ((x \ 1) \ y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) = u
    ]]></literal>
    <justification jstring="[para(13386(a,2),7397(a,1))].">
      <j1 rule="para" parents="13386 7397"/>
    </justification>
  </clause>

  <clause id="13634">
    <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(5902(a,1),13633(a,1,1,2))].">
      <j1 rule="para" parents="5902 13633"/>
    </justification>
  </clause>

  <clause id="13635">
    <literal><![CDATA[
      ((((x * y) \ x) \ T(((x * y) \ x) * z,y)) \ u) * ((z \ u) \ 1) = K(((x * y) \ x) \ 1,(((x * y) \ x) \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(5831(a,2),13390(a,1,1,1))].">
      <j1 rule="para" parents="5831 13390"/>
    </justification>
  </clause>

  <clause id="13636">
    <literal><![CDATA[
      K(x * (y \ 1),(y \ 1) \ (x \ z)) = K(x / y,(x * (y \ 1)) \ z)
    ]]></literal>
    <justification jstring="[hyper(13493,a,13402,a),flip(a)].">
      <j1 rule="hyper" parents="13493 13402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13637">
    <literal><![CDATA[
      (x \ T(y * x,z)) / T(y,x) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(22(a,2),13458(a,1,2))].">
      <j1 rule="para" parents="22 13458"/>
    </justification>
  </clause>

  <clause id="13638">
    <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(13637(a,1),559(a,1,1))].">
      <j1 rule="para" parents="13637 559"/>
    </justification>
  </clause>

  <clause id="13639">
    <literal><![CDATA[
      (x \ K(x \ y,y)) * y = T((x \ 1) * y,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,13196,a(flip),b,13469,a)].">
      <j1 rule="hyper" parents="63 13196 13469"/>
    </justification>
  </clause>

  <clause id="13640">
    <literal><![CDATA[
      T(x * y,L(z,y,x)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(486(a,1),13498(a,1))].">
      <j1 rule="para" parents="486 13498"/>
    </justification>
  </clause>

  <clause id="13641">
    <literal><![CDATA[
      T(x * (y / z),L(z,z \ y,x)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x * (y / z),z) = u
    ]]></literal>
    <justification jstring="[para(10406(a,1),13640(a,1,2))].">
      <j1 rule="para" parents="10406 13640"/>
    </justification>
  </clause>

  <clause id="13642">
    <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(6887(a,1),13502(a,1,1,2))].">
      <j1 rule="para" parents="6887 13502"/>
    </justification>
  </clause>

  <clause id="13643">
    <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(10007(a,1),13502(a,1,2,1))].">
      <j1 rule="para" parents="10007 13502"/>
    </justification>
  </clause>

  <clause id="13644">
    <literal><![CDATA[
      a(x,y,K(z,L(u,w,v5))) = L(a(x,y,K(z,u)),w,v5)
    ]]></literal>
    <justification jstring="[para(13539(a,2),13543(a,2,1))].">
      <j1 rule="para" parents="13539 13543"/>
    </justification>
  </clause>

  <clause id="13645">
    <literal><![CDATA[
      1 / (K(x,y) * z) = (1 / z) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,7323,a(flip),b,13554,a)].">
      <j1 rule="hyper" parents="63 7323 13554"/>
    </justification>
  </clause>

  <clause id="13646">
    <literal><![CDATA[
      K(x,y) * ((1 / z) * K(u,w)) = K(x,y) / (K(w,u) * z)
    ]]></literal>
    <justification jstring="[hyper(126,a,13645,a(flip),b,13238,a)].">
      <j1 rule="hyper" parents="126 13645 13238"/>
    </justification>
  </clause>

  <clause id="13647">
    <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(2381(a,1),13615(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="2381 13615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13648">
    <literal><![CDATA[
      ((x / y) * (y * K(z,u))) \ x = K(u,L(z,y,y \ x))
    ]]></literal>
    <justification jstring="[hyper(10962,a,13620,a),flip(a)].">
      <j1 rule="hyper" parents="10962 13620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13649">
    <literal><![CDATA[
      K(x \ T(y,y * z),u) = K(x \ T(y,z),u)
    ]]></literal>
    <justification jstring="[para(22(a,2),13625(a,2,1,2))].">
      <j1 rule="para" parents="22 13625"/>
    </justification>
  </clause>

  <clause id="13650">
    <literal><![CDATA[
      K(R(x / y,y,x \ T(z,z * u)) \ T(z,u),w) = K(y * (x \ T(z,z * u)),w)
    ]]></literal>
    <justification jstring="[para(527(a,1),13649(a,1,1)),flip(a)].">
      <j1 rule="para" parents="527 13649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13651">
    <literal><![CDATA[
      T(x,y \ T(z,z * u)) = (w * K(y \ T(z,u),x)) \ (w * x)
    ]]></literal>
    <justification jstring="[para(13649(a,1),5447(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="13649 5447"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13652">
    <literal><![CDATA[
      T(x * K(x * y,y \ 1),y) != z
    ]]></literal>
    <literal><![CDATA[
      y \ T(x * y,y \ 1) = z
    ]]></literal>
    <justification jstring="[para(8645(a,2),13495(a,1))].">
      <j1 rule="para" parents="8645 13495"/>
    </justification>
  </clause>

  <clause id="13653">
    <literal><![CDATA[
      K(x,K(y,z * (1 / u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z / u)) = w
    ]]></literal>
    <justification jstring="[para(4785(a,2),13531(a,1,2))].">
      <j1 rule="para" parents="4785 13531"/>
    </justification>
  </clause>

  <clause id="13654">
    <literal><![CDATA[
      T(a(x,y,z),z \ u) = T(a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,13540,a(flip),b,13587,a),flip(a)].">
      <j1 rule="hyper" parents="63 13540 13587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13655">
    <literal><![CDATA[
      T(a(x,y,z),z * u) = T(a(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(9(a,1),13654(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9 13654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13656">
    <literal><![CDATA[
      L(a(x,y,z),u,z) * (z * u) = z * (u * T(a(x,y,z),u))
    ]]></literal>
    <justification jstring="[para(13655(a,1),664(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13655 664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13657">
    <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(13648(a,1),301(a,1,2)),flip(b)].">
      <j1 rule="para" parents="13648 301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13658">
    <literal><![CDATA[
      (x \ K(y,z)) / (x \ 1) = K(y,z) * K(y,K(z,x))
    ]]></literal>
    <justification jstring="[para(7148(a,1),13188(a,2,2))].">
      <j1 rule="para" parents="7148 13188"/>
    </justification>
  </clause>

  <clause id="13659">
    <literal><![CDATA[
      K(x,T(y,z)) * (z \ 1) = z \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(7903,a,13658,a)].">
      <j1 rule="hyper" parents="7903 13658"/>
    </justification>
  </clause>

  <clause id="13660">
    <literal><![CDATA[
      K((x \ 1) \ (y \ (y \ 1)),z) = K((x * (y \ 1)) / y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5004,a(flip),b,13223,a)].">
      <j1 rule="hyper" parents="63 5004 13223"/>
    </justification>
  </clause>

  <clause id="13661">
    <literal><![CDATA[
      K((x \ y) * z,x) = K(y * (x \ z),x)
    ]]></literal>
    <justification jstring="[hyper(13198,a,13281,a),flip(a)].">
      <j1 rule="hyper" parents="13198 13281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13662">
    <literal><![CDATA[
      K(x \ (y * z),x) = K((x \ y) * z,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,10836,a,b,13661,a)].">
      <j1 rule="hyper" parents="333 10836 13661"/>
    </justification>
  </clause>

  <clause id="13663">
    <literal><![CDATA[
      K(x \ ((x * y) * z),x) = K(y * z,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),13662(a,2,1,1))].">
      <j1 rule="para" parents="9 13662"/>
    </justification>
  </clause>

  <clause id="13664">
    <literal><![CDATA[
      K(x,y \ K((z \ u) * w,z)) = K(x,y \ K(u * w,z))
    ]]></literal>
    <justification jstring="[para(13662(a,1),12689(a,1,2,2))].">
      <j1 rule="para" parents="13662 12689"/>
    </justification>
  </clause>

  <clause id="13665">
    <literal><![CDATA[
      K(x \ ((y * x) * z),x) = K(y * z,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,10112,a,b,13663,a)].">
      <j1 rule="hyper" parents="63 10112 13663"/>
    </justification>
  </clause>

  <clause id="13666">
    <literal><![CDATA[
      K((x \ y) \ (y * z),x \ y) = K(x * z,x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),13665(a,1,1,2,1))].">
      <j1 rule="para" parents="10 13665"/>
    </justification>
  </clause>

  <clause id="13667">
    <literal><![CDATA[
      K((x \ y) \ z,x \ y) = K(x * (y \ z),x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),13666(a,1,1,2))].">
      <j1 rule="para" parents="10 13666"/>
    </justification>
  </clause>

  <clause id="13668">
    <literal><![CDATA[
      K(x \ (y * z),y \ x) = K(y * (x \ z),y \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,10317,a(flip),b,13667,a)].">
      <j1 rule="hyper" parents="63 10317 13667"/>
    </justification>
  </clause>

  <clause id="13669">
    <literal><![CDATA[
      a(x,y,K(z * (u \ w),z \ u)) = a(x,y,K(w,z \ u))
    ]]></literal>
    <justification jstring="[para(13667(a,1),11149(a,1,3))].">
      <j1 rule="para" parents="13667 11149"/>
    </justification>
  </clause>

  <clause id="13670">
    <literal><![CDATA[
      K(x / (y / z),z \ y) = K(z * (y \ x),z \ y)
    ]]></literal>
    <justification jstring="[hyper(10420,a,13668,a)].">
      <j1 rule="hyper" parents="10420 13668"/>
    </justification>
  </clause>

  <clause id="13671">
    <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(6075(a,1),13311(a,1,2,1))].">
      <j1 rule="para" parents="6075 13311"/>
    </justification>
  </clause>

  <clause id="13672">
    <literal><![CDATA[
      T((x \ T(y,z)) \ T(y,x),y) = (x \ T(y,z)) \ y
    ]]></literal>
    <justification jstring="[para(13231(a,1),13314(a,2,1))].">
      <j1 rule="para" parents="13231 13314"/>
    </justification>
  </clause>

  <clause id="13673">
    <literal><![CDATA[
      K(x,y / T((z \ 1) \ 1,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(13331(a,2),13528(a,1))].">
      <j1 rule="para" parents="13331 13528"/>
    </justification>
  </clause>

  <clause id="13674">
    <literal><![CDATA[
      K(x,y / ((z * u) \ z)) = K(x,y / (z \ (z / u)))
    ]]></literal>
    <justification jstring="[hyper(13528,a,13332,a),flip(a)].">
      <j1 rule="hyper" parents="13528 13332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13675">
    <literal><![CDATA[
      T(x * x,y) * ((x * x) \ y) = T(y,x \ (x \ y))
    ]]></literal>
    <justification jstring="[para(3643(a,1),13467(a,1,2))].">
      <j1 rule="para" parents="3643 13467"/>
    </justification>
  </clause>

  <clause id="13676">
    <literal><![CDATA[
      T(x,y \ (y \ x)) = x * K(y * y,x)
    ]]></literal>
    <justification jstring="[hyper(4540,a,13675,a),flip(a)].">
      <j1 rule="hyper" parents="4540 13675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13677">
    <literal><![CDATA[
      T(x \ y,x \ (x \ (x \ y))) = (x \ y) * K(x * x,x * y)
    ]]></literal>
    <justification jstring="[para(13204(a,1),13676(a,2,2))].">
      <j1 rule="para" parents="13204 13676"/>
    </justification>
  </clause>

  <clause id="13678">
    <literal><![CDATA[
      a(x \ y,T(x,y),z) = a(y / x,x,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,13023,a(flip),b,13567,a),flip(a)].">
      <j1 rule="hyper" parents="63 13023 13567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13680">
    <literal><![CDATA[
      K(x,y) / (K(x,y) * z) = T(1 / z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(7057,a,13646,a),flip(a)].">
      <j1 rule="hyper" parents="7057 13646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13681">
    <literal><![CDATA[
      K((x * (y \ 1)) / y,z) = K(x * (y \ (y \ 1)),z)
    ]]></literal>
    <justification jstring="[hyper(13425,a,13660,a),flip(a)].">
      <j1 rule="hyper" parents="13425 13660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13682">
    <literal><![CDATA[
      K((x * (y \ 1)) / y,z) = K(x / (y * y),z)
    ]]></literal>
    <justification jstring="[para(722(a,1),13681(a,2,1))].">
      <j1 rule="para" parents="722 13681"/>
    </justification>
  </clause>

  <clause id="13687">
    <literal><![CDATA[
      L(x \ (T(y,z) \ z),x,K(y,z)) = x \ (y \ T(z,y))
    ]]></literal>
    <justification jstring="[para(4365(a,1),13488(a,1,3))].">
      <j1 rule="para" parents="4365 13488"/>
    </justification>
  </clause>

  <clause id="13688">
    <literal><![CDATA[
      (K(x,y) * z) \ (x \ y) = z \ (x \ T(y,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,4681,a(flip),b,13687,a)].">
      <j1 rule="hyper" parents="63 4681 13687"/>
    </justification>
  </clause>

  <clause id="13689">
    <literal><![CDATA[
      T(x * y,z) / T(y,x) = T(x * K(x * y,z),y)
    ]]></literal>
    <justification jstring="[hyper(13496,a,12400,a(flip))].">
      <j1 rule="hyper" parents="13496 12400"/>
    </justification>
  </clause>

  <clause id="13690">
    <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(13689(a,2),6443(a,2,2))].">
      <j1 rule="para" parents="13689 6443"/>
    </justification>
  </clause>

  <clause id="13691">
    <literal><![CDATA[
      ((x * y) * z) / L(y * z,x,a(x,y,z)) = x * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,12432,a(flip),b,13599,a),flip(a)].">
      <j1 rule="hyper" parents="333 12432 13599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13692">
    <literal><![CDATA[
      R(x * R(x \ 1,y,z),x,y * z) = a(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(1157(a,1),13605(a,1,1))].">
      <j1 rule="para" parents="1157 13605"/>
    </justification>
  </clause>

  <clause id="13693">
    <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(11208(a,1),13631(a,1,2,1,2))].">
      <j1 rule="para" parents="11208 13631"/>
    </justification>
  </clause>

  <clause id="13694">
    <literal><![CDATA[
      L(a(x,y,z),u,z) * (z * u) = z * (a(x,y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(333,a,235,a(flip),b,13656,a),flip(a)].">
      <j1 rule="hyper" parents="333 235 13656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13695">
    <literal><![CDATA[
      K(x,L(y,z \ u,z) * u) = K(x,z * ((z \ T(u,y)) * y))
    ]]></literal>
    <justification jstring="[para(11029(a,1),13177(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11029 13177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13696">
    <literal><![CDATA[
      T(x \ 1,K(y,z)) * K(u,w) = K(x,K(y,z)) * (x \ K(u,w))
    ]]></literal>
    <justification jstring="[para(7288(a,2),13184(a,2,1)),flip(a)].">
      <j1 rule="para" parents="7288 13184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13697">
    <literal><![CDATA[
      K(x,y * (z * ((u \ w) \ w))) = K(x,y * (z * T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(13421,a,13211,a),flip(a)].">
      <j1 rule="hyper" parents="13421 13211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13698">
    <literal><![CDATA[
      T(x,y * (z * ((u \ w) \ w))) = T(x,y * (z * T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(124,a,13697,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 13697 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13699">
    <literal><![CDATA[
      L(x,y,z / ((1 / u) * K(w,v5))) = L(x,y,z / (u \ K(w,v5)))
    ]]></literal>
    <justification jstring="[para(13645(a,1),13264(a,1,3,2))].">
      <j1 rule="para" parents="13645 13264"/>
    </justification>
  </clause>

  <clause id="13700">
    <literal><![CDATA[
      L(x,y,((1 / z) * K(u,w)) \ v5) = L(x,y,(z \ K(u,w)) \ v5)
    ]]></literal>
    <justification jstring="[para(13645(a,1),13265(a,1,3,1))].">
      <j1 rule="para" parents="13645 13265"/>
    </justification>
  </clause>

  <clause id="13701">
    <literal><![CDATA[
      T(T(x,y / z),K(y / z,u)) = T(x,T(y * (z \ 1),u))
    ]]></literal>
    <justification jstring="[para(13244(a,1),13277(a,1,1))].">
      <j1 rule="para" parents="13244 13277"/>
    </justification>
  </clause>

  <clause id="13702">
    <literal><![CDATA[
      T(x,T(y * (z \ 1),u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y / z,u)) = w
    ]]></literal>
    <justification jstring="[para(13701(a,1),7056(a,1))].">
      <j1 rule="para" parents="13701 7056"/>
    </justification>
  </clause>

  <clause id="13703">
    <literal><![CDATA[
      T(x,T((y \ 1) / z,u)) = T(x,T(y \ (z \ 1),u))
    ]]></literal>
    <justification jstring="[hyper(13702,a,13571,a)].">
      <j1 rule="hyper" parents="13702 13571"/>
    </justification>
  </clause>

  <clause id="13704">
    <literal><![CDATA[
      T(x,T(y \ (z \ 1),y)) = T(x,y \ (y \ (z \ y)))
    ]]></literal>
    <justification jstring="[hyper(13580,a,13703,a),flip(a)].">
      <j1 rule="hyper" parents="13580 13703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13705">
    <literal><![CDATA[
      T(x,y \ (y \ (z \ y))) = T(x,(z \ 1) / y)
    ]]></literal>
    <justification jstring="[hyper(13513,a,13704,a),flip(a)].">
      <j1 rule="hyper" parents="13513 13704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13706">
    <literal><![CDATA[
      T(x,y \ (y \ (z \ y))) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ (y \ 1)) = u
    ]]></literal>
    <justification jstring="[para(13705(a,2),13611(a,1))].">
      <j1 rule="para" parents="13705 13611"/>
    </justification>
  </clause>

  <clause id="13707">
    <literal><![CDATA[
      (T(x,y) / z) \ K(x,K(y,x / z)) = ((x / z) * K(x,y)) \ 1
    ]]></literal>
    <justification jstring="[para(6763(a,1),13302(a,1,2))].">
      <j1 rule="para" parents="6763 13302"/>
    </justification>
  </clause>

  <clause id="13708">
    <literal><![CDATA[
      ((K(x,y) * z) / K(x,y)) \ T(y,x) = (z * K(x,y)) \ y
    ]]></literal>
    <justification jstring="[para(6866(a,1),13312(a,2,1))].">
      <j1 rule="para" parents="6866 13312"/>
    </justification>
  </clause>

  <clause id="13709">
    <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(13333(a,2),13629(a,1))].">
      <j1 rule="para" parents="13333 13629"/>
    </justification>
  </clause>

  <clause id="13710">
    <literal><![CDATA[
      (K(x,y) * (z \ x)) \ K(x,K(y,z \ x)) = (z \ T(x,y)) \ 1
    ]]></literal>
    <justification jstring="[para(6763(a,1),13369(a,1,2))].">
      <j1 rule="para" parents="6763 13369"/>
    </justification>
  </clause>

  <clause id="13711">
    <literal><![CDATA[
      K(x,T(y,z)) \ K(z,z \ y) = T(z * (y / z),x) / y
    ]]></literal>
    <justification jstring="[para(4535(a,1),13387(a,1,2))].">
      <j1 rule="para" parents="4535 13387"/>
    </justification>
  </clause>

  <clause id="13712">
    <literal><![CDATA[
      K(x,T(y,z)) \ K(z,z \ y) = (z * (T(y,x) / z)) / y
    ]]></literal>
    <justification jstring="[para(4083(a,1),13711(a,2,1))].">
      <j1 rule="para" parents="4083 13711"/>
    </justification>
  </clause>

  <clause id="13713">
    <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(13418(a,1),4469(a,1))].">
      <j1 rule="para" parents="13418 4469"/>
    </justification>
  </clause>

  <clause id="13714">
    <literal><![CDATA[
      K(x \ (y * z),T(x,y)) = K(z / (y \ x),x)
    ]]></literal>
    <justification jstring="[hyper(13713,a,7281,a)].">
      <j1 rule="hyper" parents="13713 7281"/>
    </justification>
  </clause>

  <clause id="13715">
    <literal><![CDATA[
      L(x,x \ y,z) \ (z * y) != u
    ]]></literal>
    <literal><![CDATA[
      T(z * (y / x),x) = u
    ]]></literal>
    <justification jstring="[para(10413(a,1),13641(a,1))].">
      <j1 rule="para" parents="10413 13641"/>
    </justification>
  </clause>

  <clause id="13716">
    <literal><![CDATA[
      L(x,x \ (y \ z),K(y,z)) \ ((y \ z) * K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(K(y,z) * ((y \ z) / x),x) = u
    ]]></literal>
    <justification jstring="[para(6185(a,1),13715(a,1,2))].">
      <j1 rule="para" parents="6185 13715"/>
    </justification>
  </clause>

  <clause id="13717">
    <literal><![CDATA[
      T(x,y \ T(z,z * u)) = T(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[hyper(333,a,5447,a(flip),b,13651,a),flip(a)].">
      <j1 rule="hyper" parents="333 5447 13651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13718">
    <literal><![CDATA[
      T(x,y \ T(z,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(13651(a,2),5458(a,1))].">
      <j1 rule="para" parents="13651 5458"/>
    </justification>
  </clause>

  <clause id="13719">
    <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(126,a,13717,a(flip),b,8027,a),flip(a)].">
      <j1 rule="hyper" parents="126 13717 8027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13720">
    <literal><![CDATA[
      T(x \ (x \ y),x \ (x \ (x \ (x \ y)))) = (x \ (x \ y)) * K(x * x,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),13677(a,2,2,2))].">
      <j1 rule="para" parents="10 13677"/>
    </justification>
  </clause>

  <clause id="13721">
    <literal><![CDATA[
      (T(x,y) / z) \ K(x,K(y,z)) = ((x / z) * K(x,y)) \ 1
    ]]></literal>
    <justification jstring="[para(7158(a,1),13707(a,1,2))].">
      <j1 rule="para" parents="7158 13707"/>
    </justification>
  </clause>

  <clause id="13722">
    <literal><![CDATA[
      (K(x,y) * (z \ x)) \ K(x,K(y,z)) = (z \ T(x,y)) \ 1
    ]]></literal>
    <justification jstring="[para(7145(a,1),13710(a,1,2))].">
      <j1 rule="para" parents="7145 13710"/>
    </justification>
  </clause>

  <clause id="13723">
    <literal><![CDATA[
      ((x \ y) \ K(z,y)) * K(y,K(z,x)) = (x \ T(y,z)) \ 1
    ]]></literal>
    <justification jstring="[hyper(13489,a,13722,a)].">
      <j1 rule="hyper" parents="13489 13722"/>
    </justification>
  </clause>

  <clause id="13724">
    <literal><![CDATA[
      (x \ y) \ K(z,T(y,x)) = (x \ T(y,z)) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,12326,a(flip),b,13723,a)].">
      <j1 rule="hyper" parents="63 12326 13723"/>
    </justification>
  </clause>

  <clause id="13726">
    <literal><![CDATA[
      a(x * (y / x),x,z) * (y * (T(x,y) * z)) = (x * y) * z
    ]]></literal>
    <justification jstring="[hyper(333,a,236,a(flip),b,13595,a),flip(a)].">
      <j1 rule="hyper" parents="333 236 13595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13727">
    <literal><![CDATA[
      (x * (y * z)) / (L(x,z,y) * (y * z)) = a(y,z,T(x,y * z))
    ]]></literal>
    <justification jstring="[para(664(a,1),13596(a,1,2))].">
      <j1 rule="para" parents="664 13596"/>
    </justification>
  </clause>

  <clause id="13728">
    <literal><![CDATA[
      x \ T(y * x,x \ 1) = (y * x) * (y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(13652,a,12402,a)].">
      <j1 rule="hyper" parents="13652 12402"/>
    </justification>
  </clause>

  <clause id="13729">
    <literal><![CDATA[
      a(K(x,y),z,u) = a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(9916,a,13109,a),flip(a)].">
      <j1 rule="hyper" parents="9916 13109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13730">
    <literal><![CDATA[
      a(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,z,K(u,y)) = w
    ]]></literal>
    <justification jstring="[para(13109(a,1),9916(a,1))].">
      <j1 rule="para" parents="13109 9916"/>
    </justification>
  </clause>

  <clause id="13731">
    <literal><![CDATA[
      a(x,y,K(z,u)) = a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,13103,a(flip),b,13729,a),flip(a)].">
      <j1 rule="hyper" parents="63 13103 13729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13732">
    <literal><![CDATA[
      a(x,y,K(z,u)) = K(x,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,12426,a(flip),b,13729,a),flip(a)].">
      <j1 rule="hyper" parents="63 12426 13729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13733">
    <literal><![CDATA[
      (K(x,y) * (z * u)) * a(x,z,K(u,y)) = (K(x,y) * z) * u
    ]]></literal>
    <justification jstring="[hyper(126,a,13729,a(flip),b,14,a(flip))].">
      <j1 rule="hyper" parents="126 13729 14"/>
    </justification>
  </clause>

  <clause id="13734">
    <literal><![CDATA[
      (x * K(y,z)) * a(y,u,K(u \ x,T(z,x))) = (K(y,T(z,x)) * u) * (u \ x)
    ]]></literal>
    <justification jstring="[para(13729(a,1),6972(a,1,2))].">
      <j1 rule="para" parents="13729 6972"/>
    </justification>
  </clause>

  <clause id="13735">
    <literal><![CDATA[
      a(x,y,K(z,L(u,w,x))) = a(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(9466(a,1),13729(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9466 13729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13736">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(u,y)) = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(13729(a,1),11728(a,1,2))].">
      <j1 rule="para" parents="13729 11728"/>
    </justification>
  </clause>

  <clause id="13737">
    <literal><![CDATA[
      a(K(x,y),z,u) = a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(333,a,13729,a,b,13731,a)].">
      <j1 rule="hyper" parents="333 13729 13731"/>
    </justification>
  </clause>

  <clause id="13738">
    <literal><![CDATA[
      a(x,y,K(z,z \ u)) = a(z,y,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(333,a,11158,a,b,13731,a)].">
      <j1 rule="hyper" parents="333 11158 13731"/>
    </justification>
  </clause>

  <clause id="13739">
    <literal><![CDATA[
      a(x \ 1,y,K(z,u)) = a(u,y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(333,a,11162,a(flip),b,13731,a),flip(a)].">
      <j1 rule="hyper" parents="333 11162 13731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13740">
    <literal><![CDATA[
      x / a(y,z,K(u,w)) = x * a(w,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(197,a,13731,a,b,9913,a)].">
      <j1 rule="hyper" parents="197 13731 9913"/>
    </justification>
  </clause>

  <clause id="13741">
    <literal><![CDATA[
      x * a(x,y,K(z,u)) = T(x,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(126,a,13731,a,b,13178,a)].">
      <j1 rule="hyper" parents="126 13731 13178"/>
    </justification>
  </clause>

  <clause id="13742">
    <literal><![CDATA[
      x * a(y,z,K(u,w)) = x * a(w,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(126,a,13731,a,b,9,a)].">
      <j1 rule="hyper" parents="126 13731 9"/>
    </justification>
  </clause>

  <clause id="13743">
    <literal><![CDATA[
      K(L(x,y,z) \ x,u) = a(u,y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,13542,a,b,13731,a)].">
      <j1 rule="hyper" parents="63 13542 13731"/>
    </justification>
  </clause>

  <clause id="13744">
    <literal><![CDATA[
      a(x \ y,z,K(u,w)) = a(u,z,K(y \ x,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,11163,a,b,13731,a),flip(a)].">
      <j1 rule="hyper" parents="63 11163 13731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13745">
    <literal><![CDATA[
      a(x,y,K(z,u \ z)) = a(z,y,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,11160,a,b,13731,a)].">
      <j1 rule="hyper" parents="63 11160 13731"/>
    </justification>
  </clause>

  <clause id="13746">
    <literal><![CDATA[
      a(x,y,K(z,z \ u)) = a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,11158,a,b,13731,a)].">
      <j1 rule="hyper" parents="63 11158 13731"/>
    </justification>
  </clause>

  <clause id="13747">
    <literal><![CDATA[
      a(x,y,K(z * u,z)) = a(z,y,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,11152,a,b,13731,a)].">
      <j1 rule="hyper" parents="63 11152 13731"/>
    </justification>
  </clause>

  <clause id="13748">
    <literal><![CDATA[
      a(x,y,K(z \ u,z)) = a(z,y,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,11149,a,b,13731,a)].">
      <j1 rule="hyper" parents="63 11149 13731"/>
    </justification>
  </clause>

  <clause id="13749">
    <literal><![CDATA[
      a(x,y * z,K(u,z)) = a(z,y,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,10945,a,b,13731,a)].">
      <j1 rule="hyper" parents="63 10945 13731"/>
    </justification>
  </clause>

  <clause id="13750">
    <literal><![CDATA[
      K(x,L(y,z,u)) * K(y,x) = a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,10884,a,b,13731,a)].">
      <j1 rule="hyper" parents="63 10884 13731"/>
    </justification>
  </clause>

  <clause id="13751">
    <literal><![CDATA[
      K(x,y) * K(y,L(x,z,u)) = a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,10883,a,b,13731,a)].">
      <j1 rule="hyper" parents="63 10883 13731"/>
    </justification>
  </clause>

  <clause id="13752">
    <literal><![CDATA[
      K(x,y) * L(K(y,x),z,u) = a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,9729,a,b,13731,a)].">
      <j1 rule="hyper" parents="63 9729 13731"/>
    </justification>
  </clause>

  <clause id="13753">
    <literal><![CDATA[
      a(x * y,z,K(u,x)) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,11157,a(flip),b,13731,a),flip(a)].">
      <j1 rule="hyper" parents="63 11157 13731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13754">
    <literal><![CDATA[
      a(x,L(x,y,z),K(u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(63,a,10192,a(flip),b,13731,a),flip(a)].">
      <j1 rule="hyper" parents="63 10192 13731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13755">
    <literal><![CDATA[
      a(L(x,y,z),x,K(u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(63,a,9537,a(flip),b,13731,a),flip(a)].">
      <j1 rule="hyper" parents="63 9537 13731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13756">
    <literal><![CDATA[
      x * a(y,z,K(u,x)) = T(x,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(126,a,13731,a(flip),b,13178,a)].">
      <j1 rule="hyper" parents="126 13731 13178"/>
    </justification>
  </clause>

  <clause id="13757">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = a(u,y,K(x,K(w,z)))
    ]]></literal>
    <justification jstring="[para(6786(a,1),13731(a,1,3))].">
      <j1 rule="para" parents="6786 13731"/>
    </justification>
  </clause>

  <clause id="13758">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = a(u,y,K(x,K(z,w)))
    ]]></literal>
    <justification jstring="[para(6796(a,1),13731(a,1,3))].">
      <j1 rule="para" parents="6796 13731"/>
    </justification>
  </clause>

  <clause id="13759">
    <literal><![CDATA[
      a(x,y,K(z * (u / T(w,x)),v5)) = a(v5,y,K(x,z * (u / w)))
    ]]></literal>
    <justification jstring="[para(9429(a,1),13731(a,2,3))].">
      <j1 rule="para" parents="9429 13731"/>
    </justification>
  </clause>

  <clause id="13760">
    <literal><![CDATA[
      a(x,y,K(z * (T(u,x) \ w),v5)) = a(v5,y,K(x,z * (u \ w)))
    ]]></literal>
    <justification jstring="[para(9432(a,1),13731(a,2,3))].">
      <j1 rule="para" parents="9432 13731"/>
    </justification>
  </clause>

  <clause id="13761">
    <literal><![CDATA[
      K(x,y) * a(y,z,K(x,u)) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(13731(a,2),9731(a,1,2))].">
      <j1 rule="para" parents="13731 9731"/>
    </justification>
  </clause>

  <clause id="13762">
    <literal><![CDATA[
      K(x,y) * (L(K(y,x),z,u) * w) = a(y,z,K(u,x)) * w
    ]]></literal>
    <justification jstring="[para(13731(a,1),9735(a,2,1))].">
      <j1 rule="para" parents="13731 9735"/>
    </justification>
  </clause>

  <clause id="13763">
    <literal><![CDATA[
      a(x,y,K(z,u)) \ w = a(u,y,K(z,x)) * w
    ]]></literal>
    <justification jstring="[para(13731(a,2),9791(a,1,1))].">
      <j1 rule="para" parents="13731 9791"/>
    </justification>
  </clause>

  <clause id="13764">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(u,y)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(13731(a,1),10860(a,1,2))].">
      <j1 rule="para" parents="13731 10860"/>
    </justification>
  </clause>

  <clause id="13765">
    <literal><![CDATA[
      K(x,y) * a(y,z,K(x,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(13731(a,2),10860(a,1,2))].">
      <j1 rule="para" parents="13731 10860"/>
    </justification>
  </clause>

  <clause id="13766">
    <literal><![CDATA[
      K(x,L(y,z,u)) * a(x,z,K(y,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(13731(a,2),10885(a,1,2))].">
      <j1 rule="para" parents="13731 10885"/>
    </justification>
  </clause>

  <clause id="13767">
    <literal><![CDATA[
      a(x,y,K(z,u)) * K(x,u) = K(x,L(u,y,z))
    ]]></literal>
    <justification jstring="[para(13731(a,1),10928(a,1,1))].">
      <j1 rule="para" parents="13731 10928"/>
    </justification>
  </clause>

  <clause id="13768">
    <literal><![CDATA[
      a(x,y,K(z,u)) * K(x,L(z,y,u)) = K(x,z)
    ]]></literal>
    <justification jstring="[para(13731(a,2),10929(a,1,1))].">
      <j1 rule="para" parents="13731 10929"/>
    </justification>
  </clause>

  <clause id="13769">
    <literal><![CDATA[
      a(x,y,K(z,u)) * T(z,x) = T(z,L(x,y,u))
    ]]></literal>
    <justification jstring="[para(13731(a,2),10936(a,1,1))].">
      <j1 rule="para" parents="13731 10936"/>
    </justification>
  </clause>

  <clause id="13770">
    <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(13731(a,1),10933(a,1,2))].">
      <j1 rule="para" parents="13731 10933"/>
    </justification>
  </clause>

  <clause id="13771">
    <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(13731(a,2),10933(a,1,2))].">
      <j1 rule="para" parents="13731 10933"/>
    </justification>
  </clause>

  <clause id="13772">
    <literal><![CDATA[
      L(x,y,a(y,z,K(u,w))) = x
    ]]></literal>
    <justification jstring="[para(13731(a,1),13072(a,1,3))].">
      <j1 rule="para" parents="13731 13072"/>
    </justification>
  </clause>

  <clause id="13773">
    <literal><![CDATA[
      x * a(y,z,K(u,x)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,a(u,z,y)) = w
    ]]></literal>
    <justification jstring="[para(13731(a,1),13181(a,1,2))].">
      <j1 rule="para" parents="13731 13181"/>
    </justification>
  </clause>

  <clause id="13774">
    <literal><![CDATA[
      x * a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,a(u,y,z)) = w
    ]]></literal>
    <justification jstring="[para(13731(a,2),13181(a,1,2))].">
      <j1 rule="para" parents="13731 13181"/>
    </justification>
  </clause>

  <clause id="13775">
    <literal><![CDATA[
      L(K(x,y),L(z,u,w),z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(52,a,13754,a)].">
      <j1 rule="hyper" parents="52 13754"/>
    </justification>
  </clause>

  <clause id="13776">
    <literal><![CDATA[
      L(K(x,y),z,L(z,u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(52,a,13755,a)].">
      <j1 rule="hyper" parents="52 13755"/>
    </justification>
  </clause>

  <clause id="13777">
    <literal><![CDATA[
      ((x * y) * K(z,u)) / (y * K(z,u)) = x * a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(13772(a,1),13691(a,1,2))].">
      <j1 rule="para" parents="13772 13691"/>
    </justification>
  </clause>

  <clause id="13778">
    <literal><![CDATA[
      K(x,L(y,z,u) \ y) = a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(333,a,13095,a,b,13732,a)].">
      <j1 rule="hyper" parents="333 13095 13732"/>
    </justification>
  </clause>

  <clause id="13779">
    <literal><![CDATA[
      K(x,y \ R(y,z,u)) = a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(333,a,12424,a,b,13732,a)].">
      <j1 rule="hyper" parents="333 12424 13732"/>
    </justification>
  </clause>

  <clause id="13780">
    <literal><![CDATA[
      a(x,y,K(z,u)) * x = T(x,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(125,a,13732,a,b,4261,a(flip))].">
      <j1 rule="hyper" parents="125 13732 4261"/>
    </justification>
  </clause>

  <clause id="13781">
    <literal><![CDATA[
      a(x \ 1,y,K(z,u)) / x = T(1 / x,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(123,a,13732,a,b,4332,a)].">
      <j1 rule="hyper" parents="123 13732 4332"/>
    </justification>
  </clause>

  <clause id="13782">
    <literal><![CDATA[
      K(x,a(y,z,z \ 1)) = 1
    ]]></literal>
    <justification jstring="[hyper(63,a,6135,a(flip),b,13732,a),flip(a)].">
      <j1 rule="hyper" parents="63 6135 13732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13783">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (w * x) = T(x,a(u,y,z)) * T(w,x)
    ]]></literal>
    <justification jstring="[para(13732(a,2),4520(a,1,1))].">
      <j1 rule="para" parents="13732 4520"/>
    </justification>
  </clause>

  <clause id="13784">
    <literal><![CDATA[
      (x * y) * a(y,z,K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      x * T(y,a(w,z,u)) = v5
    ]]></literal>
    <justification jstring="[para(13732(a,2),6089(a,1,2))].">
      <j1 rule="para" parents="13732 6089"/>
    </justification>
  </clause>

  <clause id="13785">
    <literal><![CDATA[
      L(a(x,y,K(z,u)),w,v5) = K(x,L(a(u,y,z),w,v5))
    ]]></literal>
    <justification jstring="[para(13732(a,2),10851(a,1,1))].">
      <j1 rule="para" parents="13732 10851"/>
    </justification>
  </clause>

  <clause id="13786">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = K(z,K(x,a(w,y,u)))
    ]]></literal>
    <justification jstring="[para(13732(a,1),13107(a,2,2))].">
      <j1 rule="para" parents="13732 13107"/>
    </justification>
  </clause>

  <clause id="13787">
    <literal><![CDATA[
      T(x,a(y,z,z \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(56,a,13782,a)].">
      <j1 rule="hyper" parents="56 13782"/>
    </justification>
  </clause>

  <clause id="13788">
    <literal><![CDATA[
      T(a(x,y,y \ 1),z) = a(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(54,a,13787,a)].">
      <j1 rule="hyper" parents="54 13787"/>
    </justification>
  </clause>

  <clause id="13790">
    <literal><![CDATA[
      a(K(x,y),z,u) = K(a(u,z,y),x)
    ]]></literal>
    <justification jstring="[hyper(333,a,13539,a(flip),b,13737,a),flip(a)].">
      <j1 rule="hyper" parents="333 13539 13737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13791">
    <literal><![CDATA[
      x * a(K(y,z),u,w) = x * a(w,u,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(126,a,13737,a,b,9,a)].">
      <j1 rule="hyper" parents="126 13737 9"/>
    </justification>
  </clause>

  <clause id="13792">
    <literal><![CDATA[
      K(x,L(y,L(z,u,w),z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(10960,a,13775,a)].">
      <j1 rule="hyper" parents="10960 13775"/>
    </justification>
  </clause>

  <clause id="13793">
    <literal><![CDATA[
      K(x,L(y,z,L(z,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(10960,a,13776,a)].">
      <j1 rule="hyper" parents="10960 13776"/>
    </justification>
  </clause>

  <clause id="13794">
    <literal><![CDATA[
      K(x,L(y,L(z,u,w) \ 1,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(2596(a,2),13792(a,1,2))].">
      <j1 rule="para" parents="2596 13792"/>
    </justification>
  </clause>

  <clause id="13795">
    <literal><![CDATA[
      a(x,y,K(z \ (u * x),w)) = a(w,y,K(x,z \ u))
    ]]></literal>
    <justification jstring="[para(10333(a,1),13738(a,1,3)),flip(a)].">
      <j1 rule="para" parents="10333 13738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13796">
    <literal><![CDATA[
      a(x \ 1,y,K(z,u)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(333,a,13731,a(flip),b,13739,a),flip(a)].">
      <j1 rule="hyper" parents="333 13731 13739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13797">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(y,u)) = K(x,L(y,z,u \ 1))
    ]]></literal>
    <justification jstring="[para(13739(a,1),10860(a,1,2))].">
      <j1 rule="para" parents="13739 10860"/>
    </justification>
  </clause>

  <clause id="13798">
    <literal><![CDATA[
      x * a(x,y,a(z,u,K(w,v5))) = T(x,a(v5,y,a(z,u,w)))
    ]]></literal>
    <justification jstring="[para(13539(a,2),13741(a,1,2,3))].">
      <j1 rule="para" parents="13539 13741"/>
    </justification>
  </clause>

  <clause id="13799">
    <literal><![CDATA[
      L(x,y,z) * T(L(x,y,z) \ x,u) = x * a(u,y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(126,a,13743,a(flip),b,5859,a),flip(a)].">
      <j1 rule="hyper" parents="126 13743 5859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13800">
    <literal><![CDATA[
      a(x \ y,z,K(u,x)) = a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,13731,a(flip),b,13746,a)].">
      <j1 rule="hyper" parents="63 13731 13746"/>
    </justification>
  </clause>

  <clause id="13801">
    <literal><![CDATA[
      a(x,y,K(z,u \ (z \ w))) = a(u \ w,y,K(x,z))
    ]]></literal>
    <justification jstring="[para(10322(a,2),13746(a,1,3))].">
      <j1 rule="para" parents="10322 13746"/>
    </justification>
  </clause>

  <clause id="13802">
    <literal><![CDATA[
      a(x,y,K(z,x * u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,13731,a(flip),b,13747,a)].">
      <j1 rule="hyper" parents="63 13731 13747"/>
    </justification>
  </clause>

  <clause id="13803">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(z,y,K(u,x)) = w
    ]]></literal>
    <justification jstring="[para(13749(a,1),11005(a,1))].">
      <j1 rule="para" parents="13749 11005"/>
    </justification>
  </clause>

  <clause id="13804">
    <literal><![CDATA[
      T(x,a(y,z * y,u)) = x * a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[para(13749(a,1),13741(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13749 13741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13805">
    <literal><![CDATA[
      a(x * y,z,K(u,x)) = a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(333,a,13731,a(flip),b,13753,a),flip(a)].">
      <j1 rule="hyper" parents="333 13731 13753"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13806">
    <literal><![CDATA[
      (x * y) / T(x,L(y,z,u)) = T(y,a(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,10946,a,b,13756,a)].">
      <j1 rule="hyper" parents="63 10946 13756"/>
    </justification>
  </clause>

  <clause id="13807">
    <literal><![CDATA[
      L(x,y,z) * a(u,w,K(z \ 1,x)) = T(L(x,y,z),a(z \ 1,w,u))
    ]]></literal>
    <justification jstring="[para(9469(a,1),13756(a,1,2,3))].">
      <j1 rule="para" parents="9469 13756"/>
    </justification>
  </clause>

  <clause id="13808">
    <literal><![CDATA[
      T(T(x,a(y,z,u)),y) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(13756(a,1),10985(a,1,1))].">
      <j1 rule="para" parents="13756 10985"/>
    </justification>
  </clause>

  <clause id="13809">
    <literal><![CDATA[
      T(T(x,a(y,z,u)),a(u,z,y)) = x
    ]]></literal>
    <justification jstring="[para(13756(a,1),13545(a,1,1))].">
      <j1 rule="para" parents="13756 13545"/>
    </justification>
  </clause>

  <clause id="13810">
    <literal><![CDATA[
      T(x,a(x * y,z,u)) = x * a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[para(13747(a,1),13756(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13747 13756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13811">
    <literal><![CDATA[
      T(x,a(y \ 1,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,13787,a(flip),b,13809,a)].">
      <j1 rule="hyper" parents="63 13787 13809"/>
    </justification>
  </clause>

  <clause id="13812">
    <literal><![CDATA[
      T(x,a(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(w,a(u,z,y)) = x
    ]]></literal>
    <justification jstring="[para(13809(a,1),49(a,1)),flip(a)].">
      <j1 rule="para" parents="13809 49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13813">
    <literal><![CDATA[
      x / a(y \ 1,y,z) = a(y \ 1,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(6748,a,13811,a),flip(a)].">
      <j1 rule="hyper" parents="6748 13811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13814">
    <literal><![CDATA[
      K(x * y,z \ R(z,x,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(333,a,13110,a(flip),b,13779,a),flip(a)].">
      <j1 rule="hyper" parents="333 13110 13779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13815">
    <literal><![CDATA[
      (x * (y \ R(y,z,u))) / x = (y \ R(y,z,u)) * a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(126,a,13779,a(flip),b,4266,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="126 13779 4266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13816">
    <literal><![CDATA[
      T((T(x,y) \ R(T(x,y),z,u)) * a(y,z,K(u,x)),y) = T(x,y) \ R(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(13779(a,1),8744(a,1,1,2))].">
      <j1 rule="para" parents="13779 8744"/>
    </justification>
  </clause>

  <clause id="13817">
    <literal><![CDATA[
      T(x \ R(x,y,z),y * z) * 1 = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(126,a,13814,a(flip),b,4205,a(flip))].">
      <j1 rule="hyper" parents="126 13814 4205"/>
    </justification>
  </clause>

  <clause id="13818">
    <literal><![CDATA[
      a(x,y,K(z,u)) \ x = T(x,a(z,y,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,9791,a,b,13780,a)].">
      <j1 rule="hyper" parents="63 9791 13780"/>
    </justification>
  </clause>

  <clause id="13819">
    <literal><![CDATA[
      a(x,y,K(z,u)) * u = T(u,a(z,y,x))
    ]]></literal>
    <justification jstring="[para(13731(a,2),13780(a,1,1))].">
      <j1 rule="para" parents="13731 13780"/>
    </justification>
  </clause>

  <clause id="13820">
    <literal><![CDATA[
      x * ((L(x,y,z) \ 1) * K(u,w)) = (L(x,y,z) \ x) * K(u,w)
    ]]></literal>
    <justification jstring="[para(13794(a,1),10968(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13794 10968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13821">
    <literal><![CDATA[
      a(K(x,y) / z,u,K(w,v5)) = a(z * K(y,x),u,K(v5,w))
    ]]></literal>
    <justification jstring="[para(13252(a,1),13796(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13252 13796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13822">
    <literal><![CDATA[
      a(L(x,y,z) \ u,w,K(z,x)) = a(u,w,K(z,L(x,y,z)))
    ]]></literal>
    <justification jstring="[para(9466(a,1),13800(a,1,3))].">
      <j1 rule="para" parents="9466 13800"/>
    </justification>
  </clause>

  <clause id="13823">
    <literal><![CDATA[
      (x * y) * a(y,z,K(u,x)) = T(x * y,a(x,z,u))
    ]]></literal>
    <justification jstring="[para(13805(a,1),13741(a,1,2))].">
      <j1 rule="para" parents="13805 13741"/>
    </justification>
  </clause>

  <clause id="13824">
    <literal><![CDATA[
      T(T(x,y),a(y,z,u)) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(437,a,13808,a)].">
      <j1 rule="hyper" parents="437 13808"/>
    </justification>
  </clause>

  <clause id="13825">
    <literal><![CDATA[
      T(x,a(y,x,z)) = x
    ]]></literal>
    <justification jstring="[hyper(40,a,10360,a(flip),b,13808,a),flip(a)].">
      <j1 rule="hyper" parents="40 10360 13808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13826">
    <literal><![CDATA[
      T(x,a(y,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(40,a,6709,a(flip),b,13808,a),flip(a)].">
      <j1 rule="hyper" parents="40 6709 13808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13827">
    <literal><![CDATA[
      T(x,a(y,z,u)) * y = y * T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(126,a,13808,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="126 13808 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13828">
    <literal><![CDATA[
      T(T(x,a(y,z,u)),L(u,z,y)) = T(x,u)
    ]]></literal>
    <justification jstring="[para(13809(a,1),13808(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13809 13808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13829">
    <literal><![CDATA[
      T(a(x,y,z),y) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(54,a,13825,a)].">
      <j1 rule="hyper" parents="54 13825"/>
    </justification>
  </clause>

  <clause id="13830">
    <literal><![CDATA[
      (x * a(y,x,z)) / x = a(y,x,z)
    ]]></literal>
    <justification jstring="[hyper(197,a,13825,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="197 13825 22"/>
    </justification>
  </clause>

  <clause id="13831">
    <literal><![CDATA[
      a(x,y,z) * y = y * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(126,a,13825,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="126 13825 22"/>
    </justification>
  </clause>

  <clause id="13832">
    <literal><![CDATA[
      T(a(x,x,y),z) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(54,a,13826,a)].">
      <j1 rule="hyper" parents="54 13826"/>
    </justification>
  </clause>

  <clause id="13833">
    <literal><![CDATA[
      T(x,L(y,z,u) \ y) = a(y,z,K(u,x)) * x
    ]]></literal>
    <justification jstring="[hyper(333,a,13096,a,b,13819,a)].">
      <j1 rule="hyper" parents="333 13096 13819"/>
    </justification>
  </clause>

  <clause id="13834">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (u * w) = T(u,a(z,y,x)) * w
    ]]></literal>
    <justification jstring="[para(13819(a,1),13074(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13819 13074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13835">
    <literal><![CDATA[
      T(T(x,x * y),a(y,z,u)) = L(T(x,L(y,z,u)),y,x)
    ]]></literal>
    <justification jstring="[para(13824(a,1),636(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13824 636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13836">
    <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(13828(a,1),12222(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="13828 12222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13837">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(u,y,K(x,z)) = w
    ]]></literal>
    <justification jstring="[para(13737(a,1),13730(a,1))].">
      <j1 rule="para" parents="13737 13730"/>
    </justification>
  </clause>

  <clause id="13838">
    <literal><![CDATA[
      a(x,y,K(z,L(u,w,x))) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(333,a,13729,a(flip),b,13735,a),flip(a)].">
      <j1 rule="hyper" parents="333 13729 13735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13839">
    <literal><![CDATA[
      a(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(u,z,K(y,x)) = w
    ]]></literal>
    <justification jstring="[para(13729(a,2),13803(a,1))].">
      <j1 rule="para" parents="13729 13803"/>
    </justification>
  </clause>

  <clause id="13840">
    <literal><![CDATA[
      a(x,y,K(z \ u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(13748(a,2),13803(a,1))].">
      <j1 rule="para" parents="13748 13803"/>
    </justification>
  </clause>

  <clause id="13841">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      a(z,y,K(x,K(u,w))) = v5
    ]]></literal>
    <justification jstring="[para(6799(a,1),13837(a,1,3))].">
      <j1 rule="para" parents="6799 13837"/>
    </justification>
  </clause>

  <clause id="13842">
    <literal><![CDATA[
      K(x,y) * K(y,L(x,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(y,z,K(u,x)) = w
    ]]></literal>
    <justification jstring="[para(10883(a,2),13837(a,1))].">
      <j1 rule="para" parents="10883 13837"/>
    </justification>
  </clause>

  <clause id="13843">
    <literal><![CDATA[
      K(x,L(y,z,u)) * K(y,x) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,z,K(u,y)) = w
    ]]></literal>
    <justification jstring="[para(10884(a,2),13837(a,1))].">
      <j1 rule="para" parents="10884 13837"/>
    </justification>
  </clause>

  <clause id="13844">
    <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(13081(a,2),13837(a,1))].">
      <j1 rule="para" parents="13081 13837"/>
    </justification>
  </clause>

  <clause id="13845">
    <literal><![CDATA[
      a(x,y,K(z,u)) * L(u,w,x) = T(L(u,w,x),a(z,y,x))
    ]]></literal>
    <justification jstring="[para(13838(a,1),13819(a,1,1))].">
      <j1 rule="para" parents="13838 13819"/>
    </justification>
  </clause>

  <clause id="13846">
    <literal><![CDATA[
      x * a(y,z,K(u,w)) != x * v5
    ]]></literal>
    <literal><![CDATA[
      a(u,z,K(w,y)) = v5
    ]]></literal>
    <justification jstring="[para(13742(a,1),43(a,1))].">
      <j1 rule="para" parents="13742 43"/>
    </justification>
  </clause>

  <clause id="13847">
    <literal><![CDATA[
      K(x,L(y,y \ z,u)) * K(y,x) = a(x,z / y,K(u,y))
    ]]></literal>
    <justification jstring="[para(10406(a,1),13750(a,1,1,2))].">
      <j1 rule="para" parents="10406 13750"/>
    </justification>
  </clause>

  <clause id="13848">
    <literal><![CDATA[
      K(x,L(y,z,u)) * K(y,x) = a(x,x \ z,K(u,y))
    ]]></literal>
    <justification jstring="[para(10906(a,1),13750(a,1,1))].">
      <j1 rule="para" parents="10906 13750"/>
    </justification>
  </clause>

  <clause id="13849">
    <literal><![CDATA[
      K(x,y) * (K(y,L(x,z,u)) * w) = a(y,z,K(u,x)) * w
    ]]></literal>
    <justification jstring="[para(13750(a,1),11595(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13750 11595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13850">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w \ v5
    ]]></literal>
    <literal><![CDATA[
      w * a(z,y,K(u,x)) = v5
    ]]></literal>
    <justification jstring="[para(13752(a,1),9741(a,2)),flip(a)].">
      <j1 rule="para" parents="13752 9741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13851">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = a(w,y,K(z,K(x,u)))
    ]]></literal>
    <justification jstring="[para(6762(a,1),13757(a,2,3)),flip(a)].">
      <j1 rule="para" parents="6762 13757"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13852">
    <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(7853(a,1),13761(a,1,2,3))].">
      <j1 rule="para" parents="7853 13761"/>
    </justification>
  </clause>

  <clause id="13853">
    <literal><![CDATA[
      x / (a(y,z,K(u,w)) * T(a(w,z,K(u,y)) * x,v5)) = K(v5,x / a(y,z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(13763(a,1),4630(a,1,2,2,1))].">
      <j1 rule="para" parents="13763 4630"/>
    </justification>
  </clause>

  <clause id="13854">
    <literal><![CDATA[
      x \ (y * (a(z,u,K(w,v5)) * T(a(v5,u,K(w,z)) * (y \ x),v6))) = K((x \ (y * a(z,u,K(w,v5)))) \ 1,v6)
    ]]></literal>
    <justification jstring="[para(13763(a,1),4955(a,1,2,2,2,1))].">
      <j1 rule="para" parents="13763 4955"/>
    </justification>
  </clause>

  <clause id="13855">
    <literal><![CDATA[
      R(K(x,y),z,u) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,13736,a(flip),b,13764,a)].">
      <j1 rule="hyper" parents="63 13736 13764"/>
    </justification>
  </clause>

  <clause id="13856">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(u,y)) = K(x,L(y,z,y \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,11150,a(flip),b,13764,a)].">
      <j1 rule="hyper" parents="63 11150 13764"/>
    </justification>
  </clause>

  <clause id="13858">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(y,K(u,w))) = K(x,L(y,z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(6799(a,1),13764(a,1,2,3))].">
      <j1 rule="para" parents="6799 13764"/>
    </justification>
  </clause>

  <clause id="13859">
    <literal><![CDATA[
      K(x,L(y,R(z,u,w),z)) = K(x,y) * 1
    ]]></literal>
    <justification jstring="[para(9028(a,1),13764(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9028 13764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13861">
    <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(10515(a,1),13764(a,1,2,3))].">
      <j1 rule="para" parents="10515 13764"/>
    </justification>
  </clause>

  <clause id="13862">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(y,u)) = K(x,L(y,z,u \ y))
    ]]></literal>
    <justification jstring="[para(11161(a,1),13764(a,1,2))].">
      <j1 rule="para" parents="11161 13764"/>
    </justification>
  </clause>

  <clause id="13863">
    <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(13357(a,1),13764(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="13357 13764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13864">
    <literal><![CDATA[
      K(x,R(y,z,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(11586,a,13855,a)].">
      <j1 rule="hyper" parents="11586 13855"/>
    </justification>
  </clause>

  <clause id="13865">
    <literal><![CDATA[
      R(K(x,y),z,u) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(333,a,10851,a,b,13855,a),flip(a)].">
      <j1 rule="hyper" parents="333 10851 13855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13866">
    <literal><![CDATA[
      K(x,(y * z) / ((u \ y) * z)) = K(x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,5648,a,b,13855,a)].">
      <j1 rule="hyper" parents="63 5648 13855"/>
    </justification>
  </clause>

  <clause id="13867">
    <literal><![CDATA[
      K(R(x,y,z),u) = K(x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,11573,a(flip),b,13855,a)].">
      <j1 rule="hyper" parents="63 11573 13855"/>
    </justification>
  </clause>

  <clause id="13868">
    <literal><![CDATA[
      K(x,L(y / (z / u),y,u)) = K(x,(y * u) / z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5647,a(flip),b,13855,a),flip(a)].">
      <j1 rule="hyper" parents="63 5647 13855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13869">
    <literal><![CDATA[
      K(x,L(y / z,y,u)) = K(x,(y * u) / (z * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,5643,a(flip),b,13855,a),flip(a)].">
      <j1 rule="hyper" parents="63 5643 13855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13870">
    <literal><![CDATA[
      K(R(x,y,z) \ 1,u) = K(x \ 1,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,5111,a(flip),b,13855,a)].">
      <j1 rule="hyper" parents="63 5111 13855"/>
    </justification>
  </clause>

  <clause id="13871">
    <literal><![CDATA[
      K(x,L(y,z \ u,z)) * u = (K(x,y) * (u / z)) * z
    ]]></literal>
    <justification jstring="[hyper(125,a,13855,a(flip),b,10351,a)].">
      <j1 rule="hyper" parents="125 13855 10351"/>
    </justification>
  </clause>

  <clause id="13872">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (z * u) = (K(x,y) * z) * u
    ]]></literal>
    <justification jstring="[hyper(125,a,13855,a(flip),b,20,a(flip))].">
      <j1 rule="hyper" parents="125 13855 20"/>
    </justification>
  </clause>

  <clause id="13873">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (z * u) != w
    ]]></literal>
    <literal><![CDATA[
      (K(x,y) * z) * u = w
    ]]></literal>
    <justification jstring="[para(13855(a,1),299(a,1,1))].">
      <j1 rule="para" parents="13855 299"/>
    </justification>
  </clause>

  <clause id="13874">
    <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(13855(a,1),761(a,1,1))].">
      <j1 rule="para" parents="13855 761"/>
    </justification>
  </clause>

  <clause id="13875">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (u * z) = (K(x,y) * z) * T(u,z)
    ]]></literal>
    <justification jstring="[para(13855(a,1),10345(a,1,1))].">
      <j1 rule="para" parents="13855 10345"/>
    </justification>
  </clause>

  <clause id="13877">
    <literal><![CDATA[
      L(K(x,y),z,u) = K(x,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(333,a,10851,a,b,13864,a)].">
      <j1 rule="hyper" parents="333 10851 13864"/>
    </justification>
  </clause>

  <clause id="13878">
    <literal><![CDATA[
      K(x,R(y \ z,y,u)) = K(x,(u * y) \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(333,a,9543,a(flip),b,13864,a),flip(a)].">
      <j1 rule="hyper" parents="333 9543 13864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13879">
    <literal><![CDATA[
      T(x,R(y,z,u)) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(124,a,13864,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 13864 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13880">
    <literal><![CDATA[
      K(x,L(T(y \ z,z * u),y,u)) = K(x,T((y * u) \ (z * u),y))
    ]]></literal>
    <justification jstring="[hyper(63,a,8310,a(flip),b,13864,a),flip(a)].">
      <j1 rule="hyper" parents="63 8310 13864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13881">
    <literal><![CDATA[
      K(x,L(y / z,z,u)) = K(x,(y * u) / (z * u))
    ]]></literal>
    <justification jstring="[para(108(a,1),13864(a,1,2)),flip(a)].">
      <j1 rule="para" parents="108 13864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13882">
    <literal><![CDATA[
      K(x,L((y / z) / u,u,z)) = K(x,y / (u * z))
    ]]></literal>
    <justification jstring="[para(314(a,1),13864(a,1,2)),flip(a)].">
      <j1 rule="para" parents="314 13864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13883">
    <literal><![CDATA[
      K(x,L(y \ (z / u),y,u)) = K(x,T(z / (y * u),y))
    ]]></literal>
    <justification jstring="[para(689(a,1),13864(a,1,2)),flip(a)].">
      <j1 rule="para" parents="689 13864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13884">
    <literal><![CDATA[
      K(x,L(y,y \ z,u)) * ((y \ z) * u) = T(R(y,y \ z,u),x) \ (z * u)
    ]]></literal>
    <justification jstring="[para(13864(a,1),4695(a,1,1))].">
      <j1 rule="para" parents="13864 4695"/>
    </justification>
  </clause>

  <clause id="13885">
    <literal><![CDATA[
      R(x,y,z) * (K(u,R(x,y,z)) * (y * z)) = K(u,L(x,y,z)) * ((x * y) * z)
    ]]></literal>
    <justification jstring="[para(13864(a,1),4860(a,2,1))].">
      <j1 rule="para" parents="13864 4860"/>
    </justification>
  </clause>

  <clause id="13886">
    <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(13864(a,1),8688(a,1,2))].">
      <j1 rule="para" parents="13864 8688"/>
    </justification>
  </clause>

  <clause id="13887">
    <literal><![CDATA[
      K(x,L(y / (z / u),u \ z,u)) = K(x,(y * u) / z)
    ]]></literal>
    <justification jstring="[para(10354(a,1),13864(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10354 13864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13890">
    <literal><![CDATA[
      L(K(x / (y / z),u),x,z) = K((x * z) / y,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,5564,a(flip),b,13865,a),flip(a)].">
      <j1 rule="hyper" parents="63 5564 13865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13891">
    <literal><![CDATA[
      L(K(x,y),z,u) * (z * u) = (K(x,y) * z) * u
    ]]></literal>
    <justification jstring="[hyper(125,a,13865,a(flip),b,20,a(flip))].">
      <j1 rule="hyper" parents="125 13865 20"/>
    </justification>
  </clause>

  <clause id="13892">
    <literal><![CDATA[
      L(K(x,y),z,u) \ ((K(x,y) * z) * u) = z * u
    ]]></literal>
    <justification jstring="[para(13865(a,1),187(a,1,1))].">
      <j1 rule="para" parents="13865 187"/>
    </justification>
  </clause>

  <clause id="13893">
    <literal><![CDATA[
      L(L(K(x,y),z,u),w,v5) * (z * u) = (L(K(x,y),w,v5) * z) * u
    ]]></literal>
    <justification jstring="[para(13865(a,1),457(a,1,1,1))].">
      <j1 rule="para" parents="13865 457"/>
    </justification>
  </clause>

  <clause id="13894">
    <literal><![CDATA[
      L(K(x,y),z,T(u,K(x,y) * z)) \ (u * (K(x,y) * z)) = z * T(u,K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(13865(a,1),531(a,1,1))].">
      <j1 rule="para" parents="13865 531"/>
    </justification>
  </clause>

  <clause id="13896">
    <literal><![CDATA[
      (K(x,T(y,z * u)) * z) * u = (z * u) * L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(13865(a,1),6908(a,2,2))].">
      <j1 rule="para" parents="13865 6908"/>
    </justification>
  </clause>

  <clause id="13897">
    <literal><![CDATA[
      (K(x,T(y,z)) * u) * (u \ z) = z * L(K(x,y),u,u \ z)
    ]]></literal>
    <justification jstring="[para(13865(a,1),6909(a,2,2))].">
      <j1 rule="para" parents="13865 6909"/>
    </justification>
  </clause>

  <clause id="13898">
    <literal><![CDATA[
      L(K(x,y),z,u) * (u * z) = (K(x,y) * z) * T(u,z)
    ]]></literal>
    <justification jstring="[para(13865(a,1),10345(a,1,1))].">
      <j1 rule="para" parents="13865 10345"/>
    </justification>
  </clause>

  <clause id="13899">
    <literal><![CDATA[
      R(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(13865(a,2),10960(a,1))].">
      <j1 rule="para" parents="13865 10960"/>
    </justification>
  </clause>

  <clause id="13901">
    <literal><![CDATA[
      K(R(x,y,z),u) = K(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(333,a,10898,a,b,13867,a),flip(a)].">
      <j1 rule="hyper" parents="333 10898 13867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13902">
    <literal><![CDATA[
      K((x / y) / z,L(u,z,y)) = K(x / (z * y),u)
    ]]></literal>
    <justification jstring="[para(314(a,1),13867(a,1,1)),flip(a)].">
      <j1 rule="para" parents="314 13867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13903">
    <literal><![CDATA[
      x * (K(y,L(x,z,u)) * K(w,R(y,z,u))) = (R(y,z,u) * x) / R(T(y,w),z,u)
    ]]></literal>
    <justification jstring="[para(13867(a,1),5506(a,1,2,1))].">
      <j1 rule="para" parents="13867 5506"/>
    </justification>
  </clause>

  <clause id="13904">
    <literal><![CDATA[
      K(x / y,L(T(z,y * u),y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K((y * u) \ (x * u),z) = w
    ]]></literal>
    <justification jstring="[para(13867(a,1),7205(a,1))].">
      <j1 rule="para" parents="13867 7205"/>
    </justification>
  </clause>

  <clause id="13905">
    <literal><![CDATA[
      (R(x,y,z) * (u * K(x,L(w,y,z)))) / R(T(x,w),y,z) = (R(x,y,z) * u) / R(x,y,z)
    ]]></literal>
    <justification jstring="[para(13867(a,1),6206(a,1,1,2,2))].">
      <j1 rule="para" parents="13867 6206"/>
    </justification>
  </clause>

  <clause id="13906">
    <literal><![CDATA[
      L(K(x,y / (z / u)),u \ z,u) = K(x,(y * u) / z)
    ]]></literal>
    <justification jstring="[para(10354(a,1),13877(a,2,2))].">
      <j1 rule="para" parents="10354 13877"/>
    </justification>
  </clause>

  <clause id="13907">
    <literal><![CDATA[
      K(x,R(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(13877(a,1),10960(a,1))].">
      <j1 rule="para" parents="13877 10960"/>
    </justification>
  </clause>

  <clause id="13909">
    <literal><![CDATA[
      R(x,y,z) * T(u,L(x,y,z)) = u * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(126,a,13879,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="126 13879 22"/>
    </justification>
  </clause>

  <clause id="13910">
    <literal><![CDATA[
      T(x,L(y,z,u)) * R(T(y,x),z,u) = x * R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(125,a,13879,a(flip),b,3646,a)].">
      <j1 rule="hyper" parents="125 13879 3646"/>
    </justification>
  </clause>

  <clause id="13911">
    <literal><![CDATA[
      T(x,L(y / z,z,u)) = T(x,(y * u) / (z * u))
    ]]></literal>
    <justification jstring="[para(108(a,1),13879(a,1,2)),flip(a)].">
      <j1 rule="para" parents="108 13879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13912">
    <literal><![CDATA[
      T(x,L((y / z) / u,u,z)) = T(x,y / (u * z))
    ]]></literal>
    <justification jstring="[para(314(a,1),13879(a,1,2)),flip(a)].">
      <j1 rule="para" parents="314 13879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13913">
    <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(13879(a,1),7225(a,1,2))].">
      <j1 rule="para" parents="13879 7225"/>
    </justification>
  </clause>

  <clause id="13914">
    <literal><![CDATA[
      K(L(x,y,z),T(u,w)) \ ((R(w,v5,v6) * T(u,w)) / T(u,w)) = (T(T(u,w),R(x,y,z)) * R(T(w,u),v5,v6)) / T(u,w)
    ]]></literal>
    <justification jstring="[para(13879(a,2),7222(a,2,1,1))].">
      <j1 rule="para" parents="13879 7222"/>
    </justification>
  </clause>

  <clause id="13915">
    <literal><![CDATA[
      T(x,R(y,z * K(u,w),v5)) = T(x,L(y,K(w,u) / z,v5))
    ]]></literal>
    <justification jstring="[para(13339(a,1),13879(a,1,2))].">
      <j1 rule="para" parents="13339 13879"/>
    </justification>
  </clause>

  <clause id="13917">
    <literal><![CDATA[
      K(L(x,y,z),u) * ((x * y) * z) = (T(x,u) * y) * z
    ]]></literal>
    <justification jstring="[hyper(125,a,13901,a(flip),b,8865,a)].">
      <j1 rule="hyper" parents="125 13901 8865"/>
    </justification>
  </clause>

  <clause id="13918">
    <literal><![CDATA[
      K(L(x / y,y,z),u) = K((x * z) / (y * z),u)
    ]]></literal>
    <justification jstring="[para(108(a,1),13901(a,1,1)),flip(a)].">
      <j1 rule="para" parents="108 13901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13919">
    <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(13901(a,1),7207(a,1))].">
      <j1 rule="para" parents="13901 7207"/>
    </justification>
  </clause>

  <clause id="13920">
    <literal><![CDATA[
      K(x,L(y,R(z,u,w),z)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(13859(a,2),134(a,1)),flip(b)].">
      <j1 rule="para" parents="13859 134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13922">
    <literal><![CDATA[
      K(x,(y * z) / ((u \ y) * z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(u,y,z)) = w
    ]]></literal>
    <justification jstring="[para(5648(a,2),13899(a,1))].">
      <j1 rule="para" parents="5648 13899"/>
    </justification>
  </clause>

  <clause id="13923">
    <literal><![CDATA[
      K(x,(y * z) / (u * z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y / u,u,z)) = w
    ]]></literal>
    <justification jstring="[para(108(a,1),13907(a,1,2))].">
      <j1 rule="para" parents="108 13907"/>
    </justification>
  </clause>

  <clause id="13924">
    <literal><![CDATA[
      K(x,T((y * z) / u,u / z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L((u / z) \ y,u / z,z)) = w
    ]]></literal>
    <justification jstring="[para(807(a,1),13907(a,1,2))].">
      <j1 rule="para" parents="807 13907"/>
    </justification>
  </clause>

  <clause id="13925">
    <literal><![CDATA[
      K(x,L(y,z,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(534(a,1),13920(a,1,2,2))].">
      <j1 rule="para" parents="534 13920"/>
    </justification>
  </clause>

  <clause id="13926">
    <literal><![CDATA[
      K(L(x,y,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(10898(a,2),13925(a,1))].">
      <j1 rule="para" parents="10898 13925"/>
    </justification>
  </clause>

  <clause id="13927">
    <literal><![CDATA[
      K((x * x) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ (x \ y),z) = u
    ]]></literal>
    <justification jstring="[para(10907(a,1),13925(a,1))].">
      <j1 rule="para" parents="10907 13925"/>
    </justification>
  </clause>

  <clause id="13928">
    <literal><![CDATA[
      K(L(x,y \ 1,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(2596(a,2),13926(a,1,1))].">
      <j1 rule="para" parents="2596 13926"/>
    </justification>
  </clause>

  <clause id="13929">
    <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(5603(a,1),13928(a,1,1))].">
      <j1 rule="para" parents="5603 13928"/>
    </justification>
  </clause>

  <clause id="13930">
    <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(7924(a,1),13765(a,1,2,3))].">
      <j1 rule="para" parents="7924 13765"/>
    </justification>
  </clause>

  <clause id="13931">
    <literal><![CDATA[
      K(x,L(y,z,a(u,w,w \ 1) \ 1)) = K(x,y) * a(y,z,1)
    ]]></literal>
    <justification jstring="[para(10216(a,1),13765(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="10216 13765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13932">
    <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(13765(a,2),10893(a,1))].">
      <j1 rule="para" parents="13765 10893"/>
    </justification>
  </clause>

  <clause id="13933">
    <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(10979(a,1),13765(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="10979 13765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13934">
    <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(13348(a,1),13765(a,1,2,3))].">
      <j1 rule="para" parents="13348 13765"/>
    </justification>
  </clause>

  <clause id="13935">
    <literal><![CDATA[
      K(x,L(y,z,L(u,w,v5) \ u)) = K(x,y) * a(y,z,a(x,w,K(u,v5)))
    ]]></literal>
    <justification jstring="[para(13778(a,1),13765(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="13778 13765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13936">
    <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(13864(a,1),13765(a,1,2,3))].">
      <j1 rule="para" parents="13864 13765"/>
    </justification>
  </clause>

  <clause id="13937">
    <literal><![CDATA[
      a(x,y,K(z,u)) * K(x,u) = L(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,10851,a,b,13767,a),flip(a)].">
      <j1 rule="hyper" parents="333 10851 13767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13938">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = K(u,K(x,a(w,y,z)))
    ]]></literal>
    <justification jstring="[para(6785(a,1),13786(a,1,3))].">
      <j1 rule="para" parents="6785 13786"/>
    </justification>
  </clause>

  <clause id="13939">
    <literal><![CDATA[
      L(K(x,y),z,u) \ K(x,y) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(121,a,9744,a(flip),b,13791,a)].">
      <j1 rule="hyper" parents="121 9744 13791"/>
    </justification>
  </clause>

  <clause id="13940">
    <literal><![CDATA[
      x * a(K(y,z),u,w) != v5 * a(w,u,K(z,y))
    ]]></literal>
    <literal><![CDATA[
      v5 = x
    ]]></literal>
    <justification jstring="[para(13791(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="13791 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13941">
    <literal><![CDATA[
      T(x,a(y,z * y,u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(333,a,13180,a(flip),b,13804,a),flip(a)].">
      <j1 rule="hyper" parents="333 13180 13804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13942">
    <literal><![CDATA[
      T(x,a(x * y,z,u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(333,a,13741,a(flip),b,13810,a),flip(a)].">
      <j1 rule="hyper" parents="333 13741 13810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13943">
    <literal><![CDATA[
      T(x,a(x \ y,z,u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(10(a,1),13942(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 13942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13944">
    <literal><![CDATA[
      T(T(x,x * y),a((x * (x * y)) / x,z,u)) = T(T(x,x * y),a(y,z,u))
    ]]></literal>
    <justification jstring="[para(3353(a,2),13942(a,1,2,1))].">
      <j1 rule="para" parents="3353 13942"/>
    </justification>
  </clause>

  <clause id="13945">
    <literal><![CDATA[
      K(R(x,y,z) \ 1,u) = K(L(x,y,z) \ 1,u)
    ]]></literal>
    <justification jstring="[hyper(333,a,10871,a,b,13870,a),flip(a)].">
      <j1 rule="hyper" parents="333 10871 13870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13946">
    <literal><![CDATA[
      K(x \ 1,L(T(y,z),u,(x * u) \ z)) = K(z \ (u * ((x * u) \ z)),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,6623,a(flip),b,13870,a),flip(a)].">
      <j1 rule="hyper" parents="63 6623 13870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13947">
    <literal><![CDATA[
      K(T(x / y,z) \ 1,L(u,y,y \ z)) = K((z \ (x * (y \ z))) \ 1,u)
    ]]></literal>
    <justification jstring="[para(982(a,1),13870(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="982 13870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13948">
    <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(333,a,10896,a(flip),b,13937,a),flip(a)].">
      <j1 rule="hyper" parents="333 10896 13937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13949">
    <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(13937(a,1),44(a,1))].">
      <j1 rule="para" parents="13937 44"/>
    </justification>
  </clause>

  <clause id="13950">
    <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(13937(a,2),10902(a,1))].">
      <j1 rule="para" parents="13937 10902"/>
    </justification>
  </clause>

  <clause id="13951">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = K(x,K(z,a(u,y,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,13757,a(flip),b,13938,a)].">
      <j1 rule="hyper" parents="63 13757 13938"/>
    </justification>
  </clause>

  <clause id="13952">
    <literal><![CDATA[
      K(L(x \ (y / z),x,z) \ 1,u) = K(T(y / (x * z),x) \ 1,u)
    ]]></literal>
    <justification jstring="[para(689(a,1),13945(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="689 13945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13953">
    <literal><![CDATA[
      ((x \ 1) \ K(L(y,z,u) \ 1,x)) \ ((x \ 1) \ 1) = K(x,R(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(13945(a,1),6007(a,1,1,2))].">
      <j1 rule="para" parents="13945 6007"/>
    </justification>
  </clause>

  <clause id="13955">
    <literal><![CDATA[
      x * a(x,y,a(z,u,K(w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,a(a(v5,u,w),y,z)) = v6
    ]]></literal>
    <justification jstring="[para(13732(a,2),13774(a,1,2,3))].">
      <j1 rule="para" parents="13732 13774"/>
    </justification>
  </clause>

  <clause id="13956">
    <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(10326(a,2),13840(a,1,3))].">
      <j1 rule="para" parents="10326 13840"/>
    </justification>
  </clause>

  <clause id="13957">
    <literal><![CDATA[
      a(x,y,K(z,x \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(z,y,K(u,x)) = w
    ]]></literal>
    <justification jstring="[para(13731(a,1),13840(a,1))].">
      <j1 rule="para" parents="13731 13840"/>
    </justification>
  </clause>

  <clause id="13958">
    <literal><![CDATA[
      a(x,y,K(z,y / (u / z))) \ K(x,(y * z) / u) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[hyper(121,a,13868,a(flip),b,13767,a)].">
      <j1 rule="hyper" parents="121 13868 13767"/>
    </justification>
  </clause>

  <clause id="13959">
    <literal><![CDATA[
      K(x,L(y * z,y,u)) = K(x,(y * u) / ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[hyper(13631,a,13869,a)].">
      <j1 rule="hyper" parents="13631 13869"/>
    </justification>
  </clause>

  <clause id="13960">
    <literal><![CDATA[
      K(x,(y * z) / (u * z)) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x,y / u),y,z) = w
    ]]></literal>
    <justification jstring="[para(13869(a,1),10893(a,1))].">
      <j1 rule="para" parents="13869 10893"/>
    </justification>
  </clause>

  <clause id="13961">
    <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(13728(a,2),13869(a,2,2,1))].">
      <j1 rule="para" parents="13728 13869"/>
    </justification>
  </clause>

  <clause id="13962">
    <literal><![CDATA[
      K(x,L(y,z,z \ (u \ z))) * (z * (z \ (z / u))) = (K(x,y) * z) * (z \ (z / u))
    ]]></literal>
    <justification jstring="[para(12845(a,1),13872(a,1,1,2))].">
      <j1 rule="para" parents="12845 13872"/>
    </justification>
  </clause>

  <clause id="13963">
    <literal><![CDATA[
      K(x,T(y / (z * u),z)) = K(x,(u * z) \ (u * (y / u)))
    ]]></literal>
    <justification jstring="[para(689(a,1),13878(a,1,2))].">
      <j1 rule="para" parents="689 13878"/>
    </justification>
  </clause>

  <clause id="13964">
    <literal><![CDATA[
      K(x,(y * z) \ (y * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(z \ u,z,y)) = w
    ]]></literal>
    <justification jstring="[para(13878(a,1),13907(a,1))].">
      <j1 rule="para" parents="13878 13907"/>
    </justification>
  </clause>

  <clause id="13965">
    <literal><![CDATA[
      K(x * y,L(z / x,x,y)) = K(x * y,(x * y) \ (z * y))
    ]]></literal>
    <justification jstring="[hyper(333,a,4368,a(flip),b,13881,a),flip(a)].">
      <j1 rule="hyper" parents="333 4368 13881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13966">
    <literal><![CDATA[
      K(x,T(L(y,z / y,u),z)) = K(x,(z * u) / ((z / y) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,11080,a(flip),b,13881,a)].">
      <j1 rule="hyper" parents="63 11080 13881"/>
    </justification>
  </clause>

  <clause id="13967">
    <literal><![CDATA[
      K(x,L(y / T(z / u,w),T(z / u,w),u)) = K(x,(y * u) / (u * T(u \ z,w)))
    ]]></literal>
    <justification jstring="[para(471(a,1),13881(a,2,2,2))].">
      <j1 rule="para" parents="471 13881"/>
    </justification>
  </clause>

  <clause id="13968">
    <literal><![CDATA[
      K(x,L(y / z,z,u)) * (z * u) = (z * u) * K(x,(z * u) \ (y * u))
    ]]></literal>
    <justification jstring="[para(13881(a,2),6497(a,1,1))].">
      <j1 rule="para" parents="13881 6497"/>
    </justification>
  </clause>

  <clause id="13969">
    <literal><![CDATA[
      K(x,L((y / T(z,u \ 1)) / (w / (u * w)),w / (u * w),T(z,u \ 1))) = K(x,y / (z * (w / (u * w))))
    ]]></literal>
    <justification jstring="[para(3766(a,1),13882(a,2,2,2))].">
      <j1 rule="para" parents="3766 13882"/>
    </justification>
  </clause>

  <clause id="13970">
    <literal><![CDATA[
      T(x,K(y,L((z / u) / w,w,u))) = x * K(y,K(x,z / (w * u)))
    ]]></literal>
    <justification jstring="[para(13882(a,1),6789(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13882 6789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13971">
    <literal><![CDATA[
      K(x,K((y / z) / u,L(w,y / z,z))) = K(x,K(w,y / (u * z)))
    ]]></literal>
    <justification jstring="[para(13882(a,1),10944(a,2,2))].">
      <j1 rule="para" parents="13882 10944"/>
    </justification>
  </clause>

  <clause id="13972">
    <literal><![CDATA[
      K(((x \ y) * x) / z,T(u,x \ y)) != w
    ]]></literal>
    <literal><![CDATA[
      y \ (x * (K((x \ y) / (z / x),u) * (x \ y))) = w
    ]]></literal>
    <justification jstring="[para(13890(a,1),6718(a,1))].">
      <j1 rule="para" parents="13890 6718"/>
    </justification>
  </clause>

  <clause id="13973">
    <literal><![CDATA[
      L(K(x,y),z,u) * (z * u) = (K(y,x) \ z) * u
    ]]></literal>
    <justification jstring="[para(4567(a,2),13891(a,2,1))].">
      <j1 rule="para" parents="4567 13891"/>
    </justification>
  </clause>

  <clause id="13974">
    <literal><![CDATA[
      L(K(x,y),y * x,z) \ ((x * y) * z) = (y * x) * z
    ]]></literal>
    <justification jstring="[para(4201(a,1),13892(a,1,2,1))].">
      <j1 rule="para" parents="4201 13892"/>
    </justification>
  </clause>

  <clause id="13975">
    <literal><![CDATA[
      R(x,x,y) * T(z,x) = z * R(x,x,y)
    ]]></literal>
    <justification jstring="[para(6709(a,1),13909(a,1,2))].">
      <j1 rule="para" parents="6709 13909"/>
    </justification>
  </clause>

  <clause id="13977">
    <literal><![CDATA[
      (x * y) \ (x \ ((x * x) * y)) = (y * x) \ (y * R(x,x,y))
    ]]></literal>
    <justification jstring="[para(13975(a,1),9127(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13975 9127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13978">
    <literal><![CDATA[
      T(x,L(y / (z / ((u \ 1) \ 1)),z / ((u \ 1) \ 1),u)) = T(x,(y * u) / ((u * (1 / u)) \ z))
    ]]></literal>
    <justification jstring="[para(10067(a,1),13911(a,2,2,2))].">
      <j1 rule="para" parents="10067 13911"/>
    </justification>
  </clause>

  <clause id="13979">
    <literal><![CDATA[
      T(x,L(y / (z \ u),z \ u,K(u,K(w,v5)))) = T(x,(y * K(u,K(w,v5))) / (z \ T(u,K(w,v5))))
    ]]></literal>
    <justification jstring="[para(12334(a,1),13911(a,2,2,2))].">
      <j1 rule="para" parents="12334 13911"/>
    </justification>
  </clause>

  <clause id="13981">
    <literal><![CDATA[
      K((x * y) \ z,T(u,y)) = K(((x \ z) * x) / (y * x),u)
    ]]></literal>
    <justification jstring="[hyper(7200,a,13918,a)].">
      <j1 rule="hyper" parents="7200 13918"/>
    </justification>
  </clause>

  <clause id="13983">
    <literal><![CDATA[
      K(x / (y * y),T(z,y * y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ (y \ x),z) = u
    ]]></literal>
    <justification jstring="[para(6431(a,2),13927(a,1))].">
      <j1 rule="para" parents="6431 13927"/>
    </justification>
  </clause>

  <clause id="13984">
    <literal><![CDATA[
      L(K(x,y),z,z \ u) * u = (K(y,x) \ z) * (z \ u)
    ]]></literal>
    <justification jstring="[hyper(343,a,13973,a)].">
      <j1 rule="hyper" parents="343 13973"/>
    </justification>
  </clause>

  <clause id="13985">
    <literal><![CDATA[
      L(K(x,y),z,(K(y,x) \ z) \ u) \ u = z * ((K(y,x) \ z) \ u)
    ]]></literal>
    <justification jstring="[hyper(121,a,10,a(flip),b,13973,a)].">
      <j1 rule="hyper" parents="121 10 13973"/>
    </justification>
  </clause>

  <clause id="13986">
    <literal><![CDATA[
      T(1 / x,a(y,z,u)) = a(x,z,K(y,u)) / x
    ]]></literal>
    <justification jstring="[para(13796(a,1),13781(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13796 13781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13987">
    <literal><![CDATA[
      a(x,y,K(z,L(u,w,v5))) = K(x,L(a(u,y,z),w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,13644,a,b,13785,a)].">
      <j1 rule="hyper" parents="63 13644 13785"/>
    </justification>
  </clause>

  <clause id="13988">
    <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(6302(a,1),13797(a,1,2,3))].">
      <j1 rule="para" parents="6302 13797"/>
    </justification>
  </clause>

  <clause id="13989">
    <literal><![CDATA[
      K(x,y) * a(x,z,a(y,u,K(w,v5))) = K(x,L(y,z,a(v5,u,w) \ 1))
    ]]></literal>
    <justification jstring="[para(13732(a,2),13797(a,1,2,3))].">
      <j1 rule="para" parents="13732 13797"/>
    </justification>
  </clause>

  <clause id="13990">
    <literal><![CDATA[
      K(x,y) * a(z \ u,w,K(y,x)) = K(x,L(y,w,z \ (x \ u)))
    ]]></literal>
    <justification jstring="[para(13801(a,1),13765(a,1,2))].">
      <j1 rule="para" parents="13801 13765"/>
    </justification>
  </clause>

  <clause id="13991">
    <literal><![CDATA[
      T(x \ R(x,y,z),y * z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(135,a,13817,a)].">
      <j1 rule="hyper" parents="135 13817"/>
    </justification>
  </clause>

  <clause id="13992">
    <literal><![CDATA[
      a(x,x \ y,K(z,u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,13750,a(flip),b,13848,a),flip(a)].">
      <j1 rule="hyper" parents="63 13750 13848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13993">
    <literal><![CDATA[
      K(x,L(y,z \ u,z)) = K(y,x) \ a(z,u,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(121,a,13992,a(flip),b,10883,a),flip(a)].">
      <j1 rule="hyper" parents="121 13992 10883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13994">
    <literal><![CDATA[
      K(x,L(y,z \ u,z)) = K(x,y) * a(z,u,K(y,x))
    ]]></literal>
    <justification jstring="[para(13992(a,1),10860(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13992 10860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13995">
    <literal><![CDATA[
      T(x,a(y,x \ z,u)) = x * a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[para(13992(a,1),13741(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13992 13741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13996">
    <literal><![CDATA[
      T(x,a(y,z \ u,z)) = x * a(z,u,K(y,x))
    ]]></literal>
    <justification jstring="[para(13992(a,1),13756(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13992 13756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13997">
    <literal><![CDATA[
      T(x,a(y,x \ z,u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(333,a,13741,a(flip),b,13995,a),flip(a)].">
      <j1 rule="hyper" parents="333 13741 13995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13998">
    <literal><![CDATA[
      T(x * K(y,z),a(u,K(z,y),w)) = T(x * K(y,z),a(u,x,w))
    ]]></literal>
    <justification jstring="[para(5990(a,1),13997(a,1,2,2))].">
      <j1 rule="para" parents="5990 13997"/>
    </justification>
  </clause>

  <clause id="13999">
    <literal><![CDATA[
      T(x,a(y,z \ u,z)) = T(x,a(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(333,a,13756,a(flip),b,13996,a),flip(a)].">
      <j1 rule="hyper" parents="333 13756 13996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14000">
    <literal><![CDATA[
      T(x,a(y,z * u,z)) = T(x,a(y,u,z))
    ]]></literal>
    <justification jstring="[para(9(a,1),13999(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 13999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14001">
    <literal><![CDATA[
      K(x,L(y,z,y \ u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,13764,a(flip),b,13856,a),flip(a)].">
      <j1 rule="hyper" parents="63 13764 13856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14002">
    <literal><![CDATA[
      K(x,L(y,z,u \ 1)) = K(x,L(y,z,u \ y))
    ]]></literal>
    <justification jstring="[hyper(63,a,13797,a(flip),b,13862,a)].">
      <j1 rule="hyper" parents="63 13797 13862"/>
    </justification>
  </clause>

  <clause id="14003">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(u \ w,y)) = K(x,L(y,z,(w \ u) \ y))
    ]]></literal>
    <justification jstring="[para(11163(a,2),13862(a,1,2))].">
      <j1 rule="para" parents="11163 13862"/>
    </justification>
  </clause>

  <clause id="14004">
    <literal><![CDATA[
      K(x,L(y,z \ u,z)) = K(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(333,a,10860,a(flip),b,13994,a),flip(a)].">
      <j1 rule="hyper" parents="333 10860 13994"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14005">
    <literal><![CDATA[
      K(x,L(y,z \ u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,u,z)) = w
    ]]></literal>
    <justification jstring="[para(13994(a,2),10933(a,1))].">
      <j1 rule="para" parents="13994 10933"/>
    </justification>
  </clause>

  <clause id="14006">
    <literal><![CDATA[
      K(x,L(y \ (z \ u),u,z)) = K(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[hyper(10886,a,14004,a),flip(a)].">
      <j1 rule="hyper" parents="10886 14004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14007">
    <literal><![CDATA[
      K((x \ y) \ z,L(u,y,x)) = K(y \ (x * z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,10909,a(flip),b,14004,a),flip(a)].">
      <j1 rule="hyper" parents="63 10909 14004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14008">
    <literal><![CDATA[
      K(x,L(y,z * u,z)) = K(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[para(9(a,1),14004(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 14004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14009">
    <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(767(a,1),14004(a,1,2,2))].">
      <j1 rule="para" parents="767 14004"/>
    </justification>
  </clause>

  <clause id="14010">
    <literal><![CDATA[
      K(x,L((y \ z) \ u,z,y)) = K(x,z \ (y * u))
    ]]></literal>
    <justification jstring="[para(515(a,1),14004(a,1,2)),flip(a)].">
      <j1 rule="para" parents="515 14004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14011">
    <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(3203(a,1),14004(a,1,2,2))].">
      <j1 rule="para" parents="3203 14004"/>
    </justification>
  </clause>

  <clause id="14012">
    <literal><![CDATA[
      K(x,L(y,z,u \ z)) = K(x,L(y,u,u \ z))
    ]]></literal>
    <justification jstring="[para(10087(a,1),14004(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10087 14004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14013">
    <literal><![CDATA[
      x * K(y,L(z,x,u)) = u * ((u \ x) * K(y,z))
    ]]></literal>
    <justification jstring="[para(14004(a,1),10872(a,1,2))].">
      <j1 rule="para" parents="14004 10872"/>
    </justification>
  </clause>

  <clause id="14014">
    <literal><![CDATA[
      K(x \ (y \ z),L(u,z,y)) != w
    ]]></literal>
    <literal><![CDATA[
      K((y * x) \ z,u) = w
    ]]></literal>
    <justification jstring="[para(14004(a,1),10882(a,1))].">
      <j1 rule="para" parents="14004 10882"/>
    </justification>
  </clause>

  <clause id="14015">
    <literal><![CDATA[
      K(x,L(y,z * u,z \ 1)) = K(x,L(y,u,z \ 1))
    ]]></literal>
    <justification jstring="[para(2955(a,1),14008(a,1,2))].">
      <j1 rule="para" parents="2955 14008"/>
    </justification>
  </clause>

  <clause id="14016">
    <literal><![CDATA[
      K(x,L(y,z * u,T(u,z))) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(10153(a,2),14008(a,1,2))].">
      <j1 rule="para" parents="10153 14008"/>
    </justification>
  </clause>

  <clause id="14017">
    <literal><![CDATA[
      K(x,(y * (y \ z)) / (u * (y \ z))) = K(x,L(y / u,z,y \ z))
    ]]></literal>
    <justification jstring="[hyper(333,a,13869,a(flip),b,14012,a)].">
      <j1 rule="hyper" parents="333 13869 14012"/>
    </justification>
  </clause>

  <clause id="14018">
    <literal><![CDATA[
      K(x,L(y \ z,u,y \ u)) = K(x,u \ ((u / y) * z))
    ]]></literal>
    <justification jstring="[para(10102(a,1),14012(a,2,2))].">
      <j1 rule="para" parents="10102 14012"/>
    </justification>
  </clause>

  <clause id="14019">
    <literal><![CDATA[
      K(x,y \ ((y / z) * (u * z))) = K(x,L(T(u,z),y,z \ y))
    ]]></literal>
    <justification jstring="[para(10123(a,1),14012(a,2,2)),flip(a)].">
      <j1 rule="para" parents="10123 14012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14020">
    <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(13561(a,1),14012(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="13561 14012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14021">
    <literal><![CDATA[
      K(x * y,L(z,x,y)) = K(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(10386,a,14016,a),flip(a)].">
      <j1 rule="hyper" parents="10386 14016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14022">
    <literal><![CDATA[
      K(x,L(y * z,y,z)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(9476,a,14016,a),flip(a)].">
      <j1 rule="hyper" parents="9476 14016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14023">
    <literal><![CDATA[
      K(x * y,L(z,x,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(14016(a,1),10386(a,1))].">
      <j1 rule="para" parents="14016 10386"/>
    </justification>
  </clause>

  <clause id="14024">
    <literal><![CDATA[
      T(x * y,L(z,x,y)) = T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(124,a,14021,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 14021 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14025">
    <literal><![CDATA[
      T(K(x,L((x * y) * z,x * y,z)),K(x,(y * x) * z)) = K(x,(y * x) * z)
    ]]></literal>
    <justification jstring="[hyper(451,a,14022,a,b,7486,a)].">
      <j1 rule="hyper" parents="451 14022 7486"/>
    </justification>
  </clause>

  <clause id="14026">
    <literal><![CDATA[
      R(x,y,z) * T(y * z,x) = (y * z) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(14024(a,1),13909(a,1,2))].">
      <j1 rule="para" parents="14024 13909"/>
    </justification>
  </clause>

  <clause id="14027">
    <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(2956(a,1),14005(a,1,2))].">
      <j1 rule="para" parents="2956 14005"/>
    </justification>
  </clause>

  <clause id="14028">
    <literal><![CDATA[
      K(x,(y * z) \ L(y,u,w)) = K(x,z \ (y \ L(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,13792,a(flip),b,14006,a),flip(a)].">
      <j1 rule="hyper" parents="63 13792 14006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14029">
    <literal><![CDATA[
      K((x \ y) \ z,y) = K(y \ (x * z),y)
    ]]></literal>
    <justification jstring="[hyper(9476,a,14007,a)].">
      <j1 rule="hyper" parents="9476 14007"/>
    </justification>
  </clause>

  <clause id="14030">
    <literal><![CDATA[
      K(T(x,y) \ z,L(u,y,x \ y)) = K(y \ ((x \ y) * z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,12781,a(flip),b,14007,a)].">
      <j1 rule="hyper" parents="63 12781 14007"/>
    </justification>
  </clause>

  <clause id="14031">
    <literal><![CDATA[
      K(x \ ((y \ x) * z),x) = K(y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(8328,a,14029,a),flip(a)].">
      <j1 rule="hyper" parents="8328 14029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14032">
    <literal><![CDATA[
      K(x \ ((x / y) * z),x) = K(y \ z,x)
    ]]></literal>
    <justification jstring="[para(79(a,1),14029(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="79 14029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14033">
    <literal><![CDATA[
      K(x \ (y * z),z) = K((x \ z) * y,z)
    ]]></literal>
    <justification jstring="[hyper(10832,a,14031,a),flip(a)].">
      <j1 rule="hyper" parents="10832 14031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14034">
    <literal><![CDATA[
      K(x \ ((x \ y) \ z),y) = K(y \ z,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),14031(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10 14031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14035">
    <literal><![CDATA[
      K(x \ ((y / x) \ z),y) = K(y \ z,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),14032(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10 14032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14036">
    <literal><![CDATA[
      K((x \ y) * z,y) = K(y * (x \ z),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,10672,a(flip),b,14033,a),flip(a)].">
      <j1 rule="hyper" parents="63 10672 14033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14037">
    <literal><![CDATA[
      K((1 / x) \ ((x * y) \ z),L(y,x,x \ 1)) = K(L(y,x,x \ 1) \ z,L(y,x,x \ 1))
    ]]></literal>
    <justification jstring="[para(2656(a,1),14034(a,1,1,2,1))].">
      <j1 rule="para" parents="2656 14034"/>
    </justification>
  </clause>

  <clause id="14038">
    <literal><![CDATA[
      K((x \ 1) \ ((y * x) \ z),R(y,x,x \ 1)) = K(R(y,x,x \ 1) \ z,R(y,x,x \ 1))
    ]]></literal>
    <justification jstring="[para(537(a,1),14035(a,1,1,2,1))].">
      <j1 rule="para" parents="537 14035"/>
    </justification>
  </clause>

  <clause id="14039">
    <literal><![CDATA[
      K((x / y) * z,x) = K(x * (y \ z),x)
    ]]></literal>
    <justification jstring="[hyper(8329,a,14036,a)].">
      <j1 rule="hyper" parents="8329 14036"/>
    </justification>
  </clause>

  <clause id="14040">
    <literal><![CDATA[
      K((x * y) * (T(x,y) \ z),x * y) = K(y * z,x * y)
    ]]></literal>
    <justification jstring="[para(191(a,1),14039(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="191 14039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14041">
    <literal><![CDATA[
      K(x,(y \ R(y,z,u)) \ w) = K(x,R(y,z,u) \ (y * w))
    ]]></literal>
    <justification jstring="[hyper(13920,a,14010,a)].">
      <j1 rule="hyper" parents="13920 14010"/>
    </justification>
  </clause>

  <clause id="14042">
    <literal><![CDATA[
      K(x,L((a(y \ 1,y,z) \ 1) \ u,L(z,y,y \ 1),z)) = K(x,L(z,y,y \ 1) \ (z * u))
    ]]></literal>
    <justification jstring="[para(3259(a,2),14010(a,1,2,1,1))].">
      <j1 rule="para" parents="3259 14010"/>
    </justification>
  </clause>

  <clause id="14043">
    <literal><![CDATA[
      x \ (K(y,L(z,u,x)) * u) = (x \ u) * K(y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(6719,a,14013,a)].">
      <j1 rule="hyper" parents="6719 14013"/>
    </justification>
  </clause>

  <clause id="14044">
    <literal><![CDATA[
      x \ (y * K(z,L(u,y,x))) = (x \ y) * K(z,u)
    ]]></literal>
    <justification jstring="[hyper(564,a,14013,a)].">
      <j1 rule="hyper" parents="564 14013"/>
    </justification>
  </clause>

  <clause id="14045">
    <literal><![CDATA[
      (L(x,y,z) \ x) * (L(x,y,z) * K(u,w)) = x * K(u,L(w,x,L(x,y,z) \ x))
    ]]></literal>
    <justification jstring="[para(2559(a,1),14013(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="2559 14013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14046">
    <literal><![CDATA[
      x \ ((1 / y) * K(z,y)) = (x \ (1 / y)) * K(z,y)
    ]]></literal>
    <justification jstring="[para(6708(a,1),14044(a,1,2,2))].">
      <j1 rule="para" parents="6708 14044"/>
    </justification>
  </clause>

  <clause id="14047">
    <literal><![CDATA[
      K(x,L((y * z) \ u,z,y \ 1)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L((y * z) \ u,u,y \ 1)) = w
    ]]></literal>
    <justification jstring="[para(14015(a,1),10961(a,1))].">
      <j1 rule="para" parents="14015 10961"/>
    </justification>
  </clause>

  <clause id="14048">
    <literal><![CDATA[
      a(x,y,z) = ((y * z) * x) \ ((y * z) * R(x,y,z))
    ]]></literal>
    <justification jstring="[para(14026(a,1),9128(a,2,2))].">
      <j1 rule="para" parents="14026 9128"/>
    </justification>
  </clause>

  <clause id="14049">
    <literal><![CDATA[
      (x \ (1 / y)) * K(z,y) = x \ (1 / T(y,z))
    ]]></literal>
    <justification jstring="[para(4220(a,1),14046(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4220 14046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14050">
    <literal><![CDATA[
      (x \ (1 / T(y,z))) * K(T(u,z),T(y,z)) = x \ (1 / (K(y,u) * T(y,z)))
    ]]></literal>
    <justification jstring="[para(7993(a,1),14046(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7993 14046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14051">
    <literal><![CDATA[
      a(x,y,z) = L(x \ R(x,y,z),x,y * z)
    ]]></literal>
    <justification jstring="[hyper(333,a,99,a,b,14048,a),flip(a)].">
      <j1 rule="hyper" parents="333 99 14048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14052">
    <literal><![CDATA[
      ((x * y) * z) * a(z,x,y) = (x * y) * R(z,x,y)
    ]]></literal>
    <justification jstring="[hyper(126,a,14048,a,b,xx)].">
      <j1 rule="hyper" parents="126 14048"/>
    </justification>
  </clause>

  <clause id="14053">
    <literal><![CDATA[
      (K(x,y) * ((y * z) * x)) \ ((y * (K(x,y) * z)) * R(x,y,K(x,y) * z)) = a(x,y,K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(6331(a,1),14048(a,2,1)),flip(a)].">
      <j1 rule="para" parents="6331 14048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14055">
    <literal><![CDATA[
      (x * ((y * z) * u)) \ (x * ((y * z) * R(u,y,z))) != w
    ]]></literal>
    <literal><![CDATA[
      L(a(u,y,z),(y * z) * u,x) = w
    ]]></literal>
    <justification jstring="[para(14052(a,1),504(a,1,2,2))].">
      <j1 rule="para" parents="14052 504"/>
    </justification>
  </clause>

  <clause id="14056">
    <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(6390(a,1),14052(a,1,1,1))].">
      <j1 rule="para" parents="6390 14052"/>
    </justification>
  </clause>

  <clause id="14057">
    <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(11161(a,1),13770(a,1,2))].">
      <j1 rule="para" parents="11161 13770"/>
    </justification>
  </clause>

  <clause id="14058">
    <literal><![CDATA[
      K(x,y) * a(y,z,a(x,u,K(w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,a(v5,u,w))) = v6
    ]]></literal>
    <justification jstring="[para(13732(a,2),13771(a,1,2,3))].">
      <j1 rule="para" parents="13732 13771"/>
    </justification>
  </clause>

  <clause id="14059">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      a(u,y,K(z,K(x,w))) = v5
    ]]></literal>
    <justification jstring="[para(13758(a,1),13841(a,1))].">
      <j1 rule="para" parents="13758 13841"/>
    </justification>
  </clause>

  <clause id="14060">
    <literal><![CDATA[
      K(x,x * (y \ L(y,z,u))) != w \ v5
    ]]></literal>
    <literal><![CDATA[
      w * a(y,z,K(x,u)) = v5
    ]]></literal>
    <justification jstring="[para(13085(a,2),13850(a,1))].">
      <j1 rule="para" parents="13085 13850"/>
    </justification>
  </clause>

  <clause id="14061">
    <literal><![CDATA[
      K(x,L(y,z,u)) * z = (K(x,y) * (z / u)) * u
    ]]></literal>
    <justification jstring="[para(14004(a,1),13871(a,1,1))].">
      <j1 rule="para" parents="14004 13871"/>
    </justification>
  </clause>

  <clause id="14062">
    <literal><![CDATA[
      (x * K(y,L(z,x,u))) / u = K(y,T(z,x)) * (x / u)
    ]]></literal>
    <justification jstring="[hyper(7686,a,14061,a)].">
      <j1 rule="hyper" parents="7686 14061"/>
    </justification>
  </clause>

  <clause id="14063">
    <literal><![CDATA[
      (K(x,L(y,z,u)) * z) / u = K(x,y) * (z / u)
    ]]></literal>
    <justification jstring="[hyper(602,a,14061,a)].">
      <j1 rule="hyper" parents="602 14061"/>
    </justification>
  </clause>

  <clause id="14064">
    <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(444,a,14063,a(flip),b,13500,a)].">
      <j1 rule="hyper" parents="444 14063 13500"/>
    </justification>
  </clause>

  <clause id="14065">
    <literal><![CDATA[
      K(x,T(1 / (y * z),y)) = K(x,(z * y) \ K(z,1 / z))
    ]]></literal>
    <justification jstring="[para(522(a,1),13883(a,1,2)),flip(a)].">
      <j1 rule="para" parents="522 13883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14066">
    <literal><![CDATA[
      K(x,L(y / (z / u),z,u)) = K(x,(y * u) / z)
    ]]></literal>
    <justification jstring="[hyper(14005,a,13887,a)].">
      <j1 rule="hyper" parents="14005 13887"/>
    </justification>
  </clause>

  <clause id="14067">
    <literal><![CDATA[
      x * (y * K(z,T(u,x * y))) = (K(z,u) * y) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(7336,a,13898,a)].">
      <j1 rule="hyper" parents="7336 13898"/>
    </justification>
  </clause>

  <clause id="14069">
    <literal><![CDATA[
      L(K(x,((y / z) / u) \ x),z \ y,z) = K(x,((x * u) * z) / y)
    ]]></literal>
    <justification jstring="[para(5661(a,1),13906(a,1,1))].">
      <j1 rule="para" parents="5661 13906"/>
    </justification>
  </clause>

  <clause id="14070">
    <literal><![CDATA[
      T(T(x,y),L(y,z,u)) * R(T(y,x),z,u) = T(x,y) * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(3613(a,1),13910(a,1,2,1))].">
      <j1 rule="para" parents="3613 13910"/>
    </justification>
  </clause>

  <clause id="14071">
    <literal><![CDATA[
      ((x * y) * z) / ((T(x,u) * y) * z) = K(u,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(197,a,13917,a(flip),b,4567,a)].">
      <j1 rule="hyper" parents="197 13917 4567"/>
    </justification>
  </clause>

  <clause id="14072">
    <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(4677(a,1),13959(a,2,2,1))].">
      <j1 rule="para" parents="4677 13959"/>
    </justification>
  </clause>

  <clause id="14073">
    <literal><![CDATA[
      a(x,y,K(y * z,u)) * K(x,(y * u) / ((z \ 1) * u)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(13959(a,1),13768(a,1,2))].">
      <j1 rule="para" parents="13959 13768"/>
    </justification>
  </clause>

  <clause id="14074">
    <literal><![CDATA[
      L(K(x,y),y * x,L(z,y,x)) \ (x * (y * z)) = (y * x) * L(z,y,x)
    ]]></literal>
    <justification jstring="[para(97(a,1),13974(a,1,2))].">
      <j1 rule="para" parents="97 13974"/>
    </justification>
  </clause>

  <clause id="14075">
    <literal><![CDATA[
      x * L(K(y,T(z,x)),u,u \ x) = (K(z,y) \ u) * (u \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,6399,a,b,13984,a)].">
      <j1 rule="hyper" parents="63 6399 13984"/>
    </justification>
  </clause>

  <clause id="14076">
    <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(14059,a,11039,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="14059 11039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14077">
    <literal><![CDATA[
      K(x,L(y,z,(T(y,x) * z) \ u)) * u = (y * z) * ((T(y,x) * z) \ u)
    ]]></literal>
    <justification jstring="[para(14071(a,1),335(a,1,1))].">
      <j1 rule="para" parents="14071 335"/>
    </justification>
  </clause>

  <clause id="14078">
    <literal><![CDATA[
      a(L(x,y,z) \ u,w,K(z,x)) = a(u,w,K(z,x))
    ]]></literal>
    <justification jstring="[para(9466(a,1),13822(a,2,3))].">
      <j1 rule="para" parents="9466 13822"/>
    </justification>
  </clause>

  <clause id="14080">
    <literal><![CDATA[
      a(x,y,K(z,u)) * L(u,w,x) != v5
    ]]></literal>
    <literal><![CDATA[
      L(T(u,a(z,y,x)),w,x) = v5
    ]]></literal>
    <justification jstring="[para(13845(a,2),10114(a,1))].">
      <j1 rule="para" parents="13845 10114"/>
    </justification>
  </clause>

  <clause id="14081">
    <literal><![CDATA[
      a(x,y / z,K(u,z)) = a(x,z \ y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(13843,a,13847,a),flip(a)].">
      <j1 rule="hyper" parents="13843 13847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14082">
    <literal><![CDATA[
      a(x,y \ z,K(u,y)) = a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,10948,a(flip),b,14081,a),flip(a)].">
      <j1 rule="hyper" parents="63 10948 14081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14083">
    <literal><![CDATA[
      K(x,y) * (T(K(y,L(x,z,u)) * K(w,K(y,L(x,z,u))),w) * v5) = a(y,z,K(u,x)) * v5
    ]]></literal>
    <justification jstring="[para(4239(a,2),13849(a,1,2,1))].">
      <j1 rule="para" parents="4239 13849"/>
    </justification>
  </clause>

  <clause id="14084">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(y,K(u,w))) = L(K(x,y),z,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(333,a,10851,a,b,13858,a),flip(a)].">
      <j1 rule="hyper" parents="333 10851 13858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14085">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(y,K(u,w))) = L(K(x,y),y * z,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(333,a,9721,a,b,13858,a),flip(a)].">
      <j1 rule="hyper" parents="333 9721 13858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14086">
    <literal><![CDATA[
      K(x,L(y,z,u)) * ((y * z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      (K(x,y) * (y * z)) * u = w
    ]]></literal>
    <justification jstring="[para(10866(a,1),13873(a,1,1))].">
      <j1 rule="para" parents="10866 13873"/>
    </justification>
  </clause>

  <clause id="14087">
    <literal><![CDATA[
      T(x,L(y,K(z,u) / w,v5)) = T(x,L(y,w * K(u,z),v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,13879,a(flip),b,13915,a),flip(a)].">
      <j1 rule="hyper" parents="63 13879 13915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14088">
    <literal><![CDATA[
      K((x * y) \ z,T(u,y)) = K(T(z,x) / (y * x),u)
    ]]></literal>
    <justification jstring="[hyper(333,a,12907,a(flip),b,13981,a),flip(a)].">
      <j1 rule="hyper" parents="333 12907 13981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14089">
    <literal><![CDATA[
      K(T(x,y),(z * y) \ u) = 1 / K(((z \ u) * z) / (y * z),x)
    ]]></literal>
    <justification jstring="[hyper(197,a,13981,a(flip),b,4367,a),flip(a)].">
      <j1 rule="hyper" parents="197 13981 4367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14090">
    <literal><![CDATA[
      K((x \ T(y,x \ 1)) \ z,T(u,(x \ y) / y)) = K(((y \ z) * y) / (((x \ y) / y) * y),u)
    ]]></literal>
    <justification jstring="[para(3107(a,2),13981(a,1,1,1))].">
      <j1 rule="para" parents="3107 13981"/>
    </justification>
  </clause>

  <clause id="14091">
    <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(63,a,13396,a(flip),b,14088,a)].">
      <j1 rule="hyper" parents="63 13396 14088"/>
    </justification>
  </clause>

  <clause id="14092">
    <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(13844,a,14040,a),flip(a)].">
      <j1 rule="hyper" parents="13844 14040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14093">
    <literal><![CDATA[
      K(x,R(y,z,z \ 1) \ (y * u)) = K(x,a(y,z,z \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(767(a,1),14041(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="767 14041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14094">
    <literal><![CDATA[
      K(x,R(y,z,z) \ (y * u)) = K(x,a(y,z,z) \ u)
    ]]></literal>
    <justification jstring="[para(13601(a,1),14041(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13601 14041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14095">
    <literal><![CDATA[
      T(x,L(y,K(z,u) * w,v5)) = T(x,L(y,w * K(u,z),v5))
    ]]></literal>
    <justification jstring="[para(13308(a,1),14087(a,1,2))].">
      <j1 rule="para" parents="13308 14087"/>
    </justification>
  </clause>

  <clause id="14096">
    <literal><![CDATA[
      ((K(x,y) * z) * u) * a(x,z,K(y,u)) = K(x,y) * (z * u)
    ]]></literal>
    <justification jstring="[hyper(125,a,13733,a(flip),b,9912,a)].">
      <j1 rule="hyper" parents="125 13733 9912"/>
    </justification>
  </clause>

  <clause id="14097">
    <literal><![CDATA[
      x * a(x,y,K(z,u)) = R(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(544,a,13777,a),flip(a)].">
      <j1 rule="hyper" parents="544 13777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14098">
    <literal><![CDATA[
      ((x * y) * K(z,u)) / L(y * K(z,u),w,a(w,v5,K(v6,v7))) = x * a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(13772(a,2),13777(a,1,2))].">
      <j1 rule="para" parents="13772 13777"/>
    </justification>
  </clause>

  <clause id="14099">
    <literal><![CDATA[
      R(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,a(u,y,z)) = w
    ]]></literal>
    <justification jstring="[para(14097(a,1),13774(a,1))].">
      <j1 rule="para" parents="14097 13774"/>
    </justification>
  </clause>

  <clause id="14100">
    <literal><![CDATA[
      T(x * y,a(x,z,u)) = x * T(y,a(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(13784,a,13823,a),flip(a)].">
      <j1 rule="hyper" parents="13784 13823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14101">
    <literal><![CDATA[
      T(x,a(y,z,u)) / y = T(x / y,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(4093,a,14100,a)].">
      <j1 rule="hyper" parents="4093 14100"/>
    </justification>
  </clause>

  <clause id="14102">
    <literal><![CDATA[
      T(K(x,T(y,z * u)) * z,u) = T(z,u) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(253,a,13896,a,b,10085,a(flip))].">
      <j1 rule="hyper" parents="253 13896 10085"/>
    </justification>
  </clause>

  <clause id="14103">
    <literal><![CDATA[
      T(x,y) * K(z,T(u,x * y)) = T(K(z,u) * x,y)
    ]]></literal>
    <justification jstring="[para(6900(a,1),14102(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6900 14102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14104">
    <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(14103(a,2),827(a,1))].">
      <j1 rule="para" parents="14103 827"/>
    </justification>
  </clause>

  <clause id="14105">
    <literal><![CDATA[
      K(x,L(y,z,a(u,w,w \ 1) \ 1)) = K(x,y) * 1
    ]]></literal>
    <justification jstring="[para(380(a,1),13931(a,2,2))].">
      <j1 rule="para" parents="380 13931"/>
    </justification>
  </clause>

  <clause id="14106">
    <literal><![CDATA[
      K(x,L(y,z,a(u,w,w \ 1) \ 1)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(14105(a,2),134(a,1)),flip(b)].">
      <j1 rule="para" parents="14105 134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14108">
    <literal><![CDATA[
      K(x * (y \ z),L(y / x,x,y \ z)) = K(x * (y \ z),(x * (y \ z)) \ z)
    ]]></literal>
    <justification jstring="[para(10(a,1),13965(a,2,2,2))].">
      <j1 rule="para" parents="10 13965"/>
    </justification>
  </clause>

  <clause id="14109">
    <literal><![CDATA[
      K(x,(y * z) / ((y / u) * z)) = T(L(K(x,u),y,z),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,9460,a(flip),b,13966,a),flip(a)].">
      <j1 rule="hyper" parents="63 9460 13966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14110">
    <literal><![CDATA[
      T(L(K(x,y),z / u,u),z / u) = K(x,z / (((z / u) / y) * u))
    ]]></literal>
    <justification jstring="[para(12(a,1),14109(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12 14109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14111">
    <literal><![CDATA[
      (x * y) \ (x \ ((x * x) * y)) = y \ ((y / x) * R(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(333,a,3232,a(flip),b,13977,a),flip(a)].">
      <j1 rule="hyper" parents="333 3232 13977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14112">
    <literal><![CDATA[
      x * K(y,L(T(z,u),x,u \ x)) = (x / u) * (K(y,z) * u)
    ]]></literal>
    <justification jstring="[para(14019(a,1),11086(a,1,2))].">
      <j1 rule="para" parents="14019 11086"/>
    </justification>
  </clause>

  <clause id="14113">
    <literal><![CDATA[
      K(x,y) * a(x,z,a(y,u,K(w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,(L(w,u,v5) \ w) \ y)) = v6
    ]]></literal>
    <justification jstring="[para(13778(a,1),14057(a,1,2,3))].">
      <j1 rule="para" parents="13778 14057"/>
    </justification>
  </clause>

  <clause id="14114">
    <literal><![CDATA[
      K(x,L(K(y,T(z,x)),u,u \ x)) \ ((K(z,y) \ u) * (u \ x)) = L(K(y,T(z,x)),u,u \ x) * x
    ]]></literal>
    <justification jstring="[hyper(121,a,14075,a(flip),b,4201,a)].">
      <j1 rule="hyper" parents="121 14075 4201"/>
    </justification>
  </clause>

  <clause id="14115">
    <literal><![CDATA[
      a(x,y,K(z,u * u)) = 1
    ]]></literal>
    <justification jstring="[hyper(120,a,33,a,b,14096,a),flip(a)].">
      <j1 rule="hyper" parents="120 33 14096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14116">
    <literal><![CDATA[
      T(a(x,y,z),u * u) = 1 * a(x,y,z)
    ]]></literal>
    <justification jstring="[para(14115(a,1),13540(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14115 13540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14117">
    <literal><![CDATA[
      T(a(x,y,z),u * u) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,7,a(flip),b,14116,a),flip(a)].">
      <j1 rule="hyper" parents="333 7 14116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14118">
    <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(13262(a,1),14112(a,2,2))].">
      <j1 rule="para" parents="13262 14112"/>
    </justification>
  </clause>

  <clause id="14119">
    <literal><![CDATA[
      (L(x,y,z) \ x) * K(u,w) = x * (L(x,y,z) \ K(u,w))
    ]]></literal>
    <justification jstring="[para(13126(a,1),13820(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13126 13820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14121">
    <literal><![CDATA[
      L(x,y,z) * (x \ (x * (L(x,y,z) \ K(u,(L(x,y,z) \ x) \ w)))) = K(u,L(x,y,z) * (x \ w))
    ]]></literal>
    <justification jstring="[para(14119(a,1),11190(a,1,2,2))].">
      <j1 rule="para" parents="14119 11190"/>
    </justification>
  </clause>

  <clause id="14122">
    <literal><![CDATA[
      K(x,y) / (z * (L(z,u,w) \ K(x,y))) = (L(z,u,w) \ z) \ 1
    ]]></literal>
    <justification jstring="[para(14119(a,1),13490(a,1,2))].">
      <j1 rule="para" parents="14119 13490"/>
    </justification>
  </clause>

  <clause id="14123">
    <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(13936(a,1),13771(a,1))].">
      <j1 rule="para" parents="13936 13771"/>
    </justification>
  </clause>

  <clause id="14124">
    <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(14123,a,11102,a)].">
      <j1 rule="hyper" parents="14123 11102"/>
    </justification>
  </clause>

  <clause id="14125">
    <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(98(a,2),13948(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="98 13948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14126">
    <literal><![CDATA[
      K(x,L(y,z,u \ (x \ w))) = K(x,L(y,z,u \ w))
    ]]></literal>
    <justification jstring="[hyper(10933,a,13990,a),flip(a)].">
      <j1 rule="hyper" parents="10933 13990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14127">
    <literal><![CDATA[
      K(x,L(y,z,u \ 1)) = K(x,L(y,z,u \ x))
    ]]></literal>
    <justification jstring="[para(66(a,1),14126(a,1,2,3,2))].">
      <j1 rule="para" parents="66 14126"/>
    </justification>
  </clause>

  <clause id="14129">
    <literal><![CDATA[
      K(x,L(y,z,(u \ w) \ y)) = K(x,L(y,z,w \ u))
    ]]></literal>
    <justification jstring="[hyper(13770,a,14003,a),flip(a)].">
      <j1 rule="hyper" parents="13770 14003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14130">
    <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(14003(a,1),13770(a,1))].">
      <j1 rule="para" parents="14003 13770"/>
    </justification>
  </clause>

  <clause id="14131">
    <literal><![CDATA[
      K(x,L(y,z,(u \ w) \ 1)) = K(x,L(y,z,w \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,14002,a,b,14129,a)].">
      <j1 rule="hyper" parents="63 14002 14129"/>
    </justification>
  </clause>

  <clause id="14132">
    <literal><![CDATA[
      K(x,L(y,z,(u * w) \ u)) = K(x,L(y,z,w \ 1))
    ]]></literal>
    <justification jstring="[para(9(a,1),14131(a,1,2,3,1)),flip(a)].">
      <j1 rule="para" parents="9 14131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14133">
    <literal><![CDATA[
      K(x,L(y,z,L(u \ 1,u,w))) = K(x,L(y,z,u \ 1))
    ]]></literal>
    <justification jstring="[para(227(a,2),14132(a,1,2,3))].">
      <j1 rule="para" parents="227 14132"/>
    </justification>
  </clause>

  <clause id="14134">
    <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(14002(a,2),14130(a,1))].">
      <j1 rule="para" parents="14002 14130"/>
    </justification>
  </clause>

  <clause id="14135">
    <literal><![CDATA[
      K(x,L(y,a(z,u,u \ 1),z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(13920,a,14009,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="13920 14009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14136">
    <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(63,a,10868,a(flip),b,14135,a)].">
      <j1 rule="hyper" parents="63 10868 14135"/>
    </justification>
  </clause>

  <clause id="14137">
    <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(6800(a,1),14076(a,1,2))].">
      <j1 rule="para" parents="6800 14076"/>
    </justification>
  </clause>

  <clause id="14138">
    <literal><![CDATA[
      a(x,y * z,K(y,K(u,w))) = a(x,z,K(y,K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(34,a,14084,a,b,14085,a)].">
      <j1 rule="hyper" parents="34 14084 14085"/>
    </justification>
  </clause>

  <clause id="14139">
    <literal><![CDATA[
      a(x,y \ z,K(y,K(u,w))) = a(x,z,K(y,K(u,w)))
    ]]></literal>
    <justification jstring="[para(10(a,1),14138(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 14138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14140">
    <literal><![CDATA[
      a(x,y * z,K(u,K(w,y))) = a(x,z,K(y,K(u,w)))
    ]]></literal>
    <justification jstring="[para(6788(a,2),14138(a,1,3))].">
      <j1 rule="para" parents="6788 14138"/>
    </justification>
  </clause>

  <clause id="14141">
    <literal><![CDATA[
      a(x,y * z,K(u,K(w,y))) = a(x,z,K(u,K(w,y)))
    ]]></literal>
    <justification jstring="[para(6788(a,2),14140(a,2,3))].">
      <j1 rule="para" parents="6788 14140"/>
    </justification>
  </clause>

  <clause id="14142">
    <literal><![CDATA[
      K(T(x,y),(z * y) \ u) = K(x,((z \ u) * z) / (y * z))
    ]]></literal>
    <justification jstring="[hyper(333,a,4371,a(flip),b,14089,a),flip(a)].">
      <j1 rule="hyper" parents="333 4371 14089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14143">
    <literal><![CDATA[
      K(x,T((y * z) \ u,z)) = K(x,((y \ u) * y) / (z * y))
    ]]></literal>
    <justification jstring="[hyper(6695,a,14142,a)].">
      <j1 rule="hyper" parents="6695 14142"/>
    </justification>
  </clause>

  <clause id="14144">
    <literal><![CDATA[
      K(x,T((y * z) \ u,z)) = K(x,T(u,y) / (z * y))
    ]]></literal>
    <justification jstring="[hyper(333,a,12719,a(flip),b,14143,a),flip(a)].">
      <j1 rule="hyper" parents="333 12719 14143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14145">
    <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(5147(a,1),14144(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5147 14144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14146">
    <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(10330(a,2),14144(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="10330 14144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14147">
    <literal><![CDATA[
      a(T(x,y),z,K(u,x * y)) = K(L(x,z,u) * y,x * y)
    ]]></literal>
    <justification jstring="[para(251(a,1),14092(a,1,1)),flip(a)].">
      <j1 rule="para" parents="251 14092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14148">
    <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(63,a,11678,a(flip),b,14137,a)].">
      <j1 rule="hyper" parents="63 11678 14137"/>
    </justification>
  </clause>

  <clause id="14149">
    <literal><![CDATA[
      K(a(x,y * z,K(z,u)),w) = a(z,y,K(w,K(x,u)))
    ]]></literal>
    <justification jstring="[para(9745(a,1),14148(a,1,1))].">
      <j1 rule="para" parents="9745 14148"/>
    </justification>
  </clause>

  <clause id="14150">
    <literal><![CDATA[
      K(a(x,y * z,K(z,u)),w) = a(z,y,K(w,K(u,x)))
    ]]></literal>
    <justification jstring="[para(6800(a,1),14149(a,2,3))].">
      <j1 rule="para" parents="6800 14149"/>
    </justification>
  </clause>

  <clause id="14151">
    <literal><![CDATA[
      K(L(x \ (y / z),x,z) \ 1,u) = K((y / (x * z)) \ 1,T(u,x))
    ]]></literal>
    <justification jstring="[hyper(333,a,6378,a(flip),b,13952,a),flip(a)].">
      <j1 rule="hyper" parents="333 6378 13952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14152">
    <literal><![CDATA[
      T(x,a(a(y,z,u),w,v5)) = T(x,a(y,w,a(v5,z,u)))
    ]]></literal>
    <justification jstring="[hyper(13955,a,13798,a)].">
      <j1 rule="hyper" parents="13955 13798"/>
    </justification>
  </clause>

  <clause id="14153">
    <literal><![CDATA[
      T(x,K(y,L((z / u) / w,w,u))) = x * K(x,K(y,z / (w * u)))
    ]]></literal>
    <justification jstring="[para(6785(a,1),13970(a,2,2))].">
      <j1 rule="para" parents="6785 13970"/>
    </justification>
  </clause>

  <clause id="14154">
    <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(13276(a,1),13971(a,1,2))].">
      <j1 rule="para" parents="13276 13971"/>
    </justification>
  </clause>

  <clause id="14155">
    <literal><![CDATA[
      K(x,L(y / z,u,y \ u)) = K(x,u / (z * (y \ u)))
    ]]></literal>
    <justification jstring="[para(10(a,1),14017(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 14017"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14156">
    <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(3716(a,2),14155(a,2,2,2,2))].">
      <j1 rule="para" parents="3716 14155"/>
    </justification>
  </clause>

  <clause id="14157">
    <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(14060,a,8245,a(flip))].">
      <j1 rule="hyper" parents="14060 8245"/>
    </justification>
  </clause>

  <clause id="14158">
    <literal><![CDATA[
      K(x,(y * z) \ R(y,u,u \ 1)) = K(x,z \ a(y,u,u \ 1))
    ]]></literal>
    <justification jstring="[para(769(a,1),14136(a,1,2))].">
      <j1 rule="para" parents="769 14136"/>
    </justification>
  </clause>

  <clause id="14159">
    <literal><![CDATA[
      K(x,L(y \ (z / u),y,u) \ 1) = (w * K((z / (y * u)) \ 1,T(x,y))) \ w
    ]]></literal>
    <justification jstring="[para(14151(a,1),5990(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="14151 5990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14160">
    <literal><![CDATA[
      T(x * (y * (z \ 1)),z * z) = (z * z) \ (x * (y * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,3166,a(flip),b,13283,a)].">
      <j1 rule="hyper" parents="63 3166 13283"/>
    </justification>
  </clause>

  <clause id="14161">
    <literal><![CDATA[
      K(x,x \ y) * K(x * (y / x),z) = y \ (x * (T(y,z) / x))
    ]]></literal>
    <justification jstring="[para(4460(a,1),13368(a,1,1))].">
      <j1 rule="para" parents="4460 13368"/>
    </justification>
  </clause>

  <clause id="14162">
    <literal><![CDATA[
      K(x,x \ y) * K(y,T(z,x)) = y \ (x * (T(y,z) / x))
    ]]></literal>
    <justification jstring="[para(12208(a,1),14161(a,1,2))].">
      <j1 rule="para" parents="12208 14161"/>
    </justification>
  </clause>

  <clause id="14163">
    <literal><![CDATA[
      K(x \ y,x) \ K(y,T(z,x)) = y \ (x * (T(y,z) / x))
    ]]></literal>
    <justification jstring="[hyper(4585,a,14162,a)].">
      <j1 rule="hyper" parents="4585 14162"/>
    </justification>
  </clause>

  <clause id="14164">
    <literal><![CDATA[
      T(((a(x,y,z) \ 1) * u) * a(x,y,z),a(x,y,z) \ u) = L(u,a(x,y,z),a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(333,a,2599,a(flip),b,13380,a),flip(a)].">
      <j1 rule="hyper" parents="333 2599 13380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14165">
    <literal><![CDATA[
      K(x * (y * (x \ 1)),z) = K(y,T(z,x \ 1))
    ]]></literal>
    <justification jstring="[hyper(34,a,6504,a,b,13399,a),flip(a)].">
      <j1 rule="hyper" parents="34 6504 13399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14166">
    <literal><![CDATA[
      K(x * (y * (x \ 1)),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(14165(a,2),7282(a,1))].">
      <j1 rule="para" parents="14165 7282"/>
    </justification>
  </clause>

  <clause id="14167">
    <literal><![CDATA[
      K(x,T(y,y \ (z * (y \ u))) * w) = K(x,T(y,y \ (z * u)) * w)
    ]]></literal>
    <justification jstring="[para(13417(a,1),13419(a,1,2,1))].">
      <j1 rule="para" parents="13417 13419"/>
    </justification>
  </clause>

  <clause id="14168">
    <literal><![CDATA[
      T(x,T((y / z) \ K(y,u),w)) = T(x,T((z / y) * K(y,u),w))
    ]]></literal>
    <justification jstring="[para(13162(a,1),13450(a,1,2,1))].">
      <j1 rule="para" parents="13162 13450"/>
    </justification>
  </clause>

  <clause id="14169">
    <literal><![CDATA[
      ((x * ((x * y) / x)) / z) \ y = ((x * y) / z) \ T(y,T(x,y))
    ]]></literal>
    <justification jstring="[para(111(a,1),13568(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="111 13568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14170">
    <literal><![CDATA[
      ((x * ((x * y) / x)) / z) \ y = ((x * y) / z) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(3613(a,1),14169(a,2,2))].">
      <j1 rule="para" parents="3613 14169"/>
    </justification>
  </clause>

  <clause id="14171">
    <literal><![CDATA[
      K(x * (y \ 1),y * (x \ z)) = K(x / y,(x * (y \ 1)) \ z)
    ]]></literal>
    <justification jstring="[hyper(13421,a,13636,a)].">
      <j1 rule="hyper" parents="13421 13636"/>
    </justification>
  </clause>

  <clause id="14172">
    <literal><![CDATA[
      K(x / y,(x * (y \ 1)) \ z) = K(x / y,y * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(13493,a,14171,a),flip(a)].">
      <j1 rule="hyper" parents="13493 14171"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14173">
    <literal><![CDATA[
      K(x / y,(x * (y \ 1)) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,(x \ z) * y) = u
    ]]></literal>
    <justification jstring="[para(14172(a,2),12251(a,1))].">
      <j1 rule="para" parents="14172 12251"/>
    </justification>
  </clause>

  <clause id="14174">
    <literal><![CDATA[
      K(x / y,(x / y) \ z) = K(y \ x,(x \ z) * y)
    ]]></literal>
    <justification jstring="[hyper(14173,a,10659,a),flip(a)].">
      <j1 rule="hyper" parents="14173 10659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14175">
    <literal><![CDATA[
      K(x / y,(x / y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,(x \ z) * y) = u
    ]]></literal>
    <justification jstring="[para(10659(a,1),14173(a,1))].">
      <j1 rule="para" parents="10659 14173"/>
    </justification>
  </clause>

  <clause id="14176">
    <literal><![CDATA[
      K(x \ y,(y \ z) * x) * K(y,K(x,R(y / x,u,w) \ z)) = K(x \ y,R(y / x,u,w) \ z)
    ]]></literal>
    <justification jstring="[para(14174(a,1),10662(a,1,1))].">
      <j1 rule="para" parents="14174 10662"/>
    </justification>
  </clause>

  <clause id="14177">
    <literal><![CDATA[
      L(x,y,z) * a(u,w,K(z \ 1,x)) = L(T(x,a(z \ 1,w,u)),y,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,25,a,b,13807,a),flip(a)].">
      <j1 rule="hyper" parents="333 25 13807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14178">
    <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(13852(a,1),13932(a,1))].">
      <j1 rule="para" parents="13852 13932"/>
    </justification>
  </clause>

  <clause id="14179">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(u / w,y)) = K(x,L(y,z,u / (y * w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,11150,a(flip),b,13861,a)].">
      <j1 rule="hyper" parents="63 11150 13861"/>
    </justification>
  </clause>

  <clause id="14180">
    <literal><![CDATA[
      K(x,L(L(y,z,u),z,u \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,13766,a(flip),b,13988,a),flip(a)].">
      <j1 rule="hyper" parents="63 13766 13988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14181">
    <literal><![CDATA[
      K(x,L(L(y,z,u \ 1),z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(30(a,1),14180(a,1,2))].">
      <j1 rule="para" parents="30 14180"/>
    </justification>
  </clause>

  <clause id="14182">
    <literal><![CDATA[
      K(x,L((y * z) \ u,z,y \ 1)) = K(x,z \ (y \ u))
    ]]></literal>
    <justification jstring="[para(311(a,1),14180(a,1,2,1))].">
      <j1 rule="para" parents="311 14180"/>
    </justification>
  </clause>

  <clause id="14183">
    <literal><![CDATA[
      x * (y * K(z,L(u,y,x \ 1))) = (x * y) * K(z,u)
    ]]></literal>
    <justification jstring="[para(14181(a,1),10874(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14181 10874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14184">
    <literal><![CDATA[
      (K(x,L(y,z,u \ 1)) * z) * u = K(x,y) * (z * u)
    ]]></literal>
    <justification jstring="[para(14181(a,1),13872(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14181 13872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14185">
    <literal><![CDATA[
      (x \ y) * K(z,L(u,y,x \ 1)) = x \ (y * K(z,u))
    ]]></literal>
    <justification jstring="[para(14181(a,1),14044(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14181 14044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14186">
    <literal><![CDATA[
      K(x,L(y,z,u \ 1)) * (z / u) = (K(x,y) * z) / u
    ]]></literal>
    <justification jstring="[para(14181(a,1),14063(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="14181 14063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14187">
    <literal><![CDATA[
      K(x,L(T(y,z * u),u,z \ 1)) = K(x,u \ (z \ (y * (z * u))))
    ]]></literal>
    <justification jstring="[para(22(a,2),14182(a,1,2,1))].">
      <j1 rule="para" parents="22 14182"/>
    </justification>
  </clause>

  <clause id="14188">
    <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(85(a,1),14182(a,1,2,1))].">
      <j1 rule="para" parents="85 14182"/>
    </justification>
  </clause>

  <clause id="14189">
    <literal><![CDATA[
      x * K(y,L(T(z,u * x),x,u \ 1)) = u \ (K(y,z) * (u * x))
    ]]></literal>
    <justification jstring="[hyper(121,a,6390,a(flip),b,14183,a),flip(a)].">
      <j1 rule="hyper" parents="121 6390 14183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14190">
    <literal><![CDATA[
      x * (y * K(z,L(u,y,x \ u))) = (x * y) * K(z,u)
    ]]></literal>
    <justification jstring="[para(14002(a,1),14183(a,1,2,2))].">
      <j1 rule="para" parents="14002 14183"/>
    </justification>
  </clause>

  <clause id="14191">
    <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(5742(a,1),14184(a,2,2))].">
      <j1 rule="para" parents="5742 14184"/>
    </justification>
  </clause>

  <clause id="14192">
    <literal><![CDATA[
      K(x,L(y \ (z * u),y,z \ 1)) = K(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[hyper(34,a,10996,a(flip),b,14185,a),flip(a)].">
      <j1 rule="hyper" parents="34 10996 14185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14193">
    <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(13583(a,1),14190(a,2,1))].">
      <j1 rule="para" parents="13583 14190"/>
    </justification>
  </clause>

  <clause id="14194">
    <literal><![CDATA[
      x * K(y,x \ (z \ (u * (z * x)))) = z \ (K(y,u) * (z * x))
    ]]></literal>
    <justification jstring="[para(14187(a,1),14189(a,1,2))].">
      <j1 rule="para" parents="14187 14189"/>
    </justification>
  </clause>

  <clause id="14195">
    <literal><![CDATA[
      x \ (K(y,R(z,x,u)) * (x * u)) = u * K(y,u \ (x \ ((z * x) * u)))
    ]]></literal>
    <justification jstring="[para(107(a,1),14194(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="107 14194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14196">
    <literal><![CDATA[
      K(x,T(y,y \ (z * u)) * w) = K(x,T(y,z * (y \ u)) * w)
    ]]></literal>
    <justification jstring="[hyper(12771,a,14167,a),flip(a)].">
      <j1 rule="hyper" parents="12771 14167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14197">
    <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(14196(a,1),12771(a,1))].">
      <j1 rule="para" parents="14196 12771"/>
    </justification>
  </clause>

  <clause id="14198">
    <literal><![CDATA[
      L(T(x,a(y \ 1,z,u)),w,y) = L(x,w,y) * a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(11162(a,1),14177(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11162 14177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14199">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (y \ T(R(y,z,u),T(x,y))) = R(y,z,u) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(13864(a,1),13483(a,1,1))].">
      <j1 rule="para" parents="13864 13483"/>
    </justification>
  </clause>

  <clause id="14200">
    <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(10851(a,1),13503(a,1,1))].">
      <j1 rule="para" parents="10851 13503"/>
    </justification>
  </clause>

  <clause id="14201">
    <literal><![CDATA[
      K(x / (a(y,z,y) \ (u \ K(y * z,y))),w) = K(x * (K(y,z) * u),w)
    ]]></literal>
    <justification jstring="[para(12850(a,1),13632(a,1,1,2))].">
      <j1 rule="para" parents="12850 13632"/>
    </justification>
  </clause>

  <clause id="14203">
    <literal><![CDATA[
      K(T(x / y,z) \ 1,L(u,y,y \ z)) = K((x * (y \ z)) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(333,a,5852,a(flip),b,13947,a),flip(a)].">
      <j1 rule="hyper" parents="333 5852 13947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14204">
    <literal><![CDATA[
      K((x / y) \ 1,T(L(z,y,y \ u),u)) = K((x * (y \ u)) \ u,z)
    ]]></literal>
    <justification jstring="[hyper(6692,a,14203,a)].">
      <j1 rule="hyper" parents="6692 14203"/>
    </justification>
  </clause>

  <clause id="14205">
    <literal><![CDATA[
      K((x / y) \ 1,L(T(z,u),y,y \ u)) = K((x * (y \ u)) \ u,z)
    ]]></literal>
    <justification jstring="[para(25(a,2),14204(a,1,2))].">
      <j1 rule="para" parents="25 14204"/>
    </justification>
  </clause>

  <clause id="14206">
    <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(6785(a,1),13950(a,1,1,3))].">
      <j1 rule="para" parents="6785 13950"/>
    </justification>
  </clause>

  <clause id="14207">
    <literal><![CDATA[
      a(x,y,K(z,(u / y) \ z)) \ K(x,(y * z) / u) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[para(9624(a,1),13958(a,1,1,3))].">
      <j1 rule="para" parents="9624 13958"/>
    </justification>
  </clause>

  <clause id="14208">
    <literal><![CDATA[
      (x * y) * K(z,(x * y) \ (u * y)) = (K(z,u / x) * x) * y
    ]]></literal>
    <justification jstring="[hyper(13873,a,13968,a),flip(a)].">
      <j1 rule="hyper" parents="13873 13968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14209">
    <literal><![CDATA[
      (x * y) * K(z,(x * y) \ (u * y)) = (x * K(z,x \ u)) * y
    ]]></literal>
    <justification jstring="[para(6497(a,1),14208(a,2,1))].">
      <j1 rule="para" parents="6497 14208"/>
    </justification>
  </clause>

  <clause id="14210">
    <literal><![CDATA[
      R(T(x * K(y,x),z),y,u) \ ((y * x) * u) = (y * K(z,y \ (y * x))) * u
    ]]></literal>
    <justification jstring="[hyper(8973,a,14209,a)].">
      <j1 rule="hyper" parents="8973 14209"/>
    </justification>
  </clause>

  <clause id="14211">
    <literal><![CDATA[
      K(x,L(y,z,L(u,w,v5) \ u)) = K(x,L(y,z,a(v5,w,u)))
    ]]></literal>
    <justification jstring="[hyper(14058,a,13935,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="14058 13935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14212">
    <literal><![CDATA[
      L(K(x,K(y,z)),z * K(x,y),L(u,z,K(x,y))) \ (K(x,y) * (z * u)) = (z * K(x,y)) * L(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(6763(a,1),14074(a,1,1,1))].">
      <j1 rule="para" parents="6763 14074"/>
    </justification>
  </clause>

  <clause id="14213">
    <literal><![CDATA[
      x * K(y,x \ (z \ ((u * z) * x))) = z \ ((K(y,u) * z) * x)
    ]]></literal>
    <justification jstring="[para(11580(a,1),14195(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11580 14195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14214">
    <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(121,a,14213,a(flip),b,3624,a)].">
      <j1 rule="hyper" parents="121 14213 3624"/>
    </justification>
  </clause>

  <clause id="14215">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (y \ R(T(y,T(x,y)),z,u)) = R(y,z,u) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(27(a,2),14199(a,1,2,2))].">
      <j1 rule="para" parents="27 14199"/>
    </justification>
  </clause>

  <clause id="14216">
    <literal><![CDATA[
      K(x,L(y,z,u)) * T(u * (z / y),K(x,y)) = u * (z / T(y,x))
    ]]></literal>
    <justification jstring="[para(10862(a,1),14200(a,1,1))].">
      <j1 rule="para" parents="10862 14200"/>
    </justification>
  </clause>

  <clause id="14217">
    <literal><![CDATA[
      K((x / (y \ K(z * u,z))) * a(z,u,z),w) = K(x * (K(z,u) * y),w)
    ]]></literal>
    <justification jstring="[para(12854(a,1),14201(a,1,1))].">
      <j1 rule="para" parents="12854 14201"/>
    </justification>
  </clause>

  <clause id="14218">
    <literal><![CDATA[
      a(x,y,K(z,u / y)) \ K(z,(y * x) / u) = K(z,y / (u / x))
    ]]></literal>
    <justification jstring="[para(13745(a,1),14207(a,1,1))].">
      <j1 rule="para" parents="13745 14207"/>
    </justification>
  </clause>

  <clause id="14219">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (y \ R(T(y,x),z,u)) = R(y,z,u) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(3613(a,1),14215(a,1,2,2,1))].">
      <j1 rule="para" parents="3613 14215"/>
    </justification>
  </clause>

  <clause id="14220">
    <literal><![CDATA[
      T(x,L(y,z,u)) \ R(T(x,y),z,u) = R(x,z,u) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(10910,a,14219,a)].">
      <j1 rule="hyper" parents="10910 14219"/>
    </justification>
  </clause>

  <clause id="14221">
    <literal><![CDATA[
      T(x,L(y,z,u)) \ R(T(x,y),z,u) = x \ R(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(333,a,1314,a(flip),b,14220,a),flip(a)].">
      <j1 rule="hyper" parents="333 1314 14220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14222">
    <literal><![CDATA[
      K(x / (y \ K(z * u,z)),w) = K(x * (K(z,u) * y),w)
    ]]></literal>
    <justification jstring="[hyper(12623,a,14217,a)].">
      <j1 rule="hyper" parents="12623 14217"/>
    </justification>
  </clause>

  <clause id="14223">
    <literal><![CDATA[
      K(x * (K(y,y * z) * u),w) = K(x * (K(y,z) * u),w)
    ]]></literal>
    <justification jstring="[hyper(13510,a,14222,a)].">
      <j1 rule="hyper" parents="13510 14222"/>
    </justification>
  </clause>

  <clause id="14225">
    <literal><![CDATA[
      K(x,y) * L(K(x,y) \ (z \ 1),u,w) = L(z \ K(x,y),u,w) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,5994,a(flip),b,13193,a),flip(a)].">
      <j1 rule="hyper" parents="333 5994 13193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14226">
    <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(13207(a,1),13452(a,1))].">
      <j1 rule="para" parents="13207 13452"/>
    </justification>
  </clause>

  <clause id="14227">
    <literal><![CDATA[
      T(x,T(y / (1 / z),u) * w) = T(x,T(y / (z \ 1),u) * w)
    ]]></literal>
    <justification jstring="[para(13224(a,1),13297(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13224 13297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14228">
    <literal><![CDATA[
      T(x,T(y / (1 / z),z \ 1) * u) = T(x,((z \ 1) \ y) * u)
    ]]></literal>
    <justification jstring="[para(113(a,1),14227(a,2,2,1))].">
      <j1 rule="para" parents="113 14227"/>
    </justification>
  </clause>

  <clause id="14229">
    <literal><![CDATA[
      T(x,((1 / y) \ z) * u) = T(x,((y \ 1) \ z) * u)
    ]]></literal>
    <justification jstring="[para(2990(a,1),14228(a,1,2,1))].">
      <j1 rule="para" parents="2990 14228"/>
    </justification>
  </clause>

  <clause id="14230">
    <literal><![CDATA[
      T((x / y) \ 1,x) \ K(x \ y,y \ x) = T(x,(x / y) \ 1) / y
    ]]></literal>
    <justification jstring="[para(3512(a,1),13445(a,1,2))].">
      <j1 rule="para" parents="3512 13445"/>
    </justification>
  </clause>

  <clause id="14231">
    <literal><![CDATA[
      K(x \ y,y \ x) / (T(x,(x / y) \ 1) / y) = T((x / y) \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(198,a,14230,a)].">
      <j1 rule="hyper" parents="198 14230"/>
    </justification>
  </clause>

  <clause id="14232">
    <literal><![CDATA[
      K(x \ y,y \ x) / (T(x,x \ y) / y) = T((x / y) \ 1,x)
    ]]></literal>
    <justification jstring="[para(3593(a,1),14231(a,1,2,1))].">
      <j1 rule="para" parents="3593 14231"/>
    </justification>
  </clause>

  <clause id="14233">
    <literal><![CDATA[
      1 / T(T(x,x \ y) / y,x \ y) = T((x / y) \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(12738,a,14232,a)].">
      <j1 rule="hyper" parents="12738 14232"/>
    </justification>
  </clause>

  <clause id="14234">
    <literal><![CDATA[
      1 / R((x \ y) \ 1,x \ y,x) = T((x / y) \ 1,x)
    ]]></literal>
    <justification jstring="[para(3782(a,1),14233(a,1,2))].">
      <j1 rule="para" parents="3782 14233"/>
    </justification>
  </clause>

  <clause id="14235">
    <literal><![CDATA[
      R((x \ y) \ 1,x \ y,x) = T((x / y) \ 1,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(192,a,14234,a),flip(a)].">
      <j1 rule="hyper" parents="192 14234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14236">
    <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(13647(a,2),13623(a,1))].">
      <j1 rule="para" parents="13647 13623"/>
    </justification>
  </clause>

  <clause id="14237">
    <literal><![CDATA[
      T(x,T(y \ T(z,z * u),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y \ T(z,u),w)) = v5
    ]]></literal>
    <justification jstring="[para(13719(a,2),8028(a,1))].">
      <j1 rule="para" parents="13719 8028"/>
    </justification>
  </clause>

  <clause id="14238">
    <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(13746(a,1),13933(a,2,2))].">
      <j1 rule="para" parents="13746 13933"/>
    </justification>
  </clause>

  <clause id="14239">
    <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(14238(a,2),10933(a,1))].">
      <j1 rule="para" parents="14238 10933"/>
    </justification>
  </clause>

  <clause id="14240">
    <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(110(a,1),14239(a,1,2,3,1,2))].">
      <j1 rule="para" parents="110 14239"/>
    </justification>
  </clause>

  <clause id="14241">
    <literal><![CDATA[
      K(x,L(y,z,(u * x) \ w)) = K(x,L(y,z,u \ w))
    ]]></literal>
    <justification jstring="[hyper(14240,a,xx),flip(a)].">
      <j1 rule="hyper" parents="14240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14242">
    <literal><![CDATA[
      K(x \ 1,L(y,z,x \ u)) = K(x \ 1,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(166(a,1),14241(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="166 14241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14243">
    <literal><![CDATA[
      K(x,R(y,z,u) \ 1) = K(x,L(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(13198,a,13953,a),flip(a)].">
      <j1 rule="hyper" parents="13198 13953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14244">
    <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(807(a,1),14243(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="807 14243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14245">
    <literal><![CDATA[
      x \ (1 / (K(y,z) * T(y,u))) = (x \ (1 / T(y,u))) * K(z,y)
    ]]></literal>
    <justification jstring="[para(6901(a,1),14050(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6901 14050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14247">
    <literal><![CDATA[
      (x \ (1 / T(y,z))) * K(u,y) = x \ (K(u,y) / T(y,z))
    ]]></literal>
    <justification jstring="[para(8056(a,1),14245(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8056 14245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14248">
    <literal><![CDATA[
      K(x,y) * L(K(y,x) * (z \ 1),u,w) = L(z \ K(x,y),u,w) * K(y,x)
    ]]></literal>
    <justification jstring="[para(4567(a,1),14225(a,1,2,1))].">
      <j1 rule="para" parents="4567 14225"/>
    </justification>
  </clause>

  <clause id="14249">
    <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(3678(a,1),13548(a,1,1,1))].">
      <j1 rule="para" parents="3678 13548"/>
    </justification>
  </clause>

  <clause id="14250">
    <literal><![CDATA[
      ((x * y) * z) / (x * ((y * (z * (u * u))) / (u * u))) = a(x,y,z * (u * u))
    ]]></literal>
    <justification jstring="[para(809(a,1),13594(a,1,2))].">
      <j1 rule="para" parents="809 13594"/>
    </justification>
  </clause>

  <clause id="14251">
    <literal><![CDATA[
      x \ R(x * R(x \ 1,y,z),x,y * z) = (x \ 1) * a(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(1927(a,1),13602(a,1,2))].">
      <j1 rule="para" parents="1927 13602"/>
    </justification>
  </clause>

  <clause id="14252">
    <literal><![CDATA[
      (x \ 1) * a(x \ 1,y,z) = x \ a(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(13692(a,1),14251(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13692 14251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14253">
    <literal><![CDATA[
      T((1 / x) \ a((1 / x) \ 1,y,z),x * a((1 / x) \ 1,y,z)) = x * a((1 / x) \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(451,a,14252,a(flip),b,195,a(flip))].">
      <j1 rule="hyper" parents="451 14252 195"/>
    </justification>
  </clause>

  <clause id="14254">
    <literal><![CDATA[
      (x * K(y,z)) * a(y,u,K(x / u,z)) = (K(y,T(z,x)) * u) * (u \ x)
    ]]></literal>
    <justification jstring="[para(6904(a,1),13734(a,1,2,3))].">
      <j1 rule="para" parents="6904 13734"/>
    </justification>
  </clause>

  <clause id="14255">
    <literal><![CDATA[
      (x * K(y,z)) * a(y,u,K(x / u,z)) = x * L(K(y,z),u,u \ x)
    ]]></literal>
    <justification jstring="[hyper(333,a,13897,a(flip),b,14254,a),flip(a)].">
      <j1 rule="hyper" parents="333 13897 14254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14256">
    <literal><![CDATA[
      a(x \ y,x,K(z,u)) = a(u,x,K(y / x,z))
    ]]></literal>
    <justification jstring="[hyper(9781,a,14255,a)].">
      <j1 rule="hyper" parents="9781 14255"/>
    </justification>
  </clause>

  <clause id="14257">
    <literal><![CDATA[
      a(x,y,K((y * z) / y,u)) = a(z,y,K(u,x))
    ]]></literal>
    <justification jstring="[para(9(a,1),14256(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 14256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14259">
    <literal><![CDATA[
      a(x,y,K(z,T(u,y))) = a(z,y,K(u,x))
    ]]></literal>
    <justification jstring="[para(6921(a,1),14257(a,1,3))].">
      <j1 rule="para" parents="6921 14257"/>
    </justification>
  </clause>

  <clause id="14260">
    <literal><![CDATA[
      K(x,L(y,z,u)) * ((y * z) * u) = R(y,z,u) * ((K(x,y) * z) * u)
    ]]></literal>
    <justification jstring="[para(11580(a,1),13885(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11580 13885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14261">
    <literal><![CDATA[
      R(x,y,z) * ((K(u,x) * y) * z) = (K(u,x) * (x * y)) * z
    ]]></literal>
    <justification jstring="[hyper(14086,a,14260,a),flip(a)].">
      <j1 rule="hyper" parents="14086 14260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14262">
    <literal><![CDATA[
      R(x,y,z) * ((K(u,x) * y) * z) = (x * (K(u,x) * y)) * z
    ]]></literal>
    <justification jstring="[para(4712(a,1),14261(a,2,1))].">
      <j1 rule="para" parents="4712 14261"/>
    </justification>
  </clause>

  <clause id="14263">
    <literal><![CDATA[
      R(x,K(y,x) * z,u) = R(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(35,a,107,a,b,14262,a)].">
      <j1 rule="hyper" parents="35 107 14262"/>
    </justification>
  </clause>

  <clause id="14264">
    <literal><![CDATA[
      R(x,T(y,x),z) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(2065(a,2),14263(a,1,2))].">
      <j1 rule="para" parents="2065 14263"/>
    </justification>
  </clause>

  <clause id="14271">
    <literal><![CDATA[
      R(x,y,z) * (T(y,x) * z) = (y * x) * z
    ]]></literal>
    <justification jstring="[hyper(125,a,14264,a(flip),b,247,a)].">
      <j1 rule="hyper" parents="125 14264 247"/>
    </justification>
  </clause>

  <clause id="14272">
    <literal><![CDATA[
      R(x,y,(y * x) \ z) \ z = T(y,x) * ((y * x) \ z)
    ]]></literal>
    <justification jstring="[para(14264(a,1),796(a,1,1))].">
      <j1 rule="para" parents="14264 796"/>
    </justification>
  </clause>

  <clause id="14273">
    <literal><![CDATA[
      ((x * y) * z) / (T(y,x) * (K(x,y) * z)) = R(x,y,K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(123,a,10007,a(flip),b,14271,a)].">
      <j1 rule="hyper" parents="123 10007 14271"/>
    </justification>
  </clause>

  <clause id="14274">
    <literal><![CDATA[
      (T(x,y) * z) * K(R(y,x,z),T(x,y) * z) = ((x * y) * z) / R(y,x,z)
    ]]></literal>
    <justification jstring="[hyper(123,a,14271,a(flip),b,4291,a),flip(a)].">
      <j1 rule="hyper" parents="123 14271 4291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14275">
    <literal><![CDATA[
      R(x,y,(y * x) \ z) \ z = y * ((x * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(333,a,10026,a(flip),b,14272,a),flip(a)].">
      <j1 rule="hyper" parents="333 10026 14272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14276">
    <literal><![CDATA[
      R(x,y,L(x \ 1,x,y)) \ y = y * ((x * y) \ y)
    ]]></literal>
    <justification jstring="[para(227(a,2),14275(a,1,1,3))].">
      <j1 rule="para" parents="227 14275"/>
    </justification>
  </clause>

  <clause id="14277">
    <literal><![CDATA[
      R(x,y,L(x,x,y)) \ y = y * ((x * y) \ y)
    ]]></literal>
    <justification jstring="[para(5572(a,1),14276(a,1,1))].">
      <j1 rule="para" parents="5572 14276"/>
    </justification>
  </clause>

  <clause id="14278">
    <literal><![CDATA[
      R(x,y,x) \ y = y * ((x * y) \ y)
    ]]></literal>
    <justification jstring="[para(10801(a,1),14277(a,1,1))].">
      <j1 rule="para" parents="10801 14277"/>
    </justification>
  </clause>

  <clause id="14280">
    <literal><![CDATA[
      T(T(x,K(y,z * R(u,z \ 1,u))),y * (R(u,z \ 1,u) \ (z \ 1))) = T(x,((z \ 1) * ((u * (z \ 1)) \ (z \ 1))) * y)
    ]]></literal>
    <justification jstring="[para(14278(a,1),12302(a,2,2,1))].">
      <j1 rule="para" parents="14278 12302"/>
    </justification>
  </clause>

  <clause id="14281">
    <literal><![CDATA[
      R(x,y,K(x,y) * z) = ((x * y) * z) / (y * z)
    ]]></literal>
    <justification jstring="[para(4250(a,1),14273(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4250 14273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14282">
    <literal><![CDATA[
      R(x,y,K(x,y) * z) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,20,a,b,14281,a),flip(a)].">
      <j1 rule="hyper" parents="333 20 14281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14284">
    <literal><![CDATA[
      R(x,y,K(x,y) \ z) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),14282(a,1,3)),flip(a)].">
      <j1 rule="para" parents="10 14282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14285">
    <literal><![CDATA[
      (T(x,y) * z) * K(y,L(T(x,y) * z,x,z)) = ((x * y) * z) / R(y,x,z)
    ]]></literal>
    <justification jstring="[para(13867(a,1),14274(a,1,2))].">
      <j1 rule="para" parents="13867 14274"/>
    </justification>
  </clause>

  <clause id="14286">
    <literal><![CDATA[
      K(x,(((y * x) * z) / R(x,y,z)) \ u) = K(x,(T(y,x) * z) \ u)
    ]]></literal>
    <justification jstring="[para(14285(a,1),7643(a,1,2,1))].">
      <j1 rule="para" parents="14285 7643"/>
    </justification>
  </clause>

  <clause id="14287">
    <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(14286(a,2),7651(a,1))].">
      <j1 rule="para" parents="14286 7651"/>
    </justification>
  </clause>

  <clause id="14288">
    <literal><![CDATA[
      K(x,x * (((y * x) * z) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * z) \ u) = w
    ]]></literal>
    <justification jstring="[para(11393(a,1),14287(a,1))].">
      <j1 rule="para" parents="11393 14287"/>
    </justification>
  </clause>

  <clause id="14290">
    <literal><![CDATA[
      K(x,L(y,a(z \ 1,z,u),L(u,z,z \ 1))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,13793,a(flip),b,14011,a),flip(a)].">
      <j1 rule="hyper" parents="333 13793 14011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14292">
    <literal><![CDATA[
      T(K(x,L((x * y) * z,y,z)),K(x,(y * x) * z)) = K(x,(y * x) * z)
    ]]></literal>
    <justification jstring="[para(10923(a,1),14025(a,1,1))].">
      <j1 rule="para" parents="10923 14025"/>
    </justification>
  </clause>

  <clause id="14293">
    <literal><![CDATA[
      K(x,L((x * y) * z,y,z)) = K(x,(y * x) * z)
    ]]></literal>
    <justification jstring="[hyper(5316,a,14292,a)].">
      <j1 rule="hyper" parents="5316 14292"/>
    </justification>
  </clause>

  <clause id="14296">
    <literal><![CDATA[
      K(x,L((y * z) \ u,u,y \ 1)) = K(x,z \ (y \ u))
    ]]></literal>
    <justification jstring="[hyper(14047,a,14182,a)].">
      <j1 rule="hyper" parents="14047 14182"/>
    </justification>
  </clause>

  <clause id="14297">
    <literal><![CDATA[
      K(x * (y \ z),(x * (y \ z)) \ z) = K(x * (y \ z),y / x)
    ]]></literal>
    <justification jstring="[hyper(14023,a,14108,a),flip(a)].">
      <j1 rule="hyper" parents="14023 14108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14298">
    <literal><![CDATA[
      K(x,L((y * z) \ u,u,y \ 1)) = K(x,z \ (R(1 / y,y,z) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,14133,a(flip),b,14124,a)].">
      <j1 rule="hyper" parents="63 14133 14124"/>
    </justification>
  </clause>

  <clause id="14300">
    <literal><![CDATA[
      K(x,y \ (R(1 / z,z,y) * u)) = K(x,y \ (z \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,14296,a(flip),b,14298,a),flip(a)].">
      <j1 rule="hyper" parents="63 14296 14298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14301">
    <literal><![CDATA[
      K(x,y \ ((z / y) \ u)) = K(x,y \ ((y / z) * u))
    ]]></literal>
    <justification jstring="[para(400(a,1),14300(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="400 14300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14302">
    <literal><![CDATA[
      K(x \ (y / (x \ 1)),z \ ((z / u) * w)) = K(y,T(z \ ((u / z) \ w),x))
    ]]></literal>
    <justification jstring="[hyper(13550,a,14301,a),flip(a)].">
      <j1 rule="hyper" parents="13550 14301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14303">
    <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(14302(a,1),13550(a,1))].">
      <j1 rule="para" parents="14302 13550"/>
    </justification>
  </clause>

  <clause id="14304">
    <literal><![CDATA[
      K(x,L(y \ (z / u),y,u) \ 1) = K(x,T((z / (y * u)) \ 1,y))
    ]]></literal>
    <justification jstring="[hyper(333,a,6420,a(flip),b,14159,a),flip(a)].">
      <j1 rule="hyper" parents="333 6420 14159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14305">
    <literal><![CDATA[
      K(x,L(y \ (z / u),y,u) \ 1) = K(x,T((y * u) / z,y))
    ]]></literal>
    <justification jstring="[hyper(333,a,8700,a(flip),b,14304,a),flip(a)].">
      <j1 rule="hyper" parents="333 8700 14304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14306">
    <literal><![CDATA[
      L(K(x,(y / z) \ u),u,z) = K(x,T((u * z) / y,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,9404,a(flip),b,14305,a)].">
      <j1 rule="hyper" parents="63 9404 14305"/>
    </justification>
  </clause>

  <clause id="14307">
    <literal><![CDATA[
      R(T(x * K(y,x),z),y,u) \ ((y * x) * u) = (y * K(z,x)) * u
    ]]></literal>
    <justification jstring="[para(9(a,1),14210(a,2,1,2,2))].">
      <j1 rule="para" parents="9 14210"/>
    </justification>
  </clause>

  <clause id="14308">
    <literal><![CDATA[
      K(x,(y * z) \ ((y * u) * z)) = (y * z) \ ((y * K(x,u)) * z)
    ]]></literal>
    <justification jstring="[para(14307(a,1),8954(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14307 8954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14309">
    <literal><![CDATA[
      K(x,(y * z) \ ((y * (u / y)) * z)) = R(T(K(x,y \ u),y * z),y,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,7114,a(flip),b,14308,a),flip(a)].">
      <j1 rule="hyper" parents="333 7114 14308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14310">
    <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(333,a,6379,a,b,14244,a),flip(a)].">
      <j1 rule="hyper" parents="333 6379 14244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14311">
    <literal><![CDATA[
      T(T(x,x * y) * K(x * y,z),y) = y \ T(T(x,y * x) * y,z)
    ]]></literal>
    <justification jstring="[para(12615(a,1),14249(a,1,1,2))].">
      <j1 rule="para" parents="12615 14249"/>
    </justification>
  </clause>

  <clause id="14312">
    <literal><![CDATA[
      T(T(x * K(x * y,z),x * y),y) = y \ T(T(x,y * x) * y,z)
    ]]></literal>
    <justification jstring="[para(6650(a,2),14311(a,1,1))].">
      <j1 rule="para" parents="6650 14311"/>
    </justification>
  </clause>

  <clause id="14314">
    <literal><![CDATA[
      T(T(x * K(x * y,z),y),x * y) = y \ T(T(x,y * x) * y,z)
    ]]></literal>
    <justification jstring="[hyper(437,a,14312,a)].">
      <j1 rule="hyper" parents="437 14312"/>
    </justification>
  </clause>

  <clause id="14315">
    <literal><![CDATA[
      T(T(x * K(x * y,z),y),x * y) = y \ T(T(x,x * y) * y,z)
    ]]></literal>
    <justification jstring="[para(3678(a,1),14314(a,2,2,1,1))].">
      <j1 rule="para" parents="3678 14314"/>
    </justification>
  </clause>

  <clause id="14316">
    <literal><![CDATA[
      ((x * y) * z) / (x * (y * ((z * (u * u)) / (u * u)))) = a(x,y,z * (u * u))
    ]]></literal>
    <justification jstring="[para(809(a,1),14250(a,1,2,2))].">
      <j1 rule="para" parents="809 14250"/>
    </justification>
  </clause>

  <clause id="14317">
    <literal><![CDATA[
      K(x,L((y / z) \ u,y / z,z) \ 1) = K(x,T(y / (u * z),y / z))
    ]]></literal>
    <justification jstring="[hyper(333,a,8700,a(flip),b,14310,a),flip(a)].">
      <j1 rule="hyper" parents="333 8700 14310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14318">
    <literal><![CDATA[
      K(x,T(y / (z * u),y / u)) = K(x,(u * z) \ (u * (y / u)))
    ]]></literal>
    <justification jstring="[hyper(5951,a,14317,a),flip(a)].">
      <j1 rule="hyper" parents="5951 14317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14319">
    <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(333,a,12700,a(flip),b,14318,a),flip(a)].">
      <j1 rule="hyper" parents="333 12700 14318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14320">
    <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(5197(a,1),14318(a,2,2,1))].">
      <j1 rule="para" parents="5197 14318"/>
    </justification>
  </clause>

  <clause id="14321">
    <literal><![CDATA[
      a(x,y,z * (u * u)) = ((x * y) * z) / (x * (y * z))
    ]]></literal>
    <justification jstring="[para(11(a,1),14316(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="11 14316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14322">
    <literal><![CDATA[
      a(x,y,z * (u * u)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,13588,a,b,14321,a),flip(a)].">
      <j1 rule="hyper" parents="333 13588 14321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14323">
    <literal><![CDATA[
      a(x,y,z \ 1) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(223(a,1),14322(a,1,3)),flip(a)].">
      <j1 rule="para" parents="223 14322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14324">
    <literal><![CDATA[
      a(x,y,1 / z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(228(a,1),14322(a,1,3))].">
      <j1 rule="para" parents="228 14322"/>
    </justification>
  </clause>

  <clause id="14325">
    <literal><![CDATA[
      a(x,y,z \ (u * u)) = a(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[para(443(a,1),14322(a,1,3))].">
      <j1 rule="para" parents="443 14322"/>
    </justification>
  </clause>

  <clause id="14326">
    <literal><![CDATA[
      a(x,y,(z * z) \ u) = a(x,y,u \ (z * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,3284,a(flip),b,14323,a),flip(a)].">
      <j1 rule="hyper" parents="63 3284 14323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14327">
    <literal><![CDATA[
      T(x,a(y,z,z) \ 1) = x
    ]]></literal>
    <justification jstring="[para(14323(a,1),10218(a,1,2,1))].">
      <j1 rule="para" parents="14323 10218"/>
    </justification>
  </clause>

  <clause id="14328">
    <literal><![CDATA[
      x / (a(y,z,z) \ 1) = (a(y,z,z) \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(6748,a,14327,a),flip(a)].">
      <j1 rule="hyper" parents="6748 14327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14329">
    <literal><![CDATA[
      a(x,y,z \ (u * u)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,14323,a(flip),b,14325,a),flip(a)].">
      <j1 rule="hyper" parents="333 14323 14325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14330">
    <literal><![CDATA[
      a(x,y,(z * z) \ u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(333,a,14329,a(flip),b,14326,a),flip(a)].">
      <j1 rule="hyper" parents="333 14329 14326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14331">
    <literal><![CDATA[
      a(x,y \ 1,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(1647,a,14330,a)].">
      <j1 rule="hyper" parents="1647 14330"/>
    </justification>
  </clause>

  <clause id="14333">
    <literal><![CDATA[
      a(x,y,(z \ 1) \ u) = a(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(710(a,1),14330(a,1,3)),flip(a)].">
      <j1 rule="para" parents="710 14330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14334">
    <literal><![CDATA[
      a(x,1 / y,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(3218,a,14331,a)].">
      <j1 rule="hyper" parents="3218 14331"/>
    </justification>
  </clause>

  <clause id="14335">
    <literal><![CDATA[
      L(x,y,y) \ x = a(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,2602,a(flip),b,14331,a)].">
      <j1 rule="hyper" parents="63 2602 14331"/>
    </justification>
  </clause>

  <clause id="14336">
    <literal><![CDATA[
      a(1 / x,x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      1 = u
    ]]></literal>
    <justification jstring="[para(14334(a,1),13108(a,1))].">
      <j1 rule="para" parents="14334 13108"/>
    </justification>
  </clause>

  <clause id="14337">
    <literal><![CDATA[
      L(x \ L(x,y,y),z,u) \ 1 = a(y,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,4035,a(flip),b,14335,a)].">
      <j1 rule="hyper" parents="63 4035 14335"/>
    </justification>
  </clause>

  <clause id="14339">
    <literal><![CDATA[
      a(x,x,y) \ 1 = y \ L(y,x,x)
    ]]></literal>
    <justification jstring="[para(14335(a,1),3253(a,1,1))].">
      <j1 rule="para" parents="14335 3253"/>
    </justification>
  </clause>

  <clause id="14340">
    <literal><![CDATA[
      L(a(x,x,K(y,z) * u),L(K(y,z) * u,x,x),K(z,y)) = (K(z,y) * L(K(y,z) * u,x,x)) \ u
    ]]></literal>
    <justification jstring="[para(14335(a,1),4581(a,1,1))].">
      <j1 rule="para" parents="14335 4581"/>
    </justification>
  </clause>

  <clause id="14341">
    <literal><![CDATA[
      T(x,(y * a(z,z,y)) \ u) = T(x,L(y \ 1,z,z) * u)
    ]]></literal>
    <justification jstring="[para(14335(a,1),13382(a,1,2,1,2))].">
      <j1 rule="para" parents="14335 13382"/>
    </justification>
  </clause>

  <clause id="14342">
    <literal><![CDATA[
      x * (a(y,y,x) \ 1) = L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(126,a,14339,a,b,xx)].">
      <j1 rule="hyper" parents="126 14339"/>
    </justification>
  </clause>

  <clause id="14343">
    <literal><![CDATA[
      T(x,(y \ L(y,z,z)) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,a(z,z,y) \ u) = w
    ]]></literal>
    <justification jstring="[para(14339(a,1),13608(a,1,2,1))].">
      <j1 rule="para" parents="14339 13608"/>
    </justification>
  </clause>

  <clause id="14344">
    <literal><![CDATA[
      L(a(x,x,y) \ 1,z,u) \ 1 = a(x,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(14339(a,2),14337(a,1,1,1))].">
      <j1 rule="para" parents="14339 14337"/>
    </justification>
  </clause>

  <clause id="14345">
    <literal><![CDATA[
      T(x,(L(y \ 1,z,z) \ 1) \ u) = T(x,(y * a(z,z,y)) \ u)
    ]]></literal>
    <justification jstring="[hyper(333,a,13206,a,b,14341,a)].">
      <j1 rule="hyper" parents="333 13206 14341"/>
    </justification>
  </clause>

  <clause id="14346">
    <literal><![CDATA[
      T(x,(y * a(z,z,y)) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,L(y \ 1,z,z) * u) = w
    ]]></literal>
    <justification jstring="[para(14345(a,1),13423(a,1))].">
      <j1 rule="para" parents="14345 13423"/>
    </justification>
  </clause>

  <clause id="14347">
    <literal><![CDATA[
      K(K(x,y) * z,(K(x,y) * z) \ K(x,y)) = (z \ 1) \ T(1 / z,K(x,y))
    ]]></literal>
    <justification jstring="[para(13680(a,1),13373(a,2,2))].">
      <j1 rule="para" parents="13680 13373"/>
    </justification>
  </clause>

  <clause id="14348">
    <literal><![CDATA[
      K(K(x,y) * z,(K(x,y) * z) \ K(x,y)) = z * T(1 / z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(333,a,3577,a(flip),b,14347,a),flip(a)].">
      <j1 rule="hyper" parents="333 3577 14347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14349">
    <literal><![CDATA[
      K(K(x,y) * z,z \ 1) = z * T(1 / z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(5949,a,14348,a)].">
      <j1 rule="hyper" parents="5949 14348"/>
    </justification>
  </clause>

  <clause id="14351">
    <literal><![CDATA[
      K(x,y) * (y / L((x * y) / x,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      (L(y * K(x,y),z,u) \ y) * K(x,y) = w
    ]]></literal>
    <justification jstring="[para(13462(a,1),13415(a,1))].">
      <j1 rule="para" parents="13462 13415"/>
    </justification>
  </clause>

  <clause id="14353">
    <literal><![CDATA[
      x * (K(y,L(x,z,u)) * K(w,L(y,z,u))) = (R(y,z,u) * x) / R(T(y,w),z,u)
    ]]></literal>
    <justification jstring="[para(13864(a,1),13903(a,1,2,2))].">
      <j1 rule="para" parents="13864 13903"/>
    </justification>
  </clause>

  <clause id="14354">
    <literal><![CDATA[
      (L(x,y,z) \ x) * (L(x,y,z) * K(u,w)) = x * K(u,L(w,x,a(z,y,x)))
    ]]></literal>
    <justification jstring="[para(14211(a,1),14045(a,2,2))].">
      <j1 rule="para" parents="14211 14045"/>
    </justification>
  </clause>

  <clause id="14355">
    <literal><![CDATA[
      (R(x,y,z) * u) / R(T(x,w),y,z) = (L(x,y,z) * u) / L(T(x,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,11132,a(flip),b,14353,a),flip(a)].">
      <j1 rule="hyper" parents="63 11132 14353"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14356">
    <literal><![CDATA[
      L(K(x,y),z,u) \ (u * (K(x,y) * z)) = z * T(u,K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(10154(a,1),13894(a,1,1))].">
      <j1 rule="para" parents="10154 13894"/>
    </justification>
  </clause>

  <clause id="14357">
    <literal><![CDATA[
      L(K(x,y),z,u) * (u * (K(y,x) * z)) = z * T(u,K(y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(9515,a,14356,a)].">
      <j1 rule="hyper" parents="9515 14356"/>
    </justification>
  </clause>

  <clause id="14359">
    <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(63,a,11061,a,b,14357,a)].">
      <j1 rule="hyper" parents="63 11061 14357"/>
    </justification>
  </clause>

  <clause id="14360">
    <literal><![CDATA[
      x / L(y * K(z,u),w,a(w,v5,K(v6,v7))) != v8 * a(v8,y,K(z,u))
    ]]></literal>
    <literal><![CDATA[
      (v8 * y) * K(z,u) = x
    ]]></literal>
    <justification jstring="[para(14098(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="14098 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14361">
    <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(14139(a,1),14125(a,2,1))].">
      <j1 rule="para" parents="14139 14125"/>
    </justification>
  </clause>

  <clause id="14362">
    <literal><![CDATA[
      K(x,K(y,z \ (u * ((u \ z) * w)))) = K(x,K(y,L(w,z,u)))
    ]]></literal>
    <justification jstring="[hyper(333,a,13948,a(flip),b,14361,a),flip(a)].">
      <j1 rule="hyper" parents="333 13948 14361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14363">
    <literal><![CDATA[
      K(x,K(y,L(z,u \ w,u))) = K(x,K(y,L(z,w,u)))
    ]]></literal>
    <justification jstring="[para(98(a,1),14362(a,1,2,2))].">
      <j1 rule="para" parents="98 14362"/>
    </justification>
  </clause>

  <clause id="14364">
    <literal><![CDATA[
      K(x,K(y,L(z,u / w,w))) = K(x,K(y,L(z,u,w)))
    ]]></literal>
    <justification jstring="[para(10083(a,2),14363(a,1,2,2))].">
      <j1 rule="para" parents="10083 14363"/>
    </justification>
  </clause>

  <clause id="14365">
    <literal><![CDATA[
      x \ (T(y,z) * L(T(y,z) \ y,u,w)) = (x \ T(y,z)) * L(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[para(10(a,1),13371(a,1,2,2,1,2))].">
      <j1 rule="para" parents="10 13371"/>
    </justification>
  </clause>

  <clause id="14366">
    <literal><![CDATA[
      x \ (T(y,z) * L(K(z,y),u,w)) = (x \ T(y,z)) * L(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[para(4205(a,2),14365(a,1,2,2,1))].">
      <j1 rule="para" parents="4205 14365"/>
    </justification>
  </clause>

  <clause id="14367">
    <literal><![CDATA[
      x \ (T(y,z) * K(z,L(y,u,w))) = (x \ T(y,z)) * L(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[para(10851(a,1),14366(a,1,2,2))].">
      <j1 rule="para" parents="10851 14366"/>
    </justification>
  </clause>

  <clause id="14368">
    <literal><![CDATA[
      x \ T(y * K(z,L(y,u,w)),z) = (x \ T(y,z)) * L(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[para(6650(a,2),14367(a,1,2))].">
      <j1 rule="para" parents="6650 14367"/>
    </justification>
  </clause>

  <clause id="14369">
    <literal><![CDATA[
      K(x \ ((y \ z) \ 1),((y \ z) \ 1) * (T(y,u) \ z)) = K(u,K(((y \ z) \ 1) / x,y))
    ]]></literal>
    <justification jstring="[hyper(333,a,6785,a,b,13461,a),flip(a)].">
      <j1 rule="hyper" parents="333 6785 13461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14370">
    <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(5767(a,1),13551(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5767 13551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14371">
    <literal><![CDATA[
      K(x,y * K((z * (1 / u)) \ w,u)) = K(x,y * K(u * (z \ w),w \ z))
    ]]></literal>
    <justification jstring="[para(5766(a,1),14370(a,2,2,2))].">
      <j1 rule="para" parents="5766 14370"/>
    </justification>
  </clause>

  <clause id="14373">
    <literal><![CDATA[
      K(x,y * K(z * (u \ w),w \ u)) = K(x,y * K(z * (u \ w),z))
    ]]></literal>
    <justification jstring="[para(13296(a,1),14371(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13296 14371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14374">
    <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(14373(a,2),12754(a,1))].">
      <j1 rule="para" parents="14373 12754"/>
    </justification>
  </clause>

  <clause id="14375">
    <literal><![CDATA[
      K(x * y,L(z,u,u \ 1)) = (x \ T(y * x,z)) * (T(y,x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(13638,a,13521,a),flip(a)].">
      <j1 rule="hyper" parents="13638 13521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14376">
    <literal><![CDATA[
      (x \ T(y * x,z)) * (T(y,x) \ 1) = K(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(14106,a,14375,a),flip(a)].">
      <j1 rule="hyper" parents="14106 14375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14377">
    <literal><![CDATA[
      (x \ T(y * x,z)) * (T(y,x) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(14375(a,1),9476(a,1))].">
      <j1 rule="para" parents="14375 9476"/>
    </justification>
  </clause>

  <clause id="14378">
    <literal><![CDATA[
      a(x,y \ z,K(u,L(y,(y \ z) * u,y \ 1))) = K(x,((y \ z) * u) \ (y \ (z * u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,13987,a,b,14188,a)].">
      <j1 rule="hyper" parents="63 13987 14188"/>
    </justification>
  </clause>

  <clause id="14379">
    <literal><![CDATA[
      K(x,T(y / z,y / (u \ z))) = K(x,T(z,u) \ ((u \ z) * (y / (u \ z))))
    ]]></literal>
    <justification jstring="[para(10(a,1),14319(a,1,2,1,2))].">
      <j1 rule="para" parents="10 14319"/>
    </justification>
  </clause>

  <clause id="14380">
    <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(11261(a,1),14359(a,1,1))].">
      <j1 rule="para" parents="11261 14359"/>
    </justification>
  </clause>

  <clause id="14381">
    <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(6840(a,1),14380(a,1,1,2))].">
      <j1 rule="para" parents="6840 14380"/>
    </justification>
  </clause>

  <clause id="14382">
    <literal><![CDATA[
      K(x \ ((y \ z) \ 1),((y \ z) \ 1) * (T(y,u) \ z)) = K(u,K((y \ z) \ (x \ 1),y))
    ]]></literal>
    <justification jstring="[para(13292(a,1),14369(a,2,2))].">
      <j1 rule="para" parents="13292 14369"/>
    </justification>
  </clause>

  <clause id="14383">
    <literal><![CDATA[
      a(x,y \ z,K(u,L(y,(y \ z) * u,1))) = K(x,((y \ z) * u) \ (y \ (z * u)))
    ]]></literal>
    <justification jstring="[para(14001(a,1),14378(a,1,3))].">
      <j1 rule="para" parents="14001 14378"/>
    </justification>
  </clause>

  <clause id="14384">
    <literal><![CDATA[
      K(x,((y \ z) * u) \ (y \ (z * u))) = a(x,y \ z,K(u,y))
    ]]></literal>
    <justification jstring="[para(371(a,1),14383(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="371 14383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14385">
    <literal><![CDATA[
      K(x,((y \ z) * u) \ (y \ (z * u))) = a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(333,a,14082,a(flip),b,14384,a),flip(a)].">
      <j1 rule="hyper" parents="333 14082 14384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14386">
    <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(5256(a,1),14385(a,1,2,1))].">
      <j1 rule="para" parents="5256 14385"/>
    </justification>
  </clause>

  <clause id="14387">
    <literal><![CDATA[
      K(x \ ((y \ z) \ 1),((y \ z) \ 1) * (T(y,u) \ z)) = K(u,K(z \ (y * (x \ 1)),y))
    ]]></literal>
    <justification jstring="[para(6293(a,1),14382(a,2,2))].">
      <j1 rule="para" parents="6293 14382"/>
    </justification>
  </clause>

  <clause id="14388">
    <literal><![CDATA[
      K(x \ ((y \ z) \ 1),((y \ z) \ 1) * (T(y,u) \ z)) = K(y,K(u,z \ (y * (x \ 1))))
    ]]></literal>
    <justification jstring="[hyper(333,a,6788,a(flip),b,14387,a),flip(a)].">
      <j1 rule="hyper" parents="333 6788 14387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14389">
    <literal><![CDATA[
      K(x \ ((y \ z) \ 1),((y \ z) \ 1) * (T(y,u) \ z)) = K(y,K(u,z \ (x \ 1)))
    ]]></literal>
    <justification jstring="[hyper(333,a,10403,a(flip),b,14388,a),flip(a)].">
      <j1 rule="hyper" parents="333 10403 14388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14390">
    <literal><![CDATA[
      K(a(x,y,z),a(x,y,z) \ u) = u \ T(u,u / a(x,y,z))
    ]]></literal>
    <justification jstring="[para(12(a,1),13002(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12 13002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14391">
    <literal><![CDATA[
      K(a(x,y,z),a(x,y,z) \ u) = u \ T(u,a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(3363(a,1),14390(a,2,2))].">
      <j1 rule="para" parents="3363 14390"/>
    </justification>
  </clause>

  <clause id="14392">
    <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(14391(a,2),4306(a,1))].">
      <j1 rule="para" parents="14391 4306"/>
    </justification>
  </clause>

  <clause id="14393">
    <literal><![CDATA[
      K(x,a(y,z,u) \ x) = a(y,z,K(u,a(y,z,u) \ x))
    ]]></literal>
    <justification jstring="[hyper(14392,a,13539,a(flip))].">
      <j1 rule="hyper" parents="14392 13539"/>
    </justification>
  </clause>

  <clause id="14394">
    <literal><![CDATA[
      R(R(x,y,z),y * z,a(u,w,u)) = R(x,y,z * a(u,w,u))
    ]]></literal>
    <justification jstring="[hyper(544,a,13050,a),flip(a)].">
      <j1 rule="hyper" parents="544 13050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14395">
    <literal><![CDATA[
      R(x,y,z * a(u,w,u)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,12592,a(flip),b,14394,a),flip(a)].">
      <j1 rule="hyper" parents="63 12592 14394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14397">
    <literal><![CDATA[
      R(x,y,a(z,u,z) \ w) = R(x,y,w)
    ]]></literal>
    <justification jstring="[para(9247(a,1),14395(a,1,3)),flip(a)].">
      <j1 rule="para" parents="9247 14395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14398">
    <literal><![CDATA[
      R(x,y,T(z * u,z)) = R(x,y,u * z)
    ]]></literal>
    <justification jstring="[para(9256(a,1),14395(a,1,3))].">
      <j1 rule="para" parents="9256 14395"/>
    </justification>
  </clause>

  <clause id="14399">
    <literal><![CDATA[
      R(x,a(y,z,y) \ u,w) = R(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,13010,a,b,14397,a)].">
      <j1 rule="hyper" parents="63 13010 14397"/>
    </justification>
  </clause>

  <clause id="14400">
    <literal><![CDATA[
      R(x,y,z \ L(u,w,u)) = R(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(12813(a,1),14397(a,1,3))].">
      <j1 rule="para" parents="12813 14397"/>
    </justification>
  </clause>

  <clause id="14402">
    <literal><![CDATA[
      R(x,((y \ 1) * y) \ z,u) = R(x,z,u)
    ]]></literal>
    <justification jstring="[para(2445(a,1),14399(a,1,2,1))].">
      <j1 rule="para" parents="2445 14399"/>
    </justification>
  </clause>

  <clause id="14403">
    <literal><![CDATA[
      R(x,y,z * y) = R(x,y,y * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,10340,a(flip),b,14398,a),flip(a)].">
      <j1 rule="hyper" parents="63 10340 14398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14404">
    <literal><![CDATA[
      R(x,y,(z \ u) * z) = R(x,y,T(u,z))
    ]]></literal>
    <justification jstring="[para(10(a,1),14398(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="10 14398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14405">
    <literal><![CDATA[
      R(x,((y \ 1) * y) \ (((z \ 1) \ 1) \ u),w) = R(x,z \ u,w)
    ]]></literal>
    <justification jstring="[hyper(333,a,3157,a(flip),b,14402,a),flip(a)].">
      <j1 rule="hyper" parents="333 3157 14402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14406">
    <literal><![CDATA[
      R(x,y,z * (u / z)) = R(x,y,T(u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,5192,a(flip),b,14404,a)].">
      <j1 rule="hyper" parents="63 5192 14404"/>
    </justification>
  </clause>

  <clause id="14407">
    <literal><![CDATA[
      R(x,y,z \ T(u,u * w)) = R(x,y,z \ T(u,w))
    ]]></literal>
    <justification jstring="[para(3742(a,1),14400(a,1,3,2))].">
      <j1 rule="para" parents="3742 14400"/>
    </justification>
  </clause>

  <clause id="14408">
    <literal><![CDATA[
      R(x,y,z \ ((u \ w) \ w)) = R(x,y,z \ T(u,w))
    ]]></literal>
    <justification jstring="[para(11339(a,1),14400(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="11339 14400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14409">
    <literal><![CDATA[
      K(R(x / y,y,x \ T(z,u)) \ T(z,u),w) = K(y * (x \ T(z,z * u)),w)
    ]]></literal>
    <justification jstring="[para(14407(a,1),13650(a,1,1,1))].">
      <j1 rule="para" parents="14407 13650"/>
    </justification>
  </clause>

  <clause id="14410">
    <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(13146(a,1),14408(a,1,3,2,1)),flip(a)].">
      <j1 rule="para" parents="13146 14408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14411">
    <literal><![CDATA[
      R(x,y,z \ T(T(u,K(w,v5)) \ v6,K(w,T(v5,u)))) = R(x,y,z \ (((u \ v6) \ K(w,v5)) \ K(w,T(v5,u))))
    ]]></literal>
    <justification jstring="[para(13438(a,1),14408(a,1,3,2,1)),flip(a)].">
      <j1 rule="para" parents="13438 14408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14412">
    <literal><![CDATA[
      R(x,((y \ 1) \ ((z \ 1) * z)) \ u,w) = R(x,y \ u,w)
    ]]></literal>
    <justification jstring="[para(10150(a,1),14405(a,1,2))].">
      <j1 rule="para" parents="10150 14405"/>
    </justification>
  </clause>

  <clause id="14413">
    <literal><![CDATA[
      R(x,(y / ((z \ 1) \ 1)) \ u,w) = R(x,(y / z) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,11272,a(flip),b,14412,a)].">
      <j1 rule="hyper" parents="63 11272 14412"/>
    </justification>
  </clause>

  <clause id="14415">
    <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(6200(a,1),14410(a,1,3,2))].">
      <j1 rule="para" parents="6200 14410"/>
    </justification>
  </clause>

  <clause id="14416">
    <literal><![CDATA[
      K(x * (y \ T(z,z * u)),w) = K(x * (y \ T(z,u)),w)
    ]]></literal>
    <justification jstring="[para(527(a,1),14409(a,1,1)),flip(a)].">
      <j1 rule="para" parents="527 14409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14417">
    <literal><![CDATA[
      1 * K(x,L(y \ L(y,z,u),y,w)) = K(x,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[para(9859(a,1),13077(a,1,1))].">
      <j1 rule="para" parents="9859 13077"/>
    </justification>
  </clause>

  <clause id="14418">
    <literal><![CDATA[
      K(x,L(y \ L(y,z,u),y,w)) = K(x,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(127,a,14417,a)].">
      <j1 rule="hyper" parents="127 14417"/>
    </justification>
  </clause>

  <clause id="14420">
    <literal><![CDATA[
      K(x,a(y,z,u) \ 1) = K(x,u \ L(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,7858,a(flip),b,14418,a)].">
      <j1 rule="hyper" parents="63 7858 14418"/>
    </justification>
  </clause>

  <clause id="14422">
    <literal><![CDATA[
      T(x,a(y,z,u) \ 1) = T(x,u \ L(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(124,a,14420,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 14420 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14423">
    <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(14422(a,2),634(a,1,1))].">
      <j1 rule="para" parents="14422 634"/>
    </justification>
  </clause>

  <clause id="14424">
    <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(333,a,13086,a(flip),b,14423,a),flip(a)].">
      <j1 rule="hyper" parents="333 13086 14423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14425">
    <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(3215(a,1),13556(a,1,2))].">
      <j1 rule="para" parents="3215 13556"/>
    </justification>
  </clause>

  <clause id="14426">
    <literal><![CDATA[
      (L(x,y,z) * (u * K(x,L(w,y,z)))) / L(T(x,w),y,z) = (R(x,y,z) * u) / R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,14355,a(flip),b,13905,a)].">
      <j1 rule="hyper" parents="63 14355 13905"/>
    </justification>
  </clause>

  <clause id="14427">
    <literal><![CDATA[
      K(L(x,y,y \ 1) \ z,L(x,y,y \ 1)) = K((1 / y) \ ((y * x) \ z),x)
    ]]></literal>
    <justification jstring="[hyper(13527,a,14037,a),flip(a)].">
      <j1 rule="hyper" parents="13527 14037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14429">
    <literal><![CDATA[
      K(L(x,y,y \ 1) \ z,L(x,y,y \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y * ((y * x) \ z),x) = u
    ]]></literal>
    <justification jstring="[para(14427(a,2),13511(a,1))].">
      <j1 rule="para" parents="14427 13511"/>
    </justification>
  </clause>

  <clause id="14430">
    <literal><![CDATA[
      K(R(x,y,y \ 1) \ z,R(x,y,y \ 1)) = K((y \ 1) \ ((x * y) \ z),x)
    ]]></literal>
    <justification jstring="[hyper(13526,a,14038,a),flip(a)].">
      <j1 rule="hyper" parents="13526 14038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14432">
    <literal><![CDATA[
      K(R(x,y,y \ 1) \ z,R(x,y,y \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y * ((x * y) \ z),x) = u
    ]]></literal>
    <justification jstring="[para(14430(a,2),13425(a,1))].">
      <j1 rule="para" parents="14430 13425"/>
    </justification>
  </clause>

  <clause id="14433">
    <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(3143(a,1),14072(a,1,2))].">
      <j1 rule="para" parents="3143 14072"/>
    </justification>
  </clause>

  <clause id="14435">
    <literal><![CDATA[
      (L(x * K(y,x),z,u) \ x) * K(y,x) = x / ((y * L(x,z,u)) / T(y,x))
    ]]></literal>
    <justification jstring="[hyper(14351,a,13565,a)].">
      <j1 rule="hyper" parents="14351 13565"/>
    </justification>
  </clause>

  <clause id="14436">
    <literal><![CDATA[
      x / y != (L(x * K(z,x),u,w) \ x) * K(z,x)
    ]]></literal>
    <literal><![CDATA[
      (z * L(x,u,w)) / T(z,x) = y
    ]]></literal>
    <justification jstring="[para(14435(a,2),45(a,1)),flip(a)].">
      <j1 rule="para" parents="14435 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14437">
    <literal><![CDATA[
      (R(x,y,z) * u) / R(x,y,z) = (L(x,y,z) * u) / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,10919,a(flip),b,14426,a),flip(a)].">
      <j1 rule="hyper" parents="63 10919 14426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14438">
    <literal><![CDATA[
      T(x,y * T(z * T(u,u \ w),(u \ w) \ w)) = T(x,y * (T(z,T(u,w)) * T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(333,a,13698,a(flip),b,12747,a),flip(a)].">
      <j1 rule="hyper" parents="333 13698 12747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14439">
    <literal><![CDATA[
      L(x,y,((z \ u) * z) \ (u * (1 / z))) = L(x,y,K(u,z \ 1) / z)
    ]]></literal>
    <justification jstring="[para(8634(a,1),12843(a,1,3,1))].">
      <j1 rule="para" parents="8634 12843"/>
    </justification>
  </clause>

  <clause id="14440">
    <literal><![CDATA[
      L(x,y,K(z,z \ u) * (1 / z)) = L(x,y,K(u,z \ 1) / z)
    ]]></literal>
    <justification jstring="[para(10013(a,1),14439(a,1,3))].">
      <j1 rule="para" parents="10013 14439"/>
    </justification>
  </clause>

  <clause id="14441">
    <literal><![CDATA[
      L(x,y,K(z,u \ 1) / u) = L(x,y,K(u,u \ z) / u)
    ]]></literal>
    <justification jstring="[para(3560(a,1),14440(a,1,3)),flip(a)].">
      <j1 rule="para" parents="3560 14440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14442">
    <literal><![CDATA[
      ((x * ((y * (x / y)) \ y)) / x) \ 1 = x / (x * ((((x / (1 / (x \ y))) / x) \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(7567(a,1),13347(a,1,1,1,2))].">
      <j1 rule="para" parents="7567 13347"/>
    </justification>
  </clause>

  <clause id="14443">
    <literal><![CDATA[
      x / (x * ((((x / (1 / (x \ y))) / x) \ 1) \ 1)) = ((x / (x / y)) / x) \ 1
    ]]></literal>
    <justification jstring="[para(4827(a,1),14442(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4827 14442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14444">
    <literal><![CDATA[
      x / (x * ((1 / ((x / ((x \ y) \ 1)) / x)) \ 1)) = ((x / (x / y)) / x) \ 1
    ]]></literal>
    <justification jstring="[para(2909(a,2),14443(a,1,2,2,1))].">
      <j1 rule="para" parents="2909 14443"/>
    </justification>
  </clause>

  <clause id="14445">
    <literal><![CDATA[
      x / (x * ((x / ((x \ y) \ 1)) / x)) = ((x / (x / y)) / x) \ 1
    ]]></literal>
    <justification jstring="[para(79(a,1),14444(a,1,2,2))].">
      <j1 rule="para" parents="79 14444"/>
    </justification>
  </clause>

  <clause id="14447">
    <literal><![CDATA[
      x / (x / ((y / x) \ 1)) = ((x / (x / y)) / x) \ 1
    ]]></literal>
    <justification jstring="[para(10248(a,1),14445(a,1,2))].">
      <j1 rule="para" parents="10248 14445"/>
    </justification>
  </clause>

  <clause id="14448">
    <literal><![CDATA[
      1 / (x / (x / ((y / x) \ 1))) = (x / (x / y)) / x
    ]]></literal>
    <justification jstring="[hyper(197,a,14447,a,b,xx)].">
      <j1 rule="hyper" parents="197 14447"/>
    </justification>
  </clause>

  <clause id="14449">
    <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="[hyper(13716,a,xx),flip(a)].">
      <j1 rule="hyper" parents="13716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14450">
    <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(11896(a,1),14020(a,2,2))].">
      <j1 rule="para" parents="11896 14020"/>
    </justification>
  </clause>

  <clause id="14451">
    <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(13561(a,1),14450(a,1,2,3))].">
      <j1 rule="para" parents="13561 14450"/>
    </justification>
  </clause>

  <clause id="14452">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1) \ (y * u)) = K(x,(a(z \ 1,z,y) \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,13792,a(flip),b,14042,a),flip(a)].">
      <j1 rule="hyper" parents="63 13792 14042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14454">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1) \ (y * u)) = K(x,a(z \ 1,z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(333,a,13141,a(flip),b,14452,a),flip(a)].">
      <j1 rule="hyper" parents="333 13141 14452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14455">
    <literal><![CDATA[
      K(x,y * (L(y,z,z \ 1) \ u)) = K(x,a(z \ 1,z,y) * u)
    ]]></literal>
    <justification jstring="[para(1258(a,1),14454(a,1,2))].">
      <j1 rule="para" parents="1258 14454"/>
    </justification>
  </clause>

  <clause id="14456">
    <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(14259(a,1),14056(a,1,2))].">
      <j1 rule="para" parents="14259 14056"/>
    </justification>
  </clause>

  <clause id="14457">
    <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(63,a,14096,a(flip),b,14456,a),flip(a)].">
      <j1 rule="hyper" parents="63 14096 14456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14458">
    <literal><![CDATA[
      (K(x,y) * z) * R(u,z,K(x,T(y,z))) = K(x,y) * (z * u)
    ]]></literal>
    <justification jstring="[para(6390(a,1),14457(a,1,1))].">
      <j1 rule="para" parents="6390 14457"/>
    </justification>
  </clause>

  <clause id="14459">
    <literal><![CDATA[
      (K(x,y) * z) * R(u,z,K(x,y)) = K(x,y) * (z * u)
    ]]></literal>
    <justification jstring="[para(10347(a,1),14458(a,1,2))].">
      <j1 rule="para" parents="10347 14458"/>
    </justification>
  </clause>

  <clause id="14460">
    <literal><![CDATA[
      R(x,y,K(z,u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(501,a,14459,a),flip(a)].">
      <j1 rule="hyper" parents="501 14459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14461">
    <literal><![CDATA[
      L(x,y,K(z,u)) = T(x,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(14099,a,14460,a),flip(a)].">
      <j1 rule="hyper" parents="14099 14460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14462">
    <literal><![CDATA[
      L(R(x,y,z),y * z,K(z,u)) = R(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(8655,a,14460,a),flip(a)].">
      <j1 rule="hyper" parents="8655 14460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14463">
    <literal><![CDATA[
      L((x * K(y,z)) / u,u,K(z,y)) = x / (u * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(6027,a,14460,a),flip(a)].">
      <j1 rule="hyper" parents="6027 14460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14464">
    <literal><![CDATA[
      L(x,x \ y,K(z,u)) = (y * K(z,u)) / ((x \ y) * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(913,a,14460,a),flip(a)].">
      <j1 rule="hyper" parents="913 14460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14465">
    <literal><![CDATA[
      L(x / y,y,K(z,u)) = (x * K(z,u)) / (y * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(883,a,14460,a),flip(a)].">
      <j1 rule="hyper" parents="883 14460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14466">
    <literal><![CDATA[
      x * a(x,y,K(z,u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,14097,a,b,14460,a)].">
      <j1 rule="hyper" parents="63 14097 14460"/>
    </justification>
  </clause>

  <clause id="14467">
    <literal><![CDATA[
      ((x * y) * K(z,T(u,y))) / (K(z,u) * y) = L(x,y,K(z,T(u,y)))
    ]]></literal>
    <justification jstring="[hyper(63,a,6493,a,b,14460,a)].">
      <j1 rule="hyper" parents="63 6493 14460"/>
    </justification>
  </clause>

  <clause id="14468">
    <literal><![CDATA[
      ((x * (y * z)) * K(z,u)) / (y * T(z,u)) = L(x,y * z,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,6078,a,b,14460,a)].">
      <j1 rule="hyper" parents="63 6078 14460"/>
    </justification>
  </clause>

  <clause id="14469">
    <literal><![CDATA[
      L(R(x / y,y,z),y * z,K(y,u)) = ((x * z) * K(y,u)) / (y * (z * K(y,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,6146,a(flip),b,14460,a),flip(a)].">
      <j1 rule="hyper" parents="63 6146 14460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14470">
    <literal><![CDATA[
      L(x,y,K(z,u)) * (y * K(z,u)) = (x * y) * K(z,u)
    ]]></literal>
    <justification jstring="[hyper(125,a,14460,a(flip),b,20,a(flip))].">
      <j1 rule="hyper" parents="125 14460 20"/>
    </justification>
  </clause>

  <clause id="14471">
    <literal><![CDATA[
      x \ L(x,y,K(z,u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(121,a,14460,a(flip),b,14097,a)].">
      <j1 rule="hyper" parents="121 14460 14097"/>
    </justification>
  </clause>

  <clause id="14472">
    <literal><![CDATA[
      L(x,x \ y,K(z,u)) \ (y * K(z,u)) = (x \ y) * K(z,u)
    ]]></literal>
    <justification jstring="[para(14460(a,1),529(a,1,1))].">
      <j1 rule="para" parents="14460 529"/>
    </justification>
  </clause>

  <clause id="14473">
    <literal><![CDATA[
      L((x * y) / z,z,K(y,x)) \ (y * x) = z * ((x * y) \ (y * x))
    ]]></literal>
    <justification jstring="[para(14460(a,1),795(a,1,1))].">
      <j1 rule="para" parents="14460 795"/>
    </justification>
  </clause>

  <clause id="14474">
    <literal><![CDATA[
      L(x,x \ y,K(z,z \ y)) \ (z * (y / z)) = (x \ y) * K(z,z \ y)
    ]]></literal>
    <justification jstring="[para(14460(a,1),4672(a,1,1))].">
      <j1 rule="para" parents="14460 4672"/>
    </justification>
  </clause>

  <clause id="14475">
    <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(14460(a,1),8655(a,1))].">
      <j1 rule="para" parents="14460 8655"/>
    </justification>
  </clause>

  <clause id="14476">
    <literal><![CDATA[
      R(x,y,a(z,u,K(w,v5))) = L(x,y,K(a(z,u,w),v5))
    ]]></literal>
    <justification jstring="[para(13539(a,2),14460(a,1,3))].">
      <j1 rule="para" parents="13539 14460"/>
    </justification>
  </clause>

  <clause id="14477">
    <literal><![CDATA[
      L(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,a(u,y,z)) = w
    ]]></literal>
    <justification jstring="[para(14460(a,1),14099(a,1))].">
      <j1 rule="para" parents="14460 14099"/>
    </justification>
  </clause>

  <clause id="14478">
    <literal><![CDATA[
      T(x,a(y,z \ u,z)) = L(x,u,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(333,a,13999,a,b,14461,a)].">
      <j1 rule="hyper" parents="333 13999 14461"/>
    </justification>
  </clause>

  <clause id="14479">
    <literal><![CDATA[
      a(x,y,K(z,u)) * x = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(333,a,13780,a,b,14461,a)].">
      <j1 rule="hyper" parents="333 13780 14461"/>
    </justification>
  </clause>

  <clause id="14480">
    <literal><![CDATA[
      x * a(y,z,K(u,x)) = L(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(333,a,13756,a,b,14461,a)].">
      <j1 rule="hyper" parents="333 13756 14461"/>
    </justification>
  </clause>

  <clause id="14481">
    <literal><![CDATA[
      x * a(y,z,K(x,u)) = L(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(333,a,13180,a,b,14461,a)].">
      <j1 rule="hyper" parents="333 13180 14461"/>
    </justification>
  </clause>

  <clause id="14482">
    <literal><![CDATA[
      T(x,L(y,z,u) \ y) = L(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(333,a,13096,a,b,14461,a)].">
      <j1 rule="hyper" parents="333 13096 14461"/>
    </justification>
  </clause>

  <clause id="14483">
    <literal><![CDATA[
      a(x,y,z) \ R(u,a(x,y,z),a(x,y,z)) = L(u * (a(x,y,z) \ 1),y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(333,a,12446,a,b,14461,a)].">
      <j1 rule="hyper" parents="333 12446 14461"/>
    </justification>
  </clause>

  <clause id="14484">
    <literal><![CDATA[
      L(1 / x,y,K(z,u)) = a(x,y,K(u,z)) / x
    ]]></literal>
    <justification jstring="[hyper(333,a,13986,a(flip),b,14461,a),flip(a)].">
      <j1 rule="hyper" parents="333 13986 14461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14485">
    <literal><![CDATA[
      L(a(x,x,y),z,K(u,w)) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,13832,a(flip),b,14461,a),flip(a)].">
      <j1 rule="hyper" parents="333 13832 14461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14486">
    <literal><![CDATA[
      L(T(x,y),z,K(u,y)) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(333,a,13824,a(flip),b,14461,a),flip(a)].">
      <j1 rule="hyper" parents="333 13824 14461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14487">
    <literal><![CDATA[
      L(a(x,y,y \ 1),z,K(u,w)) = a(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(333,a,13788,a(flip),b,14461,a),flip(a)].">
      <j1 rule="hyper" parents="333 13788 14461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14488">
    <literal><![CDATA[
      L(x,y,K(L(z,u,x),w)) = T(x,a(w,y,z))
    ]]></literal>
    <justification jstring="[hyper(333,a,13582,a(flip),b,14461,a),flip(a)].">
      <j1 rule="hyper" parents="333 13582 14461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14489">
    <literal><![CDATA[
      L(x / a(y,z,u),z,K(u,y)) = a(y,z,u) \ x
    ]]></literal>
    <justification jstring="[hyper(333,a,113,a(flip),b,14461,a),flip(a)].">
      <j1 rule="hyper" parents="333 113 14461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14490">
    <literal><![CDATA[
      (x / y) * L(y,z,K(u,w)) = x * K(y,a(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(126,a,14461,a,b,5978,a)].">
      <j1 rule="hyper" parents="126 14461 5978"/>
    </justification>
  </clause>

  <clause id="14491">
    <literal><![CDATA[
      x \ L(x,y,K(z,u)) = a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(121,a,14461,a,b,13180,a)].">
      <j1 rule="hyper" parents="121 14461 13180"/>
    </justification>
  </clause>

  <clause id="14492">
    <literal><![CDATA[
      T(L(x,y,K(z,u)),a(z,y,u)) = x
    ]]></literal>
    <justification jstring="[hyper(41,a,13809,a(flip),b,14461,a),flip(a)].">
      <j1 rule="hyper" parents="41 13809 14461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14494">
    <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(14461(a,2),423(a,1))].">
      <j1 rule="para" parents="14461 423"/>
    </justification>
  </clause>

  <clause id="14495">
    <literal><![CDATA[
      x * (L(x,y,K(z,u)) \ w) = K(a(u,y,z),x) * w
    ]]></literal>
    <justification jstring="[para(14461(a,2),4556(a,1,2,1))].">
      <j1 rule="para" parents="14461 4556"/>
    </justification>
  </clause>

  <clause id="14497">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (w * x) = L(x,y,K(z,u)) * T(w,x)
    ]]></literal>
    <justification jstring="[para(14461(a,2),13783(a,2,1))].">
      <j1 rule="para" parents="14461 13783"/>
    </justification>
  </clause>

  <clause id="14498">
    <literal><![CDATA[
      L(x,y,K(z,u)) / u = T(x / u,a(u,y,z))
    ]]></literal>
    <justification jstring="[para(14461(a,2),14101(a,1,1))].">
      <j1 rule="para" parents="14461 14101"/>
    </justification>
  </clause>

  <clause id="14499">
    <literal><![CDATA[
      L(L(x,y,K(z,u)),y,K(u,z)) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,14461,a,b,14492,a)].">
      <j1 rule="hyper" parents="63 14461 14492"/>
    </justification>
  </clause>

  <clause id="14500">
    <literal><![CDATA[
      L(x,y,K(z,u)) * a(z,y,u) = a(z,y,u) * x
    ]]></literal>
    <justification jstring="[hyper(126,a,14492,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="126 14492 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14501">
    <literal><![CDATA[
      L(x,y,T(z,a(u,w,v5) \ 1)) = L(x,y,L(z,w,K(u,v5)))
    ]]></literal>
    <justification jstring="[para(14492(a,1),12795(a,1,3,1))].">
      <j1 rule="para" parents="14492 12795"/>
    </justification>
  </clause>

  <clause id="14502">
    <literal><![CDATA[
      L((K(x,y) * z) \ u,z,K(y,x)) = z \ (K(y,x) * u)
    ]]></literal>
    <justification jstring="[hyper(5156,a,14499,a),flip(a)].">
      <j1 rule="hyper" parents="5156 14499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14503">
    <literal><![CDATA[
      x \ L(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(14466(a,1),342(a,1,2))].">
      <j1 rule="para" parents="14466 342"/>
    </justification>
  </clause>

  <clause id="14504">
    <literal><![CDATA[
      x * a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(14471(a,1),273(a,1,2)),flip(b)].">
      <j1 rule="para" parents="14471 273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14505">
    <literal><![CDATA[
      a(x,y,K(z,u)) * x != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(14471(a,1),2523(a,1,1))].">
      <j1 rule="para" parents="14471 2523"/>
    </justification>
  </clause>

  <clause id="14506">
    <literal><![CDATA[
      L(x,y \ z,K(y,u)) = L(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,14461,a,b,14478,a)].">
      <j1 rule="hyper" parents="63 14461 14478"/>
    </justification>
  </clause>

  <clause id="14507">
    <literal><![CDATA[
      L(x,y,z) * T(L(x,y,z) \ x,u) = L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,13799,a,b,14480,a)].">
      <j1 rule="hyper" parents="63 13799 14480"/>
    </justification>
  </clause>

  <clause id="14508">
    <literal><![CDATA[
      T(x * K(y,x),L(y,z,u)) = L(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,10982,a,b,14480,a)].">
      <j1 rule="hyper" parents="63 10982 14480"/>
    </justification>
  </clause>

  <clause id="14509">
    <literal><![CDATA[
      T(x * a(y,z,K(u,x)),w) = L(T(x,w),z,K(y,u))
    ]]></literal>
    <justification jstring="[para(14480(a,2),25(a,2,1)),flip(a)].">
      <j1 rule="para" parents="14480 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14510">
    <literal><![CDATA[
      L(x,y,K(z,u)) \ x = a(u,y,K(z,x))
    ]]></literal>
    <justification jstring="[para(14481(a,1),9913(a,1,1))].">
      <j1 rule="para" parents="14481 9913"/>
    </justification>
  </clause>

  <clause id="14511">
    <literal><![CDATA[
      L(x \ y,z,K(u,x)) = T(y / x,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(113(a,1),14486(a,1,1))].">
      <j1 rule="para" parents="113 14486"/>
    </justification>
  </clause>

  <clause id="14512">
    <literal><![CDATA[
      L(x,y * z,K(y,u)) = L(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[para(9(a,1),14506(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9 14506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14513">
    <literal><![CDATA[
      L(L(x,y,z),y,K(z,u)) = L(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(5601,a,14512,a),flip(a)].">
      <j1 rule="hyper" parents="5601 14512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14514">
    <literal><![CDATA[
      L(L(x,y,K(z,u)),y,z) = L(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[para(14512(a,1),5602(a,1,1))].">
      <j1 rule="para" parents="14512 5602"/>
    </justification>
  </clause>

  <clause id="14515">
    <literal><![CDATA[
      L(x,y,K(z,L(u,w,x))) = T(x,a(u,y,z))
    ]]></literal>
    <justification jstring="[para(10212(a,1),14488(a,1,3))].">
      <j1 rule="para" parents="10212 14488"/>
    </justification>
  </clause>

  <clause id="14517">
    <literal><![CDATA[
      L(x,T(y,z),T(u,y)) = L(x,T(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,5666,a(flip),b,14513,a),flip(a)].">
      <j1 rule="hyper" parents="63 5666 14513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14518">
    <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(14513(a,1),1254(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14513 1254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14519">
    <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(14513(a,1),14510(a,1,1))].">
      <j1 rule="para" parents="14513 14510"/>
    </justification>
  </clause>

  <clause id="14520">
    <literal><![CDATA[
      L(L(x,y,K(z * u,u \ 1)),y,z * u) = L(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(333,a,11890,a(flip),b,14514,a),flip(a)].">
      <j1 rule="hyper" parents="333 11890 14514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14521">
    <literal><![CDATA[
      L(x,y,K(z,L(u,w,x))) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(333,a,14461,a,b,14515,a),flip(a)].">
      <j1 rule="hyper" parents="333 14461 14515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14522">
    <literal><![CDATA[
      L(x / y,z,K(u,y)) = L(x,z,K(u,y)) / y
    ]]></literal>
    <justification jstring="[hyper(333,a,14461,a,b,14498,a)].">
      <j1 rule="hyper" parents="333 14461 14498"/>
    </justification>
  </clause>

  <clause id="14523">
    <literal><![CDATA[
      L(x * K(y,x),z,u) \ (x * K(y,x)) = L(x,z,u) \ L(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[para(14508(a,1),11015(a,2,2))].">
      <j1 rule="para" parents="14508 11015"/>
    </justification>
  </clause>

  <clause id="14524">
    <literal><![CDATA[
      T(x * K(y,L(x,z,u)),y) = L(y \ (y * x),z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(333,a,11164,a(flip),b,14511,a)].">
      <j1 rule="hyper" parents="333 11164 14511"/>
    </justification>
  </clause>

  <clause id="14525">
    <literal><![CDATA[
      L(x * y,z,K(u,x)) = x * L(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(37,a,891,a(flip),b,14522,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="37 891 14522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14526">
    <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(444,a,14489,a,b,14044,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="444 14489 14044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14527">
    <literal><![CDATA[
      x * a(y,z,K(u,x)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z,K(y,u)) = w
    ]]></literal>
    <justification jstring="[para(13731(a,2),14504(a,1,2))].">
      <j1 rule="para" parents="13731 14504"/>
    </justification>
  </clause>

  <clause id="14528">
    <literal><![CDATA[
      T(x,a(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z,K(u,y)) = w
    ]]></literal>
    <justification jstring="[para(13741(a,1),14504(a,1))].">
      <j1 rule="para" parents="13741 14504"/>
    </justification>
  </clause>

  <clause id="14529">
    <literal><![CDATA[
      R(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(14097(a,1),14504(a,1))].">
      <j1 rule="para" parents="14097 14504"/>
    </justification>
  </clause>

  <clause id="14530">
    <literal><![CDATA[
      T(x,a(y,z * y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z,K(u,y)) = w
    ]]></literal>
    <justification jstring="[para(13941(a,2),14528(a,1))].">
      <j1 rule="para" parents="13941 14528"/>
    </justification>
  </clause>

  <clause id="14531">
    <literal><![CDATA[
      L(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z \ y,K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(14478(a,1),14528(a,1))].">
      <j1 rule="para" parents="14478 14528"/>
    </justification>
  </clause>

  <clause id="14532">
    <literal><![CDATA[
      (L(x,y,z) * K(u,w)) / (x * K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x \ L(x,y,z),x,K(u,w)) = v5
    ]]></literal>
    <justification jstring="[para(2519(a,1),14529(a,1))].">
      <j1 rule="para" parents="2519 14529"/>
    </justification>
  </clause>

  <clause id="14533">
    <literal><![CDATA[
      R(x,y,a(z,u,K(w,v5))) = L(x,y,a(z,u,K(w,v5)))
    ]]></literal>
    <justification jstring="[para(13539(a,2),14476(a,2,3))].">
      <j1 rule="para" parents="13539 14476"/>
    </justification>
  </clause>

  <clause id="14534">
    <literal><![CDATA[
      (x / y) * L(y,z,K(u,w)) = x * a(y,z,K(u,w))
    ]]></literal>
    <justification jstring="[para(13732(a,2),14490(a,2,2))].">
      <j1 rule="para" parents="13732 14490"/>
    </justification>
  </clause>

  <clause id="14535">
    <literal><![CDATA[
      x * (L(x,y,K(z,u)) \ w) = a(u,y,K(z,x)) * w
    ]]></literal>
    <justification jstring="[para(13539(a,2),14495(a,2,1))].">
      <j1 rule="para" parents="13539 14495"/>
    </justification>
  </clause>

  <clause id="14536">
    <literal><![CDATA[
      L(T(x,y),z,K(u,y)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(14509(a,1),10986(a,1))].">
      <j1 rule="para" parents="14509 10986"/>
    </justification>
  </clause>

  <clause id="14537">
    <literal><![CDATA[
      T(T(x,y),a(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(14461(a,1),14536(a,1))].">
      <j1 rule="para" parents="14461 14536"/>
    </justification>
  </clause>

  <clause id="14538">
    <literal><![CDATA[
      T(x,a(a(y,x,z),u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,L(a(y,x,z),u,w)) = v5
    ]]></literal>
    <justification jstring="[para(13825(a,1),14537(a,1,1))].">
      <j1 rule="para" parents="13825 14537"/>
    </justification>
  </clause>

  <clause id="14539">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (u \ w) = L(u,y,K(z,x)) \ w
    ]]></literal>
    <justification jstring="[hyper(1275,a,14535,a),flip(a)].">
      <j1 rule="hyper" parents="1275 14535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14540">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (u \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(u,y,K(z,x)) \ w = v5
    ]]></literal>
    <justification jstring="[para(14535(a,1),1275(a,1))].">
      <j1 rule="para" parents="14535 1275"/>
    </justification>
  </clause>

  <clause id="14541">
    <literal><![CDATA[
      a(x,(y * K(z,u)) * L(w / y,y,K(z,u)),x) = a(x,w * K(z,u),x)
    ]]></literal>
    <justification jstring="[para(14465(a,2),13028(a,1,2,2))].">
      <j1 rule="para" parents="14465 13028"/>
    </justification>
  </clause>

  <clause id="14542">
    <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(8169(a,1),14470(a,1,2))].">
      <j1 rule="para" parents="8169 14470"/>
    </justification>
  </clause>

  <clause id="14543">
    <literal><![CDATA[
      (K(x,y) * (x * y)) \ z = (x * y) \ (K(y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(10079,a,14502,a)].">
      <j1 rule="hyper" parents="10079 14502"/>
    </justification>
  </clause>

  <clause id="14544">
    <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(767(a,1),14502(a,1,1)),flip(a)].">
      <j1 rule="para" parents="767 14502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14545">
    <literal><![CDATA[
      (x * y) \ (K(y,x) * z) = (T(x,y) * y) \ z
    ]]></literal>
    <justification jstring="[para(4273(a,1),14543(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4273 14543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14546">
    <literal><![CDATA[
      L(x,y,z) \ L(x,y,K(z,u)) = T(L(x,y,z) \ x,u \ 1)
    ]]></literal>
    <justification jstring="[hyper(121,a,11907,a(flip),b,14507,a)].">
      <j1 rule="hyper" parents="121 11907 14507"/>
    </justification>
  </clause>

  <clause id="14547">
    <literal><![CDATA[
      L(x,y,T(z,u)) \ L(x,y,z) = a(u,y,K(z,x))
    ]]></literal>
    <justification jstring="[para(9466(a,1),14519(a,2,3))].">
      <j1 rule="para" parents="9466 14519"/>
    </justification>
  </clause>

  <clause id="14548">
    <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(14547(a,1),515(a,1,1,1))].">
      <j1 rule="para" parents="14547 515"/>
    </justification>
  </clause>

  <clause id="14550">
    <literal><![CDATA[
      T(x * K(y,L(x,z,u)),y) = L(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[para(9(a,1),14524(a,2,1))].">
      <j1 rule="para" parents="9 14524"/>
    </justification>
  </clause>

  <clause id="14551">
    <literal><![CDATA[
      T(x * K(y,L(x,z,u)),y) = L(x,x * z,K(u,y))
    ]]></literal>
    <justification jstring="[para(10866(a,1),14550(a,1,1,2))].">
      <j1 rule="para" parents="10866 14550"/>
    </justification>
  </clause>

  <clause id="14552">
    <literal><![CDATA[
      (x \ T(y,z)) * L(K(z,y),u,w) = x \ L(y,u,K(w,z))
    ]]></literal>
    <justification jstring="[para(14550(a,1),14368(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14550 14368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14553">
    <literal><![CDATA[
      L(x,x * y,K(z,u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,14550,a(flip),b,14551,a),flip(a)].">
      <j1 rule="hyper" parents="63 14550 14551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14554">
    <literal><![CDATA[
      L(x,x \ y,K(z,u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(10(a,1),14553(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 14553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14555">
    <literal><![CDATA[
      L(T(x,y),x \ z,K(u,w)) = T(L(x,z,K(u,w)),y)
    ]]></literal>
    <justification jstring="[para(14554(a,1),25(a,2,1))].">
      <j1 rule="para" parents="14554 25"/>
    </justification>
  </clause>

  <clause id="14556">
    <literal><![CDATA[
      L(x,x \ y,a(z,u,K(w,v5))) = L(x,y,K(a(z,u,w),v5))
    ]]></literal>
    <justification jstring="[para(13539(a,2),14554(a,1,3))].">
      <j1 rule="para" parents="13539 14554"/>
    </justification>
  </clause>

  <clause id="14557">
    <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(14554(a,1),14449(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14554 14449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14558">
    <literal><![CDATA[
      L(T(x,y),x \ z,K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(T(x,y),z,K(u,w)) = v5
    ]]></literal>
    <justification jstring="[para(14555(a,2),10114(a,1))].">
      <j1 rule="para" parents="14555 10114"/>
    </justification>
  </clause>

  <clause id="14559">
    <literal><![CDATA[
      L(x,x \ y,a(z,u,K(w,v5))) = L(x,y,a(z,u,K(w,v5)))
    ]]></literal>
    <justification jstring="[para(13539(a,2),14556(a,2,3))].">
      <j1 rule="para" parents="13539 14556"/>
    </justification>
  </clause>

  <clause id="14560">
    <literal><![CDATA[
      (x * K(y,z)) / ((u \ x) * K(y,z)) = L(u,x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,14554,a(flip),b,14464,a),flip(a)].">
      <j1 rule="hyper" parents="63 14554 14464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14561">
    <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(3207(a,1),14560(a,1,2,1))].">
      <j1 rule="para" parents="3207 14560"/>
    </justification>
  </clause>

  <clause id="14562">
    <literal><![CDATA[
      T(K(x,y) * ((x \ y) / z),z) = (z \ (x \ y)) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(13716,a,14472,a)].">
      <j1 rule="hyper" parents="13716 14472"/>
    </justification>
  </clause>

  <clause id="14563">
    <literal><![CDATA[
      L(L(x,y,K(z,u * z)),y,u * z) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(11905(a,1),14520(a,1,1))].">
      <j1 rule="para" parents="11905 14520"/>
    </justification>
  </clause>

  <clause id="14564">
    <literal><![CDATA[
      L(L(x,y,K(z,u)),y,u * z) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(11837(a,1),14563(a,1,1))].">
      <j1 rule="para" parents="11837 14563"/>
    </justification>
  </clause>

  <clause id="14565">
    <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(63,a,13403,a(flip),b,14564,a)].">
      <j1 rule="hyper" parents="63 13403 14564"/>
    </justification>
  </clause>

  <clause id="14566">
    <literal><![CDATA[
      T(x,a(y,z,a(u,x,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,L(a(y,x,w),z,u)) = v5
    ]]></literal>
    <justification jstring="[para(14152(a,1),14538(a,1))].">
      <j1 rule="para" parents="14152 14538"/>
    </justification>
  </clause>

  <clause id="14567">
    <literal><![CDATA[
      ((x * (T(y * z,x) / x)) * K(z,u)) / (y * T(z,u)) = L(a(x,x \ (y * z),x),y * z,K(z,u))
    ]]></literal>
    <justification jstring="[para(9251(a,1),14468(a,1,1,1))].">
      <j1 rule="para" parents="9251 14468"/>
    </justification>
  </clause>

  <clause id="14568">
    <literal><![CDATA[
      L((x * y) / z,z,K(y,x)) \ (y * x) = z * K(y,x)
    ]]></literal>
    <justification jstring="[para(16(a,2),14473(a,2,2))].">
      <j1 rule="para" parents="16 14473"/>
    </justification>
  </clause>

  <clause id="14569">
    <literal><![CDATA[
      ((x * y) / z) \ (y * x) = z * K(y,x)
    ]]></literal>
    <justification jstring="[para(13164(a,1),14568(a,1,1))].">
      <j1 rule="para" parents="13164 14568"/>
    </justification>
  </clause>

  <clause id="14570">
    <literal><![CDATA[
      (x * y) / (z * K(x,y)) = (y * x) / z
    ]]></literal>
    <justification jstring="[hyper(6000,a,14569,a),flip(a)].">
      <j1 rule="hyper" parents="6000 14569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14571">
    <literal><![CDATA[
      (x * y) / (z * K(y,x)) = K(x,y) * ((x * y) / z)
    ]]></literal>
    <justification jstring="[hyper(197,a,14569,a(flip),b,13470,a)].">
      <j1 rule="hyper" parents="197 14569 13470"/>
    </justification>
  </clause>

  <clause id="14572">
    <literal><![CDATA[
      R(x,y,z) \ (z * (x * y)) = (y * z) * K(z,x * y)
    ]]></literal>
    <justification jstring="[para(20(a,2),14569(a,1,1))].">
      <j1 rule="para" parents="20 14569"/>
    </justification>
  </clause>

  <clause id="14573">
    <literal><![CDATA[
      (x \ (y * z)) * K(z,y) = x \ (z * y)
    ]]></literal>
    <justification jstring="[para(76(a,1),14569(a,1,1)),flip(a)].">
      <j1 rule="para" parents="76 14569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14574">
    <literal><![CDATA[
      x / (y * K(x / z,z)) = (z * (x / z)) / y
    ]]></literal>
    <justification jstring="[para(14569(a,1),336(a,1,2))].">
      <j1 rule="para" parents="14569 336"/>
    </justification>
  </clause>

  <clause id="14575">
    <literal><![CDATA[
      a(x,y,z) = (z * (x * y)) / ((x * (y * z)) * K(z,x * y))
    ]]></literal>
    <justification jstring="[hyper(333,a,13588,a,b,14570,a)].">
      <j1 rule="hyper" parents="333 13588 14570"/>
    </justification>
  </clause>

  <clause id="14576">
    <literal><![CDATA[
      (x * y) / (z * K(y,T(x,y))) = (T(x,y) * y) / z
    ]]></literal>
    <justification jstring="[para(111(a,1),14570(a,1,1))].">
      <j1 rule="para" parents="111 14570"/>
    </justification>
  </clause>

  <clause id="14577">
    <literal><![CDATA[
      (x \ (y * z)) * T(z,y) = (x \ (z * y)) * z
    ]]></literal>
    <justification jstring="[hyper(125,a,14573,a(flip),b,5979,a),flip(a)].">
      <j1 rule="hyper" parents="125 14573 5979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14578">
    <literal><![CDATA[
      (x \ (y * z)) / T(y,z) = (x \ (z * y)) / y
    ]]></literal>
    <justification jstring="[hyper(123,a,14573,a(flip),b,5974,a)].">
      <j1 rule="hyper" parents="123 14573 5974"/>
    </justification>
  </clause>

  <clause id="14579">
    <literal><![CDATA[
      (x \ y) * K(z \ y,z) = x \ ((z \ y) * z)
    ]]></literal>
    <justification jstring="[para(10(a,1),14573(a,1,1,2))].">
      <j1 rule="para" parents="10 14573"/>
    </justification>
  </clause>

  <clause id="14580">
    <literal><![CDATA[
      x / (y * K(z \ x,z)) = (z * (x / z)) / y
    ]]></literal>
    <justification jstring="[para(4375(a,1),14574(a,1,2,2))].">
      <j1 rule="para" parents="4375 14574"/>
    </justification>
  </clause>

  <clause id="14581">
    <literal><![CDATA[
      ((x \ y) * (z * z)) / T(y,z * z) = (x \ ((z * z) * y)) / y
    ]]></literal>
    <justification jstring="[para(441(a,1),14578(a,1,1))].">
      <j1 rule="para" parents="441 14578"/>
    </justification>
  </clause>

  <clause id="14582">
    <literal><![CDATA[
      (x * (y / x)) / (z * (y / x)) = y / (z * (x \ y))
    ]]></literal>
    <justification jstring="[para(6011(a,1),14580(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6011 14580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14583">
    <literal><![CDATA[
      (L(x,y,z) * (u / L(x,y,z))) / K(x,L(x,y,z) \ u) = u / a(L(x,y,z) \ u,y,K(z,x))
    ]]></literal>
    <justification jstring="[para(13751(a,1),14580(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13751 14580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14584">
    <literal><![CDATA[
      (x * y) / (z * K(y,x)) = (T(x,y) * y) / z
    ]]></literal>
    <justification jstring="[para(4370(a,1),14576(a,1,2,2))].">
      <j1 rule="para" parents="4370 14576"/>
    </justification>
  </clause>

  <clause id="14585">
    <literal><![CDATA[
      K(x,y) * ((x * y) / z) = (T(x,y) * y) / z
    ]]></literal>
    <justification jstring="[hyper(63,a,14571,a(flip),b,14584,a)].">
      <j1 rule="hyper" parents="63 14571 14584"/>
    </justification>
  </clause>

  <clause id="14586">
    <literal><![CDATA[
      R(x,y,z) \ (z * (x * y)) = y * T(z,x * y)
    ]]></literal>
    <justification jstring="[hyper(333,a,5984,a(flip),b,14572,a),flip(a)].">
      <j1 rule="hyper" parents="333 5984 14572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14587">
    <literal><![CDATA[
      a(x,y,z) = (z * (x * y)) / (L(z,y,x) * (x * y))
    ]]></literal>
    <justification jstring="[para(13406(a,1),14575(a,2,2))].">
      <j1 rule="para" parents="13406 14575"/>
    </justification>
  </clause>

  <clause id="14588">
    <literal><![CDATA[
      a(x,y,T(z,x * y)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,13727,a(flip),b,14587,a)].">
      <j1 rule="hyper" parents="333 13727 14587"/>
    </justification>
  </clause>

  <clause id="14589">
    <literal><![CDATA[
      (x * y) / a(y / z,z,x) = L(x,z,z \ y) * y
    ]]></literal>
    <justification jstring="[para(14588(a,1),10742(a,1,2))].">
      <j1 rule="para" parents="14588 10742"/>
    </justification>
  </clause>

  <clause id="14590">
    <literal><![CDATA[
      K(x,y) * ((y / z) * (z * x)) = L(x,z,z \ y) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,13472,a,b,14589,a)].">
      <j1 rule="hyper" parents="63 13472 14589"/>
    </justification>
  </clause>

  <clause id="14591">
    <literal><![CDATA[
      (x \ y) / (T(y,z * z) / (z * z)) = (x \ ((z * z) * y)) / y
    ]]></literal>
    <justification jstring="[hyper(806,a,14581,a)].">
      <j1 rule="hyper" parents="806 14581"/>
    </justification>
  </clause>

  <clause id="14592">
    <literal><![CDATA[
      (x \ ((y * y) * z)) / z = (x \ z) / ((y * y) \ z)
    ]]></literal>
    <justification jstring="[para(723(a,1),14591(a,1,2)),flip(a)].">
      <j1 rule="para" parents="723 14591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14593">
    <literal><![CDATA[
      (x \ ((y * y) * z)) / z = ((x \ z) / z) * (y * y)
    ]]></literal>
    <justification jstring="[hyper(333,a,794,a(flip),b,14592,a),flip(a)].">
      <j1 rule="hyper" parents="333 794 14592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14594">
    <literal><![CDATA[
      ((x \ y) / y) * (x * x) = R(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(1517,a,14593,a),flip(a)].">
      <j1 rule="hyper" parents="1517 14593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14595">
    <literal><![CDATA[
      ((x \ y) / y) * L(x,x,(x \ y) / y) = R(x,x,y) / x
    ]]></literal>
    <justification jstring="[para(14594(a,1),1823(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14594 1823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14596">
    <literal><![CDATA[
      ((x \ y) / y) * T(x,x \ 1) = R(x,x,y) / x
    ]]></literal>
    <justification jstring="[para(8304(a,1),14595(a,1,2))].">
      <j1 rule="para" parents="8304 14595"/>
    </justification>
  </clause>

  <clause id="14597">
    <literal><![CDATA[
      R(x,x,y) / x = x * ((x \ y) / y)
    ]]></literal>
    <justification jstring="[hyper(3761,a,14596,a),flip(a)].">
      <j1 rule="hyper" parents="3761 14596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14599">
    <literal><![CDATA[
      x \ (x \ R(x,x,y)) = (x \ y) / y
    ]]></literal>
    <justification jstring="[hyper(3026,a,14597,a)].">
      <j1 rule="hyper" parents="3026 14597"/>
    </justification>
  </clause>

  <clause id="14600">
    <literal><![CDATA[
      x \ R(x,x,y) = x * ((x \ y) / y)
    ]]></literal>
    <justification jstring="[hyper(3024,a,14597,a)].">
      <j1 rule="hyper" parents="3024 14597"/>
    </justification>
  </clause>

  <clause id="14601">
    <literal><![CDATA[
      x \ y != (x \ z) / z
    ]]></literal>
    <literal><![CDATA[
      x \ R(x,x,z) = y
    ]]></literal>
    <justification jstring="[para(14599(a,1),47(a,1)),flip(a)].">
      <j1 rule="para" parents="14599 47"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14602">
    <literal><![CDATA[
      x \ R(x,x,x * y) = x * (y / (x * y))
    ]]></literal>
    <justification jstring="[para(9(a,1),14600(a,2,2,1))].">
      <j1 rule="para" parents="9 14600"/>
    </justification>
  </clause>

  <clause id="14603">
    <literal><![CDATA[
      (x \ 1) \ R(x \ 1,x \ 1,x * y) = (x \ 1) * (((x * x) * y) / (x * y))
    ]]></literal>
    <justification jstring="[para(709(a,1),14600(a,2,2,1))].">
      <j1 rule="para" parents="709 14600"/>
    </justification>
  </clause>

  <clause id="14604">
    <literal><![CDATA[
      (x * (y / (x * y))) * x = R(x,x,x * y)
    ]]></literal>
    <justification jstring="[hyper(125,a,14602,a(flip),b,3022,a)].">
      <j1 rule="hyper" parents="125 14602 3022"/>
    </justification>
  </clause>

  <clause id="14605">
    <literal><![CDATA[
      (x * T(y / (x * y),x)) * T(x,y / (x * y)) = R(x,x,x * y)
    ]]></literal>
    <justification jstring="[hyper(6156,a,14604,a)].">
      <j1 rule="hyper" parents="6156 14604"/>
    </justification>
  </clause>

  <clause id="14606">
    <literal><![CDATA[
      (x * R(x \ 1,x,y)) * T(x,y / (x * y)) = R(x,x,x * y)
    ]]></literal>
    <justification jstring="[para(686(a,1),14605(a,1,1,2))].">
      <j1 rule="para" parents="686 14605"/>
    </justification>
  </clause>

  <clause id="14607">
    <literal><![CDATA[
      (x * R(x \ 1,x,y)) * T(x,x \ 1) = R(x,x,x * y)
    ]]></literal>
    <justification jstring="[para(2228(a,1),14606(a,1,2))].">
      <j1 rule="para" parents="2228 14606"/>
    </justification>
  </clause>

  <clause id="14608">
    <literal><![CDATA[
      (x * R(x \ 1,x,((x \ 1) \ y) * (x \ 1))) * T(x,x \ 1) = R(x,x,T(x * y,x \ 1))
    ]]></literal>
    <justification jstring="[para(962(a,1),14607(a,2,3))].">
      <j1 rule="para" parents="962 14607"/>
    </justification>
  </clause>

  <clause id="14610">
    <literal><![CDATA[
      L(x,x \ y,K(z,y)) \ (z * (y / z)) = (x \ y) * K(z,z \ y)
    ]]></literal>
    <justification jstring="[para(11826(a,1),14474(a,1,1))].">
      <j1 rule="para" parents="11826 14474"/>
    </justification>
  </clause>

  <clause id="14611">
    <literal><![CDATA[
      (x \ y) * K(z,z \ y) = x \ (z * (y / z))
    ]]></literal>
    <justification jstring="[para(13145(a,1),14610(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13145 14610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14612">
    <literal><![CDATA[
      ((x \ y) * x) \ (y * (z / y)) = (K(x,x \ y) * z) / y
    ]]></literal>
    <justification jstring="[hyper(63,a,12939,a(flip),b,14611,a),flip(a)].">
      <j1 rule="hyper" parents="63 12939 14611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14613">
    <literal><![CDATA[
      (K(x,x \ y) * z) / y = K(x,x \ y) * (z / y)
    ]]></literal>
    <justification jstring="[hyper(10039,a,14612,a),flip(a)].">
      <j1 rule="hyper" parents="10039 14612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14614">
    <literal><![CDATA[
      L(x,y,z) \ L(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      (L(x * K(u,x),y,z) \ x) * K(u,x) = w
    ]]></literal>
    <justification jstring="[para(14523(a,1),13415(a,1))].">
      <j1 rule="para" parents="14523 13415"/>
    </justification>
  </clause>

  <clause id="14615">
    <literal><![CDATA[
      T(K(x,y) * ((x \ y) / z),z) = z \ ((x \ y) * K(x,y))
    ]]></literal>
    <justification jstring="[para(11849(a,1),14557(a,2,1))].">
      <j1 rule="para" parents="11849 14557"/>
    </justification>
  </clause>

  <clause id="14616">
    <literal><![CDATA[
      T(K(x,y) * ((x \ y) / z),z) = z \ (K(x,y) * (x \ y))
    ]]></literal>
    <justification jstring="[para(6185(a,2),14615(a,2,2))].">
      <j1 rule="para" parents="6185 14615"/>
    </justification>
  </clause>

  <clause id="14617">
    <literal><![CDATA[
      x \ (K(y,z) * (y \ z)) = (x \ (y \ z)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,14562,a(flip),b,14616,a),flip(a)].">
      <j1 rule="hyper" parents="63 14562 14616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14618">
    <literal><![CDATA[
      x \ (y \ ((y * z) / y)) = (x \ (y \ z)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,4828,a,b,14617,a)].">
      <j1 rule="hyper" parents="63 4828 14617"/>
    </justification>
  </clause>

  <clause id="14619">
    <literal><![CDATA[
      (K(x,y) * z) \ (x \ ((x * y) / x)) = (z \ (x \ T(y,x))) * K(x,y)
    ]]></literal>
    <justification jstring="[para(13688(a,1),14618(a,2,1))].">
      <j1 rule="para" parents="13688 14618"/>
    </justification>
  </clause>

  <clause id="14620">
    <literal><![CDATA[
      (x \ (y \ T(z,y))) * K(y,z) = x \ (y \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,13487,a(flip),b,14619,a),flip(a)].">
      <j1 rule="hyper" parents="63 13487 14619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14621">
    <literal><![CDATA[
      (x \ (y \ z)) * K(z,y) = x \ (y \ T(z,y))
    ]]></literal>
    <justification jstring="[hyper(5997,a,14620,a)].">
      <j1 rule="hyper" parents="5997 14620"/>
    </justification>
  </clause>

  <clause id="14622">
    <literal><![CDATA[
      (x \ 1) * (((x * x) * y) / (x * y)) = (x \ 1) \ R(x \ 1,x,x * y)
    ]]></literal>
    <justification jstring="[para(1927(a,1),14603(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1927 14603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14623">
    <literal><![CDATA[
      (x \ 1) * (((x * x) * y) / (x * y)) = x * R(x \ 1,x,x * y)
    ]]></literal>
    <justification jstring="[hyper(333,a,3029,a(flip),b,14622,a),flip(a)].">
      <j1 rule="hyper" parents="333 3029 14622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14624">
    <literal><![CDATA[
      x * R(x \ 1,x,x * y) = (x \ 1) * R(x,x,y)
    ]]></literal>
    <justification jstring="[para(20(a,2),14623(a,1,2)),flip(a)].">
      <j1 rule="para" parents="20 14623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14625">
    <literal><![CDATA[
      x * R(x \ 1,x,y * x) = (x \ 1) * R(x,x,y)
    ]]></literal>
    <justification jstring="[para(14403(a,2),14624(a,1,2))].">
      <j1 rule="para" parents="14403 14624"/>
    </justification>
  </clause>

  <clause id="14626">
    <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(14513(a,1),14518(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14513 14518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14627">
    <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(2604(a,1),14542(a,1,1))].">
      <j1 rule="para" parents="2604 14542"/>
    </justification>
  </clause>

  <clause id="14628">
    <literal><![CDATA[
      (x * (1 / T(y,z))) * K(y,u) = x * (K(y,u) / T(y,z))
    ]]></literal>
    <justification jstring="[para(6933(a,1),14627(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6933 14627"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14629">
    <literal><![CDATA[
      R(x,T(y,z) \ 1,y) / y = x * (K(y,z) / T(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,7865,a,b,14628,a)].">
      <j1 rule="hyper" parents="63 7865 14628"/>
    </justification>
  </clause>

  <clause id="14630">
    <literal><![CDATA[
      R(x,T(y,z) \ 1,y) / y = x * (1 / y)
    ]]></literal>
    <justification jstring="[para(4277(a,1),14629(a,2,2))].">
      <j1 rule="para" parents="4277 14629"/>
    </justification>
  </clause>

  <clause id="14631">
    <literal><![CDATA[
      R(x,T(y,z) \ 1,y) = R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(1949,a,14630,a),flip(a)].">
      <j1 rule="hyper" parents="1949 14630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14633">
    <literal><![CDATA[
      R(x,T(y,z) \ 1,T(y,z)) = R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(5540,a,14631,a)].">
      <j1 rule="hyper" parents="5540 14631"/>
    </justification>
  </clause>

  <clause id="14634">
    <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(14633(a,1),9155(a,2,2))].">
      <j1 rule="para" parents="14633 9155"/>
    </justification>
  </clause>

  <clause id="14635">
    <literal><![CDATA[
      x / (T(y,z) \ R(x,y \ 1,y)) = (x * (1 / T(T(y,1),z))) \ x
    ]]></literal>
    <justification jstring="[para(14634(a,1),7895(a,1,2))].">
      <j1 rule="para" parents="14634 7895"/>
    </justification>
  </clause>

  <clause id="14637">
    <literal><![CDATA[
      (x * (1 / T(T(y,1),z))) \ x = T((x * (1 / y)) \ x,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,9141,a(flip),b,14635,a),flip(a)].">
      <j1 rule="hyper" parents="63 9141 14635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14638">
    <literal><![CDATA[
      T((x * (1 / y)) \ x,z) = (x * (1 / T(y,z))) \ x
    ]]></literal>
    <justification jstring="[para(199(a,1),14637(a,1,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="199 14637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14639">
    <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(333,a,14487,a(flip),b,14544,a),flip(a)].">
      <j1 rule="hyper" parents="333 14487 14544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14641">
    <literal><![CDATA[
      K((x \ T(y,x \ 1)) \ z,T(u,x \ 1)) = K(((y \ z) * y) / (((x \ y) / y) * y),u)
    ]]></literal>
    <justification jstring="[para(3757(a,1),14090(a,1,2))].">
      <j1 rule="para" parents="3757 14090"/>
    </justification>
  </clause>

  <clause id="14642">
    <literal><![CDATA[
      K((x \ T(y,x \ 1)) \ z,T(u,x)) = K(((y \ z) * y) / (((x \ y) / y) * y),u)
    ]]></literal>
    <justification jstring="[hyper(7282,a,14641,a)].">
      <j1 rule="hyper" parents="7282 14641"/>
    </justification>
  </clause>

  <clause id="14644">
    <literal><![CDATA[
      K((x \ T(y,x \ 1)) \ z,T(u,x)) = K(((y \ z) * y) / (x \ y),u)
    ]]></literal>
    <justification jstring="[para(12(a,1),14642(a,2,1,2))].">
      <j1 rule="para" parents="12 14642"/>
    </justification>
  </clause>

  <clause id="14645">
    <literal><![CDATA[
      K((x \ T(y,x \ 1)) \ z,T(u,x)) = K(T(z,y) / (x \ y),u)
    ]]></literal>
    <justification jstring="[hyper(333,a,12907,a(flip),b,14644,a),flip(a)].">
      <j1 rule="hyper" parents="333 12907 14644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14647">
    <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(12(a,1),14146(a,2,2,1,1))].">
      <j1 rule="para" parents="12 14146"/>
    </justification>
  </clause>

  <clause id="14648">
    <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(333,a,13163,a(flip),b,14647,a),flip(a)].">
      <j1 rule="hyper" parents="333 13163 14647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14650">
    <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(13379(a,1),14648(a,1,2,1))].">
      <j1 rule="para" parents="13379 14648"/>
    </justification>
  </clause>

  <clause id="14651">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ 1)) / (u * ((z \ 1) / u))) = K(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[para(10330(a,1),14650(a,1,2,2))].">
      <j1 rule="para" parents="10330 14650"/>
    </justification>
  </clause>

  <clause id="14652">
    <literal><![CDATA[
      (x * R(x \ 1,x,((x \ 1) \ y) * x)) * T(x,x \ 1) = R(x,x,T(x * y,x \ 1))
    ]]></literal>
    <justification jstring="[para(1873(a,1),14608(a,1,1,2))].">
      <j1 rule="para" parents="1873 14608"/>
    </justification>
  </clause>

  <clause id="14653">
    <literal><![CDATA[
      ((x \ 1) * R(x,x,(x \ 1) \ y)) * T(x,x \ 1) = R(x,x,T(x * y,x \ 1))
    ]]></literal>
    <justification jstring="[para(14625(a,1),14652(a,1,1))].">
      <j1 rule="para" parents="14625 14652"/>
    </justification>
  </clause>

  <clause id="14654">
    <literal><![CDATA[
      ((x \ 1) * R(x,x,x \ y)) * T(x,x \ 1) = R(x,x,T(x * y,x \ 1))
    ]]></literal>
    <justification jstring="[para(1890(a,1),14653(a,1,1,2))].">
      <j1 rule="para" parents="1890 14653"/>
    </justification>
  </clause>

  <clause id="14655">
    <literal><![CDATA[
      L((x \ L(x,y,z)) \ 1,u,x) = (L(x,y,z) \ x) * ((x \ L(x,y,z)) \ (x \ L(x,y,z)))
    ]]></literal>
    <justification jstring="[para(3257(a,1),12980(a,2,1))].">
      <j1 rule="para" parents="3257 12980"/>
    </justification>
  </clause>

  <clause id="14656">
    <literal><![CDATA[
      L((x \ L(x,y,z)) \ 1,u,x) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(333,a,173,a(flip),b,14655,a),flip(a)].">
      <j1 rule="hyper" parents="333 173 14655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14658">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,x) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[para(3257(a,1),14656(a,1,1))].">
      <j1 rule="para" parents="3257 14656"/>
    </justification>
  </clause>

  <clause id="14659">
    <literal><![CDATA[
      L(L(x,y,z) \ x,L(x,y,z),z * y) = L((z * (y * x)) \ ((z * y) * x),u,x)
    ]]></literal>
    <justification jstring="[para(14658(a,1),1639(a,1,1))].">
      <j1 rule="para" parents="14658 1639"/>
    </justification>
  </clause>

  <clause id="14660">
    <literal><![CDATA[
      L((x * (y * z)) \ ((x * y) * z),u,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(1640,a,14659,a),flip(a)].">
      <j1 rule="hyper" parents="1640 14659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14661">
    <literal><![CDATA[
      L(a(x,y,z),u,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(14(a,2),14660(a,1,1))].">
      <j1 rule="para" parents="14 14660"/>
    </justification>
  </clause>

  <clause id="14662">
    <literal><![CDATA[
      a(x,y,z) * (z * u) = z * (a(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(14661(a,1),13694(a,1,1))].">
      <j1 rule="para" parents="14661 13694"/>
    </justification>
  </clause>

  <clause id="14663">
    <literal><![CDATA[
      x \ (a(y,z,x) * u) = a(y,z,x) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(631,a,14662,a)].">
      <j1 rule="hyper" parents="631 14662"/>
    </justification>
  </clause>

  <clause id="14665">
    <literal><![CDATA[
      T(x,L(y / (z / ((u \ 1) \ 1)),z / u,u)) = T(x,(y * u) / ((u * (1 / u)) \ z))
    ]]></literal>
    <justification jstring="[para(3224(a,1),13978(a,1,2))].">
      <j1 rule="para" parents="3224 13978"/>
    </justification>
  </clause>

  <clause id="14666">
    <literal><![CDATA[
      T(x,L(y / (z / ((u \ 1) \ 1)),u \ z,u)) = T(x,(y * u) / ((u * (1 / u)) \ z))
    ]]></literal>
    <justification jstring="[para(10083(a,1),14665(a,1,2))].">
      <j1 rule="para" parents="10083 14665"/>
    </justification>
  </clause>

  <clause id="14667">
    <literal><![CDATA[
      T(x,L(y / (z / ((u \ 1) \ 1)),u \ z,u)) = T(x,(y * T(u,u \ 1)) / z)
    ]]></literal>
    <justification jstring="[para(10131(a,1),14666(a,2,2))].">
      <j1 rule="para" parents="10131 14666"/>
    </justification>
  </clause>

  <clause id="14668">
    <literal><![CDATA[
      T(x,L(y / (z / ((u \ 1) \ 1)),u \ z,u)) = T(x,(y * u) / z)
    ]]></literal>
    <justification jstring="[hyper(333,a,10151,a(flip),b,14667,a),flip(a)].">
      <j1 rule="hyper" parents="333 10151 14667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14669">
    <literal><![CDATA[
      T((1 / x) \ a((1 / x) \ 1,y,z),x * a((1 / x) \ 1,y,z)) = x * a(x,y,z)
    ]]></literal>
    <justification jstring="[para(79(a,1),14253(a,2,2,1))].">
      <j1 rule="para" parents="79 14253"/>
    </justification>
  </clause>

  <clause id="14670">
    <literal><![CDATA[
      T((1 / x) \ a(x,y,z),x * a((1 / x) \ 1,y,z)) = x * a(x,y,z)
    ]]></literal>
    <justification jstring="[para(79(a,1),14669(a,1,1,2,1))].">
      <j1 rule="para" parents="79 14669"/>
    </justification>
  </clause>

  <clause id="14671">
    <literal><![CDATA[
      T((1 / x) \ a(x,y,z),x * a(x,y,z)) = x * a(x,y,z)
    ]]></literal>
    <justification jstring="[para(79(a,1),14670(a,1,2,2,1))].">
      <j1 rule="para" parents="79 14670"/>
    </justification>
  </clause>

  <clause id="14672">
    <literal><![CDATA[
      (1 / x) \ a(x,y,z) = x * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(181,a,14671,a),flip(a)].">
      <j1 rule="hyper" parents="181 14671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14673">
    <literal><![CDATA[
      L(a(x,y,z),x,x \ 1) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(2662,a,14672,a)].">
      <j1 rule="hyper" parents="2662 14672"/>
    </justification>
  </clause>

  <clause id="14675">
    <literal><![CDATA[
      (L(x,y,z) * (u / L(x,y,z))) / K(x,L(x,y,z) \ u) = u / a(u,y,K(z,x))
    ]]></literal>
    <justification jstring="[para(14078(a,1),14583(a,2,2))].">
      <j1 rule="para" parents="14078 14583"/>
    </justification>
  </clause>

  <clause id="14679">
    <literal><![CDATA[
      L(L(x,a(y,z,y),u),u * a(y,z,y),w) = a(y,z,y) \ L(x * a(y,z,y),u,w)
    ]]></literal>
    <justification jstring="[para(18(a,2),12869(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18 12869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14680">
    <literal><![CDATA[
      L(L(x,a(y,z,y),u),u * a(y,z,y),w) = L(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(333,a,12926,a(flip),b,14679,a),flip(a)].">
      <j1 rule="hyper" parents="333 12926 14679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14682">
    <literal><![CDATA[
      L(x,y * a(z,u,z),w) = L(x,y,w)
    ]]></literal>
    <justification jstring="[para(12849(a,1),14680(a,1,1))].">
      <j1 rule="para" parents="12849 14680"/>
    </justification>
  </clause>

  <clause id="14684">
    <literal><![CDATA[
      L(x,R(y,z,y),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(8214(a,1),14682(a,1,2))].">
      <j1 rule="para" parents="8214 14682"/>
    </justification>
  </clause>

  <clause id="14685">
    <literal><![CDATA[
      L(x,K(y * z,y),u) = L(x,K(z,y),u)
    ]]></literal>
    <justification jstring="[para(8243(a,1),14682(a,1,2))].">
      <j1 rule="para" parents="8243 14682"/>
    </justification>
  </clause>

  <clause id="14686">
    <literal><![CDATA[
      L(x,K(y,y * z),u) = L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[para(8244(a,1),14682(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8244 14682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14687">
    <literal><![CDATA[
      L(x,y / L(z,u,z),w) = L(x,y / z,w)
    ]]></literal>
    <justification jstring="[para(8247(a,1),14682(a,1,2))].">
      <j1 rule="para" parents="8247 14682"/>
    </justification>
  </clause>

  <clause id="14688">
    <literal><![CDATA[
      L(x,T(y * (z / y),y),u) = L(x,z,u)
    ]]></literal>
    <justification jstring="[para(9241(a,1),14682(a,1,2))].">
      <j1 rule="para" parents="9241 14682"/>
    </justification>
  </clause>

  <clause id="14689">
    <literal><![CDATA[
      L(x,a(y,z,y) \ u,w) = L(x,u,w)
    ]]></literal>
    <justification jstring="[para(9247(a,1),14682(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9247 14682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14690">
    <literal><![CDATA[
      L(x,T(y * z,y),u) = L(x,z * y,u)
    ]]></literal>
    <justification jstring="[para(9256(a,1),14682(a,1,2))].">
      <j1 rule="para" parents="9256 14682"/>
    </justification>
  </clause>

  <clause id="14691">
    <literal><![CDATA[
      L(x,y * (z * a(u,w,u)),v5) = L(x,y * z,v5)
    ]]></literal>
    <justification jstring="[para(12514(a,1),14682(a,1,2))].">
      <j1 rule="para" parents="12514 14682"/>
    </justification>
  </clause>

  <clause id="14692">
    <literal><![CDATA[
      L(x,T(y,y \ z),u) = L(x,T(y,z),u)
    ]]></literal>
    <justification jstring="[para(3849(a,1),14684(a,1,2))].">
      <j1 rule="para" parents="3849 14684"/>
    </justification>
  </clause>

  <clause id="14693">
    <literal><![CDATA[
      L(x,(y \ z) \ z,u) = L(x,T(y,z),u)
    ]]></literal>
    <justification jstring="[para(8668(a,1),14684(a,1,2))].">
      <j1 rule="para" parents="8668 14684"/>
    </justification>
  </clause>

  <clause id="14694">
    <literal><![CDATA[
      L(x,K(y \ z,y),u) = L(x,K(z,y),u)
    ]]></literal>
    <justification jstring="[para(8206(a,1),14689(a,1,2))].">
      <j1 rule="para" parents="8206 14689"/>
    </justification>
  </clause>

  <clause id="14695">
    <literal><![CDATA[
      L(x,R(y,z,y) \ u,w) = L(x,y \ u,w)
    ]]></literal>
    <justification jstring="[para(9339(a,1),14689(a,1,2))].">
      <j1 rule="para" parents="9339 14689"/>
    </justification>
  </clause>

  <clause id="14696">
    <literal><![CDATA[
      L(x,K(y * z,(y * z) * (z \ 1)),u) = L(x,K(z * y,z \ 1),u)
    ]]></literal>
    <justification jstring="[para(8582(a,1),14686(a,2,2))].">
      <j1 rule="para" parents="8582 14686"/>
    </justification>
  </clause>

  <clause id="14697">
    <literal><![CDATA[
      L(x,(y \ z) * y,u) = L(x,T(z,y),u)
    ]]></literal>
    <justification jstring="[para(75(a,1),14688(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="75 14688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14698">
    <literal><![CDATA[
      L(x,y * (z / T(y,z)),u) = L(x,z,u)
    ]]></literal>
    <justification jstring="[para(3656(a,1),14688(a,1,2))].">
      <j1 rule="para" parents="3656 14688"/>
    </justification>
  </clause>

  <clause id="14699">
    <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(14692(a,1),5107(a,1))].">
      <j1 rule="para" parents="14692 5107"/>
    </justification>
  </clause>

  <clause id="14700">
    <literal><![CDATA[
      L(x,T(y * z,z \ 1),u) = L(x,T(y * z,y),u)
    ]]></literal>
    <justification jstring="[para(5801(a,1),14692(a,1,2))].">
      <j1 rule="para" parents="5801 14692"/>
    </justification>
  </clause>

  <clause id="14701">
    <literal><![CDATA[
      L(x,T(y,z),y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,y \ z) = u
    ]]></literal>
    <justification jstring="[para(14692(a,1),10099(a,1))].">
      <j1 rule="para" parents="14692 10099"/>
    </justification>
  </clause>

  <clause id="14702">
    <literal><![CDATA[
      L(x,T(T(y,z),z \ 1),u) = L(x,T(T(y,z),z \ y),u)
    ]]></literal>
    <justification jstring="[para(12745(a,1),14692(a,1,2))].">
      <j1 rule="para" parents="12745 14692"/>
    </justification>
  </clause>

  <clause id="14703">
    <literal><![CDATA[
      L(x,T(y \ z,z),u) = L(x,z / y,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,4884,a(flip),b,14693,a),flip(a)].">
      <j1 rule="hyper" parents="63 4884 14693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14704">
    <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(14693(a,1),9563(a,1,2))].">
      <j1 rule="para" parents="14693 9563"/>
    </justification>
  </clause>

  <clause id="14705">
    <literal><![CDATA[
      L(x,K(y * z,y \ 1),u) = L(x,K(z,y \ 1),u)
    ]]></literal>
    <justification jstring="[para(4867(a,1),14694(a,1,2))].">
      <j1 rule="para" parents="4867 14694"/>
    </justification>
  </clause>

  <clause id="14706">
    <literal><![CDATA[
      L(x,T(y,z \ y),u) = L(x,z * (y / z),u)
    ]]></literal>
    <justification jstring="[para(3412(a,1),14697(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3412 14697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14707">
    <literal><![CDATA[
      L(x,T((y / T(z,y)) * z,y / T(z,y)),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,14690,a,b,14698,a)].">
      <j1 rule="hyper" parents="63 14690 14698"/>
    </justification>
  </clause>

  <clause id="14708">
    <literal><![CDATA[
      L(x,y / z,y) = L(x,z \ y,y)
    ]]></literal>
    <justification jstring="[hyper(10099,a,14703,a),flip(a)].">
      <j1 rule="hyper" parents="10099 14703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14709">
    <literal><![CDATA[
      L(x,(y * z) / y,u) = L(x,y * (z / y),u)
    ]]></literal>
    <justification jstring="[para(569(a,1),14687(a,1,2)),flip(a)].">
      <j1 rule="para" parents="569 14687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14710">
    <literal><![CDATA[
      L(x,(y \ T(z,y \ z)) \ u,w) = L(x,(z / y) \ u,w)
    ]]></literal>
    <justification jstring="[para(3794(a,1),14695(a,1,2,1))].">
      <j1 rule="para" parents="3794 14695"/>
    </justification>
  </clause>

  <clause id="14711">
    <literal><![CDATA[
      L(x,K(y,y * z) * u,w) = L(x,K(y,z) * u,w)
    ]]></literal>
    <justification jstring="[para(9245(a,1),14691(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9245 14691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14712">
    <literal><![CDATA[
      L(x,y * T(z * u,z),w) = L(x,y * (u * z),w)
    ]]></literal>
    <justification jstring="[para(9256(a,1),14691(a,1,2,2))].">
      <j1 rule="para" parents="9256 14691"/>
    </justification>
  </clause>

  <clause id="14713">
    <literal><![CDATA[
      L(T(x,y) \ z,x,x \ y) = y \ ((T(y,x) / x) * z)
    ]]></literal>
    <justification jstring="[hyper(14701,a,11893,a)].">
      <j1 rule="hyper" parents="14701 11893"/>
    </justification>
  </clause>

  <clause id="14714">
    <literal><![CDATA[
      L(x,T(y * z,z \ 1),u) = L(x,z * y,u)
    ]]></literal>
    <justification jstring="[hyper(333,a,14690,a(flip),b,14700,a),flip(a)].">
      <j1 rule="hyper" parents="333 14690 14700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14715">
    <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(14714(a,1),10964(a,1,2))].">
      <j1 rule="para" parents="14714 10964"/>
    </justification>
  </clause>

  <clause id="14716">
    <literal><![CDATA[
      L(x,K(y,y \ z) * u,w) = L(x,K(y,z) * u,w)
    ]]></literal>
    <justification jstring="[para(10(a,1),14711(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="10 14711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14717">
    <literal><![CDATA[
      L(x,y * T(R(1 / z,z,u) * (z * u),R(1 / z,z,u)),w) = L(x,y * (u * K(z * u,z \ 1)),w)
    ]]></literal>
    <justification jstring="[para(5980(a,1),14712(a,2,2,2))].">
      <j1 rule="para" parents="5980 14712"/>
    </justification>
  </clause>

  <clause id="14718">
    <literal><![CDATA[
      L(x,T(T(y,z),y / T(z,y)),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(3619(a,1),14707(a,1,2,1))].">
      <j1 rule="para" parents="3619 14707"/>
    </justification>
  </clause>

  <clause id="14719">
    <literal><![CDATA[
      L(x,T(T(y,z),z \ y),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(12631(a,1),14718(a,1,2))].">
      <j1 rule="para" parents="12631 14718"/>
    </justification>
  </clause>

  <clause id="14720">
    <literal><![CDATA[
      L(x,T(T(y,z),z \ 1),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,14702,a,b,14719,a)].">
      <j1 rule="hyper" parents="63 14702 14719"/>
    </justification>
  </clause>

  <clause id="14721">
    <literal><![CDATA[
      L(x,T(y,z),z \ 1) = L(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(10099,a,14720,a)].">
      <j1 rule="hyper" parents="10099 14720"/>
    </justification>
  </clause>

  <clause id="14723">
    <literal><![CDATA[
      L(x,T(y,z),(z \ y) \ 1) = L(x,y,(z \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,14719,a(flip),b,14721,a),flip(a)].">
      <j1 rule="hyper" parents="63 14719 14721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14724">
    <literal><![CDATA[
      L(x,y * (z / y),(y \ z) \ 1) = L(x,z,(y \ z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,14706,a(flip),b,14721,a)].">
      <j1 rule="hyper" parents="63 14706 14721"/>
    </justification>
  </clause>

  <clause id="14725">
    <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(14721(a,1),14433(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14721 14433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14726">
    <literal><![CDATA[
      L(x,(x / y) \ z,u) = L(x,(y \ x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,11030,a(flip),b,14710,a),flip(a)].">
      <j1 rule="hyper" parents="63 11030 14710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14727">
    <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(14517(a,1),14699(a,1))].">
      <j1 rule="para" parents="14517 14699"/>
    </justification>
  </clause>

  <clause id="14728">
    <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(385(a,1),14696(a,1,2,2))].">
      <j1 rule="para" parents="385 14696"/>
    </justification>
  </clause>

  <clause id="14729">
    <literal><![CDATA[
      L(x,K(y * z,y \ 1),u) = L(x,K(z * y,z),u)
    ]]></literal>
    <justification jstring="[para(5657(a,1),14728(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5657 14728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14730">
    <literal><![CDATA[
      L(x,K(y * z,y \ 1),u) = L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(333,a,14685,a(flip),b,14729,a),flip(a)].">
      <j1 rule="hyper" parents="333 14685 14729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14733">
    <literal><![CDATA[
      L(x,K(y,z \ 1),u) = L(x,K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,14705,a(flip),b,14730,a)].">
      <j1 rule="hyper" parents="63 14705 14730"/>
    </justification>
  </clause>

  <clause id="14734">
    <literal><![CDATA[
      L(x,K(y \ 1,z),u) = L(x,K(z,y),u)
    ]]></literal>
    <justification jstring="[para(4621(a,1),14733(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4621 14733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14735">
    <literal><![CDATA[
      L(x,K(y,z),u \ (z \ u)) = x
    ]]></literal>
    <justification jstring="[hyper(7068,a,14734,a),flip(a)].">
      <j1 rule="hyper" parents="7068 14734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14736">
    <literal><![CDATA[
      (x \ y) / (K(z,x) \ y) = ((x \ y) / y) * K(z,x)
    ]]></literal>
    <justification jstring="[hyper(197,a,14735,a(flip),b,13618,a(flip))].">
      <j1 rule="hyper" parents="197 14735 13618"/>
    </justification>
  </clause>

  <clause id="14737">
    <literal><![CDATA[
      (x \ y) / (K(x,z) * y) = ((x \ y) / y) * K(z,x)
    ]]></literal>
    <justification jstring="[para(4567(a,1),14736(a,1,2))].">
      <j1 rule="para" parents="4567 14736"/>
    </justification>
  </clause>

  <clause id="14738">
    <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(63,a,5025,a(flip),b,14725,a)].">
      <j1 rule="hyper" parents="63 5025 14725"/>
    </justification>
  </clause>

  <clause id="14739">
    <literal><![CDATA[
      (K(x,y) * ((y * z) * x)) \ ((y * (K(x,y) * z)) * R(x,y,z)) = a(x,y,K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(14282(a,1),14053(a,1,2,2))].">
      <j1 rule="para" parents="14282 14053"/>
    </justification>
  </clause>

  <clause id="14740">
    <literal><![CDATA[
      (K(x,y) * ((y * z) * x)) \ (K(x,y) * ((y * z) * R(x,y,z))) = a(x,y,K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(7747(a,1),14739(a,1,2))].">
      <j1 rule="para" parents="7747 14739"/>
    </justification>
  </clause>

  <clause id="14741">
    <literal><![CDATA[
      L(a(x,y,z),(y * z) * x,K(x,y)) = a(x,y,K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(14055,a,14740,a)].">
      <j1 rule="hyper" parents="14055 14740"/>
    </justification>
  </clause>

  <clause id="14742">
    <literal><![CDATA[
      L(K(x,K(y,T(z,x))),u,u \ x) \ ((K(z,y) \ u) * (u \ x)) = L(K(y,T(z,x)),u,u \ x) * x
    ]]></literal>
    <justification jstring="[para(9565(a,2),14114(a,1,1))].">
      <j1 rule="para" parents="9565 14114"/>
    </justification>
  </clause>

  <clause id="14743">
    <literal><![CDATA[
      K(x,(L(y,z,u) \ y) \ w) = K(x,L(y,z,u) * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(307,a,14121,a)].">
      <j1 rule="hyper" parents="307 14121"/>
    </justification>
  </clause>

  <clause id="14744">
    <literal><![CDATA[
      K(x,(y \ L(y,z,u)) * w) = K(x,L(y,z,u) * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(13504,a,14743,a)].">
      <j1 rule="hyper" parents="13504 14743"/>
    </justification>
  </clause>

  <clause id="14746">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1) * (y \ u)) = K(x,a(z \ 1,z,y) \ u)
    ]]></literal>
    <justification jstring="[para(3203(a,1),14743(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3203 14743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14747">
    <literal><![CDATA[
      K(x \ y,(y \ z) * x) * K(y,K(x,R(x \ y,u,w) \ z)) = K(x \ y,R(y / x,u,w) \ z)
    ]]></literal>
    <justification jstring="[para(7439(a,1),14176(a,1,2,2))].">
      <j1 rule="para" parents="7439 14176"/>
    </justification>
  </clause>

  <clause id="14748">
    <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(4406(a,2),14191(a,1,1,1,2,3))].">
      <j1 rule="para" parents="4406 14191"/>
    </justification>
  </clause>

  <clause id="14749">
    <literal><![CDATA[
      (K(x,y) * L(K(y,x) * z,u,u)) \ z = a(u,u,K(y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,14485,a(flip),b,14340,a),flip(a)].">
      <j1 rule="hyper" parents="63 14485 14340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14752">
    <literal><![CDATA[
      ((x * (T(y * z,x) / x)) * K(z,u)) / (y * T(z,u)) = a(x,x \ (y * z),x)
    ]]></literal>
    <justification jstring="[hyper(333,a,12505,a(flip),b,14567,a),flip(a)].">
      <j1 rule="hyper" parents="333 12505 14567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14753">
    <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(14690(a,1),14704(a,1,2))].">
      <j1 rule="para" parents="14690 14704"/>
    </justification>
  </clause>

  <clause id="14754">
    <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(63,a,14015,a(flip),b,14753,a)].">
      <j1 rule="hyper" parents="63 14015 14753"/>
    </justification>
  </clause>

  <clause id="14755">
    <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(12903,a,14754,a)].">
      <j1 rule="hyper" parents="12903 14754"/>
    </justification>
  </clause>

  <clause id="14756">
    <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(12902,a,14755,a)].">
      <j1 rule="hyper" parents="12902 14755"/>
    </justification>
  </clause>

  <clause id="14757">
    <literal><![CDATA[
      K(x,R(y,z,z \ 1) \ ((z \ 1) * u)) = K(x,y \ (z \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,14182,a(flip),b,14756,a),flip(a)].">
      <j1 rule="hyper" parents="63 14182 14756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14758">
    <literal><![CDATA[
      K(x,(y * (z \ 1)) \ ((z \ 1) * u)) = K(x,(y / z) \ (z \ u))
    ]]></literal>
    <justification jstring="[para(554(a,1),14757(a,1,2,1))].">
      <j1 rule="para" parents="554 14757"/>
    </justification>
  </clause>

  <clause id="14759">
    <literal><![CDATA[
      K(x,(y * (z \ 1)) \ ((z \ 1) * (z * u))) = K(x,(y / z) \ u)
    ]]></literal>
    <justification jstring="[para(9(a,1),14758(a,2,2,2))].">
      <j1 rule="para" parents="9 14758"/>
    </justification>
  </clause>

  <clause id="14760">
    <literal><![CDATA[
      K(x,(y * (z \ 1)) \ L(u,z,z \ 1)) = K(x,(y / z) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,5142,a(flip),b,14759,a)].">
      <j1 rule="hyper" parents="63 5142 14759"/>
    </justification>
  </clause>

  <clause id="14761">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,u \ x) \ ((K(y,z) \ u) * (u \ x)) = L(K(z,T(y,x)),u,u \ x) * x
    ]]></literal>
    <justification jstring="[para(6838(a,1),14742(a,1,1,1))].">
      <j1 rule="para" parents="6838 14742"/>
    </justification>
  </clause>

  <clause id="14762">
    <literal><![CDATA[
      K(x \ y,R(y / x,z,u) \ w) = K(x \ y,(y \ w) * x) * K(y,K(x,w))
    ]]></literal>
    <justification jstring="[para(10603(a,1),14747(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10603 14747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14763">
    <literal><![CDATA[
      K(x \ y,(y \ z) * x) * K(y,K(x,z)) = K(x \ y,x * (y \ z))
    ]]></literal>
    <justification jstring="[para(527(a,1),14762(a,1,2)),flip(a)].">
      <j1 rule="para" parents="527 14762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14765">
    <literal><![CDATA[
      (K(x,L(y,z * u,T(T(z,1),u))) * (z * u)) * (z \ K(u,z)) = K(x,y) * R(u,z,z \ 1)
    ]]></literal>
    <justification jstring="[para(11891(a,1),14748(a,1,1,1,2))].">
      <j1 rule="para" parents="11891 14748"/>
    </justification>
  </clause>

  <clause id="14766">
    <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(199(a,1),14765(a,1,1,1,2,3,1))].">
      <j1 rule="para" parents="199 14765"/>
    </justification>
  </clause>

  <clause id="14767">
    <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(10685,a,12589,a)].">
      <j1 rule="hyper" parents="10685 12589"/>
    </justification>
  </clause>

  <clause id="14768">
    <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(63,a,12882,a(flip),b,14767,a)].">
      <j1 rule="hyper" parents="63 12882 14767"/>
    </justification>
  </clause>

  <clause id="14769">
    <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(18(a,2),14768(a,1,2,2))].">
      <j1 rule="para" parents="18 14768"/>
    </justification>
  </clause>

  <clause id="14770">
    <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(2360(a,1),14769(a,1,2))].">
      <j1 rule="para" parents="2360 14769"/>
    </justification>
  </clause>

  <clause id="14771">
    <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(63,a,3216,a(flip),b,14770,a)].">
      <j1 rule="hyper" parents="63 3216 14770"/>
    </justification>
  </clause>

  <clause id="14772">
    <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(333,a,12549,a(flip),b,14771,a)].">
      <j1 rule="hyper" parents="333 12549 14771"/>
    </justification>
  </clause>

  <clause id="14774">
    <literal><![CDATA[
      a(x,a(y,z,u) \ 1,x) = a(x,u \ L(u,z,y),x)
    ]]></literal>
    <justification jstring="[para(206(a,1),14772(a,1,2,2))].">
      <j1 rule="para" parents="206 14772"/>
    </justification>
  </clause>

  <clause id="14775">
    <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(14774(a,1),9364(a,1,1,2))].">
      <j1 rule="para" parents="14774 9364"/>
    </justification>
  </clause>

  <clause id="14776">
    <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(12841(a,1),13961(a,1,2))].">
      <j1 rule="para" parents="12841 13961"/>
    </justification>
  </clause>

  <clause id="14777">
    <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(14062(a,1),14526(a,1,2,1))].">
      <j1 rule="para" parents="14062 14526"/>
    </justification>
  </clause>

  <clause id="14778">
    <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(4580,a,14777,a)].">
      <j1 rule="hyper" parents="4580 14777"/>
    </justification>
  </clause>

  <clause id="14779">
    <literal><![CDATA[
      L(x,y * T(((1 / z) * z) * u,R(1 / z,z,u)),w) = L(x,y * (u * K(z * u,z \ 1)),w)
    ]]></literal>
    <justification jstring="[para(107(a,1),14717(a,1,2,2,1))].">
      <j1 rule="para" parents="107 14717"/>
    </justification>
  </clause>

  <clause id="14780">
    <literal><![CDATA[
      L(x,y * (z * K(u * z,u \ 1)),w) = L(x,y * T(z,R(1 / u,u,z)),w)
    ]]></literal>
    <justification jstring="[para(77(a,1),14779(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="77 14779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14781">
    <literal><![CDATA[
      L(x,y * (z * K(u * z,u \ 1)),w) = L(x,y * T(z,u \ 1),w)
    ]]></literal>
    <justification jstring="[para(3768(a,1),14780(a,2,2,2))].">
      <j1 rule="para" parents="3768 14780"/>
    </justification>
  </clause>

  <clause id="14783">
    <literal><![CDATA[
      (K(x,T(y,z)) \ L((z \ T(x,y)) / (z \ x),u,w)) * (z \ x) = (z \ T(x,y)) * L(K(y,x),u,w)
    ]]></literal>
    <justification jstring="[para(13363(a,1),13372(a,1,1,1))].">
      <j1 rule="para" parents="13363 13372"/>
    </justification>
  </clause>

  <clause id="14784">
    <literal><![CDATA[
      (K(x,T(y,z)) \ L(K(x,T(y,z)),u,w)) * (z \ x) = (z \ T(x,y)) * L(K(y,x),u,w)
    ]]></literal>
    <justification jstring="[para(13363(a,1),14783(a,1,1,2,1))].">
      <j1 rule="para" parents="13363 14783"/>
    </justification>
  </clause>

  <clause id="14785">
    <literal><![CDATA[
      (K(x,T(y,z)) \ K(x,L(T(y,z),u,w))) * (z \ x) = (z \ T(x,y)) * L(K(y,x),u,w)
    ]]></literal>
    <justification jstring="[para(10851(a,1),14784(a,1,1,2))].">
      <j1 rule="para" parents="10851 14784"/>
    </justification>
  </clause>

  <clause id="14786">
    <literal><![CDATA[
      (K(x,T(y,z)) * K(y,L(T(x,z),u,w))) * (z \ y) = (z \ T(y,x)) * L(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(6427(a,1),14785(a,1,1))].">
      <j1 rule="para" parents="6427 14785"/>
    </justification>
  </clause>

  <clause id="14787">
    <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(12254(a,1),14145(a,2,2))].">
      <j1 rule="para" parents="12254 14145"/>
    </justification>
  </clause>

  <clause id="14788">
    <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(6740(a,1),14787(a,1,2,1))].">
      <j1 rule="para" parents="6740 14787"/>
    </justification>
  </clause>

  <clause id="14789">
    <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(5045(a,1),14788(a,1,2,2))].">
      <j1 rule="para" parents="5045 14788"/>
    </justification>
  </clause>

  <clause id="14790">
    <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(8637(a,2),14789(a,1,2,2))].">
      <j1 rule="para" parents="8637 14789"/>
    </justification>
  </clause>

  <clause id="14791">
    <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(12199(a,1),14790(a,1,2,2,1))].">
      <j1 rule="para" parents="12199 14790"/>
    </justification>
  </clause>

  <clause id="14792">
    <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(13226(a,1),14791(a,1,2,2))].">
      <j1 rule="para" parents="13226 14791"/>
    </justification>
  </clause>

  <clause id="14793">
    <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(11835(a,1),12258(a,1,2))].">
      <j1 rule="para" parents="11835 12258"/>
    </justification>
  </clause>

  <clause id="14794">
    <literal><![CDATA[
      L(K(x,y / ((x \ z) * u)),w,v5) \ L(K(x,x \ (y / ((x \ z) * u))),w,v5) = a(x,x \ (y / ((z / x) * u)),x)
    ]]></literal>
    <justification jstring="[para(11048(a,1),12934(a,1,2,1))].">
      <j1 rule="para" parents="11048 12934"/>
    </justification>
  </clause>

  <clause id="14795">
    <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(13763(a,1),14548(a,1,1))].">
      <j1 rule="para" parents="13763 14548"/>
    </justification>
  </clause>

  <clause id="14796">
    <literal><![CDATA[
      a(x,x \ (y / ((z / x) * u)),x) = a(x,x \ (y / ((x \ z) * u)),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,12932,a(flip),b,14794,a),flip(a)].">
      <j1 rule="hyper" parents="63 12932 14794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14797">
    <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(14547(a,1),14795(a,1,2))].">
      <j1 rule="para" parents="14547 14795"/>
    </justification>
  </clause>

  <clause id="14798">
    <literal><![CDATA[
      L(x,y,z) \ (L(x,y,T(z,u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(z,u)) * w = v5
    ]]></literal>
    <justification jstring="[para(14797(a,1),13087(a,1))].">
      <j1 rule="para" parents="14797 13087"/>
    </justification>
  </clause>

  <clause id="14799">
    <literal><![CDATA[
      L(x,y,T(z,u)) * (L(x,y,z) \ w) = a(x,y,K(z,u)) * w
    ]]></literal>
    <justification jstring="[hyper(14798,a,14626,a),flip(a)].">
      <j1 rule="hyper" parents="14798 14626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14800">
    <literal><![CDATA[
      L(x,y,T(z,u)) * (L(x,y,z) \ u) = T(u,L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(333,a,13833,a,b,14799,a),flip(a)].">
      <j1 rule="hyper" parents="333 13833 14799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14801">
    <literal><![CDATA[
      T(L(x,y,z) \ x,u) \ x = L(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(35,a,13439,a,b,14800,a)].">
      <j1 rule="hyper" parents="35 13439 14800"/>
    </justification>
  </clause>

  <clause id="14802">
    <literal><![CDATA[
      T(L(x,y,z) \ x,u) = L(x,y,T(z,u)) \ x
    ]]></literal>
    <justification jstring="[hyper(39,a,2559,a,b,14801,a),flip(a)].">
      <j1 rule="hyper" parents="39 2559 14801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14803">
    <literal><![CDATA[
      L(x,y,z) \ L(x,y,K(z,u)) = L(x,y,T(z,u \ 1)) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,14546,a,b,14802,a)].">
      <j1 rule="hyper" parents="63 14546 14802"/>
    </justification>
  </clause>

  <clause id="14804">
    <literal><![CDATA[
      (L(x * K(y,x),z,u) \ x) * K(y,x) = L(x,z,T(u,y \ 1)) \ x
    ]]></literal>
    <justification jstring="[hyper(14614,a,14803,a)].">
      <j1 rule="hyper" parents="14614 14803"/>
    </justification>
  </clause>

  <clause id="14805">
    <literal><![CDATA[
      (L(x * K(y,x),z,u) \ x) * K(y,x) = x / L(x,z,T(u,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(333,a,2558,a,b,14804,a),flip(a)].">
      <j1 rule="hyper" parents="333 2558 14804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14806">
    <literal><![CDATA[
      (x * L(y,z,u)) / T(x,y) = L(y,z,T(u,x \ 1))
    ]]></literal>
    <justification jstring="[hyper(14436,a,14805,a(flip))].">
      <j1 rule="hyper" parents="14436 14805"/>
    </justification>
  </clause>

  <clause id="14807">
    <literal><![CDATA[
      (a(x,y,z) * L(y,u,w)) / a(x,y,z) = L(y,u,T(w,a(x,y,z) \ 1))
    ]]></literal>
    <justification jstring="[para(13829(a,1),14806(a,1,2))].">
      <j1 rule="para" parents="13829 14806"/>
    </justification>
  </clause>

  <clause id="14808">
    <literal><![CDATA[
      L((a(x,y,z) * y) / a(x,y,z),u,w) = L(y,u,T(w,a(x,y,z) \ 1))
    ]]></literal>
    <justification jstring="[hyper(893,a,14807,a)].">
      <j1 rule="hyper" parents="893 14807"/>
    </justification>
  </clause>

  <clause id="14809">
    <literal><![CDATA[
      L((x * a(y,x,z)) / a(y,x,z),u,w) = L(x,u,T(w,a(y,x,z) \ 1))
    ]]></literal>
    <justification jstring="[para(13831(a,1),14808(a,1,1,1))].">
      <j1 rule="para" parents="13831 14808"/>
    </justification>
  </clause>

  <clause id="14810">
    <literal><![CDATA[
      L(x,y,T(z,a(u,x,w) \ 1)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),14809(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 14809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14811">
    <literal><![CDATA[
      L(x,y,L(z,x,K(u,w))) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,14501,a(flip),b,14810,a)].">
      <j1 rule="hyper" parents="63 14501 14810"/>
    </justification>
  </clause>

  <clause id="14812">
    <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(5994(a,1),13447(a,1,1,2))].">
      <j1 rule="para" parents="5994 13447"/>
    </justification>
  </clause>

  <clause id="14813">
    <literal><![CDATA[
      ((((x * y) \ x) \ T(((x * y) \ x) * z,y)) \ u) * ((z \ u) \ 1) = K(((x * y) \ x) \ 1,z * ((x * y) \ x))
    ]]></literal>
    <justification jstring="[hyper(333,a,8549,a(flip),b,13635,a),flip(a)].">
      <j1 rule="hyper" parents="333 8549 13635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14814">
    <literal><![CDATA[
      ((((x * y) \ x) \ T(((x * y) \ x) * z,y)) \ u) * ((z \ u) \ 1) = K(y,z * ((x * y) \ x))
    ]]></literal>
    <justification jstring="[hyper(333,a,5857,a(flip),b,14813,a),flip(a)].">
      <j1 rule="hyper" parents="333 5857 14813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14816">
    <literal><![CDATA[
      K(L(x,y,z),T(T(u,w),v5)) \ ((R(w,v6,v7) * T(u,w)) / T(u,w)) = (T(T(u,w),R(T(x,v5),y,z)) * R(T(w,u),v6,v7)) / T(u,w)
    ]]></literal>
    <justification jstring="[para(6429(a,1),13914(a,1,1))].">
      <j1 rule="para" parents="6429 13914"/>
    </justification>
  </clause>

  <clause id="14817">
    <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(12(a,1),14320(a,1,2,1,2))].">
      <j1 rule="para" parents="12 14320"/>
    </justification>
  </clause>

  <clause id="14821">
    <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(193(a,1),12351(a,1,2,1))].">
      <j1 rule="para" parents="193 12351"/>
    </justification>
  </clause>

  <clause id="14822">
    <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(6695,a,14821,a),flip(a)].">
      <j1 rule="hyper" parents="6695 14821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14825">
    <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(333,a,12295,a,b,14822,a),flip(a)].">
      <j1 rule="hyper" parents="333 12295 14822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14827">
    <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(333,a,12312,a(flip),b,14825,a),flip(a)].">
      <j1 rule="hyper" parents="333 12312 14825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14829">
    <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(333,a,4968,a(flip),b,14827,a),flip(a)].">
      <j1 rule="hyper" parents="333 4968 14827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14831">
    <literal><![CDATA[
      K((((x / y) \ 1) \ y) \ y,z / (y / (((x / y) \ 1) \ y))) = K(x \ y,z * (x / y))
    ]]></literal>
    <justification jstring="[hyper(333,a,12361,a(flip),b,14829,a),flip(a)].">
      <j1 rule="hyper" parents="333 12361 14829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14833">
    <literal><![CDATA[
      K((((x / y) \ 1) \ y) \ y,z / ((x / y) \ 1)) = K(x \ y,z * (x / y))
    ]]></literal>
    <justification jstring="[para(76(a,1),14831(a,1,2,2))].">
      <j1 rule="para" parents="76 14831"/>
    </justification>
  </clause>

  <clause id="14835">
    <literal><![CDATA[
      K((((x / y) \ 1) \ y) \ y,z / (1 / (x / y))) = K(x \ y,z * (x / y))
    ]]></literal>
    <justification jstring="[hyper(63,a,4799,a,b,14833,a)].">
      <j1 rule="hyper" parents="63 4799 14833"/>
    </justification>
  </clause>

  <clause id="14836">
    <literal><![CDATA[
      K((x / y) \ 1,T(z / (1 / (x / y)),y)) = K(x \ y,z * (x / y))
    ]]></literal>
    <justification jstring="[hyper(6694,a,14835,a)].">
      <j1 rule="hyper" parents="6694 14835"/>
    </justification>
  </clause>

  <clause id="14837">
    <literal><![CDATA[
      K(1 / (x / y),T(z / (1 / (x / y)),y)) = K(x \ y,z * (x / y))
    ]]></literal>
    <justification jstring="[hyper(3400,a,14836,a)].">
      <j1 rule="hyper" parents="3400 14836"/>
    </justification>
  </clause>

  <clause id="14838">
    <literal><![CDATA[
      K(1 / (x / y),(x / y) * T(z,y)) = K(x \ y,z * (x / y))
    ]]></literal>
    <justification jstring="[hyper(63,a,12321,a(flip),b,14837,a)].">
      <j1 rule="hyper" parents="63 12321 14837"/>
    </justification>
  </clause>

  <clause id="14839">
    <literal><![CDATA[
      K(x / y,(y / x) * T(z,x)) = K(y \ x,z * (y / x))
    ]]></literal>
    <justification jstring="[hyper(5091,a,14838,a)].">
      <j1 rule="hyper" parents="5091 14838"/>
    </justification>
  </clause>

  <clause id="14840">
    <literal><![CDATA[
      K((x / y) \ x,z * ((x / y) / x)) = K(y,T(((x / y) / x) * T(z,x),x))
    ]]></literal>
    <justification jstring="[hyper(6983,a,14839,a),flip(a)].">
      <j1 rule="hyper" parents="6983 14839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14841">
    <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(3361(a,1),14839(a,2,1))].">
      <j1 rule="para" parents="3361 14839"/>
    </justification>
  </clause>

  <clause id="14842">
    <literal><![CDATA[
      K(x,T(((y / x) / y) * T(z,y),y)) = K(x,z * ((y / x) / y))
    ]]></literal>
    <justification jstring="[hyper(4739,a,14840,a),flip(a)].">
      <j1 rule="hyper" parents="4739 14840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14844">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),y * (R(u,z \ 1,u) \ (z \ 1))) = T(x,((z \ 1) * ((u * (z \ 1)) \ (z \ 1))) * y)
    ]]></literal>
    <justification jstring="[para(12642(a,1),14280(a,1,1,2))].">
      <j1 rule="para" parents="12642 14280"/>
    </justification>
  </clause>

  <clause id="14845">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),y * (u \ (z \ 1))) = T(x,((z \ 1) * ((u * (z \ 1)) \ (z \ 1))) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,12692,a(flip),b,14844,a)].">
      <j1 rule="hyper" parents="63 12692 14844"/>
    </justification>
  </clause>

  <clause id="14847">
    <literal><![CDATA[
      T(x,((y \ 1) * ((z * (y \ 1)) \ (y \ 1))) * u) = T(x,(z \ (y \ 1)) * u)
    ]]></literal>
    <justification jstring="[hyper(12304,a,14845,a),flip(a)].">
      <j1 rule="hyper" parents="12304 14845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14849">
    <literal><![CDATA[
      T(x,(y * ((z * y) \ (y \ 1))) * u) = T(x,(z \ (y \ 1)) * u)
    ]]></literal>
    <justification jstring="[para(2964(a,1),14847(a,1,2,1))].">
      <j1 rule="para" parents="2964 14847"/>
    </justification>
  </clause>

  <clause id="14852">
    <literal><![CDATA[
      L(R(x,a(y,z,u) \ 1,a(y,z,u) \ 1),a(y,z,u) \ 1,x) = T(((a(y,z,u) \ 1) * x) * a(y,z,u),a(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(333,a,13284,a(flip),b,12443,a),flip(a)].">
      <j1 rule="hyper" parents="333 13284 12443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14853">
    <literal><![CDATA[
      L(R(x,a(y,z,u) \ 1,a(y,z,u) \ 1),a(y,z,u) \ 1,x) = L(x,a(y,z,u),a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(333,a,14164,a(flip),b,14852,a),flip(a)].">
      <j1 rule="hyper" parents="333 14164 14852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14854">
    <literal><![CDATA[
      L(R(x,a(y,z,u),a(y,z,u)),a(y,z,u) \ 1,x) = L(x,a(y,z,u),a(y,z,u))
    ]]></literal>
    <justification jstring="[para(1930(a,1),14853(a,1,1))].">
      <j1 rule="para" parents="1930 14853"/>
    </justification>
  </clause>

  <clause id="14855">
    <literal><![CDATA[
      L(R(x,a(y,z,u),a(y,z,u)),a(y,z,u),x) = L(x,a(y,z,u),a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(2631,a,14854,a)].">
      <j1 rule="hyper" parents="2631 14854"/>
    </justification>
  </clause>

  <clause id="14856">
    <literal><![CDATA[
      R(x,a(y,z,u),a(y,z,u)) = L(x,a(y,z,u),a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,12999,a(flip),b,14855,a)].">
      <j1 rule="hyper" parents="63 12999 14855"/>
    </justification>
  </clause>

  <clause id="14858">
    <literal><![CDATA[
      a(x,y,z) \ L(u,a(x,y,z),a(x,y,z)) = L(u * (a(x,y,z) \ 1),y,K(z,x))
    ]]></literal>
    <justification jstring="[para(14856(a,1),14483(a,1,2))].">
      <j1 rule="para" parents="14856 14483"/>
    </justification>
  </clause>

  <clause id="14859">
    <literal><![CDATA[
      L(x * (a(y,z,u) \ 1),z,K(u,y)) = (a(y,z,u) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(2610,a,14858,a),flip(a)].">
      <j1 rule="hyper" parents="2610 14858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14860">
    <literal><![CDATA[
      K(L(x,y,z),T(u,w)) \ ((R(w,v5,v6) * T(u,w)) / T(u,w)) = (T(T(u,w),R(T(x,u),y,z)) * R(T(w,u),v5,v6)) / T(u,w)
    ]]></literal>
    <justification jstring="[para(179(a,1),14816(a,1,1,2))].">
      <j1 rule="para" parents="179 14816"/>
    </justification>
  </clause>

  <clause id="14861">
    <literal><![CDATA[
      (T(T(x,y),R(T(y,x),z,u)) * R(T(y,x),w,v5)) / T(x,y) = K(L(y,z,u),x) \ ((R(y,w,v5) * T(x,y)) / T(x,y))
    ]]></literal>
    <justification jstring="[para(6436(a,1),14860(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6436 14860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14862">
    <literal><![CDATA[
      (T(T(x,y),R(T(y,x),z,u)) * R(T(y,x),w,v5)) / T(x,y) = K(L(y,z,u),x) \ R(y,w,v5)
    ]]></literal>
    <justification jstring="[para(11(a,1),14861(a,2,2))].">
      <j1 rule="para" parents="11 14861"/>
    </justification>
  </clause>

  <clause id="14864">
    <literal><![CDATA[
      (T(T(x,y),L(T(y,x),z,u)) * R(T(y,x),w,v5)) / T(x,y) = K(L(y,z,u),x) \ R(y,w,v5)
    ]]></literal>
    <justification jstring="[para(13879(a,1),14862(a,1,1,1))].">
      <j1 rule="para" parents="13879 14862"/>
    </justification>
  </clause>

  <clause id="14865">
    <literal><![CDATA[
      (T(T(x,L(y,z,u)),y) * R(T(y,x),w,v5)) / T(x,y) = K(L(y,z,u),x) \ R(y,w,v5)
    ]]></literal>
    <justification jstring="[para(3707(a,1),14864(a,1,1,1))].">
      <j1 rule="para" parents="3707 14864"/>
    </justification>
  </clause>

  <clause id="14866">
    <literal><![CDATA[
      (T(T(x,y),L(y,z,u)) * R(T(y,x),w,v5)) / T(x,y) = K(L(y,z,u),x) \ R(y,w,v5)
    ]]></literal>
    <justification jstring="[para(23(a,1),14865(a,1,1,1))].">
      <j1 rule="para" parents="23 14865"/>
    </justification>
  </clause>

  <clause id="14867">
    <literal><![CDATA[
      K(L(x,y,z),u) \ R(x,y,z) = (T(u,x) * R(x,y,z)) / T(u,x)
    ]]></literal>
    <justification jstring="[para(14070(a,1),14866(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14070 14866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14868">
    <literal><![CDATA[
      K(L(x,y,z),u) \ R(x,y,z) = R(K(x,u) \ x,y,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,4953,a(flip),b,14867,a),flip(a)].">
      <j1 rule="hyper" parents="333 4953 14867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14869">
    <literal><![CDATA[
      R(K(x,y) \ x,y,z) = K(x,y) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(10357(a,1),14868(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10357 14868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14870">
    <literal><![CDATA[
      K(x,y) \ R(x,y,z) = ((y * x) * z) / (y * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,4459,a(flip),b,14869,a),flip(a)].">
      <j1 rule="hyper" parents="63 4459 14869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14878">
    <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(8932(a,1),12551(a,1,1))].">
      <j1 rule="para" parents="8932 12551"/>
    </justification>
  </clause>

  <clause id="14879">
    <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(14521(a,1),14064(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14521 14064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14884">
    <literal><![CDATA[
      L(x \ y,z,u) * ((x \ y) \ ((x \ L(y,w,y)) * v5)) = (a(y,w,y) \ v5) * L((a(y,w,y) \ v5) \ ((x \ L(y,w,y)) * v5),z,u)
    ]]></literal>
    <justification jstring="[para(12817(a,1),12837(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="12817 12837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14885">
    <literal><![CDATA[
      L(x \ y,z,u) * ((x \ y) \ ((x \ L(y,w,y)) * v5)) = (a(y,w,y) \ v5) * L((v5 \ ((x \ L(y,w,y)) * v5)) * a(y,w,y),z,u)
    ]]></literal>
    <justification jstring="[para(12818(a,1),14884(a,2,2,1))].">
      <j1 rule="para" parents="12818 14884"/>
    </justification>
  </clause>

  <clause id="14887">
    <literal><![CDATA[
      L(x \ y,z,u) * ((x \ y) \ ((x \ L(y,w,y)) * v5)) = (a(y,w,y) \ v5) * L(T((x \ L(y,w,y)) * a(y,w,y),v5),z,u)
    ]]></literal>
    <justification jstring="[para(12600(a,1),14885(a,2,2,1))].">
      <j1 rule="para" parents="12600 14885"/>
    </justification>
  </clause>

  <clause id="14888">
    <literal><![CDATA[
      L(x \ y,z,u) * ((x \ y) \ ((x \ L(y,w,y)) * v5)) = (a(y,w,y) \ v5) * L(T(x \ L(R(y,w,y),w,y),v5),z,u)
    ]]></literal>
    <justification jstring="[para(12930(a,1),14887(a,2,2,1,1))].">
      <j1 rule="para" parents="12930 14887"/>
    </justification>
  </clause>

  <clause id="14889">
    <literal><![CDATA[
      L(x \ y,z,u) * ((x \ y) \ ((x \ L(y,w,y)) * v5)) = (a(y,w,y) \ v5) * L(T(x \ y,v5),z,u)
    ]]></literal>
    <justification jstring="[para(3736(a,1),14888(a,2,2,1,1,2))].">
      <j1 rule="para" parents="3736 14888"/>
    </justification>
  </clause>

  <clause id="14890">
    <literal><![CDATA[
      L(x \ y,z,u) * ((x \ y) \ ((x \ L(y,w,y)) * v5)) = v5 * (a(y,w,y) \ L(T(x \ y,v5),z,u))
    ]]></literal>
    <justification jstring="[hyper(333,a,12805,a(flip),b,14889,a),flip(a)].">
      <j1 rule="hyper" parents="333 12805 14889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14891">
    <literal><![CDATA[
      L(x \ y,z,u) * ((x \ y) \ ((x \ L(y,w,y)) * v5)) = v5 * L(a(y,w,y) \ T(x \ y,v5),z,u)
    ]]></literal>
    <justification jstring="[para(12928(a,2),14890(a,2,2))].">
      <j1 rule="para" parents="12928 14890"/>
    </justification>
  </clause>

  <clause id="14892">
    <literal><![CDATA[
      L(x \ y,z,u) * ((x \ y) \ ((x \ L(y,w,y)) * v5)) = v5 * L(T(a(y,w,y) \ (x \ y),v5),z,u)
    ]]></literal>
    <justification jstring="[para(12602(a,2),14891(a,2,2,1))].">
      <j1 rule="para" parents="12602 14891"/>
    </justification>
  </clause>

  <clause id="14893">
    <literal><![CDATA[
      L(x \ y,z,u) * ((x \ y) \ ((x \ L(y,w,y)) * v5)) = v5 * L(T(x \ L(y,w,y),v5),z,u)
    ]]></literal>
    <justification jstring="[para(12813(a,1),14892(a,2,2,1,1))].">
      <j1 rule="para" parents="12813 14892"/>
    </justification>
  </clause>

  <clause id="14894">
    <literal><![CDATA[
      L(x \ y,z,u) * ((x \ y) \ ((x \ L(y,w,y)) * v5)) = L(x \ L(y,w,y),z,u) * v5
    ]]></literal>
    <justification jstring="[hyper(333,a,251,a(flip),b,14893,a),flip(a)].">
      <j1 rule="hyper" parents="333 251 14893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14895">
    <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(12817(a,1),14894(a,1,2))].">
      <j1 rule="para" parents="12817 14894"/>
    </justification>
  </clause>

  <clause id="14897">
    <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(63,a,12335,a(flip),b,12152,a)].">
      <j1 rule="hyper" parents="63 12335 12152"/>
    </justification>
  </clause>

  <clause id="14898">
    <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(9993(a,1),14897(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9993 14897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14901">
    <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(13400(a,1),14898(a,2,2,2))].">
      <j1 rule="para" parents="13400 14898"/>
    </justification>
  </clause>

  <clause id="14902">
    <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(6785(a,1),14901(a,2,2))].">
      <j1 rule="para" parents="6785 14901"/>
    </justification>
  </clause>

  <clause id="14903">
    <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(10851(a,1),14902(a,1,1,2))].">
      <j1 rule="para" parents="10851 14902"/>
    </justification>
  </clause>

  <clause id="14904">
    <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(63,a,11690,a,b,14903,a)].">
      <j1 rule="hyper" parents="63 11690 14903"/>
    </justification>
  </clause>

  <clause id="14905">
    <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(11261(a,1),14904(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11261 14904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14906">
    <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(121,a,14905,a,b,14381,a(flip))].">
      <j1 rule="hyper" parents="121 14905 14381"/>
    </justification>
  </clause>

  <clause id="14908">
    <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(7086(a,2),14906(a,1,2,2))].">
      <j1 rule="para" parents="7086 14906"/>
    </justification>
  </clause>

  <clause id="14909">
    <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(7840(a,2),14908(a,1,2))].">
      <j1 rule="para" parents="7840 14908"/>
    </justification>
  </clause>

  <clause id="14910">
    <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(7381(a,2),14909(a,1,2,2,2))].">
      <j1 rule="para" parents="7381 14909"/>
    </justification>
  </clause>

  <clause id="14911">
    <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(6371(a,2),14910(a,1,2,2))].">
      <j1 rule="para" parents="6371 14910"/>
    </justification>
  </clause>

  <clause id="14912">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(z,u)) = T(y,K(u,z) * x)
    ]]></literal>
    <justification jstring="[para(5042(a,2),14911(a,1,2))].">
      <j1 rule="para" parents="5042 14911"/>
    </justification>
  </clause>

  <clause id="14914">
    <literal><![CDATA[
      T(x * T(1 / x,K(y,z)),K(y,z)) = K(x,K(z,y) * (1 / x))
    ]]></literal>
    <justification jstring="[hyper(38,a,4278,a(flip),b,14912,a),flip(a)].">
      <j1 rule="hyper" parents="38 4278 14912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14915">
    <literal><![CDATA[
      (x * K(K(y,z),x)) \ T(u * x,K(y,z)) = T(u,K(z,y) * (x * K(K(y,z),x)))
    ]]></literal>
    <justification jstring="[para(4239(a,1),14912(a,1,2,1,2))].">
      <j1 rule="para" parents="4239 14912"/>
    </justification>
  </clause>

  <clause id="14916">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(u,z)) = T(y,K(z,u) * x)
    ]]></literal>
    <justification jstring="[para(6840(a,1),14912(a,1,2,1,2))].">
      <j1 rule="para" parents="6840 14912"/>
    </justification>
  </clause>

  <clause id="14917">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(z,1 / u)) = T(y,K(1 / u,z) * x)
    ]]></literal>
    <justification jstring="[para(7189(a,1),14912(a,1,2,1,2))].">
      <j1 rule="para" parents="7189 14912"/>
    </justification>
  </clause>

  <clause id="14918">
    <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(14912(a,1),13624(a,2,1,2))].">
      <j1 rule="para" parents="14912 13624"/>
    </justification>
  </clause>

  <clause id="14919">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(z,u)) = T(y,K(z,u) * x)
    ]]></literal>
    <justification jstring="[para(6840(a,1),14916(a,1,2))].">
      <j1 rule="para" parents="6840 14916"/>
    </justification>
  </clause>

  <clause id="14920">
    <literal><![CDATA[
      T(x,K(y,z) * u) = T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,14912,a(flip),b,14919,a)].">
      <j1 rule="hyper" parents="63 14912 14919"/>
    </justification>
  </clause>

  <clause id="14921">
    <literal><![CDATA[
      T(x,K(y,y \ z) * u) = T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(333,a,12760,a,b,14920,a)].">
      <j1 rule="hyper" parents="333 12760 14920"/>
    </justification>
  </clause>

  <clause id="14922">
    <literal><![CDATA[
      x \ T(x,K(y,z) * u) = K(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(121,a,14920,a,b,4222,a(flip))].">
      <j1 rule="hyper" parents="121 14920 4222"/>
    </justification>
  </clause>

  <clause id="14923">
    <literal><![CDATA[
      T(x,K(y,z) * T(u,K(z,y))) = T(x,u * K(z,y))
    ]]></literal>
    <justification jstring="[para(111(a,1),14920(a,1,2)),flip(a)].">
      <j1 rule="para" parents="111 14920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14924">
    <literal><![CDATA[
      T(x,K(y,z) * (z * u)) = T(x,T(z,y) * u)
    ]]></literal>
    <justification jstring="[para(4273(a,1),14920(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4273 14920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14925">
    <literal><![CDATA[
      T(x,K(y,z) * (y \ u)) = T(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(4555(a,1),14920(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4555 14920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14926">
    <literal><![CDATA[
      K(x,K(y,z) * u) = K(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(4306,a,14922,a)].">
      <j1 rule="hyper" parents="4306 14922"/>
    </justification>
  </clause>

  <clause id="14927">
    <literal><![CDATA[
      K(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y) * u) = w
    ]]></literal>
    <justification jstring="[para(14922(a,1),4306(a,1))].">
      <j1 rule="para" parents="14922 4306"/>
    </justification>
  </clause>

  <clause id="14928">
    <literal><![CDATA[
      K(x,K(y,y \ z) * u) = K(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(12838,a,14926,a),flip(a)].">
      <j1 rule="hyper" parents="12838 14926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14929">
    <literal><![CDATA[
      K(x,K(y,z) \ u) = K(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[para(4567(a,2),14926(a,1,2))].">
      <j1 rule="para" parents="4567 14926"/>
    </justification>
  </clause>

  <clause id="14930">
    <literal><![CDATA[
      K(x,K(y,z) * (y \ u)) = K(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(4555(a,1),14926(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4555 14926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14931">
    <literal><![CDATA[
      K(x,K(y,z \ u) * (u / z)) = K(x,T(u / z,T(y,z)))
    ]]></literal>
    <justification jstring="[para(6511(a,1),14926(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6511 14926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14932">
    <literal><![CDATA[
      K(x,K(y,y \ z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y) * u) = w
    ]]></literal>
    <justification jstring="[para(14926(a,1),12838(a,1))].">
      <j1 rule="para" parents="14926 12838"/>
    </justification>
  </clause>

  <clause id="14933">
    <literal><![CDATA[
      K(x,K(L(y,y \ z,u),w) * ((y \ z) * u)) = K(x,T(R(y,y \ z,u),w) \ (z * u))
    ]]></literal>
    <justification jstring="[para(13884(a,1),14926(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13884 14926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14934">
    <literal><![CDATA[
      K(x,K(y,z) \ u) = K(x,K(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(4567(a,2),14929(a,2,2))].">
      <j1 rule="para" parents="4567 14929"/>
    </justification>
  </clause>

  <clause id="14935">
    <literal><![CDATA[
      K(x,K(y,z) \ (y * u)) = K(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[para(4273(a,1),14929(a,2,2))].">
      <j1 rule="para" parents="4273 14929"/>
    </justification>
  </clause>

  <clause id="14936">
    <literal><![CDATA[
      K(x,K(y,z) \ (z \ u)) = K(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(4555(a,1),14929(a,2,2))].">
      <j1 rule="para" parents="4555 14929"/>
    </justification>
  </clause>

  <clause id="14937">
    <literal><![CDATA[
      K(x,K(y,y \ z) \ u) = K(x,K(z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(333,a,12864,a(flip),b,14934,a),flip(a)].">
      <j1 rule="hyper" parents="333 12864 14934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14938">
    <literal><![CDATA[
      T(x,K(y,z) \ u) = T(x,K(z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(124,a,14934,a,b,4837,a)].">
      <j1 rule="hyper" parents="124 14934 4837"/>
    </justification>
  </clause>

  <clause id="14939">
    <literal><![CDATA[
      T(x,K(y,z) \ (y / u)) = T(x,T(y,z) / u)
    ]]></literal>
    <justification jstring="[para(13299(a,1),14938(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13299 14938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14940">
    <literal><![CDATA[
      T(x,((y * z) / y) * u) = T(x,T(z,y) * u)
    ]]></literal>
    <justification jstring="[para(4817(a,1),14924(a,1,2))].">
      <j1 rule="para" parents="4817 14924"/>
    </justification>
  </clause>

  <clause id="14941">
    <literal><![CDATA[
      T(x,T(y,y \ z) * u) = T(x,(z / (z / y)) * u)
    ]]></literal>
    <justification jstring="[para(4876(a,1),14924(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4876 14924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14942">
    <literal><![CDATA[
      T(x,((y * z) / y) \ u) = T(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(4519(a,2),14925(a,1,2))].">
      <j1 rule="para" parents="4519 14925"/>
    </justification>
  </clause>

  <clause id="14943">
    <literal><![CDATA[
      T(x,K(y \ 1,z) * (((y \ u) / u) \ w)) = T(x,T((y \ u) / u,z) \ w)
    ]]></literal>
    <justification jstring="[para(4972(a,1),14925(a,1,2,1))].">
      <j1 rule="para" parents="4972 14925"/>
    </justification>
  </clause>

  <clause id="14944">
    <literal><![CDATA[
      T(x,T(y \ z,y) \ u) = T(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[para(4830(a,1),14925(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4830 14925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14945">
    <literal><![CDATA[
      T(x,T(y,z) \ (z \ u)) = T(x,y \ (T(z,y) \ u))
    ]]></literal>
    <justification jstring="[para(4836(a,1),14925(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4836 14925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14946">
    <literal><![CDATA[
      T(x,(y \ K(z,y \ 1)) \ u) = T(x,T(y \ 1,z) \ u)
    ]]></literal>
    <justification jstring="[para(4834(a,1),14925(a,1,2))].">
      <j1 rule="para" parents="4834 14925"/>
    </justification>
  </clause>

  <clause id="14947">
    <literal><![CDATA[
      K(x,K(y,y \ z) * u) = K(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(333,a,14926,a,b,14928,a),flip(a)].">
      <j1 rule="hyper" parents="333 14926 14928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14948">
    <literal><![CDATA[
      K(x,K(y,z) * T(u,K(z,z \ y))) = K(x,u * K(z,z \ y))
    ]]></literal>
    <justification jstring="[para(111(a,1),14928(a,1,2)),flip(a)].">
      <j1 rule="para" parents="111 14928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14949">
    <literal><![CDATA[
      K(x,K((y \ 1) \ z,y) * u) = K(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[para(10263(a,1),14928(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10263 14928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14950">
    <literal><![CDATA[
      K(x,((y * z) / y) \ u) = K(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(4519(a,2),14930(a,1,2))].">
      <j1 rule="para" parents="4519 14930"/>
    </justification>
  </clause>

  <clause id="14951">
    <literal><![CDATA[
      K(x,T(y \ z,y) \ u) = K(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[para(4830(a,1),14930(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4830 14930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14952">
    <literal><![CDATA[
      K(x,T(y,y \ z) \ u) = K(x,(z / (z / y)) \ u)
    ]]></literal>
    <justification jstring="[para(4832(a,2),14930(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4832 14930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14953">
    <literal><![CDATA[
      T(x,K(y,y \ z) \ u) = T(x,K(z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(124,a,14937,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 14937 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14954">
    <literal><![CDATA[
      K(x,K(y,z \ y) \ u) = K(x,K(y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,12865,a,b,14937,a)].">
      <j1 rule="hyper" parents="63 12865 14937"/>
    </justification>
  </clause>

  <clause id="14955">
    <literal><![CDATA[
      K(x,K(y \ z,z) \ u) = K(x,K(z,y \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(5069(a,1),14937(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5069 14937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14956">
    <literal><![CDATA[
      T(x,K(y,z) \ (z / u)) = T(x,T(z,y) / u)
    ]]></literal>
    <justification jstring="[hyper(63,a,14938,a,b,14939,a)].">
      <j1 rule="hyper" parents="63 14938 14939"/>
    </justification>
  </clause>

  <clause id="14957">
    <literal><![CDATA[
      T(x,T(T(y,z),z) * u) = T(x,y * u)
    ]]></literal>
    <justification jstring="[para(239(a,1),14940(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="239 14940"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14958">
    <literal><![CDATA[
      T(x,y * (T(T(y,z),z) \ u)) = T(x,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),14957(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 14957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14959">
    <literal><![CDATA[
      T(x,y * (T(T(y,z),z) \ u)) = x * K(x,u)
    ]]></literal>
    <justification jstring="[hyper(333,a,4222,a(flip),b,14958,a),flip(a)].">
      <j1 rule="hyper" parents="333 4222 14958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14960">
    <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(13388(a,1),14942(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="13388 14942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14961">
    <literal><![CDATA[
      T(x,T((y / (z \ 1)) / y,y) \ u) = T(x,((y / (z \ K(z,y))) / y) \ u)
    ]]></literal>
    <justification jstring="[para(8493(a,1),14944(a,1,2,1,1))].">
      <j1 rule="para" parents="8493 14944"/>
    </justification>
  </clause>

  <clause id="14962">
    <literal><![CDATA[
      K(x,K(y,z * y) * u) = K(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[para(4394(a,1),14947(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4394 14947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14963">
    <literal><![CDATA[
      K(x,K(y,z) * ((y \ z) * u)) = K(x,(z / y) * u)
    ]]></literal>
    <justification jstring="[para(4875(a,1),14947(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4875 14947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14964">
    <literal><![CDATA[
      K(x,K(y * (z \ u),(y * (z \ u)) \ u) * w) = K(x,K(y * (u / z),u) * w)
    ]]></literal>
    <justification jstring="[para(12901(a,2),14947(a,2,2,1))].">
      <j1 rule="para" parents="12901 14947"/>
    </justification>
  </clause>

  <clause id="14965">
    <literal><![CDATA[
      K(x,T(T(y,z),z) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(239(a,1),14950(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="239 14950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14966">
    <literal><![CDATA[
      K(x,T(T(y \ z,u),y) \ w) = K(x,T(z / y,u) \ w)
    ]]></literal>
    <justification jstring="[para(474(a,1),14950(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="474 14950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14967">
    <literal><![CDATA[
      K(x,((L(y,z,z \ 1) * z) / z) \ u) = K(x,T((1 / z) * (y * z),z) \ u)
    ]]></literal>
    <justification jstring="[para(2661(a,1),14950(a,1,2,1,1))].">
      <j1 rule="para" parents="2661 14950"/>
    </justification>
  </clause>

  <clause id="14968">
    <literal><![CDATA[
      K(x,(L(y,z,y) * z) \ u) = K(x,T(z * y,y) \ u)
    ]]></literal>
    <justification jstring="[para(3722(a,1),14950(a,1,2,1))].">
      <j1 rule="para" parents="3722 14950"/>
    </justification>
  </clause>

  <clause id="14969">
    <literal><![CDATA[
      K(x,T(y,z) \ (T(z,y) * u)) = K(x,y \ (z * u))
    ]]></literal>
    <justification jstring="[para(4751(a,1),14950(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4751 14950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14970">
    <literal><![CDATA[
      K(x,T((y \ 1) * (z * y),y) \ u) = K(x,((y \ 1) * (y * z)) \ u)
    ]]></literal>
    <justification jstring="[para(1715(a,1),14965(a,1,2,1,1))].">
      <j1 rule="para" parents="1715 14965"/>
    </justification>
  </clause>

  <clause id="14971">
    <literal><![CDATA[
      K(x,T(((y * z) \ z) \ 1,z) \ u) = K(x,(((z * y) \ z) \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(11205(a,1),14965(a,1,2,1,1))].">
      <j1 rule="para" parents="11205 14965"/>
    </justification>
  </clause>

  <clause id="14972">
    <literal><![CDATA[
      K(x,K(y \ z,z) \ u) = K(x,K(z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,14934,a,b,14954,a)].">
      <j1 rule="hyper" parents="63 14934 14954"/>
    </justification>
  </clause>

  <clause id="14973">
    <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(6753(a,2),14956(a,2,2,1))].">
      <j1 rule="para" parents="6753 14956"/>
    </justification>
  </clause>

  <clause id="14974">
    <literal><![CDATA[
      K(x,y * (T(T(y,z),z) \ u)) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(4305,a,14959,a)].">
      <j1 rule="hyper" parents="4305 14959"/>
    </justification>
  </clause>

  <clause id="14975">
    <literal><![CDATA[
      K(x,T(T(y,z),z) * u) = K(x,y * u)
    ]]></literal>
    <justification jstring="[para(9(a,1),14974(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 14974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14976">
    <literal><![CDATA[
      K(x,T(y \ z,y) * u) = K(x,(z / y) * u)
    ]]></literal>
    <justification jstring="[para(113(a,1),14975(a,1,2,1,1))].">
      <j1 rule="para" parents="113 14975"/>
    </justification>
  </clause>

  <clause id="14977">
    <literal><![CDATA[
      K(x,T(T(R(y,z,u),w),w) * (z * u)) = K(x,(y * z) * u)
    ]]></literal>
    <justification jstring="[para(107(a,1),14975(a,2,2))].">
      <j1 rule="para" parents="107 14975"/>
    </justification>
  </clause>

  <clause id="14978">
    <literal><![CDATA[
      K(x,T(L(y \ z,u,w),y) * v5) = K(x,L(z / y,u,w) * v5)
    ]]></literal>
    <justification jstring="[para(260(a,1),14975(a,1,2,1,1))].">
      <j1 rule="para" parents="260 14975"/>
    </justification>
  </clause>

  <clause id="14979">
    <literal><![CDATA[
      K(x,(y * K(z,y)) * u) = K(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[para(4239(a,1),14975(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="4239 14975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14980">
    <literal><![CDATA[
      K(x,y * T(T(z,u),u)) = K(x,z * T(y,z))
    ]]></literal>
    <justification jstring="[para(6945(a,1),14975(a,1,2))].">
      <j1 rule="para" parents="6945 14975"/>
    </justification>
  </clause>

  <clause id="14981">
    <literal><![CDATA[
      K(x,T(y \ z,y) / u) = K(x,(z / y) * (u \ 1))
    ]]></literal>
    <justification jstring="[hyper(13528,a,14976,a)].">
      <j1 rule="hyper" parents="13528 14976"/>
    </justification>
  </clause>

  <clause id="14982">
    <literal><![CDATA[
      K(T(x \ y,x) * z,u) = (w * K(u,(y / x) * z)) \ w
    ]]></literal>
    <justification jstring="[para(14976(a,1),5990(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="14976 5990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14983">
    <literal><![CDATA[
      K(x,T((y * z) \ u,y * z) * (z * K(y,z))) = K(x,(u / (z * y)) * z)
    ]]></literal>
    <justification jstring="[para(10453(a,1),14976(a,2,2))].">
      <j1 rule="para" parents="10453 14976"/>
    </justification>
  </clause>

  <clause id="14984">
    <literal><![CDATA[
      K(x,y * (K(z,y) * u)) = K(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[para(3542(a,1),14979(a,1,2))].">
      <j1 rule="para" parents="3542 14979"/>
    </justification>
  </clause>

  <clause id="14985">
    <literal><![CDATA[
      K(x,y * T(T(z,u),u)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(111(a,1),14980(a,2,2))].">
      <j1 rule="para" parents="111 14980"/>
    </justification>
  </clause>

  <clause id="14986">
    <literal><![CDATA[
      T(x,y * T(T(z,u),u)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(124,a,14985,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 14985 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14987">
    <literal><![CDATA[
      K(x,y * T(z \ u,z)) = K(x,y * (u / z))
    ]]></literal>
    <justification jstring="[para(113(a,1),14985(a,1,2,2,1))].">
      <j1 rule="para" parents="113 14985"/>
    </justification>
  </clause>

  <clause id="14988">
    <literal><![CDATA[
      K(x,y * ((z * u) / z)) = K(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[para(238(a,1),14985(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="238 14985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14989">
    <literal><![CDATA[
      K(x,y * T(z,z \ u)) = K(x,y * (u / (u / z)))
    ]]></literal>
    <justification jstring="[para(3701(a,1),14985(a,1,2,2,1))].">
      <j1 rule="para" parents="3701 14985"/>
    </justification>
  </clause>

  <clause id="14990">
    <literal><![CDATA[
      K(x,y * (z * K(u,z))) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(4239(a,1),14985(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4239 14985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14991">
    <literal><![CDATA[
      K(x,y * T(((z * u) \ u) \ 1,u)) = K(x,y * (((u * z) \ u) \ 1))
    ]]></literal>
    <justification jstring="[para(11205(a,1),14985(a,1,2,2,1))].">
      <j1 rule="para" parents="11205 14985"/>
    </justification>
  </clause>

  <clause id="14992">
    <literal><![CDATA[
      T(x,y * ((z * u) / z)) = T(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[para(238(a,1),14986(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="238 14986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14993">
    <literal><![CDATA[
      T(x,y * (z * K(u,z))) = T(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(4239(a,1),14986(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4239 14986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14994">
    <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(14986(a,1),12267(a,1,2,1))].">
      <j1 rule="para" parents="14986 12267"/>
    </justification>
  </clause>

  <clause id="14995">
    <literal><![CDATA[
      K(x,y * T(z \ T(u,z),z)) = K(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(333,a,12675,a(flip),b,14987,a),flip(a)].">
      <j1 rule="hyper" parents="333 12675 14987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14996">
    <literal><![CDATA[
      K(x,y * (T(z,u \ 1) \ (u \ z))) = K(x,y * ((u \ z) / z))
    ]]></literal>
    <justification jstring="[para(3716(a,1),14987(a,1,2,2))].">
      <j1 rule="para" parents="3716 14987"/>
    </justification>
  </clause>

  <clause id="14997">
    <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(13388(a,1),14988(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="13388 14988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14998">
    <literal><![CDATA[
      K(x,y \ (z * K(u,z))) = K(x,(y \ 1) * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(13535,a,14990,a)].">
      <j1 rule="hyper" parents="13535 14990"/>
    </justification>
  </clause>

  <clause id="14999">
    <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(3793(a,1),14990(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="3793 14990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15000">
    <literal><![CDATA[
      K(x * ((y * z) / y),u) = u / T(u,x * T(z,y))
    ]]></literal>
    <justification jstring="[hyper(197,a,14992,a(flip),b,4233,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="197 14992 4233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15002">
    <literal><![CDATA[
      K(x,K(y,y \ z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(14928(a,2),14927(a,1))].">
      <j1 rule="para" parents="14928 14927"/>
    </justification>
  </clause>

  <clause id="15003">
    <literal><![CDATA[
      T(x,K(y,z) * (u * K(K(z,y),u))) = T(x,u * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,14993,a,b,14923,a)].">
      <j1 rule="hyper" parents="63 14993 14923"/>
    </justification>
  </clause>

  <clause id="15004">
    <literal><![CDATA[
      T(x,y * K(z,u)) = T(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[para(6852(a,1),14923(a,1,2))].">
      <j1 rule="para" parents="6852 14923"/>
    </justification>
  </clause>

  <clause id="15005">
    <literal><![CDATA[
      x / T(x,y * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(y * K(u,z),x) = w
    ]]></literal>
    <justification jstring="[para(15004(a,1),4313(a,1,2))].">
      <j1 rule="para" parents="15004 4313"/>
    </justification>
  </clause>

  <clause id="15006">
    <literal><![CDATA[
      T(x,(y / z) * K(z,u)) = T(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(5450(a,1),15004(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5450 15004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15007">
    <literal><![CDATA[
      T(x,(y \ z) * K(u,z)) = T(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(13255(a,1),15004(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13255 15004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15008">
    <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(5935(a,1),15006(a,1,2,1))].">
      <j1 rule="para" parents="5935 15006"/>
    </justification>
  </clause>

  <clause id="15010">
    <literal><![CDATA[
      T(x,y / ((z * u) / z)) = T(x,y / T(u,z))
    ]]></literal>
    <justification jstring="[para(7664(a,2),15006(a,1,2))].">
      <j1 rule="para" parents="7664 15006"/>
    </justification>
  </clause>

  <clause id="15011">
    <literal><![CDATA[
      T(x,y \ ((z * u) / z)) = T(x,y \ T(u,z))
    ]]></literal>
    <justification jstring="[para(13413(a,2),15007(a,1,2))].">
      <j1 rule="para" parents="13413 15007"/>
    </justification>
  </clause>

  <clause id="15012">
    <literal><![CDATA[
      T(x,y / T(T(z,u),u)) = T(x,y / z)
    ]]></literal>
    <justification jstring="[para(239(a,1),15010(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="239 15010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15013">
    <literal><![CDATA[
      T(x,y / T(T(z \ u,w),z)) = T(x,y / T(u / z,w))
    ]]></literal>
    <justification jstring="[para(474(a,1),15010(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="474 15010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15014">
    <literal><![CDATA[
      T(x,y / T(T(z,u),u)) = x / K(y / z,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,4206,a(flip),b,15012,a),flip(a)].">
      <j1 rule="hyper" parents="333 4206 15012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15015">
    <literal><![CDATA[
      T(x,y \ ((z * u) / z)) = (w * K(y \ T(u,z),x)) \ (w * x)
    ]]></literal>
    <justification jstring="[hyper(333,a,5447,a,b,15011,a),flip(a)].">
      <j1 rule="hyper" parents="333 5447 15011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15016">
    <literal><![CDATA[
      T(x,y \ ((z * T(u,w)) / z)) = T(x,y \ T(T(u,z),w))
    ]]></literal>
    <justification jstring="[para(23(a,1),15011(a,2,2,2))].">
      <j1 rule="para" parents="23 15011"/>
    </justification>
  </clause>

  <clause id="15017">
    <literal><![CDATA[
      T(x,y \ T(T(z,u),u)) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(239(a,1),15011(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="239 15011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15018">
    <literal><![CDATA[
      K(x / T(T(y,z),z),u) = K(x / y,u)
    ]]></literal>
    <justification jstring="[hyper(4247,a,15014,a)].">
      <j1 rule="hyper" parents="4247 15014"/>
    </justification>
  </clause>

  <clause id="15019">
    <literal><![CDATA[
      K(x / T(y \ z,y),u) = K(x / (z / y),u)
    ]]></literal>
    <justification jstring="[para(113(a,1),15018(a,1,1,2,1))].">
      <j1 rule="para" parents="113 15018"/>
    </justification>
  </clause>

  <clause id="15020">
    <literal><![CDATA[
      K(x / ((y * z) / y),u) = K(x / T(z,y),u)
    ]]></literal>
    <justification jstring="[para(238(a,1),15018(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="238 15018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15023">
    <literal><![CDATA[
      K(x / (((y \ z) \ z) \ z),u) = K(x / (z / y),u)
    ]]></literal>
    <justification jstring="[para(3674(a,1),15019(a,1,1,2))].">
      <j1 rule="para" parents="3674 15019"/>
    </justification>
  </clause>

  <clause id="15024">
    <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(15020(a,1),6191(a,1,2))].">
      <j1 rule="para" parents="15020 6191"/>
    </justification>
  </clause>

  <clause id="15025">
    <literal><![CDATA[
      T(x,(y / (y / z)) * u) = T(x,T(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,12705,a(flip),b,14941,a),flip(a)].">
      <j1 rule="hyper" parents="63 12705 14941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15026">
    <literal><![CDATA[
      T(x,T(y \ z,z) * u) = T(x,(z / y) * u)
    ]]></literal>
    <justification jstring="[para(76(a,1),15025(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="76 15025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15027">
    <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(14945(a,1),7134(a,2,2,2))].">
      <j1 rule="para" parents="14945 7134"/>
    </justification>
  </clause>

  <clause id="15028">
    <literal><![CDATA[
      L(K(x,K(y,z) * (u \ w)),u \ w,u) = K(x,(u * K(y,(y \ 1) \ z)) \ w)
    ]]></literal>
    <justification jstring="[para(14949(a,1),9699(a,1,1))].">
      <j1 rule="para" parents="14949 9699"/>
    </justification>
  </clause>

  <clause id="15029">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ u) = K(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(12788,a,14952,a),flip(a)].">
      <j1 rule="hyper" parents="12788 14952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15030">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y) \ u) = w
    ]]></literal>
    <justification jstring="[para(14952(a,1),12788(a,1))].">
      <j1 rule="para" parents="14952 12788"/>
    </justification>
  </clause>

  <clause id="15031">
    <literal><![CDATA[
      T(x,(y / (y / z)) \ u) = T(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(124,a,15029,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 15029 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15032">
    <literal><![CDATA[
      K(x,T(y \ z,z) \ u) = K(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[para(76(a,1),15029(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="76 15029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15033">
    <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(15031(a,1),12284(a,1,2,1))].">
      <j1 rule="para" parents="15031 12284"/>
    </justification>
  </clause>

  <clause id="15034">
    <literal><![CDATA[
      K(x,K(y,z \ 1) \ u) = K(x,K(y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,14972,a(flip),b,14955,a),flip(a)].">
      <j1 rule="hyper" parents="63 14972 14955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15035">
    <literal><![CDATA[
      K(x,K(y \ 1,z) \ u) = K(x,K(z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,14934,a,b,15034,a)].">
      <j1 rule="hyper" parents="63 14934 15034"/>
    </justification>
  </clause>

  <clause id="15036">
    <literal><![CDATA[
      K(x,K(y,z \ (u \ 1)) \ w) = K(x,K(y,u * z) \ w)
    ]]></literal>
    <justification jstring="[para(13153(a,1),15034(a,1,2,1))].">
      <j1 rule="para" parents="13153 15034"/>
    </justification>
  </clause>

  <clause id="15037">
    <literal><![CDATA[
      K(x,K(y \ 1,z * y) \ u) = K(x,K(z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(333,a,12861,a(flip),b,15035,a),flip(a)].">
      <j1 rule="hyper" parents="333 12861 15035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15038">
    <literal><![CDATA[
      K(x,T(y \ z,y) / u) = K(x,(z / y) / u)
    ]]></literal>
    <justification jstring="[hyper(333,a,13150,a(flip),b,14981,a),flip(a)].">
      <j1 rule="hyper" parents="333 13150 14981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15039">
    <literal><![CDATA[
      T(x,T(y \ z,y) / u) = T(x,(z / y) / u)
    ]]></literal>
    <justification jstring="[hyper(124,a,15038,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 15038 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15040">
    <literal><![CDATA[
      K(x,((y * z) / y) / u) = K(x,T(z,y) / u)
    ]]></literal>
    <justification jstring="[para(9(a,1),15038(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="9 15038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15041">
    <literal><![CDATA[
      K(T(x \ y,x) / z,u) = (w * K(u,(y / x) / z)) \ w
    ]]></literal>
    <justification jstring="[para(15038(a,1),5990(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="15038 5990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15042">
    <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(11912(a,1),15038(a,1,2,1,1))].">
      <j1 rule="para" parents="11912 15038"/>
    </justification>
  </clause>

  <clause id="15043">
    <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(12732(a,1),15038(a,1,2,1))].">
      <j1 rule="para" parents="12732 15038"/>
    </justification>
  </clause>

  <clause id="15044">
    <literal><![CDATA[
      K(x,T(y * K(z,u),z / y) / w) = K(x,(T(z,u) / (z / y)) / w)
    ]]></literal>
    <justification jstring="[para(13240(a,1),15038(a,1,2,1,1))].">
      <j1 rule="para" parents="13240 15038"/>
    </justification>
  </clause>

  <clause id="15045">
    <literal><![CDATA[
      K(x,T(T(y,z),z) / u) = K(x,y / u)
    ]]></literal>
    <justification jstring="[para(239(a,1),15040(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="239 15040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15046">
    <literal><![CDATA[
      K(x,((y * z) / T(y,u)) / w) = K(x,T(z * K(u,y),y) / w)
    ]]></literal>
    <justification jstring="[para(6207(a,1),15040(a,1,2,1))].">
      <j1 rule="para" parents="6207 15040"/>
    </justification>
  </clause>

  <clause id="15047">
    <literal><![CDATA[
      K(x,(((y * z) / y) * K(y,u)) / w) = K(x,T(z * K(y,u),y) / w)
    ]]></literal>
    <justification jstring="[para(6147(a,1),15040(a,1,2,1))].">
      <j1 rule="para" parents="6147 15040"/>
    </justification>
  </clause>

  <clause id="15048">
    <literal><![CDATA[
      K(x,y \ T(z,y)) = K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(12667,a,15045,a)].">
      <j1 rule="hyper" parents="12667 15045"/>
    </justification>
  </clause>

  <clause id="15049">
    <literal><![CDATA[
      K(x,T(T(y,T(z,u)),u) / w) = K(x,(T(y,z) * K(u,y)) / w)
    ]]></literal>
    <justification jstring="[para(7713(a,1),15045(a,1,2,1,1))].">
      <j1 rule="para" parents="7713 15045"/>
    </justification>
  </clause>

  <clause id="15050">
    <literal><![CDATA[
      K(x,L(y \ T(z,y),u,w)) = L(K(x,z / y),u,w)
    ]]></literal>
    <justification jstring="[para(15048(a,1),10851(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15048 10851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15051">
    <literal><![CDATA[
      K(x,y * T((z \ u) * K(u,z),z)) = K(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[para(5454(a,2),14995(a,1,2,2,1))].">
      <j1 rule="para" parents="5454 14995"/>
    </justification>
  </clause>

  <clause id="15052">
    <literal><![CDATA[
      K(x,y \ (z * K(u,z))) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[hyper(333,a,13212,a(flip),b,14998,a),flip(a)].">
      <j1 rule="hyper" parents="333 13212 14998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15053">
    <literal><![CDATA[
      K(x,(y \ z) \ K(u,y)) = K(x,z \ T(y,u))
    ]]></literal>
    <justification jstring="[hyper(9555,a,15052,a)].">
      <j1 rule="hyper" parents="9555 15052"/>
    </justification>
  </clause>

  <clause id="15054">
    <literal><![CDATA[
      K(x,y \ T(T(z,u),u)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(4271(a,1),15052(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4271 15052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15055">
    <literal><![CDATA[
      K(x,y \ T(z \ u,z)) = K(x,y \ (u / z))
    ]]></literal>
    <justification jstring="[para(4292(a,1),15052(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4292 15052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15056">
    <literal><![CDATA[
      K(x,(y \ z) * K(u,z)) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(13412(a,1),15052(a,1,2))].">
      <j1 rule="para" parents="13412 15052"/>
    </justification>
  </clause>

  <clause id="15057">
    <literal><![CDATA[
      K(x,y \ T(T(z,u),u)) = 1 / K(y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,4371,a,b,15054,a),flip(a)].">
      <j1 rule="hyper" parents="333 4371 15054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15058">
    <literal><![CDATA[
      K(x,y \ T(z * (u / T(z,u)),z)) = K(x,y \ (z * (u / z)))
    ]]></literal>
    <justification jstring="[para(3656(a,1),15054(a,1,2,2,1))].">
      <j1 rule="para" parents="3656 15054"/>
    </justification>
  </clause>

  <clause id="15059">
    <literal><![CDATA[
      T(x,(y \ z) \ K(u,y)) = T(x,z \ T(y,u))
    ]]></literal>
    <justification jstring="[hyper(124,a,15053,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 15053 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15060">
    <literal><![CDATA[
      K(x,(y \ z) \ K(u \ 1,y)) = K(x,z \ T(y,1 / u))
    ]]></literal>
    <justification jstring="[para(2986(a,2),15053(a,2,2,2))].">
      <j1 rule="para" parents="2986 15053"/>
    </justification>
  </clause>

  <clause id="15061">
    <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(6624(a,1),15055(a,1,2,2,1))].">
      <j1 rule="para" parents="6624 15055"/>
    </justification>
  </clause>

  <clause id="15062">
    <literal><![CDATA[
      K(x,y \ T(z,z * u)) = K(x,(y \ z) * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(12754,a,15056,a),flip(a)].">
      <j1 rule="hyper" parents="12754 15056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15063">
    <literal><![CDATA[
      K(x \ T(T(y,z),z),u) = K(x \ y,u)
    ]]></literal>
    <justification jstring="[hyper(4401,a,15057,a)].">
      <j1 rule="hyper" parents="4401 15057"/>
    </justification>
  </clause>

  <clause id="15064">
    <literal><![CDATA[
      K(x \ ((y * z) / y),u) = K(x \ T(z,y),u)
    ]]></literal>
    <justification jstring="[para(238(a,1),15063(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="238 15063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15065">
    <literal><![CDATA[
      K(x \ T(y,z),x) = K(x \ y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,10953,a(flip),b,15064,a),flip(a)].">
      <j1 rule="hyper" parents="63 10953 15064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15066">
    <literal><![CDATA[
      T(x,K(y \ ((z * u) / z),w)) = K(x,K(w,y \ T(u,z))) * x
    ]]></literal>
    <justification jstring="[para(15064(a,2),6821(a,2,2)),flip(a)].">
      <j1 rule="para" parents="15064 6821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15067">
    <literal><![CDATA[
      K(x \ ((x \ 1) \ y),T(x,z)) = K(y * K((x \ 1) \ y,z),x)
    ]]></literal>
    <justification jstring="[hyper(13634,a,15065,a),flip(a)].">
      <j1 rule="hyper" parents="13634 15065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15068">
    <literal><![CDATA[
      K(x \ (y * z),T(x,y)) = K(x \ (z * y),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,12672,a(flip),b,15065,a),flip(a)].">
      <j1 rule="hyper" parents="63 12672 15065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15069">
    <literal><![CDATA[
      K(x / (y \ z),z) = K(z \ (x * y),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,13714,a(flip),b,15068,a)].">
      <j1 rule="hyper" parents="63 13714 15068"/>
    </justification>
  </clause>

  <clause id="15070">
    <literal><![CDATA[
      K(x \ (y * (x / z)),x) = K(y / z,x)
    ]]></literal>
    <justification jstring="[para(79(a,1),15069(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="79 15069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15071">
    <literal><![CDATA[
      K(R(x,y,y \ 1) \ (z * (x * y)),R(x,y,y \ 1)) = K(z / (y \ 1),R(x,y,y \ 1))
    ]]></literal>
    <justification jstring="[para(538(a,1),15069(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="538 15069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15072">
    <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(15070(a,1),13837(a,1,3))].">
      <j1 rule="para" parents="15070 13837"/>
    </justification>
  </clause>

  <clause id="15073">
    <literal><![CDATA[
      K(x * ((y * z) / y),u) = K(x * T(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(333,a,4212,a,b,15000,a),flip(a)].">
      <j1 rule="hyper" parents="333 4212 15000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15074">
    <literal><![CDATA[
      K(x * T(T(y,z),z),u) = K(x * y,u)
    ]]></literal>
    <justification jstring="[para(239(a,1),15073(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="239 15073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15076">
    <literal><![CDATA[
      K(x * (y * K(z,y)),u) = K(x * T(y,z),u)
    ]]></literal>
    <justification jstring="[para(4238(a,1),15073(a,1,1,2))].">
      <j1 rule="para" parents="4238 15073"/>
    </justification>
  </clause>

  <clause id="15077">
    <literal><![CDATA[
      K(x / T(y \ z,z),u) = K(x / (z / y),u)
    ]]></literal>
    <justification jstring="[hyper(12786,a,15023,a)].">
      <j1 rule="hyper" parents="12786 15023"/>
    </justification>
  </clause>

  <clause id="15078">
    <literal><![CDATA[
      K(x,y / T(z \ u,u)) = (w * K(y / (u / z),x)) \ w
    ]]></literal>
    <justification jstring="[para(15077(a,1),5990(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="15077 5990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15079">
    <literal><![CDATA[
      K(x,L(y \ T(z,y),u,w)) = K(x,L(z / y,u,w))
    ]]></literal>
    <justification jstring="[hyper(333,a,10851,a(flip),b,15050,a),flip(a)].">
      <j1 rule="hyper" parents="333 10851 15050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15080">
    <literal><![CDATA[
      K(x,y \ T(z,z * u)) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[hyper(333,a,15056,a(flip),b,15062,a),flip(a)].">
      <j1 rule="hyper" parents="333 15056 15062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15081">
    <literal><![CDATA[
      K(x,y \ T(z,z \ u)) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(10(a,1),15080(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="10 15080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15082">
    <literal><![CDATA[
      K(x,y \ ((z \ u) \ u)) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(112(a,1),15081(a,1,2,2))].">
      <j1 rule="para" parents="112 15081"/>
    </justification>
  </clause>

  <clause id="15083">
    <literal><![CDATA[
      T(x,y \ ((z \ u) \ u)) = T(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[hyper(124,a,15082,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 15082 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15084">
    <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(14638(a,2),15082(a,1,2,2,1))].">
      <j1 rule="para" parents="14638 15082"/>
    </justification>
  </clause>

  <clause id="15085">
    <literal><![CDATA[
      T(x,y \ T(z,z * u)) = T(x,y \ ((z \ u) \ u))
    ]]></literal>
    <justification jstring="[hyper(333,a,13717,a,b,15083,a)].">
      <j1 rule="hyper" parents="333 13717 15083"/>
    </justification>
  </clause>

  <clause id="15086">
    <literal><![CDATA[
      T(x \ T(y,y \ z),x \ T(y,z)) = x \ ((y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,695,a(flip),b,15083,a),flip(a)].">
      <j1 rule="hyper" parents="63 695 15083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15087">
    <literal><![CDATA[
      K(x,L((y / (z * y)) \ T(u,z \ 1),w,v5)) = K(x,L(u / (y / (z * y)),w,v5))
    ]]></literal>
    <justification jstring="[para(3759(a,1),15079(a,1,2,1,2))].">
      <j1 rule="para" parents="3759 15079"/>
    </justification>
  </clause>

  <clause id="15088">
    <literal><![CDATA[
      K(x,L(((y * z) \ y) \ T(u,z \ 1),w,v5)) = K(x,L(u / ((y * z) \ y),w,v5))
    ]]></literal>
    <justification jstring="[para(5801(a,1),15079(a,1,2,1,2))].">
      <j1 rule="para" parents="5801 15079"/>
    </justification>
  </clause>

  <clause id="15089">
    <literal><![CDATA[
      T(x,y \ ((z \ u) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(15085(a,1),13718(a,1))].">
      <j1 rule="para" parents="15085 13718"/>
    </justification>
  </clause>

  <clause id="15090">
    <literal><![CDATA[
      K(x,T(y * z,z) \ u) = K(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,12862,a(flip),b,14968,a),flip(a)].">
      <j1 rule="hyper" parents="63 12862 14968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15092">
    <literal><![CDATA[
      K(x,T(y,z * u) / (z * u)) = K(x,T(u * z,z) \ y)
    ]]></literal>
    <justification jstring="[hyper(333,a,12638,a,b,15090,a)].">
      <j1 rule="hyper" parents="333 12638 15090"/>
    </justification>
  </clause>

  <clause id="15093">
    <literal><![CDATA[
      T(x,T(y * z,z) \ u) = T(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[hyper(124,a,15090,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 15090 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15094">
    <literal><![CDATA[
      K(x,(y * (z / y)) \ u) = K(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(12(a,1),15090(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="12 15090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15095">
    <literal><![CDATA[
      T(x,T(y * z,z) \ u) = T(x,T(y * z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(333,a,12699,a,b,15093,a),flip(a)].">
      <j1 rule="hyper" parents="333 12699 15093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15096">
    <literal><![CDATA[
      K(x,L((y * (z / y)) \ u,w,v5)) = K(L(x,w,v5),T(z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(10963,a,15094,a)].">
      <j1 rule="hyper" parents="10963 15094"/>
    </justification>
  </clause>

  <clause id="15097">
    <literal><![CDATA[
      K(x,T(y,z) \ (z * x)) = K(x,z / (x \ y))
    ]]></literal>
    <justification jstring="[hyper(9644,a,15094,a),flip(a)].">
      <j1 rule="hyper" parents="9644 15094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15098">
    <literal><![CDATA[
      K(x,T(y \ z,z) \ u) = K(x,(y \ T(z,y \ 1)) \ u)
    ]]></literal>
    <justification jstring="[para(3107(a,2),15094(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3107 15094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15099">
    <literal><![CDATA[
      K(x,T(y,z) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(15094(a,1),5804(a,1))].">
      <j1 rule="para" parents="15094 5804"/>
    </justification>
  </clause>

  <clause id="15100">
    <literal><![CDATA[
      K(x,y \ T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(3628(a,1),15099(a,1,2))].">
      <j1 rule="para" parents="3628 15099"/>
    </justification>
  </clause>

  <clause id="15101">
    <literal><![CDATA[
      K(x,T(y,K(z,u) * w) \ (K(z,z \ u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(K(z,z \ u) * w) / y) = v5
    ]]></literal>
    <justification jstring="[para(12760(a,1),15099(a,1,2,1))].">
      <j1 rule="para" parents="12760 15099"/>
    </justification>
  </clause>

  <clause id="15102">
    <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(14920(a,1),15099(a,1,2,1))].">
      <j1 rule="para" parents="14920 15099"/>
    </justification>
  </clause>

  <clause id="15103">
    <literal><![CDATA[
      K(x,T(y,z / T(u,w)) \ ((z / u) * K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,((z / u) * K(u,w)) / y) = v5
    ]]></literal>
    <justification jstring="[para(15006(a,1),15099(a,1,2,1))].">
      <j1 rule="para" parents="15006 15099"/>
    </justification>
  </clause>

  <clause id="15104">
    <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(5772(a,1),15100(a,1,2,2))].">
      <j1 rule="para" parents="5772 15100"/>
    </justification>
  </clause>

  <clause id="15105">
    <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(12732(a,1),15100(a,1,2,2))].">
      <j1 rule="para" parents="12732 15100"/>
    </justification>
  </clause>

  <clause id="15106">
    <literal><![CDATA[
      K(x,T(y,z) \ (T(z,y) * x)) = K(x,T(z,y) / (x \ y))
    ]]></literal>
    <justification jstring="[para(3613(a,1),15097(a,1,2,1))].">
      <j1 rule="para" parents="3613 15097"/>
    </justification>
  </clause>

  <clause id="15107">
    <literal><![CDATA[
      T(x,T(y * z,z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(z * y) \ u) = w
    ]]></literal>
    <justification jstring="[para(15095(a,2),12898(a,1))].">
      <j1 rule="para" parents="15095 12898"/>
    </justification>
  </clause>

  <clause id="15108">
    <literal><![CDATA[
      K(x * K(y,z),u) = K(x * K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(15005,a,4212,a(flip))].">
      <j1 rule="hyper" parents="15005 4212"/>
    </justification>
  </clause>

  <clause id="15109">
    <literal><![CDATA[
      K(x * K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x * K(z,y),u) = w
    ]]></literal>
    <justification jstring="[para(4212(a,2),15005(a,1))].">
      <j1 rule="para" parents="4212 15005"/>
    </justification>
  </clause>

  <clause id="15110">
    <literal><![CDATA[
      K((1 / x) * K(y,z),u) = K(x \ K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(13491,a,15108,a),flip(a)].">
      <j1 rule="hyper" parents="13491 15108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15111">
    <literal><![CDATA[
      K((x * K(y,z)) * K(y,z),u) = K(x,u)
    ]]></literal>
    <justification jstring="[para(5995(a,1),15108(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5995 15108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15112">
    <literal><![CDATA[
      K(x * (K(y,z) * K(y,z)),u) = K(x,u)
    ]]></literal>
    <justification jstring="[para(8165(a,1),15111(a,1,1))].">
      <j1 rule="para" parents="8165 15111"/>
    </justification>
  </clause>

  <clause id="15113">
    <literal><![CDATA[
      K(x,y) * (x * (K(z,u) * K(z,u))) = T(x * (K(z,u) * K(z,u)),y)
    ]]></literal>
    <justification jstring="[hyper(125,a,15112,a(flip),b,4261,a(flip))].">
      <j1 rule="hyper" parents="125 15112 4261"/>
    </justification>
  </clause>

  <clause id="15114">
    <literal><![CDATA[
      K(x \ K(y,z),u) = K(x \ K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(13491,a,15110,a)].">
      <j1 rule="hyper" parents="13491 15110"/>
    </justification>
  </clause>

  <clause id="15115">
    <literal><![CDATA[
      K(x \ K(y \ z,y),u) = K(x \ K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(12766,a,15114,a),flip(a)].">
      <j1 rule="hyper" parents="12766 15114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15117">
    <literal><![CDATA[
      ((x \ 1) \ K(y \ K(z,u),x)) \ ((x \ 1) \ 1) = K(x,y \ K(u,z))
    ]]></literal>
    <justification jstring="[para(15114(a,1),6007(a,1,1,2))].">
      <j1 rule="para" parents="15114 6007"/>
    </justification>
  </clause>

  <clause id="15119">
    <literal><![CDATA[
      K(x \ K(y \ z,z),u) = K(x \ K(y,y \ z),u)
    ]]></literal>
    <justification jstring="[para(4377(a,1),15115(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4377 15115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15120">
    <literal><![CDATA[
      K(x \ K(y \ z,z),u) = K(x \ K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(333,a,12673,a(flip),b,15119,a),flip(a)].">
      <j1 rule="hyper" parents="333 12673 15119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15121">
    <literal><![CDATA[
      K(x \ K(y,z \ y),u) = K(x \ K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,15114,a,b,15120,a)].">
      <j1 rule="hyper" parents="63 15114 15120"/>
    </justification>
  </clause>

  <clause id="15122">
    <literal><![CDATA[
      T(x,y \ T(T(z,u),z \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ T(T(z,u),w)) = v5
    ]]></literal>
    <justification jstring="[para(6678(a,2),15089(a,1,2,2))].">
      <j1 rule="para" parents="6678 15089"/>
    </justification>
  </clause>

  <clause id="15123">
    <literal><![CDATA[
      T(x,((y \ z) \ K(u,z \ y)) \ w) = T(x,T((y \ z) \ 1,u) \ w)
    ]]></literal>
    <justification jstring="[para(5766(a,1),14946(a,1,2,1,2))].">
      <j1 rule="para" parents="5766 14946"/>
    </justification>
  </clause>

  <clause id="15124">
    <literal><![CDATA[
      K(T(x \ y,x) * z,u) = K((y / x) * z,u)
    ]]></literal>
    <justification jstring="[hyper(333,a,5990,a(flip),b,14982,a),flip(a)].">
      <j1 rule="hyper" parents="333 5990 14982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15125">
    <literal><![CDATA[
      K(T(x \ y,x) * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K((y / x) * z,u) = w
    ]]></literal>
    <justification jstring="[para(14982(a,2),6024(a,1))].">
      <j1 rule="para" parents="14982 6024"/>
    </justification>
  </clause>

  <clause id="15126">
    <literal><![CDATA[
      K(((x * y) / x) * z,u) = K(T(y,x) * z,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),15124(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 15124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15127">
    <literal><![CDATA[
      K(x * (K(y,x) * z),u) = K(T(x,y) * z,u)
    ]]></literal>
    <justification jstring="[para(4414(a,1),15126(a,1,1))].">
      <j1 rule="para" parents="4414 15126"/>
    </justification>
  </clause>

  <clause id="15128">
    <literal><![CDATA[
      K(((T(T(x,y),y) \ z) / K(y,x)) * u,w) = K(T(T(x,y) \ z,K(y,x)) * u,w)
    ]]></literal>
    <justification jstring="[para(4704(a,1),15126(a,1,1,1,1))].">
      <j1 rule="para" parents="4704 15126"/>
    </justification>
  </clause>

  <clause id="15129">
    <literal><![CDATA[
      T(x,y / T(((z \ u) \ u) \ u,w)) = T(x,y / T(u / z,w))
    ]]></literal>
    <justification jstring="[para(3717(a,1),15013(a,1,2,2))].">
      <j1 rule="para" parents="3717 15013"/>
    </justification>
  </clause>

  <clause id="15130">
    <literal><![CDATA[
      T(x,y \ T((z * u) / z,w)) = T(x,y \ T(T(u,z),w))
    ]]></literal>
    <justification jstring="[para(476(a,1),15016(a,1,2,2))].">
      <j1 rule="para" parents="476 15016"/>
    </justification>
  </clause>

  <clause id="15131">
    <literal><![CDATA[
      K(T(x \ y,x) / z,u) = K((y / x) / z,u)
    ]]></literal>
    <justification jstring="[hyper(333,a,5990,a(flip),b,15041,a),flip(a)].">
      <j1 rule="hyper" parents="333 5990 15041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15132">
    <literal><![CDATA[
      K(((x * y) / x) / z,u) = K(T(y,x) / z,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),15131(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 15131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15133">
    <literal><![CDATA[
      K(T(T(x,y),y) / z,u) = K(x / z,u)
    ]]></literal>
    <justification jstring="[para(239(a,1),15132(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="239 15132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15134">
    <literal><![CDATA[
      K((x * y) \ T(z,x),T(u,y)) = K(z / (y * x),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,14088,a,b,15133,a)].">
      <j1 rule="hyper" parents="63 14088 15133"/>
    </justification>
  </clause>

  <clause id="15135">
    <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(13434(a,1),15134(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13434 15134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15136">
    <literal><![CDATA[
      K(x,y * (T(z \ u,z) * K(u,z))) = K(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[para(6647(a,1),15051(a,1,2,2))].">
      <j1 rule="para" parents="6647 15051"/>
    </justification>
  </clause>

  <clause id="15137">
    <literal><![CDATA[
      K(x,y / T(z \ u,u)) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[hyper(333,a,5990,a(flip),b,15078,a),flip(a)].">
      <j1 rule="hyper" parents="333 5990 15078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15138">
    <literal><![CDATA[
      K(x,y / T(z \ u,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (u / z)) = w
    ]]></literal>
    <justification jstring="[para(15078(a,2),6024(a,1))].">
      <j1 rule="para" parents="15078 6024"/>
    </justification>
  </clause>

  <clause id="15139">
    <literal><![CDATA[
      K(x,y / (z / (z / u))) = K(x,y / T(u,z))
    ]]></literal>
    <justification jstring="[para(79(a,1),15137(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="79 15137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15140">
    <literal><![CDATA[
      K(x,T(y * z,z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z * y) \ u) = w
    ]]></literal>
    <justification jstring="[para(15092(a,1),12667(a,1))].">
      <j1 rule="para" parents="15092 12667"/>
    </justification>
  </clause>

  <clause id="15141">
    <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(12712(a,1),15140(a,1))].">
      <j1 rule="para" parents="12712 15140"/>
    </justification>
  </clause>

  <clause id="15142">
    <literal><![CDATA[
      K(x,(y \ T(z,y \ 1)) \ u) = K(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,15032,a(flip),b,15098,a),flip(a)].">
      <j1 rule="hyper" parents="63 15032 15098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15143">
    <literal><![CDATA[
      K(x,T(y,z) / (x \ z)) = K(x,z \ (y * x))
    ]]></literal>
    <justification jstring="[hyper(63,a,14969,a(flip),b,15106,a),flip(a)].">
      <j1 rule="hyper" parents="63 14969 15106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15144">
    <literal><![CDATA[
      K(x,y * (T(z,z \ u) \ T(u,z))) = K(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[para(13367(a,2),15136(a,1,2,2))].">
      <j1 rule="para" parents="13367 15136"/>
    </justification>
  </clause>

  <clause id="15145">
    <literal><![CDATA[
      K(x,y * (T(z,u \ 1) \ T(z / u,z))) = K(x,y * (z \ (z / u)))
    ]]></literal>
    <justification jstring="[para(5813(a,1),15144(a,1,2,2,1))].">
      <j1 rule="para" parents="5813 15144"/>
    </justification>
  </clause>

  <clause id="15146">
    <literal><![CDATA[
      K(x,R(T(T(y,z),z),u,w) * (u * w)) = K(x,(y * u) * w)
    ]]></literal>
    <justification jstring="[para(867(a,2),14977(a,1,2,1))].">
      <j1 rule="para" parents="867 14977"/>
    </justification>
  </clause>

  <clause id="15147">
    <literal><![CDATA[
      K(x,(T(T(y,z),z) * u) * w) = K(x,(y * u) * w)
    ]]></literal>
    <justification jstring="[para(107(a,1),15146(a,1,2))].">
      <j1 rule="para" parents="107 15146"/>
    </justification>
  </clause>

  <clause id="15148">
    <literal><![CDATA[
      K(x,(((y * z) / y) * u) * w) = K(x,(T(z,y) * u) * w)
    ]]></literal>
    <justification jstring="[para(238(a,1),15147(a,1,2,1,1,1)),flip(a)].">
      <j1 rule="para" parents="238 15147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15149">
    <literal><![CDATA[
      K(x,(T(y,z) * z) * u) = K(x,(z * y) * u)
    ]]></literal>
    <justification jstring="[para(12(a,1),15148(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12 15148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15150">
    <literal><![CDATA[
      K(x,(y * (K(z,y) * u)) * w) = K(x,(T(y,z) * u) * w)
    ]]></literal>
    <justification jstring="[para(4414(a,1),15148(a,1,2,1))].">
      <j1 rule="para" parents="4414 15148"/>
    </justification>
  </clause>

  <clause id="15151">
    <literal><![CDATA[
      K(x,T(y,z * u) * (z * u)) = K(x,(T(u,z) * z) * y)
    ]]></literal>
    <justification jstring="[hyper(333,a,12267,a,b,15149,a)].">
      <j1 rule="hyper" parents="333 12267 15149"/>
    </justification>
  </clause>

  <clause id="15152">
    <literal><![CDATA[
      K(x,(y * (K(z,y) * (u / y))) * w) = K(x,((T(y,z) \ u) * y) * w)
    ]]></literal>
    <justification jstring="[para(6635(a,1),15149(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="6635 15149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15153">
    <literal><![CDATA[
      K(x,(T(y,z) * z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z * y) * u) = w
    ]]></literal>
    <justification jstring="[para(15151(a,1),12284(a,1))].">
      <j1 rule="para" parents="15151 12284"/>
    </justification>
  </clause>

  <clause id="15154">
    <literal><![CDATA[
      K(x,(T(y \ z,K(y,u)) * T(y,u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(T(y,u) * (z / y)) * w) = v5
    ]]></literal>
    <justification jstring="[para(6188(a,1),15153(a,1,2,1,1))].">
      <j1 rule="para" parents="6188 15153"/>
    </justification>
  </clause>

  <clause id="15155">
    <literal><![CDATA[
      K(x,((y \ z) * (y * K(u,y))) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * (z / T(y,u))) * w) = v5
    ]]></literal>
    <justification jstring="[para(6230(a,1),15153(a,1,2,1))].">
      <j1 rule="para" parents="6230 15153"/>
    </justification>
  </clause>

  <clause id="15156">
    <literal><![CDATA[
      T(x * T(1 / x,K(y,z)),K(y,z)) = K(x,x \ K(z,y))
    ]]></literal>
    <justification jstring="[hyper(333,a,8568,a(flip),b,14914,a),flip(a)].">
      <j1 rule="hyper" parents="333 8568 14914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15157">
    <literal><![CDATA[
      T(K(K(x,y) * z,z \ 1),K(x,y)) = K(z,z \ K(y,x))
    ]]></literal>
    <justification jstring="[para(14349(a,2),15156(a,1,1))].">
      <j1 rule="para" parents="14349 15156"/>
    </justification>
  </clause>

  <clause id="15158">
    <literal><![CDATA[
      K(x,K(y,z) * T(u,K(z,y))) = K(x,u * K(z,z \ y))
    ]]></literal>
    <justification jstring="[para(7025(a,1),14948(a,1,2,2))].">
      <j1 rule="para" parents="7025 14948"/>
    </justification>
  </clause>

  <clause id="15159">
    <literal><![CDATA[
      K(x,y * K(z,z \ u)) = K(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[para(6852(a,1),15158(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6852 15158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15160">
    <literal><![CDATA[
      K(x,y * K(z,u)) = K(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,12676,a(flip),b,15159,a)].">
      <j1 rule="hyper" parents="63 12676 15159"/>
    </justification>
  </clause>

  <clause id="15161">
    <literal><![CDATA[
      K(x,y * K(z,z * u)) = K(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(12754,a,15160,a),flip(a)].">
      <j1 rule="hyper" parents="12754 15160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15162">
    <literal><![CDATA[
      K(x,(y / z) * K(z,u)) = K(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(5450(a,1),15160(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5450 15160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15163">
    <literal><![CDATA[
      T(x,y * K(z,z * u)) = T(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(124,a,15161,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 15161 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15164">
    <literal><![CDATA[
      K(x,y * K(R(z,u,w),(z * u) * w)) = K(x,y * K(u * w,R(z,u,w)))
    ]]></literal>
    <justification jstring="[para(107(a,1),15161(a,1,2,2,2))].">
      <j1 rule="para" parents="107 15161"/>
    </justification>
  </clause>

  <clause id="15165">
    <literal><![CDATA[
      K(x,y / T(z \ u,z)) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[para(6012(a,1),15162(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6012 15162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15166">
    <literal><![CDATA[
      K(x,y / ((z * u) / z)) = K(x,y / T(u,z))
    ]]></literal>
    <justification jstring="[para(7664(a,2),15162(a,1,2))].">
      <j1 rule="para" parents="7664 15162"/>
    </justification>
  </clause>

  <clause id="15167">
    <literal><![CDATA[
      K(x,y / T(z,z \ u)) = K(x,y / (u / (u / z)))
    ]]></literal>
    <justification jstring="[para(7672(a,2),15162(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7672 15162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15170">
    <literal><![CDATA[
      K(x,y / (z / (z / (z / u)))) = K(x,y / (u \ z))
    ]]></literal>
    <justification jstring="[para(332(a,1),15167(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="332 15167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15171">
    <literal><![CDATA[
      K(x,y / T(z / u,z)) = K(x,y / (u \ z))
    ]]></literal>
    <justification jstring="[hyper(63,a,15139,a(flip),b,15170,a)].">
      <j1 rule="hyper" parents="63 15139 15170"/>
    </justification>
  </clause>

  <clause id="15172">
    <literal><![CDATA[
      K(x,y / ((z \ u) \ u)) = K(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(76(a,1),15171(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="76 15171"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15173">
    <literal><![CDATA[
      K(x,y / T(1 / L(z,u,u \ 1),a(u \ 1,u,z))) = K(x,y / (z \ a(u \ 1,u,z)))
    ]]></literal>
    <justification jstring="[para(3206(a,1),15172(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="3206 15172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15174">
    <literal><![CDATA[
      T(x,y \ ((z * u) / z)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ T(u,z)) = w
    ]]></literal>
    <justification jstring="[para(15015(a,2),5458(a,1))].">
      <j1 rule="para" parents="15015 5458"/>
    </justification>
  </clause>

  <clause id="15175">
    <literal><![CDATA[
      T(x,(y \ z) * K(u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(13413(a,1),15174(a,1,2))].">
      <j1 rule="para" parents="13413 15174"/>
    </justification>
  </clause>

  <clause id="15176">
    <literal><![CDATA[
      K(x,T(T(y,z),T(u,z)) / w) = K(x,(T(y,u) * K(z,y)) / w)
    ]]></literal>
    <justification jstring="[para(23(a,1),15049(a,1,2,1))].">
      <j1 rule="para" parents="23 15049"/>
    </justification>
  </clause>

  <clause id="15177">
    <literal><![CDATA[
      K(x,y \ ((z / T(u,z)) * u)) = K(x,y \ (u * (z / u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,12682,a(flip),b,15058,a)].">
      <j1 rule="hyper" parents="63 12682 15058"/>
    </justification>
  </clause>

  <clause id="15178">
    <literal><![CDATA[
      K(x,y \ (z * (u / z))) = K(x,y \ T(u,z))
    ]]></literal>
    <justification jstring="[para(3619(a,1),15177(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3619 15177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15179">
    <literal><![CDATA[
      K(x,T(y / (z * u),z)) = K(x,(u * z) \ T(y,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,13963,a,b,15178,a)].">
      <j1 rule="hyper" parents="63 13963 15178"/>
    </justification>
  </clause>

  <clause id="15180">
    <literal><![CDATA[
      K(x,y \ T(z * u,u)) = K(x,y \ (u * z))
    ]]></literal>
    <justification jstring="[para(11(a,1),15178(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="11 15178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15181">
    <literal><![CDATA[
      K(x,y \ T(z \ u,u)) = K(x,y \ (z \ T(u,z \ 1)))
    ]]></literal>
    <justification jstring="[para(3107(a,2),15178(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3107 15178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15182">
    <literal><![CDATA[
      K(x,y \ T(z * u,z)) = K(x,y \ (T(z,u) * u))
    ]]></literal>
    <justification jstring="[para(3311(a,2),15178(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3311 15178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15183">
    <literal><![CDATA[
      K(x,T(y / ((z \ u) * z),z \ u)) = K(x,u \ T(y,z))
    ]]></literal>
    <justification jstring="[para(10(a,1),15179(a,2,2,1))].">
      <j1 rule="para" parents="10 15179"/>
    </justification>
  </clause>

  <clause id="15184">
    <literal><![CDATA[
      K(x,y \ (T(z,u) * u)) = K(x,y \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,12682,a(flip),b,15182,a),flip(a)].">
      <j1 rule="hyper" parents="63 12682 15182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15185">
    <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(12247(a,1),15184(a,1,2,2,1))].">
      <j1 rule="para" parents="12247 15184"/>
    </justification>
  </clause>

  <clause id="15186">
    <literal><![CDATA[
      K(x,y \ (T(z,u * w) * ((u \ 1) \ w))) = K(x,y \ (((u \ 1) \ w) * z))
    ]]></literal>
    <justification jstring="[para(13206(a,1),15184(a,1,2,2,1))].">
      <j1 rule="para" parents="13206 15184"/>
    </justification>
  </clause>

  <clause id="15187">
    <literal><![CDATA[
      K(x,y \ (T(z,u * w) * ((1 / u) \ w))) = K(x,y \ (((1 / u) \ w) * z))
    ]]></literal>
    <justification jstring="[para(13282(a,1),15184(a,1,2,2,1))].">
      <j1 rule="para" parents="13282 15184"/>
    </justification>
  </clause>

  <clause id="15188">
    <literal><![CDATA[
      K(x * K((y \ 1) \ x,z),y) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(13633,a,15067,a),flip(a)].">
      <j1 rule="hyper" parents="13633 15067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15190">
    <literal><![CDATA[
      K(x * K(y * x,z),y) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(13142(a,1),15188(a,1,1,2))].">
      <j1 rule="para" parents="13142 15188"/>
    </justification>
  </clause>

  <clause id="15191">
    <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(126,a,15190,a(flip),b,4735,a(flip))].">
      <j1 rule="hyper" parents="126 15190 4735"/>
    </justification>
  </clause>

  <clause id="15192">
    <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(15096(a,2),10963(a,1))].">
      <j1 rule="para" parents="15096 10963"/>
    </justification>
  </clause>

  <clause id="15193">
    <literal><![CDATA[
      T(x,y / T(T(z \ u,w),u)) = T(x,y / T(u / z,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,12703,a(flip),b,15129,a)].">
      <j1 rule="hyper" parents="63 12703 15129"/>
    </justification>
  </clause>

  <clause id="15194">
    <literal><![CDATA[
      T(x,y / T(T(z \ u,u),w)) = T(x,y / T(u / z,w))
    ]]></literal>
    <justification jstring="[para(23(a,1),15193(a,1,2,2))].">
      <j1 rule="para" parents="23 15193"/>
    </justification>
  </clause>

  <clause id="15195">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(z,u)) = T(y,K(1 / u,z) * x)
    ]]></literal>
    <justification jstring="[para(7189(a,1),14917(a,1,2))].">
      <j1 rule="para" parents="7189 14917"/>
    </justification>
  </clause>

  <clause id="15196">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(z,u)) = T(y,K(u \ 1,z) * x)
    ]]></literal>
    <justification jstring="[para(3333(a,1),15195(a,2,2,1))].">
      <j1 rule="para" parents="3333 15195"/>
    </justification>
  </clause>

  <clause id="15197">
    <literal><![CDATA[
      T(x,K(y \ 1,z) * u) = T(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,14912,a(flip),b,15196,a),flip(a)].">
      <j1 rule="hyper" parents="63 14912 15196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15198">
    <literal><![CDATA[
      K(x,K(y \ 1,z) * u) = x \ T(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(121,a,15197,a(flip),b,4222,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="121 15197 4222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15199">
    <literal><![CDATA[
      T(x,K(y,z) * T(u,K(z,y \ 1))) = T(x,u * K(y \ 1,z))
    ]]></literal>
    <justification jstring="[para(6852(a,1),15197(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6852 15197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15200">
    <literal><![CDATA[
      K(x,K(y \ 1,z) * u) = K(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(333,a,4215,a,b,15198,a),flip(a)].">
      <j1 rule="hyper" parents="333 4215 15198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15201">
    <literal><![CDATA[
      K(x,K(y,z \ 1) * u) = K(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(14927,a,15200,a)].">
      <j1 rule="hyper" parents="14927 15200"/>
    </justification>
  </clause>

  <clause id="15202">
    <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(15200(a,1),9860(a,1,1))].">
      <j1 rule="para" parents="15200 9860"/>
    </justification>
  </clause>

  <clause id="15203">
    <literal><![CDATA[
      K(x,K(y,z \ 1) * u) = K(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(333,a,14926,a,b,15201,a),flip(a)].">
      <j1 rule="hyper" parents="333 14926 15201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15204">
    <literal><![CDATA[
      K(x,K(y \ z,u) * w) = K(x,K(u,z \ y) * w)
    ]]></literal>
    <justification jstring="[para(5766(a,1),15201(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5766 15201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15205">
    <literal><![CDATA[
      K(x,K(y,z) * T(u,K(z,y))) = K(x,u * K(z,y \ 1))
    ]]></literal>
    <justification jstring="[para(7188(a,1),15201(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7188 15201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15206">
    <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(15201(a,1),9861(a,1,1))].">
      <j1 rule="para" parents="15201 9861"/>
    </justification>
  </clause>

  <clause id="15207">
    <literal><![CDATA[
      K(x,K(y,z \ 1) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(15201(a,2),14927(a,1))].">
      <j1 rule="para" parents="15201 14927"/>
    </justification>
  </clause>

  <clause id="15208">
    <literal><![CDATA[
      T(x,K(y,z \ 1) * u) = T(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(124,a,15203,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 15203 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15209">
    <literal><![CDATA[
      K(K(x,y \ 1) * z,u) = u / T(u,K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(197,a,15208,a(flip),b,4233,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="197 15208 4233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15210">
    <literal><![CDATA[
      K(x,T(y,K(z,u) * w) \ (K(z,u \ 1) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(K(z,u \ 1) * w) / y) = v5
    ]]></literal>
    <justification jstring="[para(15208(a,1),15099(a,1,2,1))].">
      <j1 rule="para" parents="15208 15099"/>
    </justification>
  </clause>

  <clause id="15211">
    <literal><![CDATA[
      K(x,K(y,z \ y) * u) = K(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(12838,a,15204,a),flip(a)].">
      <j1 rule="hyper" parents="12838 15204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15212">
    <literal><![CDATA[
      K(x,K(y \ z,z) * u) = K(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(333,a,14928,a(flip),b,15204,a),flip(a)].">
      <j1 rule="hyper" parents="333 14928 15204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15213">
    <literal><![CDATA[
      K(x,K(y \ (z \ 1),u) * w) = K(x,K(u,z * y) * w)
    ]]></literal>
    <justification jstring="[para(13141(a,1),15204(a,2,2,1))].">
      <j1 rule="para" parents="13141 15204"/>
    </justification>
  </clause>

  <clause id="15214">
    <literal><![CDATA[
      K(x,K(y \ z,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(15204(a,2),14932(a,1))].">
      <j1 rule="para" parents="15204 14932"/>
    </justification>
  </clause>

  <clause id="15215">
    <literal><![CDATA[
      K(x,T(y,z \ y) \ u) = K(x,K(z,y) * (y \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,14930,a(flip),b,15211,a)].">
      <j1 rule="hyper" parents="63 14930 15211"/>
    </justification>
  </clause>

  <clause id="15216">
    <literal><![CDATA[
      K(x,T(y / z,T(u \ (z \ y),z))) = K(x,K(u,z \ y) * (y / z))
    ]]></literal>
    <justification jstring="[para(6511(a,1),15211(a,1,2))].">
      <j1 rule="para" parents="6511 15211"/>
    </justification>
  </clause>

  <clause id="15217">
    <literal><![CDATA[
      T(x,K(y \ z,z) * u) = T(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(124,a,15212,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 15212 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15218">
    <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(15217(a,1),15099(a,1,2,1))].">
      <j1 rule="para" parents="15217 15099"/>
    </justification>
  </clause>

  <clause id="15219">
    <literal><![CDATA[
      K(K(x,y \ 1) * z,u) = K(K(x,y) * z,u)
    ]]></literal>
    <justification jstring="[hyper(333,a,4212,a,b,15209,a),flip(a)].">
      <j1 rule="hyper" parents="333 4212 15209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15220">
    <literal><![CDATA[
      K(T(x \ 1,y) \ z,u) = K(K(y,x) * (x * z),u)
    ]]></literal>
    <justification jstring="[hyper(13929,a,15219,a)].">
      <j1 rule="hyper" parents="13929 15219"/>
    </justification>
  </clause>

  <clause id="15221">
    <literal><![CDATA[
      K(x,T(y,z \ y) \ u) = K(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(4555(a,1),15215(a,2,2))].">
      <j1 rule="para" parents="4555 15215"/>
    </justification>
  </clause>

  <clause id="15222">
    <literal><![CDATA[
      K(T(x \ 1,y) \ z,u) = K(x * (K(y,x) * z),u)
    ]]></literal>
    <justification jstring="[para(4712(a,1),15220(a,2,1))].">
      <j1 rule="para" parents="4712 15220"/>
    </justification>
  </clause>

  <clause id="15223">
    <literal><![CDATA[
      K(T(x \ 1,y) \ z,u) = K(T(x,y) * z,u)
    ]]></literal>
    <justification jstring="[hyper(333,a,15127,a(flip),b,15222,a),flip(a)].">
      <j1 rule="hyper" parents="333 15127 15222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15224">
    <literal><![CDATA[
      K(x,y * K(z,u \ 1)) = K(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[para(6852(a,1),15205(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6852 15205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15225">
    <literal><![CDATA[
      K(x * K(y,z \ 1),u) = 1 / K(u,x * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(197,a,15224,a(flip),b,4367,a),flip(a)].">
      <j1 rule="hyper" parents="197 15224 4367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15226">
    <literal><![CDATA[
      K(x * K(y \ 1,z),u) = 1 / K(u,x * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(15109,a,15225,a)].">
      <j1 rule="hyper" parents="15109 15225"/>
    </justification>
  </clause>

  <clause id="15227">
    <literal><![CDATA[
      K(x * K(y \ 1,z),u) = K(x * K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(333,a,4371,a(flip),b,15226,a),flip(a)].">
      <j1 rule="hyper" parents="333 4371 15226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15228">
    <literal><![CDATA[
      T(x,K(y,z) * T(u,K(y,z))) = T(x,u * K(y \ 1,z))
    ]]></literal>
    <justification jstring="[para(7153(a,1),15199(a,1,2,2))].">
      <j1 rule="para" parents="7153 15199"/>
    </justification>
  </clause>

  <clause id="15229">
    <literal><![CDATA[
      T(x,y * K(z \ 1,u)) = T(x,y * K(z,u))
    ]]></literal>
    <justification jstring="[para(111(a,1),15228(a,1,2)),flip(a)].">
      <j1 rule="para" parents="111 15228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15230">
    <literal><![CDATA[
      T(x,y \ T(z,u \ 1)) = T(x,(y \ z) * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(15175,a,15229,a)].">
      <j1 rule="hyper" parents="15175 15229"/>
    </justification>
  </clause>

  <clause id="15231">
    <literal><![CDATA[
      T(x,y \ T(z,u \ 1)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(15230(a,2),15175(a,1))].">
      <j1 rule="para" parents="15230 15175"/>
    </justification>
  </clause>

  <clause id="15232">
    <literal><![CDATA[
      T(x * (K(y,z) * K(y,z)),u) = T(x,u) * (K(y,z) * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(4539,a,15113,a),flip(a)].">
      <j1 rule="hyper" parents="4539 15113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15233">
    <literal><![CDATA[
      K(x,y \ K(z,u)) = K(x,y \ K(u,z))
    ]]></literal>
    <justification jstring="[hyper(13198,a,15117,a)].">
      <j1 rule="hyper" parents="13198 15117"/>
    </justification>
  </clause>

  <clause id="15234">
    <literal><![CDATA[
      K(x,y \ K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(15117(a,1),13198(a,1))].">
      <j1 rule="para" parents="15117 13198"/>
    </justification>
  </clause>

  <clause id="15235">
    <literal><![CDATA[
      K(x,y * (T(z,u \ 1) \ (u \ z))) = K(x,y * (z \ (z / u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,12833,a(flip),b,15145,a)].">
      <j1 rule="hyper" parents="63 12833 15145"/>
    </justification>
  </clause>

  <clause id="15236">
    <literal><![CDATA[
      K(x,y * ((z \ u) / u)) = K(x,y * (u \ (u / z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,14996,a(flip),b,15235,a)].">
      <j1 rule="hyper" parents="63 14996 15235"/>
    </justification>
  </clause>

  <clause id="15237">
    <literal><![CDATA[
      K(x,((T(y,z) \ u) * y) * w) = K(x,(T(y,z) * (u / y)) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,15150,a(flip),b,15152,a),flip(a)].">
      <j1 rule="hyper" parents="63 15150 15152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15238">
    <literal><![CDATA[
      K(x,T(y / z,T(u \ (z \ y),z))) = K(x,T(y / z,T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(333,a,14931,a(flip),b,15216,a),flip(a)].">
      <j1 rule="hyper" parents="333 14931 15216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15239">
    <literal><![CDATA[
      K(x,T(y / z,y / (z * u))) = K(x,T(y / z,T(u,z)))
    ]]></literal>
    <justification jstring="[para(9965(a,1),15238(a,1,2))].">
      <j1 rule="para" parents="9965 15238"/>
    </justification>
  </clause>

  <clause id="15240">
    <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(63,a,14817,a(flip),b,15239,a)].">
      <j1 rule="hyper" parents="63 14817 15239"/>
    </justification>
  </clause>

  <clause id="15241">
    <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(5217(a,1),15239(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5217 15239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15242">
    <literal><![CDATA[
      K(x,(y \ z) * T(u,z \ y)) = K(x,u / ((y \ z) \ 1))
    ]]></literal>
    <justification jstring="[hyper(15104,a,13141,a),flip(a)].">
      <j1 rule="hyper" parents="15104 13141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15243">
    <literal><![CDATA[
      K(x,(y \ z) * T(u,z \ y)) = K(x,u * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(333,a,13247,a(flip),b,15242,a),flip(a)].">
      <j1 rule="hyper" parents="333 13247 15242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15244">
    <literal><![CDATA[
      K(x,L(y \ z,u,w) * (z \ y)) = K(x,(z \ y) * L(y \ z,u,w))
    ]]></literal>
    <justification jstring="[para(180(a,1),15243(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="180 15243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15245">
    <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(5247(a,1),15244(a,1,2,1,1))].">
      <j1 rule="para" parents="5247 15244"/>
    </justification>
  </clause>

  <clause id="15246">
    <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(9278(a,2),15244(a,1,2,2))].">
      <j1 rule="para" parents="9278 15244"/>
    </justification>
  </clause>

  <clause id="15247">
    <literal><![CDATA[
      T(x,K(y,z) * (((y \ u) / u) \ w)) = T(x,T((y \ u) / u,z) \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,15197,a(flip),b,14943,a)].">
      <j1 rule="hyper" parents="63 15197 14943"/>
    </justification>
  </clause>

  <clause id="15248">
    <literal><![CDATA[
      T(x,((y / (z \ K(z,y))) / y) \ u) = T(x,(y \ (y / (z \ 1))) \ u)
    ]]></literal>
    <justification jstring="[para(113(a,1),14961(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="113 14961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15249">
    <literal><![CDATA[
      K(x,T((y * z) \ u,y * z) * T(z,y)) = K(x,(u / (z * y)) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,14990,a(flip),b,14983,a)].">
      <j1 rule="hyper" parents="63 14990 14983"/>
    </justification>
  </clause>

  <clause id="15250">
    <literal><![CDATA[
      K(x,y * K(z,L((z * u) * w,u,w))) = K(x,y * K(u * w,R(z,u,w)))
    ]]></literal>
    <justification jstring="[para(13867(a,1),15164(a,1,2,2))].">
      <j1 rule="para" parents="13867 15164"/>
    </justification>
  </clause>

  <clause id="15251">
    <literal><![CDATA[
      K(x,y \ (T(z,u * w) * ((u \ 1) \ w))) = K(x,y \ (((1 / u) \ w) * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,5016,a(flip),b,15187,a)].">
      <j1 rule="hyper" parents="63 5016 15187"/>
    </justification>
  </clause>

  <clause id="15252">
    <literal><![CDATA[
      K(x,y * K(z * u,R(w,z,u))) = K(x,y * K(w,(z * w) * u))
    ]]></literal>
    <justification jstring="[para(14293(a,1),15250(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14293 15250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15253">
    <literal><![CDATA[
      K(x,y * K(z * u,L(w,z,u))) = K(x,y * K(w,(z * w) * u))
    ]]></literal>
    <justification jstring="[para(13864(a,1),15252(a,1,2,2))].">
      <j1 rule="para" parents="13864 15252"/>
    </justification>
  </clause>

  <clause id="15254">
    <literal><![CDATA[
      K(x,y * K(z,(u * z) * w)) = K(x,y * K(u * w,z))
    ]]></literal>
    <justification jstring="[para(14021(a,1),15253(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14021 15253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15255">
    <literal><![CDATA[
      K(x,y \ (((1 / z) \ u) * w)) = K(x,y \ (((z \ 1) \ u) * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,15186,a(flip),b,15251,a),flip(a)].">
      <j1 rule="hyper" parents="63 15186 15251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15256">
    <literal><![CDATA[
      K(x,T((1 / y) * (z * y),y) \ u) = K(x,L(z,y,y \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(11(a,1),14967(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11 14967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15258">
    <literal><![CDATA[
      K(x,(y * K(z,(z \ 1) \ u)) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * K(u,z)) \ w) = v5
    ]]></literal>
    <justification jstring="[para(15028(a,1),9849(a,1))].">
      <j1 rule="para" parents="15028 9849"/>
    </justification>
  </clause>

  <clause id="15259">
    <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(13426(a,1),15191(a,1,1,2))].">
      <j1 rule="para" parents="13426 15191"/>
    </justification>
  </clause>

  <clause id="15260">
    <literal><![CDATA[
      L(x,T(y,z),x) = L(x,y * K(x * y,u),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,12573,a,b,15259,a)].">
      <j1 rule="hyper" parents="63 12573 15259"/>
    </justification>
  </clause>

  <clause id="15262">
    <literal><![CDATA[
      L(x,T(y,z),x) = L(x,x \ T(x * y,u),x)
    ]]></literal>
    <justification jstring="[para(13221(a,2),15260(a,2,2))].">
      <j1 rule="para" parents="13221 15260"/>
    </justification>
  </clause>

  <clause id="15263">
    <literal><![CDATA[
      L(x,x \ T(x * y,z),x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(12572,a,15262,a),flip(a)].">
      <j1 rule="hyper" parents="12572 15262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15264">
    <literal><![CDATA[
      L(x,x \ T(y,z),x) = L(x,x \ y,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),15263(a,1,2,2,1))].">
      <j1 rule="para" parents="10 15263"/>
    </justification>
  </clause>

  <clause id="15265">
    <literal><![CDATA[
      L(x,x \ (y / z),x) = L(x,x \ (z \ y),x)
    ]]></literal>
    <justification jstring="[para(113(a,1),15264(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="113 15264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15266">
    <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(15265(a,1),12826(a,1,2))].">
      <j1 rule="para" parents="15265 12826"/>
    </justification>
  </clause>

  <clause id="15267">
    <literal><![CDATA[
      K(x,(K(y,z \ K(z,u)) * u) \ w) = K(x,(u * K(y,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(9849,a,15202,a),flip(a)].">
      <j1 rule="hyper" parents="9849 15202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15268">
    <literal><![CDATA[
      K(x,(y * K(z,u \ 1)) \ w) = K(x,(y * K(z,u)) \ w)
    ]]></literal>
    <justification jstring="[para(5222(a,1),15267(a,1,2,1))].">
      <j1 rule="para" parents="5222 15267"/>
    </justification>
  </clause>

  <clause id="15269">
    <literal><![CDATA[
      K(x,(K(y \ K(y,z),u) * z) \ w) = K(x,(z * K(u,y)) \ w)
    ]]></literal>
    <justification jstring="[hyper(9849,a,15206,a),flip(a)].">
      <j1 rule="hyper" parents="9849 15206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15270">
    <literal><![CDATA[
      K(x,(y * K(z \ 1,u)) \ w) = K(x,(y * K(u,z)) \ w)
    ]]></literal>
    <justification jstring="[para(7705(a,1),15269(a,1,2,1))].">
      <j1 rule="para" parents="7705 15269"/>
    </justification>
  </clause>

  <clause id="15271">
    <literal><![CDATA[
      K(x,(y * K((z \ 1) \ 1,(z \ 1) \ u)) \ w) = K(x,(y * K(z * u,z \ 1)) \ w)
    ]]></literal>
    <justification jstring="[para(4867(a,1),15270(a,2,2,1,2))].">
      <j1 rule="para" parents="4867 15270"/>
    </justification>
  </clause>

  <clause id="15272">
    <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(6792(a,1),15270(a,2,2))].">
      <j1 rule="para" parents="6792 15270"/>
    </justification>
  </clause>

  <clause id="15274">
    <literal><![CDATA[
      T(x,K(y,z) * (u * K(K(z,y),u))) = T(u,K(z,y)) \ T(x * u,K(z,y))
    ]]></literal>
    <justification jstring="[para(6804(a,1),14915(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6804 14915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15275">
    <literal><![CDATA[
      T(x,K(y,z)) \ T(u * x,K(y,z)) = T(u,x * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,15003,a(flip),b,15274,a),flip(a)].">
      <j1 rule="hyper" parents="63 15003 15274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15276">
    <literal><![CDATA[
      K(x,K(y * (z \ u),z / y) * w) = K(x,K(y * (u / z),u) * w)
    ]]></literal>
    <justification jstring="[para(14297(a,1),14964(a,1,2,1))].">
      <j1 rule="para" parents="14297 14964"/>
    </justification>
  </clause>

  <clause id="15277">
    <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(15010(a,1),15024(a,1,1))].">
      <j1 rule="para" parents="15010 15024"/>
    </justification>
  </clause>

  <clause id="15278">
    <literal><![CDATA[
      T(x,T(y / ((z * u) / z),w)) = T(x,T(y / T(u,z),w))
    ]]></literal>
    <justification jstring="[hyper(7056,a,15277,a),flip(a)].">
      <j1 rule="hyper" parents="7056 15277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15279">
    <literal><![CDATA[
      T(x,T((y / z) * K(z,u),w)) = T(x,T(y / T(z,u),w))
    ]]></literal>
    <justification jstring="[para(7664(a,1),15278(a,1,2,1))].">
      <j1 rule="para" parents="7664 15278"/>
    </justification>
  </clause>

  <clause id="15280">
    <literal><![CDATA[
      T(x,T((y / z) \ K(y,u),w)) = T(x,T(z / T(y,u),w))
    ]]></literal>
    <justification jstring="[hyper(63,a,14168,a,b,15279,a)].">
      <j1 rule="hyper" parents="63 14168 15279"/>
    </justification>
  </clause>

  <clause id="15282">
    <literal><![CDATA[
      K(((T(T(x,y),y) \ z) * K(x,y)) * u,w) = K(T(T(x,y) \ z,K(y,x)) * u,w)
    ]]></literal>
    <justification jstring="[para(5994(a,1),15128(a,1,1,1))].">
      <j1 rule="para" parents="5994 15128"/>
    </justification>
  </clause>

  <clause id="15283">
    <literal><![CDATA[
      K(x,K(L(y,y \ z,u),w) * ((y \ z) * u)) = K(x,(T(y,w) \ z) * u)
    ]]></literal>
    <justification jstring="[para(11612(a,1),14933(a,2,2))].">
      <j1 rule="para" parents="11612 14933"/>
    </justification>
  </clause>

  <clause id="15284">
    <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(5994(a,1),14960(a,2,2,1))].">
      <j1 rule="para" parents="5994 14960"/>
    </justification>
  </clause>

  <clause id="15285">
    <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(7410(a,1),14973(a,1,2,1))].">
      <j1 rule="para" parents="7410 14973"/>
    </justification>
  </clause>

  <clause id="15286">
    <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(63,a,14953,a(flip),b,15285,a),flip(a)].">
      <j1 rule="hyper" parents="63 14953 15285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15288">
    <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(5994(a,1),14997(a,2,2,2))].">
      <j1 rule="para" parents="5994 14997"/>
    </justification>
  </clause>

  <clause id="15289">
    <literal><![CDATA[
      K(x,y * ((((1 / z) * u) \ u) \ u)) = K(x,y * (((1 / z) * u) * K(z,z \ u)))
    ]]></literal>
    <justification jstring="[para(13161(a,1),14999(a,2,2,2,2))].">
      <j1 rule="para" parents="13161 14999"/>
    </justification>
  </clause>

  <clause id="15290">
    <literal><![CDATA[
      K(x,y * ((((1 / z) * u) \ u) \ u)) = K(x,y * ((1 / z) * (z * (u / z))))
    ]]></literal>
    <justification jstring="[para(10324(a,1),15289(a,2,2,2))].">
      <j1 rule="para" parents="10324 15289"/>
    </justification>
  </clause>

  <clause id="15291">
    <literal><![CDATA[
      K(x,y * L(z / u,u,u \ 1)) = K(x,y * ((((1 / u) * z) \ z) \ z))
    ]]></literal>
    <justification jstring="[para(2652(a,1),15290(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="2652 15290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15292">
    <literal><![CDATA[
      K(x,y * T((1 / z) * u,u)) = K(x,y * L(u / z,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(333,a,12658,a(flip),b,15291,a)].">
      <j1 rule="hyper" parents="333 12658 15291"/>
    </justification>
  </clause>

  <clause id="15293">
    <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(9434(a,1),15135(a,2,1,2))].">
      <j1 rule="para" parents="9434 15135"/>
    </justification>
  </clause>

  <clause id="15295">
    <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(63,a,15268,a(flip),b,15240,a)].">
      <j1 rule="hyper" parents="63 15268 15240"/>
    </justification>
  </clause>

  <clause id="15296">
    <literal><![CDATA[
      K(x,(y * K(z * u,z \ 1)) \ w) = K(x,(y * K(z,(z \ 1) \ u)) \ w)
    ]]></literal>
    <justification jstring="[para(3334(a,1),15271(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="3334 15271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15297">
    <literal><![CDATA[
      K(x,(y * K(z,(z \ 1) \ u)) \ w) = K(x,(y * K(z * u,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,15268,a(flip),b,15296,a),flip(a)].">
      <j1 rule="hyper" parents="63 15268 15296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15298">
    <literal><![CDATA[
      K(x,(y * K(z * u,z)) \ w) = K(x,(y * K(u,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(15258,a,15297,a),flip(a)].">
      <j1 rule="hyper" parents="15258 15297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15299">
    <literal><![CDATA[
      K(x,(y * K(z * u,u)) \ w) = K(x,(y * K(z,u)) \ w)
    ]]></literal>
    <justification jstring="[para(4543(a,2),15298(a,1,2,1,2))].">
      <j1 rule="para" parents="4543 15298"/>
    </justification>
  </clause>

  <clause id="15300">
    <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(63,a,15295,a(flip),b,15299,a),flip(a)].">
      <j1 rule="hyper" parents="63 15295 15299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15301">
    <literal><![CDATA[
      K(x,T(y,z) \ ((y * z) * (u / (y * z)))) = K(x,T(u / y,T(z,y)))
    ]]></literal>
    <justification jstring="[para(4222(a,2),15300(a,1,2,1))].">
      <j1 rule="para" parents="4222 15300"/>
    </justification>
  </clause>

  <clause id="15302">
    <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(3613(a,1),15301(a,1,2,1))].">
      <j1 rule="para" parents="3613 15301"/>
    </justification>
  </clause>

  <clause id="15303">
    <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(111(a,1),15302(a,1,2,2,1))].">
      <j1 rule="para" parents="111 15302"/>
    </justification>
  </clause>

  <clause id="15304">
    <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(111(a,1),15303(a,1,2,2,2,2))].">
      <j1 rule="para" parents="111 15303"/>
    </justification>
  </clause>

  <clause id="15305">
    <literal><![CDATA[
      K(x,T(y,z) \ ((z * y) * (u / (z * y)))) = K(x,T(u / y,z))
    ]]></literal>
    <justification jstring="[para(6917(a,1),15304(a,2,2))].">
      <j1 rule="para" parents="6917 15304"/>
    </justification>
  </clause>

  <clause id="15306">
    <literal><![CDATA[
      K(x,T(y,z) \ T(u,z * y)) = K(x,T(u / y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,15178,a(flip),b,15305,a)].">
      <j1 rule="hyper" parents="63 15178 15305"/>
    </justification>
  </clause>

  <clause id="15308">
    <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(8553(a,1),15306(a,1,2,2,2))].">
      <j1 rule="para" parents="8553 15306"/>
    </justification>
  </clause>

  <clause id="15309">
    <literal><![CDATA[
      K(R(x,y,y \ 1) \ (z * (x * y)),R(x,y,y \ 1)) = K(z / (y \ 1),x)
    ]]></literal>
    <justification jstring="[hyper(333,a,13159,a(flip),b,15071,a),flip(a)].">
      <j1 rule="hyper" parents="333 13159 15071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15311">
    <literal><![CDATA[
      K(R(x,y,y \ 1) \ (z * (x * y)),R(x,y,y \ 1)) = K(z * y,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,13275,a(flip),b,15309,a),flip(a)].">
      <j1 rule="hyper" parents="333 13275 15309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15312">
    <literal><![CDATA[
      K(x * ((y * x) \ (z * (y * x))),y) = K(z * x,y)
    ]]></literal>
    <justification jstring="[hyper(14432,a,15311,a)].">
      <j1 rule="hyper" parents="14432 15311"/>
    </justification>
  </clause>

  <clause id="15313">
    <literal><![CDATA[
      K(x * T(y,z * x),z) = K(y * x,z)
    ]]></literal>
    <justification jstring="[para(22(a,2),15312(a,1,1,2))].">
      <j1 rule="para" parents="22 15312"/>
    </justification>
  </clause>

  <clause id="15314">
    <literal><![CDATA[
      K(T(x,y * z) * z,y) = K(z * x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,15074,a(flip),b,15313,a),flip(a)].">
      <j1 rule="hyper" parents="63 15074 15313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15315">
    <literal><![CDATA[
      K(T((x \ y) \ z,u * K(x \ y,x)) * K(x \ y,x),u) = K((y / x) \ z,u)
    ]]></literal>
    <justification jstring="[para(4830(a,1),15314(a,2,1))].">
      <j1 rule="para" parents="4830 15314"/>
    </justification>
  </clause>

  <clause id="15316">
    <literal><![CDATA[
      K(x,y / (z \ a(u \ 1,u,z))) = K(x,y / (1 / L(z,u,u \ 1)))
    ]]></literal>
    <justification jstring="[para(13811(a,1),15173(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13811 15173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15317">
    <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(15316(a,2),13514(a,1))].">
      <j1 rule="para" parents="15316 13514"/>
    </justification>
  </clause>

  <clause id="15319">
    <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(8783(a,1),15241(a,2,2))].">
      <j1 rule="para" parents="8783 15241"/>
    </justification>
  </clause>

  <clause id="15320">
    <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(6948(a,1),15319(a,1,2))].">
      <j1 rule="para" parents="6948 15319"/>
    </justification>
  </clause>

  <clause id="15321">
    <literal><![CDATA[
      K(x,T(y / z,y / (u \ z))) = K(x,T(y / z,u \ 1))
    ]]></literal>
    <justification jstring="[para(8417(a,1),15320(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8417 15320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15322">
    <literal><![CDATA[
      K(x,T(y / z,y / (u \ z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y / z,u)) = w
    ]]></literal>
    <justification jstring="[para(15321(a,2),7282(a,1))].">
      <j1 rule="para" parents="15321 7282"/>
    </justification>
  </clause>

  <clause id="15324">
    <literal><![CDATA[
      K(x,T(y,z) \ ((z \ y) * (u / (z \ y)))) = K(x,T(u / y,z))
    ]]></literal>
    <justification jstring="[hyper(15322,a,14379,a),flip(a)].">
      <j1 rule="hyper" parents="15322 14379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15325">
    <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(3655(a,1),15324(a,1,2,2,1))].">
      <j1 rule="para" parents="3655 15324"/>
    </justification>
  </clause>

  <clause id="15326">
    <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(7391(a,1),15272(a,1,2,2,2))].">
      <j1 rule="para" parents="7391 15272"/>
    </justification>
  </clause>

  <clause id="15327">
    <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(6788(a,2),15326(a,1,2,2))].">
      <j1 rule="para" parents="6788 15326"/>
    </justification>
  </clause>

  <clause id="15329">
    <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(7171(a,1),15327(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7171 15327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15330">
    <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(333,a,5782,a(flip),b,15329,a),flip(a)].">
      <j1 rule="hyper" parents="333 5782 15329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15331">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ 1) = K(x,u \ K(y,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,12862,a(flip),b,15330,a)].">
      <j1 rule="hyper" parents="63 12862 15330"/>
    </justification>
  </clause>

  <clause id="15332">
    <literal><![CDATA[
      K(x,y \ K(z,u \ 1)) = K(x,y \ K(u,z))
    ]]></literal>
    <justification jstring="[hyper(5952,a,15331,a),flip(a)].">
      <j1 rule="hyper" parents="5952 15331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15337">
    <literal><![CDATA[
      K(x,y \ K(z \ 1,u)) = K(x,y \ K(u,z))
    ]]></literal>
    <justification jstring="[para(4621(a,1),15332(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4621 15332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15338">
    <literal><![CDATA[
      K(x,y \ K(z \ u,u)) = K(x,y \ K(u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,12690,a(flip),b,15337,a)].">
      <j1 rule="hyper" parents="63 12690 15337"/>
    </justification>
  </clause>

  <clause id="15339">
    <literal><![CDATA[
      K(x,y \ K(z \ 1,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(15337(a,2),15234(a,1))].">
      <j1 rule="para" parents="15337 15234"/>
    </justification>
  </clause>

  <clause id="15340">
    <literal><![CDATA[
      K(x,y \ K(z,u \ z)) = K(x,y \ K(z,u))
    ]]></literal>
    <justification jstring="[hyper(15234,a,15338,a)].">
      <j1 rule="hyper" parents="15234 15338"/>
    </justification>
  </clause>

  <clause id="15341">
    <literal><![CDATA[
      K(x,(y \ z) \ K(u,y)) = K(x,z \ T(y,1 / u))
    ]]></literal>
    <justification jstring="[hyper(15339,a,15060,a)].">
      <j1 rule="hyper" parents="15339 15060"/>
    </justification>
  </clause>

  <clause id="15342">
    <literal><![CDATA[
      K(x,y \ T(z,1 / u)) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,15053,a(flip),b,15341,a),flip(a)].">
      <j1 rule="hyper" parents="63 15053 15341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15343">
    <literal><![CDATA[
      K(x,y \ T(z,u \ 1)) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(76(a,1),15342(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="76 15342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15344">
    <literal><![CDATA[
      K(x,y \ T(z * (u \ 1),u)) = K(x,y \ ((u \ 1) * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,15180,a(flip),b,15343,a),flip(a)].">
      <j1 rule="hyper" parents="63 15180 15343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15345">
    <literal><![CDATA[
      K(x,y \ T(((1 / z) * u) * z,z)) = K(x,y \ R(u,z,z))
    ]]></literal>
    <justification jstring="[para(2997(a,1),15343(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2997 15343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15346">
    <literal><![CDATA[
      K(x,y \ T(z,u \ (w \ u))) = K(x,y \ T(z,T(w,u)))
    ]]></literal>
    <justification jstring="[para(6738(a,1),15343(a,1,2,2))].">
      <j1 rule="para" parents="6738 15343"/>
    </justification>
  </clause>

  <clause id="15347">
    <literal><![CDATA[
      K(x,y \ ((z \ 1) * (z * u))) = K(x,y \ R(u,z,z \ 1))
    ]]></literal>
    <justification jstring="[para(833(a,1),15344(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="833 15344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15348">
    <literal><![CDATA[
      K(x,y \ (z * ((1 / z) * u))) = K(x,y \ R(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,15180,a(flip),b,15345,a)].">
      <j1 rule="hyper" parents="63 15180 15345"/>
    </justification>
  </clause>

  <clause id="15349">
    <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(13964,a,15347,a)].">
      <j1 rule="hyper" parents="13964 15347"/>
    </justification>
  </clause>

  <clause id="15350">
    <literal><![CDATA[
      K(x,y \ R(z,u,u \ 1)) = K(x,y \ L(z,u,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,5142,a(flip),b,15347,a),flip(a)].">
      <j1 rule="hyper" parents="63 5142 15347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15351">
    <literal><![CDATA[
      K(x,(y * z) \ L(y,u,u \ 1)) = K(x,z \ a(y,u,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,14158,a(flip),b,15350,a),flip(a)].">
      <j1 rule="hyper" parents="63 14158 15350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15352">
    <literal><![CDATA[
      K(x,y \ L(z / u,u,u \ 1)) = K(x,y \ (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[para(554(a,1),15350(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="554 15350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15353">
    <literal><![CDATA[
      K(x,y \ (z \ L(z,u,u \ 1))) = K(x,y \ a(z,u,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,14028,a(flip),b,15351,a)].">
      <j1 rule="hyper" parents="63 14028 15351"/>
    </justification>
  </clause>

  <clause id="15354">
    <literal><![CDATA[
      K(x,(y \ 1) \ a(z,u,u \ 1)) = K(x,y * (z \ L(z,u,u \ 1)))
    ]]></literal>
    <justification jstring="[hyper(13421,a,15353,a),flip(a)].">
      <j1 rule="hyper" parents="13421 15353"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15355">
    <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(15354(a,1),13421(a,1))].">
      <j1 rule="para" parents="15354 13421"/>
    </justification>
  </clause>

  <clause id="15356">
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ R(u,y,y \ 1)) = K(x,(y \ z) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,14192,a(flip),b,15349,a),flip(a)].">
      <j1 rule="hyper" parents="63 14192 15349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15357">
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ L(u,y,y \ 1)) = K(x,(y \ z) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,15350,a(flip),b,15356,a)].">
      <j1 rule="hyper" parents="63 15350 15356"/>
    </justification>
  </clause>

  <clause id="15358">
    <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(9599(a,1),15325(a,1,2,1))].">
      <j1 rule="para" parents="9599 15325"/>
    </justification>
  </clause>

  <clause id="15359">
    <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(3655(a,1),15358(a,1,2,2,2,2))].">
      <j1 rule="para" parents="3655 15358"/>
    </justification>
  </clause>

  <clause id="15361">
    <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(63,a,15221,a(flip),b,15359,a)].">
      <j1 rule="hyper" parents="63 15221 15359"/>
    </justification>
  </clause>

  <clause id="15362">
    <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(12625(a,1),15361(a,2,2))].">
      <j1 rule="para" parents="12625 15361"/>
    </justification>
  </clause>

  <clause id="15363">
    <literal><![CDATA[
      K(x,T(y,z) \ T(u,T(z,y))) = K(x,T(u / y,z \ y))
    ]]></literal>
    <justification jstring="[hyper(63,a,15178,a(flip),b,15362,a)].">
      <j1 rule="hyper" parents="63 15178 15362"/>
    </justification>
  </clause>

  <clause id="15364">
    <literal><![CDATA[
      ((x * (y * z)) / x) \ L(z,z \ (z * y),z) = T(z * (z \ ((x * (z * y)) / x)),z) \ z
    ]]></literal>
    <justification jstring="[para(9(a,1),15266(a,1,2,2,2))].">
      <j1 rule="para" parents="9 15266"/>
    </justification>
  </clause>

  <clause id="15365">
    <literal><![CDATA[
      T(x * (x \ ((y * (x * z)) / y)),x) \ x = ((y * (z * x)) / y) \ L(x,z,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),15364(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 15364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15367">
    <literal><![CDATA[
      ((x * (y * z)) / x) \ L(z,y,z) = T((x * (z * y)) / x,z) \ z
    ]]></literal>
    <justification jstring="[para(10(a,1),15365(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 15365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15369">
    <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="[para(112(a,1),15308(a,1,2,1))].">
      <j1 rule="para" parents="112 15308"/>
    </justification>
  </clause>

  <clause id="15370">
    <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(15229(a,1),15369(a,1,2,2))].">
      <j1 rule="para" parents="15229 15369"/>
    </justification>
  </clause>

  <clause id="15371">
    <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(4636(a,1),15370(a,1,2,2,2,2))].">
      <j1 rule="para" parents="4636 15370"/>
    </justification>
  </clause>

  <clause id="15372">
    <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(15163(a,1),15371(a,1,2,2))].">
      <j1 rule="para" parents="15163 15371"/>
    </justification>
  </clause>

  <clause id="15373">
    <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(4222(a,2),15372(a,1,2,2,2))].">
      <j1 rule="para" parents="4222 15372"/>
    </justification>
  </clause>

  <clause id="15374">
    <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(12787,a,15373,a),flip(a)].">
      <j1 rule="hyper" parents="12787 15373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15375">
    <literal><![CDATA[
      K(x,T(y / (z * u),(z * u) \ u)) = K(x,(u * z) \ T(y,T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(333,a,15090,a(flip),b,15374,a),flip(a)].">
      <j1 rule="hyper" parents="333 15090 15374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15376">
    <literal><![CDATA[
      K(x,T(y / (z * u),u \ (z \ u))) = K(x,(u * z) \ T(y,T(u,z)))
    ]]></literal>
    <justification jstring="[para(6740(a,1),15375(a,1,2))].">
      <j1 rule="para" parents="6740 15375"/>
    </justification>
  </clause>

  <clause id="15377">
    <literal><![CDATA[
      K(x,T(y / (z * u),T(z,u))) = K(x,(u * z) \ T(y,T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(7287,a,15376,a)].">
      <j1 rule="hyper" parents="7287 15376"/>
    </justification>
  </clause>

  <clause id="15378">
    <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(4496(a,1),15377(a,2,2,1))].">
      <j1 rule="para" parents="4496 15377"/>
    </justification>
  </clause>

  <clause id="15379">
    <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(14895(a,1),15246(a,1,2))].">
      <j1 rule="para" parents="14895 15246"/>
    </justification>
  </clause>

  <clause id="15380">
    <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(15367(a,1),15379(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="15367 15379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15381">
    <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(238(a,1),15380(a,2,2,1,1,1))].">
      <j1 rule="para" parents="238 15380"/>
    </justification>
  </clause>

  <clause id="15383">
    <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(15381(a,2),13516(a,1))].">
      <j1 rule="para" parents="15381 13516"/>
    </justification>
  </clause>

  <clause id="15384">
    <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(65(a,1),15245(a,1,2,2))].">
      <j1 rule="para" parents="65 15245"/>
    </justification>
  </clause>

  <clause id="15385">
    <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(6946(a,1),15378(a,2,2,2))].">
      <j1 rule="para" parents="6946 15378"/>
    </justification>
  </clause>

  <clause id="15386">
    <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(7138(a,1),15385(a,2,2,2))].">
      <j1 rule="para" parents="7138 15385"/>
    </justification>
  </clause>

  <clause id="15387">
    <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(333,a,15346,a(flip),b,15386,a),flip(a)].">
      <j1 rule="hyper" parents="333 15346 15386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15388">
    <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(333,a,15270,a(flip),b,15387,a),flip(a)].">
      <j1 rule="hyper" parents="333 15270 15387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15389">
    <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(333,a,15299,a(flip),b,15388,a),flip(a)].">
      <j1 rule="hyper" parents="333 15299 15388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15390">
    <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(4222(a,2),15389(a,2,2,1))].">
      <j1 rule="para" parents="4222 15389"/>
    </justification>
  </clause>

  <clause id="15391">
    <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(333,a,15363,a(flip),b,15390,a),flip(a)].">
      <j1 rule="hyper" parents="333 15363 15390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15392">
    <literal><![CDATA[
      K(x,T(y / z,T(z * u,(z * u) \ z))) = K(x,T(y / z,u \ z))
    ]]></literal>
    <justification jstring="[para(10(a,1),15391(a,1,2,1,2))].">
      <j1 rule="para" parents="10 15391"/>
    </justification>
  </clause>

  <clause id="15393">
    <literal><![CDATA[
      K(x,T(y / z,T(z * u,z))) = K(x,T(y / z,u \ z))
    ]]></literal>
    <justification jstring="[para(6345(a,1),15392(a,1,2))].">
      <j1 rule="para" parents="6345 15392"/>
    </justification>
  </clause>

  <clause id="15394">
    <literal><![CDATA[
      K(x,T(y / z,u \ z)) = K(x,T(y / z,u * z))
    ]]></literal>
    <justification jstring="[para(12225(a,1),15393(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12225 15393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15395">
    <literal><![CDATA[
      K(x,T((y * z) / z,u * z)) = K(x,T(y,u \ z))
    ]]></literal>
    <justification jstring="[para(11(a,1),15394(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11 15394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15396">
    <literal><![CDATA[
      K(x,T(y,z \ u)) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(11(a,1),15395(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11 15395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15397">
    <literal><![CDATA[
      K(x * (y \ z),T(u,y * z)) = K((y \ z) * x,u)
    ]]></literal>
    <justification jstring="[hyper(12215,a,15396,a),flip(a)].">
      <j1 rule="hyper" parents="12215 15396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15398">
    <literal><![CDATA[
      K(x,T(y,z \ u)) = K(x,T(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(7286,a,15396,a)].">
      <j1 rule="hyper" parents="7286 15396"/>
    </justification>
  </clause>

  <clause id="15399">
    <literal><![CDATA[
      T(x,T(y,z \ u)) = T(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(124,a,15396,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 15396 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15400">
    <literal><![CDATA[
      K(x,L(T(y,z \ u),w,v5)) = K(x,T(L(y,w,v5),z * u))
    ]]></literal>
    <justification jstring="[para(25(a,2),15396(a,1,2))].">
      <j1 rule="para" parents="25 15396"/>
    </justification>
  </clause>

  <clause id="15401">
    <literal><![CDATA[
      K(x,T(y,z * z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(204(a,1),15396(a,1,2)),flip(a)].">
      <j1 rule="para" parents="204 15396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15402">
    <literal><![CDATA[
      K(x,y) * K(y,T(x,z * u)) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[para(15396(a,1),6805(a,1,2))].">
      <j1 rule="para" parents="15396 6805"/>
    </justification>
  </clause>

  <clause id="15404">
    <literal><![CDATA[
      K(x / (y * y),z) = K(y \ (y \ x),z)
    ]]></literal>
    <justification jstring="[hyper(13983,a,15401,a),flip(a)].">
      <j1 rule="hyper" parents="13983 15401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15405">
    <literal><![CDATA[
      T(x,T(y,z * z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(124,a,15401,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 15401 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15406">
    <literal><![CDATA[
      T(x,(y * y) * z) = T(x,z * (y * y))
    ]]></literal>
    <justification jstring="[hyper(12232,a,15405,a),flip(a)].">
      <j1 rule="hyper" parents="12232 15405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15407">
    <literal><![CDATA[
      T(x,K(y,z * z)) = x
    ]]></literal>
    <justification jstring="[hyper(6882,a,15405,a)].">
      <j1 rule="hyper" parents="6882 15405"/>
    </justification>
  </clause>

  <clause id="15408">
    <literal><![CDATA[
      K(x * x,y) * z = z * K(x * x,y)
    ]]></literal>
    <justification jstring="[hyper(40,a,6201,a,b,15405,a),flip(a)].">
      <j1 rule="hyper" parents="40 6201 15405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15409">
    <literal><![CDATA[
      T(x,(y * y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z * (y * y)) = u
    ]]></literal>
    <justification jstring="[para(15405(a,1),12232(a,1))].">
      <j1 rule="para" parents="15405 12232"/>
    </justification>
  </clause>

  <clause id="15410">
    <literal><![CDATA[
      T(x,T(y,z * z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = u
    ]]></literal>
    <justification jstring="[para(15407(a,1),6192(a,2))].">
      <j1 rule="para" parents="15407 6192"/>
    </justification>
  </clause>

  <clause id="15411">
    <literal><![CDATA[
      x \ T(y * x,K(z,u * u)) = T(y,x * K(z,u * u))
    ]]></literal>
    <justification jstring="[para(15407(a,1),15275(a,1,1))].">
      <j1 rule="para" parents="15407 15275"/>
    </justification>
  </clause>

  <clause id="15412">
    <literal><![CDATA[
      K(x,T(y,z * u)) = K(x,T(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,15396,a(flip),b,15398,a)].">
      <j1 rule="hyper" parents="63 15396 15398"/>
    </justification>
  </clause>

  <clause id="15413">
    <literal><![CDATA[
      K(x,T(y / ((z \ u) * z),u * z)) = K(x,u \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,15183,a(flip),b,15398,a),flip(a)].">
      <j1 rule="hyper" parents="63 15183 15398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15414">
    <literal><![CDATA[
      K(x,T((y \ z) * u,z * y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u * (y \ z)) = w
    ]]></literal>
    <justification jstring="[para(15398(a,1),12278(a,1))].">
      <j1 rule="para" parents="15398 12278"/>
    </justification>
  </clause>

  <clause id="15415">
    <literal><![CDATA[
      K(x,T(y * (z \ u),u * z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z \ u) * y) = w
    ]]></literal>
    <justification jstring="[para(15398(a,1),12281(a,1))].">
      <j1 rule="para" parents="15398 12281"/>
    </justification>
  </clause>

  <clause id="15416">
    <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(15398(a,1),13385(a,1))].">
      <j1 rule="para" parents="15398 13385"/>
    </justification>
  </clause>

  <clause id="15417">
    <literal><![CDATA[
      K(x,T(y,K(z,u)) \ T(w * y,K(z,u))) = K(x,T(w,K(z,u) \ y))
    ]]></literal>
    <justification jstring="[para(15275(a,2),15398(a,2,2)),flip(a)].">
      <j1 rule="para" parents="15275 15398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15418">
    <literal><![CDATA[
      K((x * (y \ 1)) / y,z) = K(y \ (y \ x),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,13682,a,b,15404,a)].">
      <j1 rule="hyper" parents="63 13682 15404"/>
    </justification>
  </clause>

  <clause id="15419">
    <literal><![CDATA[
      T(T(x,y * y),z) = T(x,(y * y) * z)
    ]]></literal>
    <justification jstring="[hyper(333,a,1124,a,b,15406,a)].">
      <j1 rule="hyper" parents="333 1124 15406"/>
    </justification>
  </clause>

  <clause id="15420">
    <literal><![CDATA[
      T(x,y * (z * z)) = T(x,z * (z * y))
    ]]></literal>
    <justification jstring="[hyper(63,a,13285,a(flip),b,15406,a),flip(a)].">
      <j1 rule="hyper" parents="63 13285 15406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15421">
    <literal><![CDATA[
      T(x \ (x \ y),x \ (x \ (x \ (x \ y)))) = K(x * x,y) * (x \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(333,a,13720,a,b,15408,a)].">
      <j1 rule="hyper" parents="333 13720 15408"/>
    </justification>
  </clause>

  <clause id="15422">
    <literal><![CDATA[
      K(x * (y * z),T(u,z * y)) = K((y * z) * x,u)
    ]]></literal>
    <justification jstring="[hyper(12215,a,15412,a),flip(a)].">
      <j1 rule="hyper" parents="12215 15412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15423">
    <literal><![CDATA[
      K(x,T(y \ (z * u),u * z)) = K(x,(z * u) / y)
    ]]></literal>
    <justification jstring="[hyper(7225,a,15412,a),flip(a)].">
      <j1 rule="hyper" parents="7225 15412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15424">
    <literal><![CDATA[
      K(x,T((y * z) \ u,z * y)) = K(x,u / (y * z))
    ]]></literal>
    <justification jstring="[hyper(7076,a,15412,a),flip(a)].">
      <j1 rule="hyper" parents="7076 15412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15425">
    <literal><![CDATA[
      K(x,T(y,z * (u * y))) = K(x,T(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(333,a,9870,a,b,15412,a)].">
      <j1 rule="hyper" parents="333 9870 15412"/>
    </justification>
  </clause>

  <clause id="15426">
    <literal><![CDATA[
      K(x,T(y,z * (u * x))) = K(x,T(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(333,a,9801,a,b,15412,a)].">
      <j1 rule="hyper" parents="333 9801 15412"/>
    </justification>
  </clause>

  <clause id="15427">
    <literal><![CDATA[
      x * K(y,T(z,u * w)) = x * K(y,T(z,w * u))
    ]]></literal>
    <justification jstring="[hyper(126,a,15412,a,b,9,a)].">
      <j1 rule="hyper" parents="126 15412 9"/>
    </justification>
  </clause>

  <clause id="15429">
    <literal><![CDATA[
      K(x,T(y,(z \ u) * z)) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[para(10(a,1),15412(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 15412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15432">
    <literal><![CDATA[
      (x * x) * T(y,x * (x * z)) = T(y,z) * (x * x)
    ]]></literal>
    <justification jstring="[hyper(126,a,15420,a(flip),b,1122,a)].">
      <j1 rule="hyper" parents="126 15420 1122"/>
    </justification>
  </clause>

  <clause id="15434">
    <literal><![CDATA[
      K(x,T(y,T(z,u))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(12224(a,1),15429(a,1,2))].">
      <j1 rule="para" parents="12224 15429"/>
    </justification>
  </clause>

  <clause id="15435">
    <literal><![CDATA[
      K(x,T(T(y,z) * u,y)) = K(x,u * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(12278,a,15434,a),flip(a)].">
      <j1 rule="hyper" parents="12278 15434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15436">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ z))) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(7324,a,15434,a)].">
      <j1 rule="hyper" parents="7324 15434"/>
    </justification>
  </clause>

  <clause id="15437">
    <literal><![CDATA[
      T(K(x,y),T(z,u)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(6552,a,15434,a)].">
      <j1 rule="hyper" parents="6552 15434"/>
    </justification>
  </clause>

  <clause id="15440">
    <literal><![CDATA[
      K(x \ y,T(z,T(y,u))) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,6904,a(flip),b,15434,a),flip(a)].">
      <j1 rule="hyper" parents="333 6904 15434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15442">
    <literal><![CDATA[
      T(x,T(y,T(z,u))) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(124,a,15434,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 15434 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15443">
    <literal><![CDATA[
      T(x,y) * K(z,T(u,x)) = K(u,z) \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(126,a,15434,a(flip),b,6380,a)].">
      <j1 rule="hyper" parents="126 15434 6380"/>
    </justification>
  </clause>

  <clause id="15444">
    <literal><![CDATA[
      K(x,T(y,z / u)) = K(x,T(y,u \ z))
    ]]></literal>
    <justification jstring="[para(113(a,1),15434(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="113 15434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15449">
    <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(15434(a,1),12210(a,1))].">
      <j1 rule="para" parents="15434 12210"/>
    </justification>
  </clause>

  <clause id="15453">
    <literal><![CDATA[
      T(K(x,y),T(z,u)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(333,a,6365,a(flip),b,15437,a),flip(a)].">
      <j1 rule="hyper" parents="333 6365 15437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15454">
    <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(15437(a,1),9197(a,1,2))].">
      <j1 rule="para" parents="15437 9197"/>
    </justification>
  </clause>

  <clause id="15455">
    <literal><![CDATA[
      T(x,T(T(y,z) \ u,y)) = T(x,u / T(y,z))
    ]]></literal>
    <justification jstring="[hyper(13513,a,15442,a),flip(a)].">
      <j1 rule="hyper" parents="13513 15442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15456">
    <literal><![CDATA[
      T(x,T(T(y,z) / u,y)) = T(x,u \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(9496,a,15442,a),flip(a)].">
      <j1 rule="hyper" parents="9496 15442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15458">
    <literal><![CDATA[
      T(x,T(T(y,z) * (y \ u),(y \ u) \ u)) = T(x,T((y \ u) \ u,z) * (y \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,12257,a(flip),b,15442,a),flip(a)].">
      <j1 rule="hyper" parents="63 12257 15442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15460">
    <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(15442(a,1),6195(a,1))].">
      <j1 rule="para" parents="15442 6195"/>
    </justification>
  </clause>

  <clause id="15461">
    <literal><![CDATA[
      T(x,y) * K(x / T(y,x),z) = y * T(y \ T(x,y),T(z,x))
    ]]></literal>
    <justification jstring="[para(15442(a,1),7247(a,2,2))].">
      <j1 rule="para" parents="15442 7247"/>
    </justification>
  </clause>

  <clause id="15464">
    <literal><![CDATA[
      T(K(x,y),K(z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6882,a,15453,a)].">
      <j1 rule="hyper" parents="6882 15453"/>
    </justification>
  </clause>

  <clause id="15465">
    <literal><![CDATA[
      T(K(x \ T(y,z),u),T(y,w)) = K((x / y) \ K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(333,a,9842,a,b,15453,a),flip(a)].">
      <j1 rule="hyper" parents="333 9842 15453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15466">
    <literal><![CDATA[
      K(x,K(y,K(z,u))) = 1
    ]]></literal>
    <justification jstring="[hyper(122,a,15453,a(flip),b,6772,a),flip(a)].">
      <j1 rule="hyper" parents="122 15453 6772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15467">
    <literal><![CDATA[
      T(K(x,y),T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(15453(a,2),6691(a,1))].">
      <j1 rule="para" parents="15453 6691"/>
    </justification>
  </clause>

  <clause id="15469">
    <literal><![CDATA[
      T(x,K(y,K(z,u))) = x
    ]]></literal>
    <justification jstring="[hyper(56,a,15466,a)].">
      <j1 rule="hyper" parents="56 15466"/>
    </justification>
  </clause>

  <clause id="15470">
    <literal><![CDATA[
      T(x,K(y,z) * u) = T(x,u * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(12264,a,15469,a)].">
      <j1 rule="hyper" parents="12264 15469"/>
    </justification>
  </clause>

  <clause id="15471">
    <literal><![CDATA[
      T(x,K(y,z) / u) = T(x,u \ K(y,z))
    ]]></literal>
    <justification jstring="[hyper(7574,a,15469,a)].">
      <j1 rule="hyper" parents="7574 15469"/>
    </justification>
  </clause>

  <clause id="15472">
    <literal><![CDATA[
      K(x,T(y,K(z,u))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(7257,a,15469,a)].">
      <j1 rule="hyper" parents="7257 15469"/>
    </justification>
  </clause>

  <clause id="15473">
    <literal><![CDATA[
      T(x,K(K(y,z),u)) = x
    ]]></literal>
    <justification jstring="[hyper(7217,a,15469,a)].">
      <j1 rule="hyper" parents="7217 15469"/>
    </justification>
  </clause>

  <clause id="15474">
    <literal><![CDATA[
      T(x,T(y,K(z,u))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(7056,a,15469,a)].">
      <j1 rule="hyper" parents="7056 15469"/>
    </justification>
  </clause>

  <clause id="15475">
    <literal><![CDATA[
      K(x,K(y,z)) * u = u * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(6860,a,15469,a)].">
      <j1 rule="hyper" parents="6860 15469"/>
    </justification>
  </clause>

  <clause id="15476">
    <literal><![CDATA[
      x * (y * K(x,K(z,u))) = T(x,K(z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(6236,a,15469,a)].">
      <j1 rule="hyper" parents="6236 15469"/>
    </justification>
  </clause>

  <clause id="15477">
    <literal><![CDATA[
      T(x \ K(y,z),K(u,x)) = x \ K(y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,7034,a(flip),b,15469,a)].">
      <j1 rule="hyper" parents="63 7034 15469"/>
    </justification>
  </clause>

  <clause id="15478">
    <literal><![CDATA[
      (x * y) * K(x,K(z,u)) = T(x,K(z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,6102,a(flip),b,15469,a)].">
      <j1 rule="hyper" parents="63 6102 15469"/>
    </justification>
  </clause>

  <clause id="15479">
    <literal><![CDATA[
      T(K(x,K(y,z)),u) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(54,a,15469,a)].">
      <j1 rule="hyper" parents="54 15469"/>
    </justification>
  </clause>

  <clause id="15481">
    <literal><![CDATA[
      K(x,T(K(y,z),u)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(37,a,9853,a(flip),b,15469,a(flip))].">
      <j1 rule="hyper" parents="37 9853 15469"/>
    </justification>
  </clause>

  <clause id="15482">
    <literal><![CDATA[
      K(x,K(y,z)) * u != w
    ]]></literal>
    <literal><![CDATA[
      u * K(x,K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(15469(a,1),300(a,1,2))].">
      <j1 rule="para" parents="15469 300"/>
    </justification>
  </clause>

  <clause id="15483">
    <literal><![CDATA[
      T(x,T(y,K(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = w
    ]]></literal>
    <justification jstring="[para(15469(a,1),6192(a,2))].">
      <j1 rule="para" parents="15469 6192"/>
    </justification>
  </clause>

  <clause id="15484">
    <literal><![CDATA[
      x * K(y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(y,K(z,u)) * x = w
    ]]></literal>
    <justification jstring="[para(15469(a,1),6860(a,1))].">
      <j1 rule="para" parents="15469 6860"/>
    </justification>
  </clause>

  <clause id="15485">
    <literal><![CDATA[
      T(x,y * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(z,u) * y) = w
    ]]></literal>
    <justification jstring="[para(15469(a,1),12264(a,1))].">
      <j1 rule="para" parents="15469 12264"/>
    </justification>
  </clause>

  <clause id="15486">
    <literal><![CDATA[
      T(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u * K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(15469(a,1),12277(a,1,1))].">
      <j1 rule="para" parents="15469 12277"/>
    </justification>
  </clause>

  <clause id="15487">
    <literal><![CDATA[
      K(x,K(y,z)) * (u \ 1) = u \ K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(13201,a,15473,a)].">
      <j1 rule="hyper" parents="13201 15473"/>
    </justification>
  </clause>

  <clause id="15489">
    <literal><![CDATA[
      K(x,K(y,z) * u) = K(x,u * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(12250,a,15464,a),flip(a)].">
      <j1 rule="hyper" parents="12250 15464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15490">
    <literal><![CDATA[
      K(T(x,K(y,z)),u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(6611,a,15464,a)].">
      <j1 rule="hyper" parents="6611 15464"/>
    </justification>
  </clause>

  <clause id="15491">
    <literal><![CDATA[
      (K(x,y) * K(z,u)) * K(y,x) = K(z,u)
    ]]></literal>
    <justification jstring="[hyper(6113,a,15464,a)].">
      <j1 rule="hyper" parents="6113 15464"/>
    </justification>
  </clause>

  <clause id="15492">
    <literal><![CDATA[
      K(x,K(y,z) / u) = K(x,u \ K(y,z))
    ]]></literal>
    <justification jstring="[hyper(5954,a,15464,a),flip(a)].">
      <j1 rule="hyper" parents="5954 15464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15495">
    <literal><![CDATA[
      K(x,L(T(y,K(z,u)),w,v5)) = K(x,L(y,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,6396,a,b,15464,a)].">
      <j1 rule="hyper" parents="63 6396 15464"/>
    </justification>
  </clause>

  <clause id="15496">
    <literal><![CDATA[
      K(K(x,y) * z,z \ 1) = K(z,z \ K(y,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,15157,a(flip),b,15464,a),flip(a)].">
      <j1 rule="hyper" parents="63 15157 15464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15498">
    <literal><![CDATA[
      K(x,y) \ K(z,u) = K(z,u) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(126,a,15464,a(flip),b,4566,a),flip(a)].">
      <j1 rule="hyper" parents="126 15464 4566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15499">
    <literal><![CDATA[
      K(x,y) * K(z,u) = K(z,u) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(126,a,15464,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="126 15464 22"/>
    </justification>
  </clause>

  <clause id="15500">
    <literal><![CDATA[
      T(L(K(x,y),z,u),K(w,v5)) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(15464(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15464 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15503">
    <literal><![CDATA[
      x * (K(y,z) * K(u,w)) = x * (K(u,w) * K(y,z))
    ]]></literal>
    <justification jstring="[para(15464(a,1),235(a,1,2,2))].">
      <j1 rule="para" parents="15464 235"/>
    </justification>
  </clause>

  <clause id="15511">
    <literal><![CDATA[
      x * (K(y,z) * K(x,u)) = T(x,u) * K(y,z)
    ]]></literal>
    <justification jstring="[para(15464(a,1),4512(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15464 4512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15512">
    <literal><![CDATA[
      T(K(x,y),K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = w
    ]]></literal>
    <justification jstring="[para(15464(a,1),5305(a,1,1)),flip(b)].">
      <j1 rule="para" parents="15464 5305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15513">
    <literal><![CDATA[
      (x * K(y,z)) * K(x,u) = T(x,u) * K(y,z)
    ]]></literal>
    <justification jstring="[para(15464(a,1),6143(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15464 6143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15514">
    <literal><![CDATA[
      T(x * K(y,z),K(x,u)) = x * K(y,z)
    ]]></literal>
    <justification jstring="[para(15464(a,1),6179(a,2,2))].">
      <j1 rule="para" parents="15464 6179"/>
    </justification>
  </clause>

  <clause id="15515">
    <literal><![CDATA[
      K(x,y) * T(x,K(z,u)) = T(T(x,K(z,u)),y)
    ]]></literal>
    <justification jstring="[para(15464(a,1),6358(a,1,1))].">
      <j1 rule="para" parents="15464 6358"/>
    </justification>
  </clause>

  <clause id="15516">
    <literal><![CDATA[
      K(x,T(y,K(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = w
    ]]></literal>
    <justification jstring="[para(15464(a,1),6960(a,1))].">
      <j1 rule="para" parents="15464 6960"/>
    </justification>
  </clause>

  <clause id="15517">
    <literal><![CDATA[
      K(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u * K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(15464(a,1),12250(a,1))].">
      <j1 rule="para" parents="15464 12250"/>
    </justification>
  </clause>

  <clause id="15518">
    <literal><![CDATA[
      K(K(x,y) * z,u) = K(z * K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(12215,a,15472,a)].">
      <j1 rule="hyper" parents="12215 15472"/>
    </justification>
  </clause>

  <clause id="15520">
    <literal><![CDATA[
      K(((x \ y) * x) / (K(z,u) * x),w) = K((x * K(z,u)) \ y,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,13981,a(flip),b,15472,a)].">
      <j1 rule="hyper" parents="63 13981 15472"/>
    </justification>
  </clause>

  <clause id="15524">
    <literal><![CDATA[
      K(x,K(y,z) \ u) = K(x,u * K(z,y))
    ]]></literal>
    <justification jstring="[para(6020(a,1),15472(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6020 15472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15525">
    <literal><![CDATA[
      K(T(x,K(y,z)),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u) = w
    ]]></literal>
    <justification jstring="[para(15472(a,1),7063(a,1))].">
      <j1 rule="para" parents="15472 7063"/>
    </justification>
  </clause>

  <clause id="15526">
    <literal><![CDATA[
      K(x,K(y,z) * (u / z)) = K(x,u / T(z,y))
    ]]></literal>
    <justification jstring="[para(7096(a,1),15472(a,1,2))].">
      <j1 rule="para" parents="7096 15472"/>
    </justification>
  </clause>

  <clause id="15527">
    <literal><![CDATA[
      K(x,K(y,z) * (u * y)) = K(x,u * T(y,z))
    ]]></literal>
    <justification jstring="[para(7097(a,1),15472(a,1,2))].">
      <j1 rule="para" parents="7097 15472"/>
    </justification>
  </clause>

  <clause id="15528">
    <literal><![CDATA[
      L(K(x,y),x,z) = (x * K(u,w)) \ (T(x,y) * K(u,w))
    ]]></literal>
    <justification jstring="[para(15472(a,1),6726(a,1,1))].">
      <j1 rule="para" parents="15472 6726"/>
    </justification>
  </clause>

  <clause id="15531">
    <literal><![CDATA[
      K(K(x,y) * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(z * K(x,y),u) = w
    ]]></literal>
    <justification jstring="[para(15472(a,1),12210(a,1))].">
      <j1 rule="para" parents="15472 12210"/>
    </justification>
  </clause>

  <clause id="15532">
    <literal><![CDATA[
      K(x * K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(y,z) * x,u) = w
    ]]></literal>
    <justification jstring="[para(15472(a,1),12215(a,1))].">
      <j1 rule="para" parents="15472 12215"/>
    </justification>
  </clause>

  <clause id="15533">
    <literal><![CDATA[
      K(x,y * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,u) * y) = w
    ]]></literal>
    <justification jstring="[para(15472(a,1),12281(a,1))].">
      <j1 rule="para" parents="15472 12281"/>
    </justification>
  </clause>

  <clause id="15536">
    <literal><![CDATA[
      T(x * K(y,z),T(u,x)) = T(x * K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,7274,a(flip),b,15474,a)].">
      <j1 rule="hyper" parents="63 7274 15474"/>
    </justification>
  </clause>

  <clause id="15537">
    <literal><![CDATA[
      T(x,T(T(y,K(z,u)),w)) = T(x,T(y,w))
    ]]></literal>
    <justification jstring="[para(23(a,1),15474(a,1,2))].">
      <j1 rule="para" parents="23 15474"/>
    </justification>
  </clause>

  <clause id="15538">
    <literal><![CDATA[
      T(x / T(y,K(z,u)),y) != w
    ]]></literal>
    <literal><![CDATA[
      T(y,K(z,u)) \ x = w
    ]]></literal>
    <justification jstring="[para(15474(a,1),423(a,1))].">
      <j1 rule="para" parents="15474 423"/>
    </justification>
  </clause>

  <clause id="15539">
    <literal><![CDATA[
      T(x,K(y,z) \ u) = T(x,u * K(z,y))
    ]]></literal>
    <justification jstring="[para(6020(a,1),15474(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6020 15474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15540">
    <literal><![CDATA[
      T(x,K(y,z) * (u / z)) = T(x,u / T(z,y))
    ]]></literal>
    <justification jstring="[para(7096(a,1),15474(a,1,2))].">
      <j1 rule="para" parents="7096 15474"/>
    </justification>
  </clause>

  <clause id="15541">
    <literal><![CDATA[
      T(x,K(y,z) * (u * y)) = T(x,u * T(y,z))
    ]]></literal>
    <justification jstring="[para(7097(a,1),15474(a,1,2))].">
      <j1 rule="para" parents="7097 15474"/>
    </justification>
  </clause>

  <clause id="15542">
    <literal><![CDATA[
      T(x * K(x * K(y,z),u),K(z,y)) = K(y,z) \ T(x * K(y,z),u)
    ]]></literal>
    <justification jstring="[para(15474(a,1),8815(a,2,2))].">
      <j1 rule="para" parents="15474 8815"/>
    </justification>
  </clause>

  <clause id="15544">
    <literal><![CDATA[
      K(T(1 / x,K(y,z)),u) = K(1 / L(x,w,x),u)
    ]]></literal>
    <justification jstring="[hyper(333,a,8594,a,b,15490,a),flip(a)].">
      <j1 rule="hyper" parents="333 8594 15490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15546">
    <literal><![CDATA[
      K(x,T(T(y,K(z,u)),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,w)) = v5
    ]]></literal>
    <justification jstring="[para(15490(a,1),7069(a,1))].">
      <j1 rule="para" parents="15490 7069"/>
    </justification>
  </clause>

  <clause id="15549">
    <literal><![CDATA[
      K(T(x,y),K(z,u)) = K(x,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(6611,a,15479,a)].">
      <j1 rule="hyper" parents="6611 15479"/>
    </justification>
  </clause>

  <clause id="15550">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,6416,a,b,15479,a)].">
      <j1 rule="hyper" parents="63 6416 15479"/>
    </justification>
  </clause>

  <clause id="15554">
    <literal><![CDATA[
      K(x,K(y,z / u)) = K(x,K(y,u \ z))
    ]]></literal>
    <justification jstring="[para(5773(a,1),15481(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5773 15481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15555">
    <literal><![CDATA[
      K(x,K(y / z,u)) = K(x,K(z \ y,u))
    ]]></literal>
    <justification jstring="[para(5910(a,1),15481(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5910 15481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15556">
    <literal><![CDATA[
      K(x,K(T(y,z),u)) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(5920(a,1),15481(a,1,2))].">
      <j1 rule="para" parents="5920 15481"/>
    </justification>
  </clause>

  <clause id="15557">
    <literal><![CDATA[
      K(x,K(y,z * u)) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[para(12230(a,1),15481(a,1,2))].">
      <j1 rule="para" parents="12230 15481"/>
    </justification>
  </clause>

  <clause id="15558">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * T(w,u) = w * (u * K(x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(15481(a,1),14067(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="15481 14067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15559">
    <literal><![CDATA[
      T(K(x,K(y,z)) * u,w) = T(u,w) * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(15481(a,1),14102(a,1,1,1))].">
      <j1 rule="para" parents="15481 14102"/>
    </justification>
  </clause>

  <clause id="15560">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(6825,a,15549,a)].">
      <j1 rule="hyper" parents="6825 15549"/>
    </justification>
  </clause>

  <clause id="15562">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(7251,a,15550,a)].">
      <j1 rule="hyper" parents="7251 15550"/>
    </justification>
  </clause>

  <clause id="15563">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(6798,a,15550,a)].">
      <j1 rule="hyper" parents="6798 15550"/>
    </justification>
  </clause>

  <clause id="15566">
    <literal><![CDATA[
      T(x,K(y,T(z,u))) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(124,a,15550,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 15550 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15567">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(y,K(x,z)) = w
    ]]></literal>
    <justification jstring="[para(15550(a,2),6798(a,1))].">
      <j1 rule="para" parents="15550 6798"/>
    </justification>
  </clause>

  <clause id="15569">
    <literal><![CDATA[
      K(x,K(y,L(z / u,u,w))) = K(x,K(y,(w * u) \ (w * z)))
    ]]></literal>
    <justification jstring="[para(7006(a,1),15550(a,1,2))].">
      <j1 rule="para" parents="7006 15550"/>
    </justification>
  </clause>

  <clause id="15571">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x \ (u * (y / u)),z) = K((u * (y / u)) / x,z)
    ]]></literal>
    <justification jstring="[para(15550(a,1),12219(a,1,1))].">
      <j1 rule="para" parents="15550 12219"/>
    </justification>
  </clause>

  <clause id="15574">
    <literal><![CDATA[
      (x \ K(y,T(z,u))) * K(y,K(z,w)) = x \ K(y,T(T(z,u),w))
    ]]></literal>
    <justification jstring="[hyper(126,a,15556,a(flip),b,12318,a)].">
      <j1 rule="hyper" parents="126 15556 12318"/>
    </justification>
  </clause>

  <clause id="15575">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x \ T(y,u),z) = K(T(y,u) / x,z)
    ]]></literal>
    <justification jstring="[para(15556(a,1),7298(a,1,1))].">
      <j1 rule="para" parents="15556 7298"/>
    </justification>
  </clause>

  <clause id="15576">
    <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(15556(a,1),10707(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="15556 10707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15577">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) = K(z,K(x,T(y,w)))
    ]]></literal>
    <justification jstring="[hyper(333,a,15550,a,b,15560,a),flip(a)].">
      <j1 rule="hyper" parents="333 15550 15560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15578">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(15560(a,2),6825(a,1))].">
      <j1 rule="para" parents="15560 6825"/>
    </justification>
  </clause>

  <clause id="15579">
    <literal><![CDATA[
      K(x * y,K(z,u)) = K(z,K(u,y * x))
    ]]></literal>
    <justification jstring="[para(12229(a,1),15560(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12229 15560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15580">
    <literal><![CDATA[
      T(x,K(y,T(z,u))) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(124,a,15562,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 15562 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15581">
    <literal><![CDATA[
      K(x,K(y \ z,u)) = K(x,K(u,z / y))
    ]]></literal>
    <justification jstring="[para(6382(a,1),15562(a,1,2))].">
      <j1 rule="para" parents="6382 15562"/>
    </justification>
  </clause>

  <clause id="15582">
    <literal><![CDATA[
      K(x,K(y,(z \ u) * z)) = K(x,K(u,y))
    ]]></literal>
    <justification jstring="[para(12241(a,2),15562(a,1,2))].">
      <j1 rule="para" parents="12241 15562"/>
    </justification>
  </clause>

  <clause id="15584">
    <literal><![CDATA[
      K(x,y) * (K(z,K(y,u)) * w) = y * (T(T(y,K(z,u)),x) \ w)
    ]]></literal>
    <justification jstring="[para(15563(a,1),8780(a,1,2,1))].">
      <j1 rule="para" parents="15563 8780"/>
    </justification>
  </clause>

  <clause id="15586">
    <literal><![CDATA[
      K(x,T(y,z)) * (u * K(y,T(x,z))) = T(u,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,7101,a,b,15566,a)].">
      <j1 rule="hyper" parents="63 7101 15566"/>
    </justification>
  </clause>

  <clause id="15587">
    <literal><![CDATA[
      T(x,K(y,z / u)) = T(x,K(y,u \ z))
    ]]></literal>
    <justification jstring="[para(113(a,1),15566(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="113 15566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15589">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(z,u) \ y) = T(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(15566(a,1),7573(a,1,1))].">
      <j1 rule="para" parents="15566 7573"/>
    </justification>
  </clause>

  <clause id="15590">
    <literal><![CDATA[
      T(x,K(y,z * u)) = T(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[para(12229(a,1),15566(a,1,2))].">
      <j1 rule="para" parents="12229 15566"/>
    </justification>
  </clause>

  <clause id="15591">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(z,u) * y) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y * T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(15566(a,1),12277(a,1,1))].">
      <j1 rule="para" parents="15566 12277"/>
    </justification>
  </clause>

  <clause id="15592">
    <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(15580(a,1),7578(a,1,1))].">
      <j1 rule="para" parents="15580 7578"/>
    </justification>
  </clause>

  <clause id="15593">
    <literal><![CDATA[
      T(x,y / K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(z,u) \ y) = w
    ]]></literal>
    <justification jstring="[para(5302(a,1),15483(a,1,2))].">
      <j1 rule="para" parents="5302 15483"/>
    </justification>
  </clause>

  <clause id="15594">
    <literal><![CDATA[
      T(x,y * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(u,z) \ y) = w
    ]]></literal>
    <justification jstring="[para(6020(a,1),15483(a,1,2))].">
      <j1 rule="para" parents="6020 15483"/>
    </justification>
  </clause>

  <clause id="15595">
    <literal><![CDATA[
      T(x,T(y,T(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(6191(a,1),15483(a,1,2))].">
      <j1 rule="para" parents="6191 15483"/>
    </justification>
  </clause>

  <clause id="15596">
    <literal><![CDATA[
      T(x,K(y,z) * (u / z)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u / T(z,y)) = w
    ]]></literal>
    <justification jstring="[para(7096(a,1),15483(a,1,2))].">
      <j1 rule="para" parents="7096 15483"/>
    </justification>
  </clause>

  <clause id="15597">
    <literal><![CDATA[
      T(x,K(y,z) * (u * y)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u * T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(7097(a,1),15483(a,1,2))].">
      <j1 rule="para" parents="7097 15483"/>
    </justification>
  </clause>

  <clause id="15598">
    <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(12260(a,1),15483(a,1))].">
      <j1 rule="para" parents="12260 15483"/>
    </justification>
  </clause>

  <clause id="15599">
    <literal><![CDATA[
      K(x,y / K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,u) \ y) = w
    ]]></literal>
    <justification jstring="[para(6906(a,1),15512(a,1))].">
      <j1 rule="para" parents="6906 15512"/>
    </justification>
  </clause>

  <clause id="15600">
    <literal><![CDATA[
      K(x,T(y,L(K(z,u),w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v6
    ]]></literal>
    <justification jstring="[para(5372(a,1),15516(a,1,2,2))].">
      <j1 rule="para" parents="5372 15516"/>
    </justification>
  </clause>

  <clause id="15601">
    <literal><![CDATA[
      K(x,y * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,z) \ y) = w
    ]]></literal>
    <justification jstring="[para(6020(a,1),15516(a,1,2))].">
      <j1 rule="para" parents="6020 15516"/>
    </justification>
  </clause>

  <clause id="15602">
    <literal><![CDATA[
      K(x,T(y,T(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(6191(a,1),15516(a,1,2))].">
      <j1 rule="para" parents="6191 15516"/>
    </justification>
  </clause>

  <clause id="15603">
    <literal><![CDATA[
      K(x,y * (z * K(y,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u) * z) = w
    ]]></literal>
    <justification jstring="[para(6174(a,1),15516(a,1,2))].">
      <j1 rule="para" parents="6174 15516"/>
    </justification>
  </clause>

  <clause id="15605">
    <literal><![CDATA[
      K(x,K(y,z) * (u * y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u * T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(7097(a,1),15516(a,1,2))].">
      <j1 rule="para" parents="7097 15516"/>
    </justification>
  </clause>

  <clause id="15606">
    <literal><![CDATA[
      K(x,T(y,z / u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u \ z)) = w
    ]]></literal>
    <justification jstring="[para(7575(a,1),15516(a,1,2))].">
      <j1 rule="para" parents="7575 15516"/>
    </justification>
  </clause>

  <clause id="15607">
    <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(10833(a,1),15516(a,1,2))].">
      <j1 rule="para" parents="10833 15516"/>
    </justification>
  </clause>

  <clause id="15608">
    <literal><![CDATA[
      K(x,T(y,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u * z)) = w
    ]]></literal>
    <justification jstring="[para(12253(a,1),15516(a,1,2))].">
      <j1 rule="para" parents="12253 15516"/>
    </justification>
  </clause>

  <clause id="15609">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u \ T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(13350(a,1),15516(a,1,2))].">
      <j1 rule="para" parents="13350 15516"/>
    </justification>
  </clause>

  <clause id="15611">
    <literal><![CDATA[
      K(x * K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(z,y) \ x,u) = w
    ]]></literal>
    <justification jstring="[para(6020(a,1),15525(a,1,1))].">
      <j1 rule="para" parents="6020 15525"/>
    </justification>
  </clause>

  <clause id="15612">
    <literal><![CDATA[
      T(x,y) * K(z \ x,u) = K(x / z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(125,a,15440,a(flip),b,6884,a),flip(a)].">
      <j1 rule="hyper" parents="125 15440 6884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15613">
    <literal><![CDATA[
      K((x \ y) \ z,x / y) * K(x / y,z) = a((x \ y) \ 1,z,(x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(15440(a,1),12386(a,1,2))].">
      <j1 rule="para" parents="15440 12386"/>
    </justification>
  </clause>

  <clause id="15614">
    <literal><![CDATA[
      K(x,L((y / z) \ u,y / z,z)) = K(x,T((u * z) / y,z \ y))
    ]]></literal>
    <justification jstring="[hyper(13924,a,15444,a)].">
      <j1 rule="hyper" parents="13924 15444"/>
    </justification>
  </clause>

  <clause id="15615">
    <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(13972,a,15444,a(flip))].">
      <j1 rule="hyper" parents="13972 15444"/>
    </justification>
  </clause>

  <clause id="15616">
    <literal><![CDATA[
      T(x,K(y,z) * u) = T(x,u * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(333,a,15004,a,b,15470,a),flip(a)].">
      <j1 rule="hyper" parents="333 15004 15470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15617">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(z,u)) = T(y,x * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,14912,a,b,15470,a)].">
      <j1 rule="hyper" parents="63 14912 15470"/>
    </justification>
  </clause>

  <clause id="15618">
    <literal><![CDATA[
      T(x,(y \ z) * K(y,u)) = T(x,T(y,u) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,14925,a(flip),b,15470,a),flip(a)].">
      <j1 rule="hyper" parents="63 14925 15470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15619">
    <literal><![CDATA[
      T(x,y * K(z \ u,z)) = T(x,K(u,z) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,12823,a(flip),b,15470,a),flip(a)].">
      <j1 rule="hyper" parents="63 12823 15470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15620">
    <literal><![CDATA[
      T(x,y * K(z,z \ u)) = T(x,K(z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,12760,a(flip),b,15470,a),flip(a)].">
      <j1 rule="hyper" parents="63 12760 15470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15621">
    <literal><![CDATA[
      T(x * T(y,K(z,u)),K(z,u)) = y * T(x,y * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(126,a,15470,a(flip),b,14919,a),flip(a)].">
      <j1 rule="hyper" parents="126 15470 14919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15622">
    <literal><![CDATA[
      T(x,K(y,y \ z) * (u * z)) = T(x,u * (y * (z / y)))
    ]]></literal>
    <justification jstring="[para(10324(a,1),15470(a,2,2))].">
      <j1 rule="para" parents="10324 15470"/>
    </justification>
  </clause>

  <clause id="15623">
    <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(15471(a,1),14118(a,1,2,2,1))].">
      <j1 rule="para" parents="15471 14118"/>
    </justification>
  </clause>

  <clause id="15624">
    <literal><![CDATA[
      (K(x,y) * z) * K(x,K(y,u)) = K(x,T(y,u)) * z
    ]]></literal>
    <justification jstring="[hyper(7905,a,15475,a),flip(a)].">
      <j1 rule="hyper" parents="7905 15475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15625">
    <literal><![CDATA[
      (x \ y) * K(x,K(z,u)) = T(x,K(z,u)) \ y
    ]]></literal>
    <justification jstring="[hyper(6834,a,15475,a),flip(a)].">
      <j1 rule="hyper" parents="6834 15475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15626">
    <literal><![CDATA[
      K(x,K(y,z)) \ u = u * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(6833,a,15475,a)].">
      <j1 rule="hyper" parents="6833 15475"/>
    </justification>
  </clause>

  <clause id="15627">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * K(x,K(y,z))) = u
    ]]></literal>
    <justification jstring="[hyper(6832,a,15475,a)].">
      <j1 rule="hyper" parents="6832 15475"/>
    </justification>
  </clause>

  <clause id="15628">
    <literal><![CDATA[
      K(x,K(y,z)) * (u / x) = u / T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(333,a,6828,a(flip),b,15475,a),flip(a)].">
      <j1 rule="hyper" parents="333 6828 15475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15629">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * K(x,y)) = u * T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(333,a,6775,a(flip),b,15475,a),flip(a)].">
      <j1 rule="hyper" parents="333 6775 15475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15630">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[hyper(125,a,15475,a,b,6827,a)].">
      <j1 rule="hyper" parents="125 15475 6827"/>
    </justification>
  </clause>

  <clause id="15631">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) / L(w,u / w,K(x,K(y,z))) = (u / w) * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,569,a,b,15475,a)].">
      <j1 rule="hyper" parents="63 569 15475"/>
    </justification>
  </clause>

  <clause id="15632">
    <literal><![CDATA[
      (x * (K(y,K(z,u)) * w)) / (w * K(y,K(z,u))) = x
    ]]></literal>
    <justification jstring="[hyper(197,a,15475,a(flip),b,9,a)].">
      <j1 rule="hyper" parents="197 15475 9"/>
    </justification>
  </clause>

  <clause id="15633">
    <literal><![CDATA[
      (T(x,K(y,z)) \ u) * K(x,K(y,z)) != w
    ]]></literal>
    <literal><![CDATA[
      x \ u = w
    ]]></literal>
    <justification jstring="[para(15475(a,1),4680(a,1))].">
      <j1 rule="para" parents="15475 4680"/>
    </justification>
  </clause>

  <clause id="15634">
    <literal><![CDATA[
      K(x,y) * (z * K(x,K(y,u))) = K(x,T(y,u)) * z
    ]]></literal>
    <justification jstring="[para(15475(a,1),8087(a,1,2))].">
      <j1 rule="para" parents="15475 8087"/>
    </justification>
  </clause>

  <clause id="15636">
    <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(15477(a,1),14916(a,1,2,1,2))].">
      <j1 rule="para" parents="15477 14916"/>
    </justification>
  </clause>

  <clause id="15637">
    <literal><![CDATA[
      K(x,K(y,z) * u) = K(x,u * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(14927,a,15489,a)].">
      <j1 rule="hyper" parents="14927 15489"/>
    </justification>
  </clause>

  <clause id="15638">
    <literal><![CDATA[
      K(x,K(y,z) * (u / y)) = K(x,u / T(y,z))
    ]]></literal>
    <justification jstring="[hyper(333,a,15162,a(flip),b,15489,a),flip(a)].">
      <j1 rule="hyper" parents="333 15162 15489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15639">
    <literal><![CDATA[
      K(x,K(y,z) \ u) = K(x,u * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,14929,a,b,15489,a)].">
      <j1 rule="hyper" parents="63 14929 15489"/>
    </justification>
  </clause>

  <clause id="15640">
    <literal><![CDATA[
      ((x * y) / z) \ (x * (y * K(z,u * K(w,v5)))) = T(z,L(K(w,v5) * u,y,x))
    ]]></literal>
    <justification jstring="[para(15489(a,1),10966(a,1,2,2,2))].">
      <j1 rule="para" parents="15489 10966"/>
    </justification>
  </clause>

  <clause id="15641">
    <literal><![CDATA[
      K(x,y * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,z) * y) = w
    ]]></literal>
    <justification jstring="[para(15489(a,1),14927(a,1))].">
      <j1 rule="para" parents="15489 14927"/>
    </justification>
  </clause>

  <clause id="15642">
    <literal><![CDATA[
      K(x,T(1 / (y * z),y)) = K(x,K(z,1 / z) / (z * y))
    ]]></literal>
    <justification jstring="[hyper(333,a,14065,a,b,15492,a)].">
      <j1 rule="hyper" parents="333 14065 15492"/>
    </justification>
  </clause>

  <clause id="15643">
    <literal><![CDATA[
      K(x,K(y \ (1 / z),L(y / u,u,z))) = K(x,K(y / u,K(z,1 / z) / (z * y)))
    ]]></literal>
    <justification jstring="[para(15492(a,2),11008(a,2,2))].">
      <j1 rule="para" parents="15492 11008"/>
    </justification>
  </clause>

  <clause id="15644">
    <literal><![CDATA[
      K(x,y) \ K(z,u) = K(u,z) \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,4567,a,b,15498,a)].">
      <j1 rule="hyper" parents="333 4567 15498"/>
    </justification>
  </clause>

  <clause id="15646">
    <literal><![CDATA[
      K(x,y) \ K(z,T(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(u,T(z,w)) \ K(y,x) = v5
    ]]></literal>
    <justification jstring="[para(15498(a,2),6448(a,1))].">
      <j1 rule="para" parents="15498 6448"/>
    </justification>
  </clause>

  <clause id="15649">
    <literal><![CDATA[
      x / y != K(z,u) * K(w,v5)
    ]]></literal>
    <literal><![CDATA[
      (K(v5,w) \ K(z,u)) * y = x
    ]]></literal>
    <justification jstring="[para(15499(a,1),4586(a,2))].">
      <j1 rule="para" parents="15499 4586"/>
    </justification>
  </clause>

  <clause id="15650">
    <literal><![CDATA[
      K(x,y) * K(z / (z / u),w) = K(u,T(w,z)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(6927(a,1),15499(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6927 15499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15651">
    <literal><![CDATA[
      T((x * K(y,z)) * u,K(x,u)) = (x * K(y,z)) * u
    ]]></literal>
    <justification jstring="[para(15514(a,1),7313(a,2,1))].">
      <j1 rule="para" parents="15514 7313"/>
    </justification>
  </clause>

  <clause id="15652">
    <literal><![CDATA[
      K(x * K(y,z),y * z) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(8327,a,15518,a),flip(a)].">
      <j1 rule="hyper" parents="8327 15518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15653">
    <literal><![CDATA[
      K(x * K(y \ z,y),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(8321,a,15518,a),flip(a)].">
      <j1 rule="hyper" parents="8321 15518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15654">
    <literal><![CDATA[
      K(K(x,y) * z,u) = K(z * K(y,x),u)
    ]]></literal>
    <justification jstring="[hyper(333,a,15108,a,b,15518,a),flip(a)].">
      <j1 rule="hyper" parents="333 15108 15518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15655">
    <literal><![CDATA[
      K(x * K(y,y * z),u) = K(K(y,z) * x,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,12616,a(flip),b,15518,a),flip(a)].">
      <j1 rule="hyper" parents="63 12616 15518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15656">
    <literal><![CDATA[
      K(x * K(y,z),x \ y) = K(x,T(x \ y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,11343,a(flip),b,15518,a),flip(a)].">
      <j1 rule="hyper" parents="63 11343 15518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15657">
    <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(15518(a,1),6697(a,1))].">
      <j1 rule="para" parents="15518 6697"/>
    </justification>
  </clause>

  <clause id="15658">
    <literal><![CDATA[
      K(K(L(x,y,z),u) * (z * (y * x)),w) = K(z * (y * T(x,u)),w)
    ]]></literal>
    <justification jstring="[para(5996(a,1),15518(a,2,1))].">
      <j1 rule="para" parents="5996 15518"/>
    </justification>
  </clause>

  <clause id="15659">
    <literal><![CDATA[
      K(x * K(y \ z,y),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(z,y) * x,u) = w
    ]]></literal>
    <justification jstring="[para(15518(a,1),12839(a,1))].">
      <j1 rule="para" parents="15518 12839"/>
    </justification>
  </clause>

  <clause id="15660">
    <literal><![CDATA[
      K(K(x,y) * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(z * K(y,x),u) = w
    ]]></literal>
    <justification jstring="[para(15518(a,2),15109(a,1))].">
      <j1 rule="para" parents="15518 15109"/>
    </justification>
  </clause>

  <clause id="15661">
    <literal><![CDATA[
      K(x / (y / z),y) = K(x / (z \ y),y)
    ]]></literal>
    <justification jstring="[para(6012(a,1),15653(a,1,1))].">
      <j1 rule="para" parents="6012 15653"/>
    </justification>
  </clause>

  <clause id="15662">
    <literal><![CDATA[
      K(x,(y * z) * K(u,y)) = K(x,T(y,u) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,14935,a(flip),b,15524,a),flip(a)].">
      <j1 rule="hyper" parents="63 14935 15524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15663">
    <literal><![CDATA[
      K(x,K(y,y \ z) \ (u / z)) = K(x,u / (y * (z / y)))
    ]]></literal>
    <justification jstring="[para(10458(a,1),15524(a,2,2))].">
      <j1 rule="para" parents="10458 15524"/>
    </justification>
  </clause>

  <clause id="15664">
    <literal><![CDATA[
      T(x,T(T(y,T(z,u)) * u,w)) = T(x,T(T(y,z) * u,w))
    ]]></literal>
    <justification jstring="[para(7315(a,1),15537(a,1,2,1))].">
      <j1 rule="para" parents="7315 15537"/>
    </justification>
  </clause>

  <clause id="15665">
    <literal><![CDATA[
      T(x,K(y,z) \ u) = T(x,u * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(333,a,15004,a,b,15539,a),flip(a)].">
      <j1 rule="hyper" parents="333 15004 15539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15666">
    <literal><![CDATA[
      T(x,(y / z) * K(u,y)) = T(x,T(y,u) / z)
    ]]></literal>
    <justification jstring="[hyper(63,a,14939,a(flip),b,15539,a),flip(a)].">
      <j1 rule="hyper" parents="63 14939 15539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15667">
    <literal><![CDATA[
      K(x,K(y,z * (u \ 1))) = K(x,K(y,u \ z))
    ]]></literal>
    <justification jstring="[hyper(63,a,11435,a,b,15554,a)].">
      <j1 rule="hyper" parents="63 11435 15554"/>
    </justification>
  </clause>

  <clause id="15669">
    <literal><![CDATA[
      T(x,K(y,L((z / u) / w,w,u))) = x * K(x,K(y,(w * u) \ z))
    ]]></literal>
    <justification jstring="[para(15554(a,1),14153(a,2,2))].">
      <j1 rule="para" parents="15554 14153"/>
    </justification>
  </clause>

  <clause id="15671">
    <literal><![CDATA[
      K(x,K(y,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(y,K(x,u * z)) = w
    ]]></literal>
    <justification jstring="[para(15557(a,1),6798(a,1))].">
      <j1 rule="para" parents="15557 6798"/>
    </justification>
  </clause>

  <clause id="15672">
    <literal><![CDATA[
      x \ T(x * y,K(z,u)) = y * K(z,K(u,y * x))
    ]]></literal>
    <justification jstring="[para(15557(a,1),12294(a,2,2))].">
      <j1 rule="para" parents="15557 12294"/>
    </justification>
  </clause>

  <clause id="15675">
    <literal><![CDATA[
      T(x,K(y,T(z,u))) = x * K(z,K(y,T(x,w)))
    ]]></literal>
    <justification jstring="[para(15577(a,1),6789(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15577 6789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15681">
    <literal><![CDATA[
      K(x,K(y,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u * z)) = w
    ]]></literal>
    <justification jstring="[para(15579(a,1),6825(a,1))].">
      <j1 rule="para" parents="15579 6825"/>
    </justification>
  </clause>

  <clause id="15682">
    <literal><![CDATA[
      K(x,K(y \ (z \ u),L(w,y,z))) = K(x,K(w,u / (z * y)))
    ]]></literal>
    <justification jstring="[para(10907(a,2),15581(a,1,2))].">
      <j1 rule="para" parents="10907 15581"/>
    </justification>
  </clause>

  <clause id="15683">
    <literal><![CDATA[
      K(x,K(y / z,(z \ u) * y)) = K(x,K(u,y / z))
    ]]></literal>
    <justification jstring="[hyper(63,a,10959,a(flip),b,15582,a)].">
      <j1 rule="hyper" parents="63 10959 15582"/>
    </justification>
  </clause>

  <clause id="15684">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),y * (u * z)) = T(x,(u * z) * y)
    ]]></literal>
    <justification jstring="[para(15590(a,1),12263(a,1,1))].">
      <j1 rule="para" parents="15590 12263"/>
    </justification>
  </clause>

  <clause id="15686">
    <literal><![CDATA[
      x \ T(y,K(z,u) * w) = x \ T(y,w * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(121,a,15616,a,b,10,a)].">
      <j1 rule="hyper" parents="121 15616 10"/>
    </justification>
  </clause>

  <clause id="15687">
    <literal><![CDATA[
      K(x,y) * T(x * K(y,x),z * K(u,w)) = T(x,T(K(w,u) * z,y))
    ]]></literal>
    <justification jstring="[hyper(126,a,15616,a(flip),b,8027,a)].">
      <j1 rule="hyper" parents="126 15616 8027"/>
    </justification>
  </clause>

  <clause id="15688">
    <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(15616(a,2),423(a,1))].">
      <j1 rule="para" parents="15616 423"/>
    </justification>
  </clause>

  <clause id="15689">
    <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(5860(a,2),15616(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5860 15616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15690">
    <literal><![CDATA[
      K(x,K(y,z)) \ T(u,x) = x \ (u * T(x,K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(333,a,6663,a,b,15626,a),flip(a)].">
      <j1 rule="hyper" parents="333 6663 15626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15691">
    <literal><![CDATA[
      K(x,K(y,z)) \ (u \ x) = u \ T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(333,a,13255,a(flip),b,15626,a),flip(a)].">
      <j1 rule="hyper" parents="333 13255 15626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15692">
    <literal><![CDATA[
      K(x,K(y,z)) \ (u * z) = u * T(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(333,a,6807,a(flip),b,15626,a),flip(a)].">
      <j1 rule="hyper" parents="333 6807 15626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15693">
    <literal><![CDATA[
      K(x,K(y,z)) \ (u * x) = u * T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(333,a,5984,a(flip),b,15626,a),flip(a)].">
      <j1 rule="hyper" parents="333 5984 15626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15694">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * K(x,K(y,z)) != w
    ]]></literal>
    <literal><![CDATA[
      u = w
    ]]></literal>
    <justification jstring="[para(15626(a,1),342(a,1))].">
      <j1 rule="para" parents="15626 342"/>
    </justification>
  </clause>

  <clause id="15695">
    <literal><![CDATA[
      K(x,K(y,z)) \ (u / T(x,K(y,z))) != w
    ]]></literal>
    <literal><![CDATA[
      u / x = w
    ]]></literal>
    <justification jstring="[para(15626(a,2),5987(a,1))].">
      <j1 rule="para" parents="15626 5987"/>
    </justification>
  </clause>

  <clause id="15697">
    <literal><![CDATA[
      (T(x,K(y,z)) \ u) * K(y,K(z,x)) = x \ u
    ]]></literal>
    <justification jstring="[hyper(34,a,6778,a,b,15627,a),flip(a)].">
      <j1 rule="hyper" parents="34 6778 15627"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15698">
    <literal><![CDATA[
      K(x,K(y,z) * (u * z)) = K(x,u * T(z,y))
    ]]></literal>
    <justification jstring="[para(5984(a,1),15637(a,2,2))].">
      <j1 rule="para" parents="5984 15637"/>
    </justification>
  </clause>

  <clause id="15699">
    <literal><![CDATA[
      L(K(x,y),z,u) \ K(w,v5) = K(v5,w) \ K(L(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(10851(a,2),15644(a,1,1))].">
      <j1 rule="para" parents="10851 15644"/>
    </justification>
  </clause>

  <clause id="15700">
    <literal><![CDATA[
      K((x * y) * K(y,z),y * z) = K(y * x,z * y)
    ]]></literal>
    <justification jstring="[hyper(333,a,12240,a,b,15652,a),flip(a)].">
      <j1 rule="hyper" parents="333 12240 15652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15701">
    <literal><![CDATA[
      K(K(x,y) * z,u) = K(K(y,x) * z,u)
    ]]></literal>
    <justification jstring="[hyper(333,a,15518,a,b,15654,a)].">
      <j1 rule="hyper" parents="333 15518 15654"/>
    </justification>
  </clause>

  <clause id="15702">
    <literal><![CDATA[
      K(K(x,y) \ z,u) = K(z * K(x,y),u)
    ]]></literal>
    <justification jstring="[para(4567(a,2),15654(a,1,1))].">
      <j1 rule="para" parents="4567 15654"/>
    </justification>
  </clause>

  <clause id="15703">
    <literal><![CDATA[
      K((x \ y) * K(x,z),u) = K(T(x,z) \ y,u)
    ]]></literal>
    <justification jstring="[para(4555(a,1),15654(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4555 15654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15704">
    <literal><![CDATA[
      K((x / y) * K(z,x),u) = K(T(x,z) / y,u)
    ]]></literal>
    <justification jstring="[para(13229(a,1),15654(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13229 15654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15705">
    <literal><![CDATA[
      K(K(x,y) * (z \ y),u) = K(z \ T(y,x),u)
    ]]></literal>
    <justification jstring="[para(13255(a,1),15654(a,2,1))].">
      <j1 rule="para" parents="13255 15654"/>
    </justification>
  </clause>

  <clause id="15706">
    <literal><![CDATA[
      K(x / ((y \ z) \ z),z) = K(x / y,z)
    ]]></literal>
    <justification jstring="[para(76(a,1),15661(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="76 15661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15707">
    <literal><![CDATA[
      T(x,K(y,z) \ x) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(333,a,12960,a(flip),b,15665,a),flip(a)].">
      <j1 rule="hyper" parents="333 12960 15665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15708">
    <literal><![CDATA[
      T(x,K(y,z) * K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(210,a,15665,a),flip(a)].">
      <j1 rule="hyper" parents="210 15665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15709">
    <literal><![CDATA[
      T(x,K(y,z) * K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(15665(a,1),210(a,1))].">
      <j1 rule="para" parents="15665 210"/>
    </justification>
  </clause>

  <clause id="15710">
    <literal><![CDATA[
      T(x,K(y,z) \ (u * y)) = T(x,u * T(y,z))
    ]]></literal>
    <justification jstring="[para(5984(a,1),15665(a,2,2))].">
      <j1 rule="para" parents="5984 15665"/>
    </justification>
  </clause>

  <clause id="15711">
    <literal><![CDATA[
      T(x,K(y,z) \ T(u,y)) = T(x,y \ (u * T(y,z)))
    ]]></literal>
    <justification jstring="[para(6663(a,2),15665(a,2,2))].">
      <j1 rule="para" parents="6663 15665"/>
    </justification>
  </clause>

  <clause id="15712">
    <literal><![CDATA[
      T(x,K(y,z) \ x) = K(y,z) * (x * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(333,a,6849,a,b,15707,a),flip(a)].">
      <j1 rule="hyper" parents="333 6849 15707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15713">
    <literal><![CDATA[
      T(x,y * (K(z,u) * K(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = w
    ]]></literal>
    <justification jstring="[para(1123(a,1),15709(a,1))].">
      <j1 rule="para" parents="1123 15709"/>
    </justification>
  </clause>

  <clause id="15714">
    <literal><![CDATA[
      K(K(x * y,x) * z,u) = K(K(x,y) * z,u)
    ]]></literal>
    <justification jstring="[hyper(333,a,12616,a(flip),b,15701,a),flip(a)].">
      <j1 rule="hyper" parents="333 12616 15701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15715">
    <literal><![CDATA[
      K(K(x,y) * (x \ z),u) = K(T(x,y) \ z,u)
    ]]></literal>
    <justification jstring="[para(4555(a,1),15701(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4555 15701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15716">
    <literal><![CDATA[
      K(K(x,y) \ (z / y),u) = K(z / T(y,x),u)
    ]]></literal>
    <justification jstring="[para(5450(a,1),15702(a,2,1))].">
      <j1 rule="para" parents="5450 15702"/>
    </justification>
  </clause>

  <clause id="15717">
    <literal><![CDATA[
      K(x \ (y * (z \ x)),x) = K(y / z,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,15069,a(flip),b,15706,a)].">
      <j1 rule="hyper" parents="63 15069 15706"/>
    </justification>
  </clause>

  <clause id="15718">
    <literal><![CDATA[
      K(L(x,y,y \ 1) \ (z * (y * x)),L(x,y,y \ 1)) = K(z / (1 / y),L(x,y,y \ 1))
    ]]></literal>
    <justification jstring="[para(2656(a,1),15717(a,1,1,2,2))].">
      <j1 rule="para" parents="2656 15717"/>
    </justification>
  </clause>

  <clause id="15719">
    <literal><![CDATA[
      K(x,K(y / z,u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y * (z \ u),u) * w) = v5
    ]]></literal>
    <justification jstring="[para(15717(a,1),12838(a,1,2,1))].">
      <j1 rule="para" parents="15717 12838"/>
    </justification>
  </clause>

  <clause id="15720">
    <literal><![CDATA[
      K(x,K(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u / z)) = w
    ]]></literal>
    <justification jstring="[para(113(a,1),15578(a,1,2,2))].">
      <j1 rule="para" parents="113 15578"/>
    </justification>
  </clause>

  <clause id="15721">
    <literal><![CDATA[
      K(x,K(T(y,z),u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u)) = w
    ]]></literal>
    <justification jstring="[para(6370(a,2),15578(a,1,2))].">
      <j1 rule="para" parents="6370 15578"/>
    </justification>
  </clause>

  <clause id="15722">
    <literal><![CDATA[
      K(x,K(y * z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z * y,u)) = w
    ]]></literal>
    <justification jstring="[para(12201(a,1),15578(a,1,2))].">
      <j1 rule="para" parents="12201 15578"/>
    </justification>
  </clause>

  <clause id="15723">
    <literal><![CDATA[
      K(x,T(y,(z \ u) * z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u)) = w
    ]]></literal>
    <justification jstring="[para(12224(a,2),15602(a,1,2))].">
      <j1 rule="para" parents="12224 15602"/>
    </justification>
  </clause>

  <clause id="15724">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(y,K(z,T(x,v5))) = w
    ]]></literal>
    <justification jstring="[para(15560(a,1),15721(a,1))].">
      <j1 rule="para" parents="15560 15721"/>
    </justification>
  </clause>

  <clause id="15725">
    <literal><![CDATA[
      K(x * (y \ (1 / y)),z) = K(y \ (y \ x),z)
    ]]></literal>
    <justification jstring="[para(1180(a,1),15418(a,1,1))].">
      <j1 rule="para" parents="1180 15418"/>
    </justification>
  </clause>

  <clause id="15726">
    <literal><![CDATA[
      T(x * K(y,T(x,z * u)),y) = T(x,K(y,u * (x * z)))
    ]]></literal>
    <justification jstring="[para(15425(a,1),7477(a,1,1,2))].">
      <j1 rule="para" parents="15425 7477"/>
    </justification>
  </clause>

  <clause id="15727">
    <literal><![CDATA[
      T(x * K(y,T(x,z * u)),y) = T(x,K(y,u * (y * z)))
    ]]></literal>
    <justification jstring="[para(15426(a,1),7601(a,1,1,2))].">
      <j1 rule="para" parents="15426 7601"/>
    </justification>
  </clause>

  <clause id="15728">
    <literal><![CDATA[
      K(x,y) \ K(z,T(u,y)) = y \ (K(u,z) \ T(y,x))
    ]]></literal>
    <justification jstring="[para(15443(a,1),4547(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15443 4547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15729">
    <literal><![CDATA[
      T(x,T(y * z,u) / T(y,w)) = T(x,T(y,w) \ T(z * y,u))
    ]]></literal>
    <justification jstring="[para(6742(a,1),15455(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6742 15455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15730">
    <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(13689(a,1),15456(a,1,2,1))].">
      <j1 rule="para" parents="13689 15456"/>
    </justification>
  </clause>

  <clause id="15731">
    <literal><![CDATA[
      T(x,K(y,z)) * (u / T(x,K(y,z))) = x * (u / x)
    ]]></literal>
    <justification jstring="[para(5975(a,1),15476(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5975 15476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15732">
    <literal><![CDATA[
      K(x,L(T(y,T(z,u)),w,v5)) = K(x,L(T(y,z),w,v5))
    ]]></literal>
    <justification jstring="[para(6191(a,1),15495(a,1,2,1))].">
      <j1 rule="para" parents="6191 15495"/>
    </justification>
  </clause>

  <clause id="15733">
    <literal><![CDATA[
      T((L(K(x,x \ K(y,z)),u,w) \ K(x,x \ K(y,z))) * L(K(x,x \ K(y,z)),u,w),K(K(z,y) * x,x \ 1)) = K(K(z,y) * x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(451,a,2550,a,b,15496,a)].">
      <j1 rule="hyper" parents="451 2550 15496"/>
    </justification>
  </clause>

  <clause id="15735">
    <literal><![CDATA[
      T(L(K(x,y),z,u),w / v5) = T(L(K(x,y),z,u),v5 \ w)
    ]]></literal>
    <justification jstring="[para(15500(a,1),7570(a,1,1))].">
      <j1 rule="para" parents="15500 7570"/>
    </justification>
  </clause>

  <clause id="15737">
    <literal><![CDATA[
      K(x,y * z) * T(x,K(y,z)) = x * K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(333,a,12273,a(flip),b,15515,a),flip(a)].">
      <j1 rule="hyper" parents="333 12273 15515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15738">
    <literal><![CDATA[
      K(x,a(y,z,K(u,w)) * (v5 / w)) = K(x,v5 / T(w,a(y,z,u)))
    ]]></literal>
    <justification jstring="[para(13539(a,2),15526(a,1,2,1))].">
      <j1 rule="para" parents="13539 15526"/>
    </justification>
  </clause>

  <clause id="15739">
    <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(7569(a,1),15527(a,2,2,2))].">
      <j1 rule="para" parents="7569 15527"/>
    </justification>
  </clause>

  <clause id="15741">
    <literal><![CDATA[
      T(x * K(y,z),T(u / x,w)) = T(x * K(y,z),T(x \ u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,6948,a(flip),b,15536,a)].">
      <j1 rule="hyper" parents="63 6948 15536"/>
    </justification>
  </clause>

  <clause id="15743">
    <literal><![CDATA[
      T(x,T(y,K(z,u) * (w * z)) \ v5) = T(x,(y \ v5) * K(y,w * T(z,u)))
    ]]></literal>
    <justification jstring="[para(15527(a,1),15618(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="15527 15618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15744">
    <literal><![CDATA[
      K(T((x \ y) \ z,K(y,x) * u) * K(x \ y,x),u) = K((y / x) \ z,u)
    ]]></literal>
    <justification jstring="[para(15619(a,1),15315(a,1,1,1))].">
      <j1 rule="para" parents="15619 15315"/>
    </justification>
  </clause>

  <clause id="15745">
    <literal><![CDATA[
      T(x / y,K(y,x) * z) = T(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(40,a,7476,a,b,15620,a)].">
      <j1 rule="hyper" parents="40 7476 15620"/>
    </justification>
  </clause>

  <clause id="15746">
    <literal><![CDATA[
      K(x / y,K(y,x) * z) = (x / y) \ T(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(121,a,15745,a(flip),b,4222,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="121 15745 4222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15747">
    <literal><![CDATA[
      (T(x,y) \ z) * K(x,K(u,w)) = T(T(x,y),K(u,w)) \ z
    ]]></literal>
    <justification jstring="[para(15549(a,1),15625(a,1,2))].">
      <j1 rule="para" parents="15549 15625"/>
    </justification>
  </clause>

  <clause id="15748">
    <literal><![CDATA[
      K(x,y * (z * K(u,y))) = K(x,T(y,u) * z)
    ]]></literal>
    <justification jstring="[para(6212(a,1),15662(a,1,2))].">
      <j1 rule="para" parents="6212 15662"/>
    </justification>
  </clause>

  <clause id="15749">
    <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(6207(a,1),15666(a,1,2,1))].">
      <j1 rule="para" parents="6207 15666"/>
    </justification>
  </clause>

  <clause id="15750">
    <literal><![CDATA[
      T(x,K(((y \ z) * y) / (u * y),w)) = x * K(w,K((y * u) \ z,T(x,v5)))
    ]]></literal>
    <justification jstring="[para(13981(a,1),15675(a,1,2))].">
      <j1 rule="para" parents="13981 15675"/>
    </justification>
  </clause>

  <clause id="15751">
    <literal><![CDATA[
      K(x,T(y,z)) \ (u * z) = K(x,y) \ (u * T(z,K(x,y)))
    ]]></literal>
    <justification jstring="[para(15692(a,1),7590(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15692 7590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15752">
    <literal><![CDATA[
      T(x,K(y,z)) \ (u * x) = x \ (u * T(x,K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(121,a,15693,a(flip),b,4296,a),flip(a)].">
      <j1 rule="hyper" parents="121 15693 4296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15753">
    <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(4397(a,1),15698(a,1,2,1))].">
      <j1 rule="para" parents="4397 15698"/>
    </justification>
  </clause>

  <clause id="15754">
    <literal><![CDATA[
      K(x,x * (K(y,z) \ (u * y))) \ T(x,u * T(y,z)) = R(x,K(y,z) \ (u * y),x)
    ]]></literal>
    <justification jstring="[para(15710(a,1),4737(a,1,2))].">
      <j1 rule="para" parents="15710 4737"/>
    </justification>
  </clause>

  <clause id="15755">
    <literal><![CDATA[
      (x * (K(y,z) \ x)) / x = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(3416,a,15712,a)].">
      <j1 rule="hyper" parents="3416 15712"/>
    </justification>
  </clause>

  <clause id="15756">
    <literal><![CDATA[
      (x * T(K(y,z) \ x,u)) / x = T(x * K(z,y),u)
    ]]></literal>
    <justification jstring="[para(15755(a,1),476(a,2,1))].">
      <j1 rule="para" parents="15755 476"/>
    </justification>
  </clause>

  <clause id="15757">
    <literal><![CDATA[
      K(K(x * y,x) * z,u) = K(K(y,x) * z,u)
    ]]></literal>
    <justification jstring="[hyper(333,a,15701,a,b,15714,a),flip(a)].">
      <j1 rule="hyper" parents="333 15701 15714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15759">
    <literal><![CDATA[
      K(K(x \ 1,y) * ((z / (x * z)) \ u),w) = K(T(z / (x * z),y) \ u,w)
    ]]></literal>
    <justification jstring="[para(4970(a,1),15715(a,1,1,1))].">
      <j1 rule="para" parents="4970 15715"/>
    </justification>
  </clause>

  <clause id="15760">
    <literal><![CDATA[
      K(T(x \ y,x) \ z,u) = K((y / x) \ z,u)
    ]]></literal>
    <justification jstring="[para(4830(a,1),15715(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4830 15715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15761">
    <literal><![CDATA[
      K(T(x,y) \ (y \ z),u) = K(x \ (T(y,x) \ z),u)
    ]]></literal>
    <justification jstring="[para(4836(a,1),15715(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4836 15715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15762">
    <literal><![CDATA[
      K(x,T(y,z) * (u * z)) = K(x,y * (u * T(z,y)))
    ]]></literal>
    <justification jstring="[para(5984(a,1),15748(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5984 15748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15763">
    <literal><![CDATA[
      K(x * K(y * z,y),u) = K(K(z,y) * x,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,15518,a(flip),b,15757,a)].">
      <j1 rule="hyper" parents="63 15518 15757"/>
    </justification>
  </clause>

  <clause id="15764">
    <literal><![CDATA[
      K(T(x \ y,y) \ z,u) = K((y / x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,12784,a,b,15760,a)].">
      <j1 rule="hyper" parents="63 12784 15760"/>
    </justification>
  </clause>

  <clause id="15765">
    <literal><![CDATA[
      K(x * K(y * (z * u),z),w) = K(K(y * u,z) * x,w)
    ]]></literal>
    <justification jstring="[para(10819(a,2),15763(a,1,1,2))].">
      <j1 rule="para" parents="10819 15763"/>
    </justification>
  </clause>

  <clause id="15766">
    <literal><![CDATA[
      T(T(x,y * y),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z * (y * y)) = u
    ]]></literal>
    <justification jstring="[para(15419(a,2),15409(a,1))].">
      <j1 rule="para" parents="15419 15409"/>
    </justification>
  </clause>

  <clause id="15767">
    <literal><![CDATA[
      K(x,K(y,z)) * u != w
    ]]></literal>
    <literal><![CDATA[
      u * K(y,K(z,x)) = w
    ]]></literal>
    <justification jstring="[para(6788(a,1),15482(a,1,1))].">
      <j1 rule="para" parents="6788 15482"/>
    </justification>
  </clause>

  <clause id="15768">
    <literal><![CDATA[
      T(x,y * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(u,z) * y) = w
    ]]></literal>
    <justification jstring="[para(15004(a,1),15485(a,1))].">
      <j1 rule="para" parents="15004 15485"/>
    </justification>
  </clause>

  <clause id="15769">
    <literal><![CDATA[
      T(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(z,y) * u) = w
    ]]></literal>
    <justification jstring="[para(15616(a,2),15485(a,1))].">
      <j1 rule="para" parents="15616 15485"/>
    </justification>
  </clause>

  <clause id="15770">
    <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(12741(a,1),15486(a,1))].">
      <j1 rule="para" parents="12741 15486"/>
    </justification>
  </clause>

  <clause id="15771">
    <literal><![CDATA[
      T(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u * K(z,y)) = w
    ]]></literal>
    <justification jstring="[para(14920(a,1),15486(a,1))].">
      <j1 rule="para" parents="14920 15486"/>
    </justification>
  </clause>

  <clause id="15773">
    <literal><![CDATA[
      K(x * K(y \ 1,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(y,z) * x,u) = w
    ]]></literal>
    <justification jstring="[para(15227(a,2),15532(a,1))].">
      <j1 rule="para" parents="15227 15532"/>
    </justification>
  </clause>

  <clause id="15774">
    <literal><![CDATA[
      K(T(1 / (x \ y),K(z,u)),w) = K(1 / L(x \ y,v5,y / x),w)
    ]]></literal>
    <justification jstring="[para(7811(a,2),15544(a,2,1,2))].">
      <j1 rule="para" parents="7811 15544"/>
    </justification>
  </clause>

  <clause id="15775">
    <literal><![CDATA[
      K(x,T(K(y,z) * (u / z),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(u / T(z,y),w)) = v5
    ]]></literal>
    <justification jstring="[para(7096(a,1),15546(a,1,2,1))].">
      <j1 rule="para" parents="7096 15546"/>
    </justification>
  </clause>

  <clause id="15776">
    <literal><![CDATA[
      T(x,(y * z) / T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(z,u) \ y) = w
    ]]></literal>
    <justification jstring="[para(5446(a,2),15594(a,1,2))].">
      <j1 rule="para" parents="5446 15594"/>
    </justification>
  </clause>

  <clause id="15777">
    <literal><![CDATA[
      K(x,(y / z) \ T(y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,y) \ z) = w
    ]]></literal>
    <justification jstring="[para(13240(a,2),15601(a,1,2))].">
      <j1 rule="para" parents="13240 15601"/>
    </justification>
  </clause>

  <clause id="15778">
    <literal><![CDATA[
      K(x,y * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,u) \ y) = w
    ]]></literal>
    <justification jstring="[para(15160(a,1),15601(a,1))].">
      <j1 rule="para" parents="15160 15601"/>
    </justification>
  </clause>

  <clause id="15779">
    <literal><![CDATA[
      K(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z) \ u) = w
    ]]></literal>
    <justification jstring="[para(15637(a,2),15601(a,1))].">
      <j1 rule="para" parents="15637 15601"/>
    </justification>
  </clause>

  <clause id="15780">
    <literal><![CDATA[
      K(x,K(y,z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y) \ u) = w
    ]]></literal>
    <justification jstring="[para(15639(a,2),15601(a,1))].">
      <j1 rule="para" parents="15639 15601"/>
    </justification>
  </clause>

  <clause id="15781">
    <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(10103(a,1),15608(a,1,2,2))].">
      <j1 rule="para" parents="10103 15608"/>
    </justification>
  </clause>

  <clause id="15782">
    <literal><![CDATA[
      K(x,T(y,z / (1 / u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u * z)) = w
    ]]></literal>
    <justification jstring="[para(13326(a,2),15608(a,1,2))].">
      <j1 rule="para" parents="13326 15608"/>
    </justification>
  </clause>

  <clause id="15783">
    <literal><![CDATA[
      K(x,T(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u * z)) = w
    ]]></literal>
    <justification jstring="[para(15396(a,2),15608(a,1))].">
      <j1 rule="para" parents="15396 15608"/>
    </justification>
  </clause>

  <clause id="15784">
    <literal><![CDATA[
      K(x,T(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z * u)) = w
    ]]></literal>
    <justification jstring="[para(15398(a,2),15608(a,1))].">
      <j1 rule="para" parents="15398 15608"/>
    </justification>
  </clause>

  <clause id="15785">
    <literal><![CDATA[
      K(K(x,y) \ z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(y,x) \ z,u) = w
    ]]></literal>
    <justification jstring="[para(15702(a,2),15611(a,1))].">
      <j1 rule="para" parents="15702 15611"/>
    </justification>
  </clause>

  <clause id="15786">
    <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(107(a,1),15681(a,1,2,2))].">
      <j1 rule="para" parents="107 15681"/>
    </justification>
  </clause>

  <clause id="15787">
    <literal><![CDATA[
      K(x,K(y,z \ (u \ 1))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z * u)) = w
    ]]></literal>
    <justification jstring="[para(12293(a,2),15681(a,1))].">
      <j1 rule="para" parents="12293 15681"/>
    </justification>
  </clause>

  <clause id="15788">
    <literal><![CDATA[
      T(x,y * (z * (K(u,w) * K(u,w)))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y * z) = v5
    ]]></literal>
    <justification jstring="[para(33(a,1),15713(a,1,2))].">
      <j1 rule="para" parents="33 15713"/>
    </justification>
  </clause>

  <clause id="15791">
    <literal><![CDATA[
      T(T(x,y * (z * z)),u) != w
    ]]></literal>
    <literal><![CDATA[
      T(T(x,y),u * (z * z)) = w
    ]]></literal>
    <justification jstring="[para(1123(a,1),15766(a,1,1))].">
      <j1 rule="para" parents="1123 15766"/>
    </justification>
  </clause>

  <clause id="15792">
    <literal><![CDATA[
      K(x,T(y,z)) * u != w
    ]]></literal>
    <literal><![CDATA[
      (K(x,y) * u) * K(y,K(x,z)) = w
    ]]></literal>
    <justification jstring="[para(6409(a,1),15767(a,1))].">
      <j1 rule="para" parents="6409 15767"/>
    </justification>
  </clause>

  <clause id="15793">
    <literal><![CDATA[
      T(x,K(y,y \ z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(z,y) * u) = w
    ]]></literal>
    <justification jstring="[para(12760(a,2),15769(a,1))].">
      <j1 rule="para" parents="12760 15769"/>
    </justification>
  </clause>

  <clause id="15794">
    <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(14919(a,2),15769(a,1))].">
      <j1 rule="para" parents="14919 15769"/>
    </justification>
  </clause>

  <clause id="15795">
    <literal><![CDATA[
      T(x,K(y,y \ z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(14921(a,2),15769(a,1))].">
      <j1 rule="para" parents="14921 15769"/>
    </justification>
  </clause>

  <clause id="15796">
    <literal><![CDATA[
      K(x,L(K(y,z),u,w) \ v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,K(L(z,u,w),y) \ v5) = v6
    ]]></literal>
    <justification jstring="[para(10851(a,2),15780(a,1,2,1))].">
      <j1 rule="para" parents="10851 15780"/>
    </justification>
  </clause>

  <clause id="15797">
    <literal><![CDATA[
      K(x,T(y,z / u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z * u)) = w
    ]]></literal>
    <justification jstring="[para(15444(a,2),15783(a,1))].">
      <j1 rule="para" parents="15444 15783"/>
    </justification>
  </clause>

  <clause id="15798">
    <literal><![CDATA[
      K(x,T(y,T(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u * (z * u))) = w
    ]]></literal>
    <justification jstring="[para(22(a,2),15784(a,1,2,2))].">
      <j1 rule="para" parents="22 15784"/>
    </justification>
  </clause>

  <clause id="15799">
    <literal><![CDATA[
      K(K(x,x * y) \ z,u) = K(K(y,x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(15785,a,12820,a)].">
      <j1 rule="hyper" parents="15785 12820"/>
    </justification>
  </clause>

  <clause id="15800">
    <literal><![CDATA[
      K(K(x * y,y \ 1) \ z,u) = K(K(y \ 1,x) \ z,u)
    ]]></literal>
    <justification jstring="[para(10941(a,1),15799(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10941 15799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15801">
    <literal><![CDATA[
      K((x \ (1 / x)) * y,z) = K(y * (x \ (1 / x)),z)
    ]]></literal>
    <justification jstring="[para(2405(a,1),15397(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2405 15397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15802">
    <literal><![CDATA[
      K(x,K(y,z \ u)) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(7050,a,15402,a),flip(a)].">
      <j1 rule="hyper" parents="7050 15402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15804">
    <literal><![CDATA[
      K(x,K(y,z / u)) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(15720,a,15802,a)].">
      <j1 rule="hyper" parents="15720 15802"/>
    </justification>
  </clause>

  <clause id="15805">
    <literal><![CDATA[
      K(x,K(y,z \ u)) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(7195,a,15802,a)].">
      <j1 rule="hyper" parents="7195 15802"/>
    </justification>
  </clause>

  <clause id="15806">
    <literal><![CDATA[
      T(x,K(y,z \ u)) = T(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(124,a,15802,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 15802 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15807">
    <literal><![CDATA[
      T(x,K(y \ ((z * u) / z),w)) = K(x,K(w,y * T(u,z))) * x
    ]]></literal>
    <justification jstring="[para(15802(a,1),15066(a,2,1))].">
      <j1 rule="para" parents="15802 15066"/>
    </justification>
  </clause>

  <clause id="15808">
    <literal><![CDATA[
      K(x,K(y,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u / z)) = w
    ]]></literal>
    <justification jstring="[para(15802(a,1),15720(a,1))].">
      <j1 rule="para" parents="15802 15720"/>
    </justification>
  </clause>

  <clause id="15809">
    <literal><![CDATA[
      T(x,K(y,z / u)) = T(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(124,a,15804,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 15804 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15810">
    <literal><![CDATA[
      T(x,K(y,z \ u)) = T(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(124,a,15805,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 15805 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15811">
    <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(15805(a,1),6779(a,1,1))].">
      <j1 rule="para" parents="15805 6779"/>
    </justification>
  </clause>

  <clause id="15812">
    <literal><![CDATA[
      T(x,K(y,z * (u \ 1))) = T(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,12299,a(flip),b,15806,a),flip(a)].">
      <j1 rule="hyper" parents="63 12299 15806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15813">
    <literal><![CDATA[
      T(x,K(y,z * (z * u))) = T(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(9(a,1),15806(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 15806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15814">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),y / (z \ u)) = T(x,(z \ u) \ y)
    ]]></literal>
    <justification jstring="[para(15806(a,1),7570(a,1,1))].">
      <j1 rule="para" parents="15806 7570"/>
    </justification>
  </clause>

  <clause id="15815">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),y * (z \ u)) = T(x,(z \ u) * y)
    ]]></literal>
    <justification jstring="[para(15806(a,1),12263(a,1,1))].">
      <j1 rule="para" parents="15806 12263"/>
    </justification>
  </clause>

  <clause id="15816">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),y * (z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(z \ u) * y) = w
    ]]></literal>
    <justification jstring="[para(15806(a,1),12297(a,1,1))].">
      <j1 rule="para" parents="15806 12297"/>
    </justification>
  </clause>

  <clause id="15817">
    <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(15806(a,1),14912(a,1,2,1,2))].">
      <j1 rule="para" parents="15806 14912"/>
    </justification>
  </clause>

  <clause id="15818">
    <literal><![CDATA[
      T(x,K(y,z * (u * z))) = T(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(11(a,1),15809(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11 15809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15819">
    <literal><![CDATA[
      T(x,K(y,z * (z / u))) = T(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(79(a,1),15810(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="79 15810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15820">
    <literal><![CDATA[
      T(x,K(y,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z \ u)) = w
    ]]></literal>
    <justification jstring="[para(15810(a,1),7196(a,1))].">
      <j1 rule="para" parents="15810 7196"/>
    </justification>
  </clause>

  <clause id="15821">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * (u * (u * z))) = T(x,(u * (u * z)) * y)
    ]]></literal>
    <justification jstring="[para(15813(a,1),12263(a,1,1))].">
      <j1 rule="para" parents="15813 12263"/>
    </justification>
  </clause>

  <clause id="15822">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * (u * (u * z))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(u * (u * z)) * y) = w
    ]]></literal>
    <justification jstring="[para(15813(a,1),12297(a,1,1))].">
      <j1 rule="para" parents="15813 12297"/>
    </justification>
  </clause>

  <clause id="15823">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),y * (u * (z \ 1))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(u * (z \ 1)) * y) = w
    ]]></literal>
    <justification jstring="[para(15812(a,1),12297(a,1,1))].">
      <j1 rule="para" parents="15812 12297"/>
    </justification>
  </clause>

  <clause id="15824">
    <literal><![CDATA[
      K((x * y) * T(z,y),T(u,y * z)) = K((z * y) * R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(10345(a,1),15422(a,1,1))].">
      <j1 rule="para" parents="10345 15422"/>
    </justification>
  </clause>

  <clause id="15825">
    <literal><![CDATA[
      K(x,T(L(y \ z,y,y \ u),z * (u / y))) = K(x,((u / y) * z) / u)
    ]]></literal>
    <justification jstring="[para(10102(a,2),15423(a,1,2,1))].">
      <j1 rule="para" parents="10102 15423"/>
    </justification>
  </clause>

  <clause id="15826">
    <literal><![CDATA[
      K(x,T(L(y \ z,y,z \ u),y * (u / z))) = K(x,u / ((u / z) * y))
    ]]></literal>
    <justification jstring="[para(13618(a,2),15424(a,1,2,1))].">
      <j1 rule="para" parents="13618 15424"/>
    </justification>
  </clause>

  <clause id="15827">
    <literal><![CDATA[
      T(x,y) \ T(K(z,u) * x,y) = K(z,T(u,y * x))
    ]]></literal>
    <justification jstring="[hyper(14104,a,15427,a)].">
      <j1 rule="hyper" parents="14104 15427"/>
    </justification>
  </clause>

  <clause id="15828">
    <literal><![CDATA[
      T(x,(y \ 1) * ((y \ 1) * z)) = T(T(x,z),y \ (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(34,a,13381,a,b,15432,a),flip(a)].">
      <j1 rule="hyper" parents="34 13381 15432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15829">
    <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(123,a,14061,a,b,15503,a)].">
      <j1 rule="hyper" parents="123 14061 15503"/>
    </justification>
  </clause>

  <clause id="15831">
    <literal><![CDATA[
      T(x * K(y,K(z,u)),w) = T(x,w) * K(y,K(z,u))
    ]]></literal>
    <justification jstring="[para(15475(a,1),15559(a,1,1))].">
      <j1 rule="para" parents="15475 15559"/>
    </justification>
  </clause>

  <clause id="15833">
    <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(15586(a,1),10120(a,1,2,2))].">
      <j1 rule="para" parents="15586 10120"/>
    </justification>
  </clause>

  <clause id="15834">
    <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(6641(a,1),15589(a,2,2))].">
      <j1 rule="para" parents="6641 15589"/>
    </justification>
  </clause>

  <clause id="15835">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * K(x,y)) = u * K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(333,a,6389,a,b,15629,a),flip(a)].">
      <j1 rule="hyper" parents="333 6389 15629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15836">
    <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(444,a,15651,a,b,13335,a)].">
      <j1 rule="hyper" parents="444 15651 13335"/>
    </justification>
  </clause>

  <clause id="15837">
    <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(15686(a,1),7489(a,2,2,1))].">
      <j1 rule="para" parents="15686 7489"/>
    </justification>
  </clause>

  <clause id="15838">
    <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(113(a,1),15690(a,2,2,2))].">
      <j1 rule="para" parents="113 15690"/>
    </justification>
  </clause>

  <clause id="15839">
    <literal><![CDATA[
      K(x,K(y,z)) \ T(u,z) = z \ (u * T(z,K(x,y)))
    ]]></literal>
    <justification jstring="[para(6788(a,2),15690(a,1,1))].">
      <j1 rule="para" parents="6788 15690"/>
    </justification>
  </clause>

  <clause id="15840">
    <literal><![CDATA[
      K(x * T(y,z),y * z) = K(y * x,z * y)
    ]]></literal>
    <justification jstring="[para(5984(a,1),15700(a,1,1))].">
      <j1 rule="para" parents="5984 15700"/>
    </justification>
  </clause>

  <clause id="15841">
    <literal><![CDATA[
      K((x * y) * R(z,y,x),x * y) = K(x * (z * y),y * x)
    ]]></literal>
    <justification jstring="[hyper(10382,a,15840,a)].">
      <j1 rule="hyper" parents="10382 15840"/>
    </justification>
  </clause>

  <clause id="15842">
    <literal><![CDATA[
      x \ (K(y,z) \ T(x,x \ z)) = z \ (x * (T(z,y) / x))
    ]]></literal>
    <justification jstring="[hyper(63,a,14163,a(flip),b,15728,a),flip(a)].">
      <j1 rule="hyper" parents="63 14163 15728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15843">
    <literal><![CDATA[
      T(x * T(y,K(z,u)),w) / y = y \ T(T(y,K(z,u)) * x,w)
    ]]></literal>
    <justification jstring="[hyper(4113,a,15731,a),flip(a)].">
      <j1 rule="hyper" parents="4113 15731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15844">
    <literal><![CDATA[
      T(x,K(y,z)) * ((x * T(x \ u,w)) / T(x,K(y,z))) = x * T(u / x,w)
    ]]></literal>
    <justification jstring="[para(474(a,1),15731(a,2,2))].">
      <j1 rule="para" parents="474 15731"/>
    </justification>
  </clause>

  <clause id="15845">
    <literal><![CDATA[
      T(x,y) * K(z,L(T(u,x),w,v5)) = K(z,L(u,w,v5)) * T(x,y)
    ]]></literal>
    <justification jstring="[para(15732(a,1),6495(a,1,2))].">
      <j1 rule="para" parents="15732 6495"/>
    </justification>
  </clause>

  <clause id="15846">
    <literal><![CDATA[
      T(x,y * z) * K(x,K(y,z)) = x * K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(4911,a,15737,a)].">
      <j1 rule="hyper" parents="4911 15737"/>
    </justification>
  </clause>

  <clause id="15847">
    <literal><![CDATA[
      K(x / y,K(y,x) * z) = K(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,4215,a,b,15746,a),flip(a)].">
      <j1 rule="hyper" parents="333 4215 15746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15848">
    <literal><![CDATA[
      K(x / y,(y / T(x,y)) * z) = K(x / y,(y / x) * z)
    ]]></literal>
    <justification jstring="[para(11847(a,1),15847(a,1,2))].">
      <j1 rule="para" parents="11847 15847"/>
    </justification>
  </clause>

  <clause id="15849">
    <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(6847(a,1),15752(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6847 15752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15850">
    <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(15762(a,2),7466(a,1))].">
      <j1 rule="para" parents="15762 7466"/>
    </justification>
  </clause>

  <clause id="15851">
    <literal><![CDATA[
      K((x \ (1 / x)) * y,z) = K(x \ (x \ y),z)
    ]]></literal>
    <justification jstring="[hyper(333,a,15725,a(flip),b,15801,a),flip(a)].">
      <j1 rule="hyper" parents="333 15725 15801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15852">
    <literal><![CDATA[
      (x * K(y \ (y \ z),u)) \ (x * u) = T(u,(y \ (1 / y)) * z)
    ]]></literal>
    <justification jstring="[para(15851(a,1),5447(a,1,1,2))].">
      <j1 rule="para" parents="15851 5447"/>
    </justification>
  </clause>

  <clause id="15853">
    <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(14525(a,2),15827(a,2,2,2))].">
      <j1 rule="para" parents="14525 15827"/>
    </justification>
  </clause>

  <clause id="15854">
    <literal><![CDATA[
      T(K(x,K(y,z)) \ u,w) = K(x,K(y,z)) \ T(u,w)
    ]]></literal>
    <justification jstring="[hyper(35,a,4105,a(flip),b,15831,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="35 4105 15831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15855">
    <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(15831(a,2),6815(a,1,1))].">
      <j1 rule="para" parents="15831 6815"/>
    </justification>
  </clause>

  <clause id="15857">
    <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(15835(a,2),43(a,1))].">
      <j1 rule="para" parents="15835 43"/>
    </justification>
  </clause>

  <clause id="15858">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,y * z) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(34,a,15511,a,b,15846,a(flip))].">
      <j1 rule="hyper" parents="34 15511 15846"/>
    </justification>
  </clause>

  <clause id="15859">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,z * y) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(6832,a,15858,a)].">
      <j1 rule="hyper" parents="6832 15858"/>
    </justification>
  </clause>

  <clause id="15860">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,x * z) = K(y,z * x)
    ]]></literal>
    <justification jstring="[para(6785(a,1),15858(a,1,1))].">
      <j1 rule="para" parents="6785 15858"/>
    </justification>
  </clause>

  <clause id="15861">
    <literal><![CDATA[
      K(x,K(y * K(z,u),T(w,K(z,u)))) * K(x,(y * K(z,T(u,w))) * w) = K(x,T(w,K(z,u)) * (y * K(z,u)))
    ]]></literal>
    <justification jstring="[para(6966(a,2),15858(a,1,2,2))].">
      <j1 rule="para" parents="6966 15858"/>
    </justification>
  </clause>

  <clause id="15863">
    <literal><![CDATA[
      K(x,K(y * K(z,u),w)) * K(x,(K(u,z) * y) * w) = K(x,w * (K(u,z) * y))
    ]]></literal>
    <justification jstring="[para(15654(a,1),15858(a,1,1,2))].">
      <j1 rule="para" parents="15654 15858"/>
    </justification>
  </clause>

  <clause id="15864">
    <literal><![CDATA[
      K(x,y * z) \ K(x,K(y,z)) = K(z * y,x)
    ]]></literal>
    <justification jstring="[para(15859(a,1),5990(a,1,1))].">
      <j1 rule="para" parents="15859 5990"/>
    </justification>
  </clause>

  <clause id="15865">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,T(z,u) * x) = K(y,x * T(z,u))
    ]]></literal>
    <justification jstring="[para(15563(a,1),15859(a,1,1))].">
      <j1 rule="para" parents="15563 15859"/>
    </justification>
  </clause>

  <clause id="15868">
    <literal><![CDATA[
      K(x,(T(y,z) \ (y * u)) * w) \ K(x,K(K(y,z) \ u,w)) = K(w * (T(y,z) \ (y * u)),x)
    ]]></literal>
    <justification jstring="[para(4685(a,1),15864(a,1,2,2))].">
      <j1 rule="para" parents="4685 15864"/>
    </justification>
  </clause>

  <clause id="15869">
    <literal><![CDATA[
      K(x,(y * z) * K(u,w)) \ K(x,K(L(y,z,K(u,w)),z * K(u,w))) = K((z * K(u,w)) * L(y,z,K(u,w)),x)
    ]]></literal>
    <justification jstring="[para(14470(a,1),15864(a,1,1,2))].">
      <j1 rule="para" parents="14470 15864"/>
    </justification>
  </clause>

  <clause id="15870">
    <literal><![CDATA[
      (T(x,K(y,z)) * (K(x,K(y,z)) \ T(u,w))) / T(x,K(y,z)) = T((x * u) / T(x,K(y,z)),w)
    ]]></literal>
    <justification jstring="[para(15854(a,1),4678(a,1,1,2))].">
      <j1 rule="para" parents="15854 4678"/>
    </justification>
  </clause>

  <clause id="15871">
    <literal><![CDATA[
      K(x,K(y,z)) \ T(x * u,w) = T(T(x,K(y,z)) * u,w)
    ]]></literal>
    <justification jstring="[para(6831(a,1),15854(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6831 15854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15872">
    <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(23(a,1),15449(a,1,2))].">
      <j1 rule="para" parents="23 15449"/>
    </justification>
  </clause>

  <clause id="15873">
    <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(15460,a,13571,a)].">
      <j1 rule="hyper" parents="15460 13571"/>
    </justification>
  </clause>

  <clause id="15874">
    <literal><![CDATA[
      L(K(x,y * K(z,u)),x,w) = (x * K(v5,v6)) \ (T(x,K(z,u) * y) * K(v5,v6))
    ]]></literal>
    <justification jstring="[para(15470(a,2),15528(a,2,2,1))].">
      <j1 rule="para" parents="15470 15528"/>
    </justification>
  </clause>

  <clause id="15875">
    <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(13435(a,1),15597(a,1,2,2))].">
      <j1 rule="para" parents="13435 15597"/>
    </justification>
  </clause>

  <clause id="15877">
    <literal><![CDATA[
      K(x,(T(y,z) * z) * (u * K(z * y,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(T(y,z) * z,w) * u) = v5
    ]]></literal>
    <justification jstring="[para(12222(a,1),15603(a,1,2,2,2))].">
      <j1 rule="para" parents="12222 15603"/>
    </justification>
  </clause>

  <clause id="15878">
    <literal><![CDATA[
      K(x,K(y / z,u) * (w * ((z / y) \ 1))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w * T((z / y) \ 1,u)) = v5
    ]]></literal>
    <justification jstring="[para(4965(a,1),15605(a,1,2,1))].">
      <j1 rule="para" parents="4965 15605"/>
    </justification>
  </clause>

  <clause id="15879">
    <literal><![CDATA[
      K(x,K(y,z) * (u * z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u * T(z,y)) = w
    ]]></literal>
    <justification jstring="[para(14926(a,1),15605(a,1))].">
      <j1 rule="para" parents="14926 15605"/>
    </justification>
  </clause>

  <clause id="15880">
    <literal><![CDATA[
      K(x,(y \ z) * K(u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(15637(a,1),15609(a,1))].">
      <j1 rule="para" parents="15637 15609"/>
    </justification>
  </clause>

  <clause id="15881">
    <literal><![CDATA[
      K(x \ ((y \ z) \ 1),((y \ z) \ 1) * (T(y,u) \ z)) = K(y,K(u,z * x))
    ]]></literal>
    <justification jstring="[hyper(15787,a,14389,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="15787 14389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15882">
    <literal><![CDATA[
      T(x,K(y \ z,y) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(z,y) * u) = w
    ]]></literal>
    <justification jstring="[para(14920(a,1),15793(a,1))].">
      <j1 rule="para" parents="14920 15793"/>
    </justification>
  </clause>

  <clause id="15883">
    <literal><![CDATA[
      K(x,T(y,z * (u * z))) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(15798,a,15434,a)].">
      <j1 rule="hyper" parents="15798 15434"/>
    </justification>
  </clause>

  <clause id="15884">
    <literal><![CDATA[
      K((x * (y * x)) * z,T(u,y)) = K(z * (x * (y * x)),u)
    ]]></literal>
    <justification jstring="[hyper(12210,a,15883,a),flip(a)].">
      <j1 rule="hyper" parents="12210 15883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15885">
    <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(5003(a,1),15880(a,1,2,2))].">
      <j1 rule="para" parents="5003 15880"/>
    </justification>
  </clause>

  <clause id="15886">
    <literal><![CDATA[
      K(x,L(T(y,z \ u),w,v5)) = K(x,L(T(y,z * u),w,v5))
    ]]></literal>
    <justification jstring="[para(25(a,2),15400(a,2,2))].">
      <j1 rule="para" parents="25 15400"/>
    </justification>
  </clause>

  <clause id="15887">
    <literal><![CDATA[
      T(x,y * K(z,u * u)) = y \ (x * y)
    ]]></literal>
    <justification jstring="[para(15407(a,1),15411(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15407 15411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15888">
    <literal><![CDATA[
      T(x,y * K(z,u * u)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,22,a,b,15887,a),flip(a)].">
      <j1 rule="hyper" parents="333 22 15887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15890">
    <literal><![CDATA[
      T(x,y * (z / (u * u))) = T(x,y * ((u * u) \ z))
    ]]></literal>
    <justification jstring="[para(6011(a,1),15888(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6011 15888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15891">
    <literal><![CDATA[
      T(x,y * (z * T(u,w * w))) = T(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(5996(a,1),15888(a,1,2))].">
      <j1 rule="para" parents="5996 15888"/>
    </justification>
  </clause>

  <clause id="15892">
    <literal><![CDATA[
      T(x,y * ((z * z) \ (u * w))) = T(x,y * (u * (w / (z * z))))
    ]]></literal>
    <justification jstring="[para(809(a,1),15890(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="809 15890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15893">
    <literal><![CDATA[
      T(x,y * (z * (u / (w * w)))) = T(x,y * (z * ((w * w) \ u)))
    ]]></literal>
    <justification jstring="[para(113(a,1),15891(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="113 15891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15895">
    <literal><![CDATA[
      K((x / y) \ K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(T(y,z) / x,u) = w
    ]]></literal>
    <justification jstring="[para(15465(a,1),7065(a,1))].">
      <j1 rule="para" parents="15465 7065"/>
    </justification>
  </clause>

  <clause id="15896">
    <literal><![CDATA[
      K((x / y) \ K(z,y),u) = K(T(y,z) / x,u)
    ]]></literal>
    <justification jstring="[hyper(15895,a,15114,a),flip(a)].">
      <j1 rule="hyper" parents="15895 15114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15897">
    <literal><![CDATA[
      K((x / y) \ K(z \ K(u,w),y),v5) = K(T(y,z \ K(w,u \ w)) / x,v5)
    ]]></literal>
    <justification jstring="[para(15121(a,1),15896(a,1,1,2))].">
      <j1 rule="para" parents="15121 15896"/>
    </justification>
  </clause>

  <clause id="15898">
    <literal><![CDATA[
      T((x * (K(y,K(z,u)) * w)) / (w * K(y,K(z,u))),w) = T(x,K(y,K(z,u)) * w)
    ]]></literal>
    <justification jstring="[hyper(253,a,12,a(flip),b,15558,a),flip(a)].">
      <j1 rule="hyper" parents="253 12 15558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15899">
    <literal><![CDATA[
      T(x / T(y,K(z,u)),y * K(u,z)) = y \ T(x,K(z,u))
    ]]></literal>
    <justification jstring="[para(12(a,1),15617(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12 15617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15900">
    <literal><![CDATA[
      T(x * T(y,x * K(z,u)),K(z,u)) = y * T(x,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(6857,a,15621,a)].">
      <j1 rule="hyper" parents="6857 15621"/>
    </justification>
  </clause>

  <clause id="15902">
    <literal><![CDATA[
      T(x,K(y,z) * (u * y)) = T(x,u * (z * (y / z)))
    ]]></literal>
    <justification jstring="[hyper(15793,a,15622,a)].">
      <j1 rule="hyper" parents="15793 15622"/>
    </justification>
  </clause>

  <clause id="15903">
    <literal><![CDATA[
      T(x,y * (z * (u / z))) = T(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[hyper(15597,a,15902,a),flip(a)].">
      <j1 rule="hyper" parents="15597 15902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15904">
    <literal><![CDATA[
      T(x,y * T(z * u,u)) = T(x,y * (u * z))
    ]]></literal>
    <justification jstring="[para(11(a,1),15903(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="11 15903"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15905">
    <literal><![CDATA[
      T(x,y * T(R(z,u,u),u \ 1)) = T(x,y * ((u \ 1) * (z * u)))
    ]]></literal>
    <justification jstring="[para(813(a,1),15903(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="813 15903"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15906">
    <literal><![CDATA[
      T(x,y * (z * ((u \ ((z * w) / z)) * u))) = T(x,y * T(z * ((u \ w) * u),z))
    ]]></literal>
    <justification jstring="[para(4147(a,1),15903(a,1,2,2,2))].">
      <j1 rule="para" parents="4147 15903"/>
    </justification>
  </clause>

  <clause id="15907">
    <literal><![CDATA[
      K(x,y * (z * (u / z))) = (w / T(x,y * T(u,z))) \ (w / x)
    ]]></literal>
    <justification jstring="[para(15903(a,1),5983(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="15903 5983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15908">
    <literal><![CDATA[
      K(x,T(1 / (y * z),y)) = K(x,1 / (z * y))
    ]]></literal>
    <justification jstring="[hyper(333,a,4809,a(flip),b,15642,a),flip(a)].">
      <j1 rule="hyper" parents="333 4809 15642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15910">
    <literal><![CDATA[
      K(x,y / (y * (y * z))) = K(x,1 / (z * y))
    ]]></literal>
    <justification jstring="[hyper(63,a,7131,a(flip),b,15908,a)].">
      <j1 rule="hyper" parents="63 7131 15908"/>
    </justification>
  </clause>

  <clause id="15911">
    <literal><![CDATA[
      K(x / (x / y),z * ((x / y) / x)) = K(y,T(((x / y) / x) * z,x))
    ]]></literal>
    <justification jstring="[hyper(12359,a,15650,a)].">
      <j1 rule="hyper" parents="12359 15650"/>
    </justification>
  </clause>

  <clause id="15912">
    <literal><![CDATA[
      K(x,K(y,z) \ (u / y)) = K(x,u / (z * (y / z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,14937,a(flip),b,15663,a)].">
      <j1 rule="hyper" parents="63 14937 15663"/>
    </justification>
  </clause>

  <clause id="15913">
    <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(63,a,12298,a,b,15664,a)].">
      <j1 rule="hyper" parents="63 12298 15664"/>
    </justification>
  </clause>

  <clause id="15914">
    <literal><![CDATA[
      T(T(x,K(y,(z * u) * (u \ 1))),y * T((u \ 1) * (u * z),u)) = T(x,((u \ 1) * (z * u)) * y)
    ]]></literal>
    <justification jstring="[para(1715(a,2),15684(a,1,2,2))].">
      <j1 rule="para" parents="1715 15684"/>
    </justification>
  </clause>

  <clause id="15915">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * (u * (z * (u \ 1)))) = T(x,(u * (z * (u \ 1))) * y)
    ]]></literal>
    <justification jstring="[para(11447(a,1),15684(a,1,1))].">
      <j1 rule="para" parents="11447 15684"/>
    </justification>
  </clause>

  <clause id="15916">
    <literal><![CDATA[
      K(x,y) \ K(L(x,z,u),y) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,13939,a(flip),b,15699,a),flip(a)].">
      <j1 rule="hyper" parents="63 13939 15699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15917">
    <literal><![CDATA[
      K(x,y) * K(a(z,u,y),x) = K(L(x,u,z),y)
    ]]></literal>
    <justification jstring="[hyper(126,a,13790,a(flip),b,15916,a)].">
      <j1 rule="hyper" parents="126 13790 15916"/>
    </justification>
  </clause>

  <clause id="15918">
    <literal><![CDATA[
      T(x,y) / T(x,a(z,u,y)) = K(L(x,u,z),y)
    ]]></literal>
    <justification jstring="[hyper(5505,a,15917,a)].">
      <j1 rule="hyper" parents="5505 15917"/>
    </justification>
  </clause>

  <clause id="15919">
    <literal><![CDATA[
      T(x,y) / (a(x,z,K(u,y)) \ x) = K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(13818(a,2),15918(a,1,2))].">
      <j1 rule="para" parents="13818 15918"/>
    </justification>
  </clause>

  <clause id="15920">
    <literal><![CDATA[
      T(x,y) / (a(K(x,y),z,u) \ x) = K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(13729(a,2),15919(a,1,2,1))].">
      <j1 rule="para" parents="13729 15919"/>
    </justification>
  </clause>

  <clause id="15921">
    <literal><![CDATA[
      K(x,L(y,z,u)) * T(y,x) = a(K(y,x),z,u) \ y
    ]]></literal>
    <justification jstring="[hyper(36,a,4569,a,b,15920,a)].">
      <j1 rule="hyper" parents="36 4569 15920"/>
    </justification>
  </clause>

  <clause id="15922">
    <literal><![CDATA[
      T(K(x,L(y,z,u)) * y,x) = a(K(y,x),z,u) \ y
    ]]></literal>
    <justification jstring="[hyper(63,a,6627,a,b,15921,a)].">
      <j1 rule="hyper" parents="63 6627 15921"/>
    </justification>
  </clause>

  <clause id="15923">
    <literal><![CDATA[
      T(x * K(y,L(x,z,u)),y) = a(K(x,y),z,u) \ x
    ]]></literal>
    <justification jstring="[para(2740(a,1),15922(a,1,1))].">
      <j1 rule="para" parents="2740 15922"/>
    </justification>
  </clause>

  <clause id="15924">
    <literal><![CDATA[
      T(x * K(y,L(x,z,u)),y) = a(x,z,K(u,y)) \ x
    ]]></literal>
    <justification jstring="[para(13729(a,1),15923(a,2,1))].">
      <j1 rule="para" parents="13729 15923"/>
    </justification>
  </clause>

  <clause id="15925">
    <literal><![CDATA[
      T(x * K(y,L(x,z,u)),y) = T(x,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(333,a,13818,a(flip),b,15924,a),flip(a)].">
      <j1 rule="hyper" parents="333 13818 15924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15926">
    <literal><![CDATA[
      L(x,y,K(z,u)) = T(x,a(z,y,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,14550,a(flip),b,15925,a)].">
      <j1 rule="hyper" parents="63 14550 15925"/>
    </justification>
  </clause>

  <clause id="15927">
    <literal><![CDATA[
      L(x,y,K(z,u)) = L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(333,a,14461,a,b,15926,a)].">
      <j1 rule="hyper" parents="333 14461 15926"/>
    </justification>
  </clause>

  <clause id="15929">
    <literal><![CDATA[
      T(T(x,a(y,z,u)),a(y,z,u)) = x
    ]]></literal>
    <justification jstring="[para(15926(a,1),14492(a,1,1))].">
      <j1 rule="para" parents="15926 14492"/>
    </justification>
  </clause>

  <clause id="15930">
    <literal><![CDATA[
      L(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(15926(a,2),14528(a,1))].">
      <j1 rule="para" parents="15926 14528"/>
    </justification>
  </clause>

  <clause id="15931">
    <literal><![CDATA[
      L(T(x,y),z,K(y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(15926(a,2),14537(a,1))].">
      <j1 rule="para" parents="15926 14537"/>
    </justification>
  </clause>

  <clause id="15933">
    <literal><![CDATA[
      (x * a(y,z,u)) / x = T(a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(197,a,15929,a(flip),b,3800,a)].">
      <j1 rule="hyper" parents="197 15929 3800"/>
    </justification>
  </clause>

  <clause id="15934">
    <literal><![CDATA[
      T(T(a(x,y,z),u),u) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(15933(a,1),238(a,1,1))].">
      <j1 rule="para" parents="15933 238"/>
    </justification>
  </clause>

  <clause id="15935">
    <literal><![CDATA[
      (x * a(y,z,u)) / T(a(y,z,u),w) = x * K(a(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(15933(a,1),7662(a,1,2))].">
      <j1 rule="para" parents="15933 7662"/>
    </justification>
  </clause>

  <clause id="15936">
    <literal><![CDATA[
      R(T(a(x,y,z),u * u),u,u) = L(a(x,y,z),u,u)
    ]]></literal>
    <justification jstring="[para(15934(a,1),13008(a,2,1))].">
      <j1 rule="para" parents="15934 13008"/>
    </justification>
  </clause>

  <clause id="15937">
    <literal><![CDATA[
      T(x,a(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z,K(y,u)) = w
    ]]></literal>
    <justification jstring="[para(14461(a,1),15930(a,1))].">
      <j1 rule="para" parents="14461 15930"/>
    </justification>
  </clause>

  <clause id="15938">
    <literal><![CDATA[
      T(x * K(y,L(x,z,u)),y) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z,K(u,y)) = w
    ]]></literal>
    <justification jstring="[para(15925(a,2),15937(a,1))].">
      <j1 rule="para" parents="15925 15937"/>
    </justification>
  </clause>

  <clause id="15939">
    <literal><![CDATA[
      R(a(x,y,z),u,u) = L(a(x,y,z),u,u)
    ]]></literal>
    <justification jstring="[para(14117(a,1),15936(a,1,1))].">
      <j1 rule="para" parents="14117 15936"/>
    </justification>
  </clause>

  <clause id="15941">
    <literal><![CDATA[
      L(a(x,y,z),1 / u,1 / u) = R(a(x,y,z),u,u)
    ]]></literal>
    <justification jstring="[hyper(1939,a,15939,a),flip(a)].">
      <j1 rule="hyper" parents="1939 15939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15943">
    <literal><![CDATA[
      L(a(x,y,z),1 / u,1 / u) = L(a(x,y,z),u,u)
    ]]></literal>
    <justification jstring="[hyper(333,a,15939,a(flip),b,15941,a),flip(a)].">
      <j1 rule="hyper" parents="333 15939 15941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15944">
    <literal><![CDATA[
      L(a(x,y,z),u,u \ 1) = L(a(x,y,z),u,u)
    ]]></literal>
    <justification jstring="[hyper(3149,a,15943,a)].">
      <j1 rule="hyper" parents="3149 15943"/>
    </justification>
  </clause>

  <clause id="15945">
    <literal><![CDATA[
      L(a(x,y,z),x,x) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,14673,a(flip),b,15944,a),flip(a)].">
      <j1 rule="hyper" parents="63 14673 15944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15946">
    <literal><![CDATA[
      (x \ 1) * a(x,y,z) = x \ a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(121,a,15945,a(flip),b,2599,a),flip(a)].">
      <j1 rule="hyper" parents="121 15945 2599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15947">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * (a(x,y,z) \ a(x,y,z)) = L(a(x,y,z) \ 1,x,x)
    ]]></literal>
    <justification jstring="[para(15945(a,1),2588(a,1,2,2))].">
      <j1 rule="para" parents="15945 2588"/>
    </justification>
  </clause>

  <clause id="15948">
    <literal><![CDATA[
      a(x,y,z) * (x \ 1) = x \ a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,12437,a,b,15946,a)].">
      <j1 rule="hyper" parents="63 12437 15946"/>
    </justification>
  </clause>

  <clause id="15949">
    <literal><![CDATA[
      T(x,K(y,z * (x * u))) = T(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(7258,a,15726,a),flip(a)].">
      <j1 rule="hyper" parents="7258 15726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15950">
    <literal><![CDATA[
      T(x,K(y,z * (y * u))) = T(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(7258,a,15727,a),flip(a)].">
      <j1 rule="hyper" parents="7258 15727"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15951">
    <literal><![CDATA[
      T(L(K(x,y),z \ u,z),u / z) = u \ (z * (K(x,y) * (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(333,a,838,a(flip),b,15735,a),flip(a)].">
      <j1 rule="hyper" parents="333 838 15735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15952">
    <literal><![CDATA[
      T(x,K(y,z)) * (T(x,u) \ w) = x * (T(T(x,u),K(y,z)) \ w)
    ]]></literal>
    <justification jstring="[para(15747(a,1),15476(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15747 15476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15953">
    <literal><![CDATA[
      K(x,T(y,z \ u)) \ (w * (u / z)) = K(x,y) \ (w * T(u / z,K(x,y)))
    ]]></literal>
    <justification jstring="[para(15444(a,1),15751(a,1,1))].">
      <j1 rule="para" parents="15444 15751"/>
    </justification>
  </clause>

  <clause id="15954">
    <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(63,a,15293,a,b,15765,a)].">
      <j1 rule="hyper" parents="63 15293 15765"/>
    </justification>
  </clause>

  <clause id="15955">
    <literal><![CDATA[
      K(K(x \ 1,y) \ z,u) = K(K(x * y,y) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(12942,a,15800,a),flip(a)].">
      <j1 rule="hyper" parents="12942 15800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15956">
    <literal><![CDATA[
      T(T(x,K(y,z * (z / (u \ 1)))),y / (z \ (z / (u \ 1)))) = T(x,L(u,u,z) \ y)
    ]]></literal>
    <justification jstring="[para(2875(a,2),15814(a,2,2,1))].">
      <j1 rule="para" parents="2875 15814"/>
    </justification>
  </clause>

  <clause id="15957">
    <literal><![CDATA[
      T(T(x,K(y,T(z,u))),y * (u \ (z / u))) = T(x,(u \ (z / u)) * y)
    ]]></literal>
    <justification jstring="[para(12249(a,1),15815(a,1,1,2))].">
      <j1 rule="para" parents="12249 15815"/>
    </justification>
  </clause>

  <clause id="15958">
    <literal><![CDATA[
      T(T(x,y),z \ (z \ 1)) = T(x,z \ ((z \ 1) * y))
    ]]></literal>
    <justification jstring="[hyper(13608,a,15828,a),flip(a)].">
      <j1 rule="hyper" parents="13608 15828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15959">
    <literal><![CDATA[
      T(T(x,y),z \ (z \ 1)) = T(x,(z * z) \ y)
    ]]></literal>
    <justification jstring="[para(712(a,1),15958(a,2,2))].">
      <j1 rule="para" parents="712 15958"/>
    </justification>
  </clause>

  <clause id="15960">
    <literal><![CDATA[
      T(T(x,y),z \ (z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ (z \ y)) = u
    ]]></literal>
    <justification jstring="[para(15959(a,2),13259(a,1))].">
      <j1 rule="para" parents="15959 13259"/>
    </justification>
  </clause>

  <clause id="15961">
    <literal><![CDATA[
      T(T(x,y \ (y \ 1)),z) = T(x,y \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(15960,a,23,a),flip(a)].">
      <j1 rule="hyper" parents="15960 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15962">
    <literal><![CDATA[
      T(T(x,y \ (y \ 1)),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ (y \ z)) = u
    ]]></literal>
    <justification jstring="[para(23(a,1),15960(a,1))].">
      <j1 rule="para" parents="23 15960"/>
    </justification>
  </clause>

  <clause id="15963">
    <literal><![CDATA[
      T(x,y \ (y \ 1)) = T(x,y \ (y \ x))
    ]]></literal>
    <justification jstring="[hyper(836,a,15961,a)].">
      <j1 rule="hyper" parents="836 15961"/>
    </justification>
  </clause>

  <clause id="15964">
    <literal><![CDATA[
      T(T(T(x,y),z),u \ (u \ 1)) = T(T(x,u \ (u \ y)),z)
    ]]></literal>
    <justification jstring="[para(15961(a,1),116(a,2,1))].">
      <j1 rule="para" parents="15961 116"/>
    </justification>
  </clause>

  <clause id="15965">
    <literal><![CDATA[
      T(x,x \ (x \ y)) = T(R(x,x,x),y)
    ]]></literal>
    <justification jstring="[para(997(a,1),15961(a,1,1)),flip(a)].">
      <j1 rule="para" parents="997 15961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15966">
    <literal><![CDATA[
      T(x,x \ (x \ y)) = R(T(x,y),x,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,27,a,b,15965,a),flip(a)].">
      <j1 rule="hyper" parents="333 27 15965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15967">
    <literal><![CDATA[
      R(T(x,x * y),x,x) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(10377,a,15966,a),flip(a)].">
      <j1 rule="hyper" parents="10377 15966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15968">
    <literal><![CDATA[
      R(T(x,y),x,x) \ y = (x \ (x \ y)) * x
    ]]></literal>
    <justification jstring="[para(15966(a,1),3713(a,1,1))].">
      <j1 rule="para" parents="15966 3713"/>
    </justification>
  </clause>

  <clause id="15969">
    <literal><![CDATA[
      L(T(x,x \ y),x,x) = T(x,x * y)
    ]]></literal>
    <justification jstring="[para(15967(a,1),3753(a,1,1))].">
      <j1 rule="para" parents="15967 3753"/>
    </justification>
  </clause>

  <clause id="15970">
    <literal><![CDATA[
      L(x,x,x) * (x \ y) = (x \ y) * T(x,x * y)
    ]]></literal>
    <justification jstring="[para(15969(a,1),251(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15969 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15971">
    <literal><![CDATA[
      (x \ y) * T(x,x * y) = a(x,x,x) \ y
    ]]></literal>
    <justification jstring="[hyper(9285,a,15970,a),flip(a)].">
      <j1 rule="hyper" parents="9285 15970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15972">
    <literal><![CDATA[
      T(x,x * y) * ((x \ y) * x) = x * (a(x,x,x) \ y)
    ]]></literal>
    <justification jstring="[para(15971(a,1),12985(a,2,2))].">
      <j1 rule="para" parents="15971 12985"/>
    </justification>
  </clause>

  <clause id="15973">
    <literal><![CDATA[
      T(x,x * y) * ((x \ y) * x) = L(x,x,x) * y
    ]]></literal>
    <justification jstring="[hyper(333,a,9272,a(flip),b,15972,a),flip(a)].">
      <j1 rule="hyper" parents="333 9272 15972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15974">
    <literal><![CDATA[
      T(L(x,x,x) * y,x) = x * ((x \ y) * x)
    ]]></literal>
    <justification jstring="[para(15973(a,1),7474(a,1,1))].">
      <j1 rule="para" parents="15973 7474"/>
    </justification>
  </clause>

  <clause id="15975">
    <literal><![CDATA[
      x * ((x \ (x \ y)) * x) = T(a(x,x,x) \ y,x)
    ]]></literal>
    <justification jstring="[para(9273(a,1),15974(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9273 15974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15976">
    <literal><![CDATA[
      T(a(x,x,x) \ y,x) / x = (x \ (y / x)) * x
    ]]></literal>
    <justification jstring="[hyper(123,a,15975,a(flip),b,4132,a)].">
      <j1 rule="hyper" parents="123 15975 4132"/>
    </justification>
  </clause>

  <clause id="15977">
    <literal><![CDATA[
      a(x,x,x) \ (T(y,x) / x) = (x \ (y / x)) * x
    ]]></literal>
    <justification jstring="[hyper(63,a,12604,a(flip),b,15976,a)].">
      <j1 rule="hyper" parents="63 12604 15976"/>
    </justification>
  </clause>

  <clause id="15978">
    <literal><![CDATA[
      T(x,y) / R(y,y,y) = (y \ (x / y)) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,9315,a(flip),b,15977,a)].">
      <j1 rule="hyper" parents="63 9315 15977"/>
    </justification>
  </clause>

  <clause id="15979">
    <literal><![CDATA[
      K(x,K(y,z * u)) * K(y,T(T(u * z,u),w) * x) = K(y,x * T(T(u * z,u),w))
    ]]></literal>
    <justification jstring="[para(12229(a,1),15865(a,1,1,2))].">
      <j1 rule="para" parents="12229 15865"/>
    </justification>
  </clause>

  <clause id="15980">
    <literal><![CDATA[
      K(x,K(y,z * u)) * K(y,T(T(u,z) * z,w) * x) = K(y,x * T(T(u,z) * z,w))
    ]]></literal>
    <justification jstring="[para(12267(a,1),15865(a,1,1,2))].">
      <j1 rule="para" parents="12267 15865"/>
    </justification>
  </clause>

  <clause id="15981">
    <literal><![CDATA[
      K(x,K(y,z)) \ (x * (T(u,w) / x)) = T(T(x,K(y,z)) * (u / x),w)
    ]]></literal>
    <justification jstring="[para(4083(a,1),15871(a,1,2))].">
      <j1 rule="para" parents="4083 15871"/>
    </justification>
  </clause>

  <clause id="15982">
    <literal><![CDATA[
      K((x * ((y * z) * z)) * K(z,y * z),u) = K((z * (y * z)) * x,T(u,y))
    ]]></literal>
    <justification jstring="[para(10341(a,2),15884(a,2,1)),flip(a)].">
      <j1 rule="para" parents="10341 15884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15983">
    <literal><![CDATA[
      K(x,L(T(y,z \ 1),u,w)) = K(x,L(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(8(a,1),15886(a,2,2,1,2))].">
      <j1 rule="para" parents="8 15886"/>
    </justification>
  </clause>

  <clause id="15984">
    <literal><![CDATA[
      K(x,L(T(y / ((z * u) \ z),u),w,v5)) = K(x,L(((z * u) \ z) \ y,w,v5))
    ]]></literal>
    <justification jstring="[para(5825(a,1),15983(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5825 15983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15985">
    <literal><![CDATA[
      T(x / T(y,K(z,u)),K(z,u) \ y) = y \ T(x,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(15594,a,15899,a)].">
      <j1 rule="hyper" parents="15594 15899"/>
    </justification>
  </clause>

  <clause id="15986">
    <literal><![CDATA[
      T((x / y) * K(y,K(z,u)),y * K(u,z)) = y \ T(x,K(z,u))
    ]]></literal>
    <justification jstring="[para(6828(a,2),15899(a,1,1))].">
      <j1 rule="para" parents="6828 15899"/>
    </justification>
  </clause>

  <clause id="15987">
    <literal><![CDATA[
      T(x * T(y,K(z,u) \ x),K(z,u)) = y * T(x,K(z,u))
    ]]></literal>
    <justification jstring="[para(15665(a,2),15900(a,1,1,2))].">
      <j1 rule="para" parents="15665 15900"/>
    </justification>
  </clause>

  <clause id="15988">
    <literal><![CDATA[
      T(T(x,y \ (y \ z)),u) = T(T(x,z),y \ (y \ u))
    ]]></literal>
    <justification jstring="[hyper(15960,a,15964,a),flip(a)].">
      <j1 rule="hyper" parents="15960 15964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15989">
    <literal><![CDATA[
      T(T(x,y * z),y \ (y \ u)) = T(T(x,y \ z),u)
    ]]></literal>
    <justification jstring="[para(9(a,1),15988(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 15988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15990">
    <literal><![CDATA[
      T(T(x,y * z),y \ T(u,y)) = T(T(x,y \ z),u * y)
    ]]></literal>
    <justification jstring="[para(22(a,2),15989(a,1,2,2))].">
      <j1 rule="para" parents="22 15989"/>
    </justification>
  </clause>

  <clause id="15991">
    <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(6072(a,2),15985(a,1,1))].">
      <j1 rule="para" parents="6072 15985"/>
    </justification>
  </clause>

  <clause id="15992">
    <literal><![CDATA[
      T(T(x,y \ z),u * y) = T(T(x,y * z),u / y)
    ]]></literal>
    <justification jstring="[hyper(63,a,12733,a(flip),b,15990,a),flip(a)].">
      <j1 rule="hyper" parents="63 12733 15990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15993">
    <literal><![CDATA[
      K(x,K(y,L(z / u,u,w))) = K(x,K(y,(w * z) / (w * u)))
    ]]></literal>
    <justification jstring="[hyper(333,a,15554,a,b,15569,a),flip(a)].">
      <j1 rule="hyper" parents="333 15554 15569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15994">
    <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(15591,a,12271,a),flip(a)].">
      <j1 rule="hyper" parents="15591 12271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15995">
    <literal><![CDATA[
      K(x,T(y,z)) \ K(z,u) = z \ (K(x,y) \ T(z,u))
    ]]></literal>
    <justification jstring="[hyper(15646,a,15728,a)].">
      <j1 rule="hyper" parents="15646 15728"/>
    </justification>
  </clause>

  <clause id="15996">
    <literal><![CDATA[
      x \ (K(y,z) \ T(x,x \ z)) = (x * (T(z,y) / x)) / z
    ]]></literal>
    <justification jstring="[hyper(63,a,13712,a(flip),b,15995,a),flip(a)].">
      <j1 rule="hyper" parents="63 13712 15995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15997">
    <literal><![CDATA[
      (x * (T(y,z) / x)) / y = y \ (x * (T(y,z) / x))
    ]]></literal>
    <justification jstring="[hyper(63,a,15842,a(flip),b,15996,a),flip(a)].">
      <j1 rule="hyper" parents="63 15842 15996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15998">
    <literal><![CDATA[
      K(x,K((y \ z) / u,L(w,u,y))) = K(x,K(w,z / (y * u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,15555,a,b,15682,a)].">
      <j1 rule="hyper" parents="63 15555 15682"/>
    </justification>
  </clause>

  <clause id="15999">
    <literal><![CDATA[
      T(x,y * (z * (u * (K(w,v5) * K(w,v5))))) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,y * (z * u)) = v6
    ]]></literal>
    <justification jstring="[para(33(a,1),15788(a,1,2,2))].">
      <j1 rule="para" parents="33 15788"/>
    </justification>
  </clause>

  <clause id="16000">
    <literal><![CDATA[
      (K(x,y) * (z \ x)) * K(y,K(x,z)) = z \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(15792,a,13360,a)].">
      <j1 rule="hyper" parents="15792 13360"/>
    </justification>
  </clause>

  <clause id="16001">
    <literal><![CDATA[
      T(x,K(y,z)) \ T(z,y) = K(z,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(35,a,15697,a,b,16000,a)].">
      <j1 rule="hyper" parents="35 15697 16000"/>
    </justification>
  </clause>

  <clause id="16002">
    <literal><![CDATA[
      ((K(x,y) * z) / K(x,y)) \ T(y,x) = K(y,x) * (z \ y)
    ]]></literal>
    <justification jstring="[para(6862(a,2),16001(a,1,1))].">
      <j1 rule="para" parents="6862 16001"/>
    </justification>
  </clause>

  <clause id="16003">
    <literal><![CDATA[
      (x * K(y,z)) \ z = K(z,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,13708,a(flip),b,16002,a)].">
      <j1 rule="hyper" parents="63 13708 16002"/>
    </justification>
  </clause>

  <clause id="16004">
    <literal><![CDATA[
      K(x,y) * ((z \ T(x,y)) \ x) = (z \ x) \ x
    ]]></literal>
    <justification jstring="[para(13254(a,1),16003(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13254 16003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16005">
    <literal><![CDATA[
      K(x,y) * ((z \ y) \ y) = (z \ T(y,x)) \ y
    ]]></literal>
    <justification jstring="[hyper(4577,a,16004,a)].">
      <j1 rule="hyper" parents="4577 16004"/>
    </justification>
  </clause>

  <clause id="16006">
    <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(6788(a,1),15857(a,1,1))].">
      <j1 rule="para" parents="6788 15857"/>
    </justification>
  </clause>

  <clause id="16007">
    <literal><![CDATA[
      x * K(a(y,z,u),w) = x * K(w,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(5457,a,15935,a),flip(a)].">
      <j1 rule="hyper" parents="5457 15935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16008">
    <literal><![CDATA[
      x * a(y,z,K(u,w)) = x * K(a(w,z,u),y)
    ]]></literal>
    <justification jstring="[para(13732(a,2),16007(a,2,2)),flip(a)].">
      <j1 rule="para" parents="13732 16007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16009">
    <literal><![CDATA[
      x * a(y,z,K(u,w)) = x * a(w,z,K(u,y))
    ]]></literal>
    <justification jstring="[para(13539(a,2),16008(a,2,2))].">
      <j1 rule="para" parents="13539 16008"/>
    </justification>
  </clause>

  <clause id="16010">
    <literal><![CDATA[
      a(x,y,K(z,u)) = a(z,y,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(13846,a,16009,a)].">
      <j1 rule="hyper" parents="13846 16009"/>
    </justification>
  </clause>

  <clause id="16013">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(16009(a,1),10933(a,1))].">
      <j1 rule="para" parents="16009 10933"/>
    </justification>
  </clause>

  <clause id="16014">
    <literal><![CDATA[
      K(x,K(y,(z * (u * w)) / (z * w))) = K(x,K(y,L(u,w,z)))
    ]]></literal>
    <justification jstring="[para(11(a,1),15993(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="11 15993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16015">
    <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(22(a,2),15998(a,1,2,1,1))].">
      <j1 rule="para" parents="22 15998"/>
    </justification>
  </clause>

  <clause id="16016">
    <literal><![CDATA[
      T(x * T(x \ y,T(z,y)),x) = T(y,x) * K(y / T(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(333,a,1394,a,b,15461,a)].">
      <j1 rule="hyper" parents="333 1394 15461"/>
    </justification>
  </clause>

  <clause id="16018">
    <literal><![CDATA[
      K((x * y) / (K(z,u) * y),w) = K((y * K(z,u)) \ (y * x),w)
    ]]></literal>
    <justification jstring="[para(9(a,1),15520(a,1,1,1,1))].">
      <j1 rule="para" parents="9 15520"/>
    </justification>
  </clause>

  <clause id="16020">
    <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(15741(a,1),15061(a,1,2,2))].">
      <j1 rule="para" parents="15741 15061"/>
    </justification>
  </clause>

  <clause id="16021">
    <literal><![CDATA[
      T(T(x,K(y,T(z,u * u))),y * (L(z,u,u) * (u * u))) = T(x,(u * (u * T(z,u * u))) * y)
    ]]></literal>
    <justification jstring="[para(664(a,1),15821(a,1,2,2))].">
      <j1 rule="para" parents="664 15821"/>
    </justification>
  </clause>

  <clause id="16022">
    <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(15843(a,1),14918(a,1,1,2,1))].">
      <j1 rule="para" parents="15843 14918"/>
    </justification>
  </clause>

  <clause id="16023">
    <literal><![CDATA[
      (T(x,K(y,L(z,u,w)) * v5) * K(y,L(T(z,x),u,w))) / (K(y,L(z,u,w)) * x) = K(x,v5 * K(y,L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(123,a,15845,a,b,12243,a)].">
      <j1 rule="hyper" parents="123 15845 12243"/>
    </justification>
  </clause>

  <clause id="16024">
    <literal><![CDATA[
      T(x,(y \ (1 / y)) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ (y \ z)) = u
    ]]></literal>
    <justification jstring="[para(15852(a,1),5458(a,1))].">
      <j1 rule="para" parents="15852 5458"/>
    </justification>
  </clause>

  <clause id="16025">
    <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(15624(a,1),15855(a,1,1,1))].">
      <j1 rule="para" parents="15624 15855"/>
    </justification>
  </clause>

  <clause id="16026">
    <literal><![CDATA[
      T(x,y * ((z * z) \ (u * w))) = T(x,y * (u * ((z * z) \ w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,15892,a,b,15893,a)].">
      <j1 rule="hyper" parents="63 15892 15893"/>
    </justification>
  </clause>

  <clause id="16027">
    <literal><![CDATA[
      K(x,y * (z * (u / z))) = K(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[hyper(333,a,5983,a(flip),b,15907,a),flip(a)].">
      <j1 rule="hyper" parents="333 5983 15907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16028">
    <literal><![CDATA[
      K(x,y * (z * ((z * u) / z))) = K(x,y * (u * z))
    ]]></literal>
    <justification jstring="[hyper(333,a,12678,a(flip),b,16027,a),flip(a)].">
      <j1 rule="hyper" parents="333 12678 16027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16029">
    <literal><![CDATA[
      K(x,y * T(z * u,u)) = K(x,y * (u * z))
    ]]></literal>
    <justification jstring="[para(11(a,1),16027(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="11 16027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16030">
    <literal><![CDATA[
      K(x,y * (z * (T(u,w) / z))) = K(x,y * T(T(u,z),w))
    ]]></literal>
    <justification jstring="[para(23(a,1),16027(a,2,2,2))].">
      <j1 rule="para" parents="23 16027"/>
    </justification>
  </clause>

  <clause id="16031">
    <literal><![CDATA[
      K(x * (y * (z / y)),u) = (w * K(u,x * T(z,y))) \ w
    ]]></literal>
    <justification jstring="[para(16027(a,1),5990(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="16027 5990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16032">
    <literal><![CDATA[
      K(x,y * L(z / u,u,u \ 1)) = K(x,y * (z * (1 / u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,15292,a(flip),b,16029,a)].">
      <j1 rule="hyper" parents="63 15292 16029"/>
    </justification>
  </clause>

  <clause id="16033">
    <literal><![CDATA[
      K(x,y * T(T(z / u,T(w,u)) * v5,K(u \ z,w) * v5)) = K(x,y * ((K(u \ z,w) * v5) * (z / u)))
    ]]></literal>
    <justification jstring="[para(6513(a,1),16029(a,1,2,2,1))].">
      <j1 rule="para" parents="6513 16029"/>
    </justification>
  </clause>

  <clause id="16034">
    <literal><![CDATA[
      K(x,y * (T(z,u) * u)) = K(x,y * (u * z))
    ]]></literal>
    <justification jstring="[para(239(a,1),16028(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="239 16028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16035">
    <literal><![CDATA[
      K(x,T((y * z) * u,y * z)) = K(x,u * (T(z,y) * y))
    ]]></literal>
    <justification jstring="[hyper(333,a,12229,a,b,16034,a)].">
      <j1 rule="hyper" parents="333 12229 16034"/>
    </justification>
  </clause>

  <clause id="16036">
    <literal><![CDATA[
      T(x,y * (T(z,u) * u)) = T(x,y * (u * z))
    ]]></literal>
    <justification jstring="[hyper(124,a,16034,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 16034 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16037">
    <literal><![CDATA[
      K(x,y * (T(z,T(u,w * v5)) * T(u,w \ v5))) = K(x,y * (T(u,w \ v5) * z))
    ]]></literal>
    <justification jstring="[para(15399(a,1),16034(a,1,2,2,1))].">
      <j1 rule="para" parents="15399 16034"/>
    </justification>
  </clause>

  <clause id="16038">
    <literal><![CDATA[
      T(x,y * T(z * T(u,u \ w),(u \ w) \ w)) = T(x,y * (T(u,w) * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,14438,a,b,16036,a)].">
      <j1 rule="hyper" parents="63 14438 16036"/>
    </justification>
  </clause>

  <clause id="16039">
    <literal><![CDATA[
      T(x,y * (T(z \ u,w) * z)) = T(x,y * (z * T(u / z,w)))
    ]]></literal>
    <justification jstring="[para(259(a,1),16036(a,1,2,2,1))].">
      <j1 rule="para" parents="259 16036"/>
    </justification>
  </clause>

  <clause id="16040">
    <literal><![CDATA[
      T(x,y * (T(z,u / T(w,u)) * (u / T(w,u)))) = T(x,y * (K(u,w) * ((u / w) * z)))
    ]]></literal>
    <justification jstring="[para(11847(a,2),16036(a,2,2,2))].">
      <j1 rule="para" parents="11847 16036"/>
    </justification>
  </clause>

  <clause id="16041">
    <literal><![CDATA[
      K(x,y * T(z * (u / z),w)) = K(x,y * T(T(u,z),w))
    ]]></literal>
    <justification jstring="[para(4083(a,2),16030(a,1,2,2))].">
      <j1 rule="para" parents="4083 16030"/>
    </justification>
  </clause>

  <clause id="16042">
    <literal><![CDATA[
      K(x * (y * (z / y)),u) = K(x * T(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(333,a,5990,a(flip),b,16031,a),flip(a)].">
      <j1 rule="hyper" parents="333 5990 16031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16043">
    <literal><![CDATA[
      K(x * T(y * z,z),u) = K(x * (z * y),u)
    ]]></literal>
    <justification jstring="[para(11(a,1),16042(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11 16042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16044">
    <literal><![CDATA[
      K(x,y * (T(z,u) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (u * z)) = w
    ]]></literal>
    <justification jstring="[para(16035(a,1),12278(a,1))].">
      <j1 rule="para" parents="16035 12278"/>
    </justification>
  </clause>

  <clause id="16045">
    <literal><![CDATA[
      T(x,y * T(z * (u / z),w)) = T(x,y * T(T(u,z),w))
    ]]></literal>
    <justification jstring="[hyper(124,a,16041,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 16041 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16046">
    <literal><![CDATA[
      K(x,y * L(z / u,u,u \ 1)) = K(x,y * (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[hyper(333,a,4803,a(flip),b,16032,a),flip(a)].">
      <j1 rule="hyper" parents="333 4803 16032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16047">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(u,x) * w) = x * (T(T(x,u),K(y,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(4913,a,15952,a)].">
      <j1 rule="hyper" parents="4913 15952"/>
    </justification>
  </clause>

  <clause id="16048">
    <literal><![CDATA[
      T(x * K(y,K(z,u)),y * K(u,z)) = y \ T(x * y,K(z,u))
    ]]></literal>
    <justification jstring="[para(11(a,1),15986(a,1,1,1))].">
      <j1 rule="para" parents="11 15986"/>
    </justification>
  </clause>

  <clause id="16049">
    <literal><![CDATA[
      T(L(x * K(y,x),z,u) * K(y,K(w,v5)),y * K(v5,w)) = y \ T(y * L(x,z,u),K(w,v5))
    ]]></literal>
    <justification jstring="[para(4426(a,2),15986(a,1,1,1))].">
      <j1 rule="para" parents="4426 15986"/>
    </justification>
  </clause>

  <clause id="16050">
    <literal><![CDATA[
      T(x,y) * K(x / T(y,x),z) = T(x * K(x / y,z),y)
    ]]></literal>
    <justification jstring="[para(6967(a,1),16016(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6967 16016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16051">
    <literal><![CDATA[
      T(x * K(x / y,z),y) = T(x,y) * K(y \ x,z)
    ]]></literal>
    <justification jstring="[para(12620(a,1),16050(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12620 16050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16052">
    <literal><![CDATA[
      T(x * K(x / y,z),y) = K(x / y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,15612,a(flip),b,16051,a),flip(a)].">
      <j1 rule="hyper" parents="333 15612 16051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16053">
    <literal><![CDATA[
      T(x * K(y,K(z,u)),K(z,u) * y) = y \ T(x * y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(15768,a,16048,a)].">
      <j1 rule="hyper" parents="15768 16048"/>
    </justification>
  </clause>

  <clause id="16054">
    <literal><![CDATA[
      T(x,K(K(y,z) * u,w * K(u,K(y,z))) * (v5 / (w * K(u,K(y,z))))) = T(x,v5 / (u \ T(w * u,K(y,z))))
    ]]></literal>
    <justification jstring="[para(16053(a,1),15540(a,2,2,2))].">
      <j1 rule="para" parents="16053 15540"/>
    </justification>
  </clause>

  <clause id="16055">
    <literal><![CDATA[
      K(x,L((y / z) \ K(u,T(T(w,z),v5)),y / z,z)) = K(x,T((z * K(u,T(w,v5))) / y,z \ y))
    ]]></literal>
    <justification jstring="[para(6886(a,1),15614(a,2,2,1,1))].">
      <j1 rule="para" parents="6886 15614"/>
    </justification>
  </clause>

  <clause id="16056">
    <literal><![CDATA[
      K(K(L(x,y,z),u) * (z * (y * x)),w) = K(z * (y * T(x,u)),T(w,K(v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(15516,a,15658,a)].">
      <j1 rule="hyper" parents="15516 15658"/>
    </justification>
  </clause>

  <clause id="16057">
    <literal><![CDATA[
      T(x,K(y,L((z / u) / w,w,u))) != x * v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,(w * u) \ z)) = v5
    ]]></literal>
    <justification jstring="[para(15669(a,2),43(a,1))].">
      <j1 rule="para" parents="15669 43"/>
    </justification>
  </clause>

  <clause id="16058">
    <literal><![CDATA[
      L(K(x \ y,z),u,x / y) = K(T(1 / (y \ x),K(w,v5)),z)
    ]]></literal>
    <justification jstring="[hyper(333,a,5877,a(flip),b,15774,a)].">
      <j1 rule="hyper" parents="333 5877 15774"/>
    </justification>
  </clause>

  <clause id="16059">
    <literal><![CDATA[
      L(K(x,y),z,u / (u * x)) = K(T(1 / ((u * x) \ u),K(w,v5)),y)
    ]]></literal>
    <justification jstring="[para(9(a,1),16058(a,1,1,1))].">
      <j1 rule="para" parents="9 16058"/>
    </justification>
  </clause>

  <clause id="16060">
    <literal><![CDATA[
      K(x,T(K(y,z) * (u / z),w)) = K(x,T(u / T(z,y),w))
    ]]></literal>
    <justification jstring="[hyper(15775,a,xx),flip(a)].">
      <j1 rule="hyper" parents="15775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16061">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * (u \ (u / z))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(u \ (u / z)) * y) = w
    ]]></literal>
    <justification jstring="[para(15819(a,1),15816(a,1,1))].">
      <j1 rule="para" parents="15819 15816"/>
    </justification>
  </clause>

  <clause id="16062">
    <literal><![CDATA[
      T(x,y * R(T(z,u \ 1),u,u)) = T(x,y * ((u \ 1) * (z * u)))
    ]]></literal>
    <justification jstring="[para(27(a,2),15905(a,1,2,2))].">
      <j1 rule="para" parents="27 15905"/>
    </justification>
  </clause>

  <clause id="16063">
    <literal><![CDATA[
      T(L(K(x,y),z / u,u),z / u) = z \ (u * (K(x,y) * (u \ z)))
    ]]></literal>
    <justification jstring="[para(10083(a,2),15951(a,1,1))].">
      <j1 rule="para" parents="10083 15951"/>
    </justification>
  </clause>

  <clause id="16064">
    <literal><![CDATA[
      L(K(x,y),z,u / (u * x)) = K(1 / ((u * x) \ u),y)
    ]]></literal>
    <justification jstring="[hyper(333,a,15490,a(flip),b,16059,a),flip(a)].">
      <j1 rule="hyper" parents="333 15490 16059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16065">
    <literal><![CDATA[
      L(K(x,y),z,u / (u * x)) = K(u \ (u * x),y)
    ]]></literal>
    <justification jstring="[hyper(333,a,5856,a(flip),b,16064,a),flip(a)].">
      <j1 rule="hyper" parents="333 5856 16064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16066">
    <literal><![CDATA[
      L(K(x,y),z,u / (u * x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,705,a(flip),b,16065,a),flip(a)].">
      <j1 rule="hyper" parents="333 705 16065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16067">
    <literal><![CDATA[
      L(K(x,y),z,u / (u * x)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = w
    ]]></literal>
    <justification jstring="[para(16065(a,2),4614(a,1))].">
      <j1 rule="para" parents="16065 4614"/>
    </justification>
  </clause>

  <clause id="16069">
    <literal><![CDATA[
      K(x,y / (((y / z) / u) * z)) = y \ (z * (K(x,u) * (z \ y)))
    ]]></literal>
    <justification jstring="[hyper(63,a,14110,a(flip),b,16063,a)].">
      <j1 rule="hyper" parents="63 14110 16063"/>
    </justification>
  </clause>

  <clause id="16070">
    <literal><![CDATA[
      K(x,(y / x) / ((((y / x) / y) / z) * y)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,8827,a(flip),b,16069,a),flip(a)].">
      <j1 rule="hyper" parents="333 8827 16069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16071">
    <literal><![CDATA[
      K(x,y / (((((y / x) / y) / z) * y) * x)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,6328,a(flip),b,16070,a)].">
      <j1 rule="hyper" parents="63 6328 16070"/>
    </justification>
  </clause>

  <clause id="16072">
    <literal><![CDATA[
      K(x,1 / ((((y / x) / y) / z) * x)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(9074,a,16071,a)].">
      <j1 rule="hyper" parents="9074 16071"/>
    </justification>
  </clause>

  <clause id="16074">
    <literal><![CDATA[
      K(x,y / (((z / x) / z) * x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,9075,a(flip),b,16072,a)].">
      <j1 rule="hyper" parents="63 9075 16072"/>
    </justification>
  </clause>

  <clause id="16075">
    <literal><![CDATA[
      K(x,y / (x * ((z / x) / z))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(10455,a,16074,a)].">
      <j1 rule="hyper" parents="10455 16074"/>
    </justification>
  </clause>

  <clause id="16076">
    <literal><![CDATA[
      L(K(x,y / x),y,(z / x) / z) = K(x,y * ((z / x) / z))
    ]]></literal>
    <justification jstring="[hyper(13960,a,16075,a)].">
      <j1 rule="hyper" parents="13960 16075"/>
    </justification>
  </clause>

  <clause id="16077">
    <literal><![CDATA[
      L(K(x,y / x),y,z / (z * x)) = K(x,y * ((z / x) / z))
    ]]></literal>
    <justification jstring="[hyper(14178,a,16076,a)].">
      <j1 rule="hyper" parents="14178 16076"/>
    </justification>
  </clause>

  <clause id="16078">
    <literal><![CDATA[
      K(x,y * ((z / x) / z)) = K(x,y / x)
    ]]></literal>
    <justification jstring="[hyper(16067,a,16077,a),flip(a)].">
      <j1 rule="hyper" parents="16067 16077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16080">
    <literal><![CDATA[
      K(x,T(y,K(z,u)) \ T(w * y,K(z,u))) = K(x,T(w,K(u,z) * y))
    ]]></literal>
    <justification jstring="[para(4567(a,1),15417(a,2,2,2))].">
      <j1 rule="para" parents="4567 15417"/>
    </justification>
  </clause>

  <clause id="16081">
    <literal><![CDATA[
      T(x * K(x * K(y,z),u),K(z,y)) = K(z,y) * T(x * K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(333,a,4567,a(flip),b,15542,a),flip(a)].">
      <j1 rule="hyper" parents="333 4567 15542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16084">
    <literal><![CDATA[
      T(x,T(K(y,z) * u,w)) = T(x,T(u * K(z,y),w))
    ]]></literal>
    <justification jstring="[hyper(8028,a,15687,a),flip(a)].">
      <j1 rule="hyper" parents="8028 15687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16085">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(z \ y,u) \ y) = T(x,T(y / z,u) \ y)
    ]]></literal>
    <justification jstring="[para(7147(a,1),15834(a,1,1))].">
      <j1 rule="para" parents="7147 15834"/>
    </justification>
  </clause>

  <clause id="16086">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(y \ z,u) \ z) = T(x,T(z / y,u) \ z)
    ]]></literal>
    <justification jstring="[para(6840(a,1),16085(a,1,1))].">
      <j1 rule="para" parents="6840 16085"/>
    </justification>
  </clause>

  <clause id="16087">
    <literal><![CDATA[
      K(x,T(((y / x) / y) * z,y)) = K(x,T(z * ((y / x) / y),y))
    ]]></literal>
    <justification jstring="[hyper(6983,a,15911,a),flip(a)].">
      <j1 rule="hyper" parents="6983 15911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16088">
    <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(333,a,12355,a(flip),b,15913,a),flip(a)].">
      <j1 rule="hyper" parents="333 12355 15913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16089">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * (u \ (z / u))) = T(x,(u \ (z / u)) * y)
    ]]></literal>
    <justification jstring="[para(15566(a,1),15957(a,1,1))].">
      <j1 rule="para" parents="15566 15957"/>
    </justification>
  </clause>

  <clause id="16091">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * T(z / y,u)) = T(x,y * T(y \ z,u))
    ]]></literal>
    <justification jstring="[para(7025(a,1),15994(a,1,1))].">
      <j1 rule="para" parents="7025 15994"/>
    </justification>
  </clause>

  <clause id="16092">
    <literal><![CDATA[
      T(T(x,K(y,z)),z * T(y / z,u)) = T(x,z * T(z \ y,u))
    ]]></literal>
    <justification jstring="[para(6840(a,1),16091(a,1,1))].">
      <j1 rule="para" parents="6840 16091"/>
    </justification>
  </clause>

  <clause id="16093">
    <literal><![CDATA[
      T(x * K(x * K(y,z),u),K(y,z)) = K(z,y) * T(x * K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(6868,a,16081,a)].">
      <j1 rule="hyper" parents="6868 16081"/>
    </justification>
  </clause>

  <clause id="16094">
    <literal><![CDATA[
      K(x,L(T(y \ z,z * (u / y)),y,y \ u)) = K(x,((u / y) * z) / u)
    ]]></literal>
    <justification jstring="[para(25(a,2),15825(a,1,2))].">
      <j1 rule="para" parents="25 15825"/>
    </justification>
  </clause>

  <clause id="16095">
    <literal><![CDATA[
      K(x,L(T(y \ z,y * (u / z)),y,z \ u)) = K(x,u / ((u / z) * y))
    ]]></literal>
    <justification jstring="[para(25(a,2),15826(a,1,2))].">
      <j1 rule="para" parents="25 15826"/>
    </justification>
  </clause>

  <clause id="16096">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,x,x) = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(209,a,15947,a),flip(a)].">
      <j1 rule="hyper" parents="209 15947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16098">
    <literal><![CDATA[
      a(x,x,L(y,x,x)) = (a(x,x,y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(16096(a,1),14344(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16096 14344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16099">
    <literal><![CDATA[
      a(x,x,L(y,x,x)) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,12441,a(flip),b,16098,a),flip(a)].">
      <j1 rule="hyper" parents="333 12441 16098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16100">
    <literal><![CDATA[
      a(x,x,(x \ 1) \ y) = a(x,x,x * y)
    ]]></literal>
    <justification jstring="[para(2601(a,1),16099(a,1,3)),flip(a)].">
      <j1 rule="para" parents="2601 16099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16101">
    <literal><![CDATA[
      a(x,x,x \ y) = a(x,x,x * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,14333,a(flip),b,16100,a)].">
      <j1 rule="hyper" parents="63 14333 16100"/>
    </justification>
  </clause>

  <clause id="16102">
    <literal><![CDATA[
      (x * y) * a(x,x,x * y) = (x * x) * (x \ y)
    ]]></literal>
    <justification jstring="[para(16101(a,1),749(a,1,2))].">
      <j1 rule="para" parents="16101 749"/>
    </justification>
  </clause>

  <clause id="16103">
    <literal><![CDATA[
      (x * y) * a(x,x,x * y) = (x \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(333,a,708,a(flip),b,16102,a),flip(a)].">
      <j1 rule="hyper" parents="333 708 16102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16104">
    <literal><![CDATA[
      ((x \ 1) * ((x \ 1) \ y)) * a(x \ 1,x \ 1,(x \ 1) * ((x \ 1) \ y)) = x \ ((1 / x) \ y)
    ]]></literal>
    <justification jstring="[hyper(333,a,5145,a(flip),b,16103,a),flip(a)].">
      <j1 rule="hyper" parents="333 5145 16103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16105">
    <literal><![CDATA[
      T(x,y * (z * (u * (K(w,v5) * K(w,v5))))) = T(x,y * (z * u))
    ]]></literal>
    <justification jstring="[hyper(15999,a,xx),flip(a)].">
      <j1 rule="hyper" parents="15999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16106">
    <literal><![CDATA[
      T(x,y * (z * (u * K(w,u)))) = T(x,y * (z * T(u,w)))
    ]]></literal>
    <justification jstring="[para(4250(a,1),16105(a,1,2,2,2))].">
      <j1 rule="para" parents="4250 16105"/>
    </justification>
  </clause>

  <clause id="16107">
    <literal><![CDATA[
      T(x,y * (z * T(u,u \ w))) = T(x,y * (z * (w / (w / u))))
    ]]></literal>
    <justification jstring="[para(4176(a,2),16106(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4176 16106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16108">
    <literal><![CDATA[
      T(x,y * (z * T((u * w) / u,v5))) = T(x,y * (z * T(T(w,v5),u)))
    ]]></literal>
    <justification jstring="[para(4319(a,2),16106(a,1,2,2,2))].">
      <j1 rule="para" parents="4319 16106"/>
    </justification>
  </clause>

  <clause id="16109">
    <literal><![CDATA[
      T(x \ (x \ y),x \ (x \ 1)) = K(x * x,y) * (x \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(63,a,15963,a,b,15421,a)].">
      <j1 rule="hyper" parents="63 15963 15421"/>
    </justification>
  </clause>

  <clause id="16110">
    <literal><![CDATA[
      K(x * x,y) * (x \ (x \ y)) = T((x \ y) / x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(4167,a,16109,a),flip(a)].">
      <j1 rule="hyper" parents="4167 16109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16112">
    <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(14315(a,1),15730(a,1,2))].">
      <j1 rule="para" parents="14315 15730"/>
    </justification>
  </clause>

  <clause id="16113">
    <literal><![CDATA[
      K(K(x,y) * T((y \ x) \ z,K(x,y) * u),u) = K((x / y) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(15659,a,15744,a)].">
      <j1 rule="hyper" parents="15659 15744"/>
    </justification>
  </clause>

  <clause id="16114">
    <literal><![CDATA[
      T(x,K(((y \ z) * y) / (u * y),w)) = x * K(x,K(w,(y * u) \ z))
    ]]></literal>
    <justification jstring="[para(6806(a,1),15750(a,2,2))].">
      <j1 rule="para" parents="6806 15750"/>
    </justification>
  </clause>

  <clause id="16115">
    <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(15806(a,1),15817(a,1,2))].">
      <j1 rule="para" parents="15806 15817"/>
    </justification>
  </clause>

  <clause id="16116">
    <literal><![CDATA[
      K(x \ ((y \ z) \ 1),(y \ z) \ (T(y,u) \ z)) = K(y,K(u,z * x))
    ]]></literal>
    <justification jstring="[hyper(13535,a,15881,a)].">
      <j1 rule="hyper" parents="13535 15881"/>
    </justification>
  </clause>

  <clause id="16117">
    <literal><![CDATA[
      K(x \ ((y \ z) \ 1),K(u,T(y,z))) = K(y,K(u,z * x))
    ]]></literal>
    <justification jstring="[para(7340(a,1),16116(a,1,2))].">
      <j1 rule="para" parents="7340 16116"/>
    </justification>
  </clause>

  <clause id="16118">
    <literal><![CDATA[
      K(x,K(y,T(z \ ((y \ u) \ 1),w))) = K(y,K(x,u * z))
    ]]></literal>
    <justification jstring="[hyper(15724,a,16117,a)].">
      <j1 rule="hyper" parents="15724 16117"/>
    </justification>
  </clause>

  <clause id="16119">
    <literal><![CDATA[
      K(x,K(y,z \ ((x \ u) \ 1))) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(15567,a,16118,a)].">
      <j1 rule="hyper" parents="15567 16118"/>
    </justification>
  </clause>

  <clause id="16121">
    <literal><![CDATA[
      K(x,K(y,z * (x \ u))) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(15787,a,16119,a)].">
      <j1 rule="hyper" parents="15787 16119"/>
    </justification>
  </clause>

  <clause id="16122">
    <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(12199(a,1),15954(a,2,1))].">
      <j1 rule="para" parents="12199 15954"/>
    </justification>
  </clause>

  <clause id="16123">
    <literal><![CDATA[
      K((x * ((y * z) * z)) * K(z,y * z),u) = K(x * (z * (y * z)),u)
    ]]></literal>
    <justification jstring="[hyper(333,a,15884,a(flip),b,15982,a),flip(a)].">
      <j1 rule="hyper" parents="333 15884 15982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16124">
    <literal><![CDATA[
      K((x * ((y * z) * z)) * K(z,z * y),u) = K(x * (z * (y * z)),u)
    ]]></literal>
    <justification jstring="[para(4636(a,1),16123(a,1,1,2))].">
      <j1 rule="para" parents="4636 16123"/>
    </justification>
  </clause>

  <clause id="16125">
    <literal><![CDATA[
      K(K(x,y) * (z * ((y * x) * x)),u) = K(z * (x * (y * x)),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,15655,a(flip),b,16124,a)].">
      <j1 rule="hyper" parents="63 15655 16124"/>
    </justification>
  </clause>

  <clause id="16126">
    <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(5999,a,16025,a),flip(a)].">
      <j1 rule="hyper" parents="5999 16025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16127">
    <literal><![CDATA[
      T(x,y * T(z * T(u,u \ w),T(u,w))) = T(x,y * (T(u,w) * z))
    ]]></literal>
    <justification jstring="[para(6465(a,1),16038(a,1,2,2))].">
      <j1 rule="para" parents="6465 16038"/>
    </justification>
  </clause>

  <clause id="16128">
    <literal><![CDATA[
      T(x,K(y \ z,u) * w) = T(x,K(y * z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(15794,a,16115,a),flip(a)].">
      <j1 rule="hyper" parents="15794 16115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16129">
    <literal><![CDATA[
      T(x,K(y * z,u) * (u * w)) = T(x,T(u,y \ z) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,14924,a(flip),b,16128,a),flip(a)].">
      <j1 rule="hyper" parents="63 14924 16128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16130">
    <literal><![CDATA[
      x / T(x,K(y * z,u) * w) = K(K(y \ z,u) * w,x)
    ]]></literal>
    <justification jstring="[hyper(197,a,16128,a(flip),b,4233,a(flip))].">
      <j1 rule="hyper" parents="197 16128 4233"/>
    </justification>
  </clause>

  <clause id="16131">
    <literal><![CDATA[
      x \ T(x,K(y * z,u) * w) = K(x,K(y \ z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(121,a,16128,a(flip),b,4222,a(flip))].">
      <j1 rule="hyper" parents="121 16128 4222"/>
    </justification>
  </clause>

  <clause id="16132">
    <literal><![CDATA[
      T(x,K(y * z,u) * (u \ w)) = T(x,T(u,y \ z) \ w)
    ]]></literal>
    <justification jstring="[para(4555(a,1),16128(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4555 16128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16133">
    <literal><![CDATA[
      T(x,K((y * z) * y,u) * w) = T(x,K(z \ 1,u) * w)
    ]]></literal>
    <justification jstring="[para(5861(a,1),16128(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5861 16128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16134">
    <literal><![CDATA[
      T(x,K(y * z,u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,w * K(y \ z,u)) = v5
    ]]></literal>
    <justification jstring="[para(16128(a,1),15486(a,1))].">
      <j1 rule="para" parents="16128 15486"/>
    </justification>
  </clause>

  <clause id="16135">
    <literal><![CDATA[
      T(x,K(y * z,y) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(z,y) * u) = w
    ]]></literal>
    <justification jstring="[para(16128(a,1),15882(a,1))].">
      <j1 rule="para" parents="16128 15882"/>
    </justification>
  </clause>

  <clause id="16136">
    <literal><![CDATA[
      T(x,T(y,z \ u) * w) = T(x,T(y,z * u) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,14924,a(flip),b,16129,a),flip(a)].">
      <j1 rule="hyper" parents="63 14924 16129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16137">
    <literal><![CDATA[
      T(x,T(y,z \ 1) * u) = T(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[para(8(a,1),16136(a,2,2,1,2))].">
      <j1 rule="para" parents="8 16136"/>
    </justification>
  </clause>

  <clause id="16139">
    <literal><![CDATA[
      T(x,T((y \ 1) * z,y) * u) = T(x,(z * (y \ 1)) * u)
    ]]></literal>
    <justification jstring="[hyper(12794,a,16137,a),flip(a)].">
      <j1 rule="hyper" parents="12794 16137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16141">
    <literal><![CDATA[
      T(x,T((y \ 1) * z,y) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(z * (y \ 1)) * u) = w
    ]]></literal>
    <justification jstring="[para(16137(a,1),12794(a,1))].">
      <j1 rule="para" parents="16137 12794"/>
    </justification>
  </clause>

  <clause id="16142">
    <literal><![CDATA[
      K(K(x \ y,z) * u,w) = K(K(x * y,z) * u,w)
    ]]></literal>
    <justification jstring="[hyper(4313,a,16130,a),flip(a)].">
      <j1 rule="hyper" parents="4313 16130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16144">
    <literal><![CDATA[
      K(K(x * 1,y) * ((z / (x * z)) \ u),w) = K(T(z / (x * z),y) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,15759,a(flip),b,16142,a),flip(a)].">
      <j1 rule="hyper" parents="63 15759 16142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16145">
    <literal><![CDATA[
      K(K(x * y,z) * (u \ z),w) = K(u \ T(z,x \ y),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,15705,a(flip),b,16142,a),flip(a)].">
      <j1 rule="hyper" parents="63 15705 16142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16146">
    <literal><![CDATA[
      K(K(x * y,z) * (z \ u),w) = K(T(z,x \ y) \ u,w)
    ]]></literal>
    <justification jstring="[para(4555(a,1),16142(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4555 16142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16147">
    <literal><![CDATA[
      K(K(x * y,x) * (y \ z),u) = K((x * (y / x)) \ z,u)
    ]]></literal>
    <justification jstring="[para(10038(a,1),16142(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10038 16142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16148">
    <literal><![CDATA[
      K(x,K(y \ z,u) * w) = K(x,K(y * z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(4306,a,16131,a),flip(a)].">
      <j1 rule="hyper" parents="4306 16131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16149">
    <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(16131(a,1),4306(a,1))].">
      <j1 rule="para" parents="16131 4306"/>
    </justification>
  </clause>

  <clause id="16150">
    <literal><![CDATA[
      K(x,K(y * z,u) * (u \ w)) = K(x,T(u,y \ z) \ w)
    ]]></literal>
    <justification jstring="[para(4555(a,1),16148(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4555 16148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16151">
    <literal><![CDATA[
      K(x,K(y * z,u) * T(w,K(u,y \ z))) = K(x,w * K(y \ z,u))
    ]]></literal>
    <justification jstring="[para(6852(a,1),16148(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6852 16148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16152">
    <literal><![CDATA[
      K(x,K(y * z,L(u,w,v5)) * (w * v5)) = K(x,(K(y \ z,u) * w) * v5)
    ]]></literal>
    <justification jstring="[para(13872(a,1),16148(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13872 16148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16153">
    <literal><![CDATA[
      T(x,T(y,z \ u) \ w) = T(x,T(y,z * u) \ w)
    ]]></literal>
    <justification jstring="[para(4555(a,1),16132(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4555 16132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16154">
    <literal><![CDATA[
      T(x,K((y * z) * y,u) * w) = T(x,K(z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(333,a,15197,a(flip),b,16133,a),flip(a)].">
      <j1 rule="hyper" parents="333 15197 16133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16155">
    <literal><![CDATA[
      T(x,K(y \ z,u) * w) = T(x,K(z * y,u) * w)
    ]]></literal>
    <justification jstring="[para(10(a,1),16154(a,1,2,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 16154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16156">
    <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(16155(a,1),14376(a,1,1,2))].">
      <j1 rule="para" parents="16155 14376"/>
    </justification>
  </clause>

  <clause id="16157">
    <literal><![CDATA[
      T(x,T(L((y \ 1) * z,y \ 1,(y \ 1) \ 1),y) * u) = T(x,(((y \ 1) * ((1 / (y \ 1)) * z)) * (y \ 1)) * u)
    ]]></literal>
    <justification jstring="[para(3137(a,1),16139(a,1,2,1,1))].">
      <j1 rule="para" parents="3137 16139"/>
    </justification>
  </clause>

  <clause id="16158">
    <literal><![CDATA[
      K(x \ T(y,z \ u),w) = K(x \ T(y,z * u),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,15705,a(flip),b,16145,a),flip(a)].">
      <j1 rule="hyper" parents="63 15705 16145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16159">
    <literal><![CDATA[
      K(x \ T(y,z \ 1),u) = K(x \ T(y,z),u)
    ]]></literal>
    <justification jstring="[para(8(a,1),16158(a,2,1,2,2))].">
      <j1 rule="para" parents="8 16158"/>
    </justification>
  </clause>

  <clause id="16161">
    <literal><![CDATA[
      (x * K(y \ T(z,u * w),v5)) \ x = K(v5,y \ T(z,u \ w))
    ]]></literal>
    <justification jstring="[para(16158(a,1),5990(a,1,1,2))].">
      <j1 rule="para" parents="16158 5990"/>
    </justification>
  </clause>

  <clause id="16162">
    <literal><![CDATA[
      K(x \ T(y * z,z),u) = K(x \ T(y * z,y),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,13627,a(flip),b,16159,a),flip(a)].">
      <j1 rule="hyper" parents="63 13627 16159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16163">
    <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(16159(a,1),10860(a,1,2,3))].">
      <j1 rule="para" parents="16159 10860"/>
    </justification>
  </clause>

  <clause id="16164">
    <literal><![CDATA[
      K(x \ T(y * z,z),u) = K(x \ (z * y),u)
    ]]></literal>
    <justification jstring="[hyper(333,a,12672,a(flip),b,16162,a),flip(a)].">
      <j1 rule="hyper" parents="333 12672 16162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16165">
    <literal><![CDATA[
      K(x \ (y * (z / y)),u) = K(x \ T(z,y),u)
    ]]></literal>
    <justification jstring="[para(12(a,1),16164(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12 16164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16166">
    <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(16164(a,1),10860(a,1,2,3))].">
      <j1 rule="para" parents="16164 10860"/>
    </justification>
  </clause>

  <clause id="16167">
    <literal><![CDATA[
      K(x \ T(y * z,y),u) = K(x \ (T(y,z) * z),u)
    ]]></literal>
    <justification jstring="[para(3311(a,2),16165(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3311 16165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16168">
    <literal><![CDATA[
      K((x * (y / x)) / z,u) = K(z,K(y,u)) * K(z \ T(y,x),u)
    ]]></literal>
    <justification jstring="[para(16165(a,1),15571(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16165 15571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16169">
    <literal><![CDATA[
      K(x \ (T(y,z) * z),u) = K(x \ (z * y),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,12672,a(flip),b,16167,a),flip(a)].">
      <j1 rule="hyper" parents="63 12672 16167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16170">
    <literal><![CDATA[
      K(T(x,y \ z) \ u,w) = K(T(x,y * z) \ u,w)
    ]]></literal>
    <justification jstring="[para(4555(a,1),16146(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4555 16146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16172">
    <literal><![CDATA[
      K((x * (y / x)) \ z,u) = K(K(x,y) * (y \ z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,15714,a(flip),b,16147,a),flip(a)].">
      <j1 rule="hyper" parents="63 15714 16147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16173">
    <literal><![CDATA[
      K((x * (y / x)) \ z,u) = K(T(y,x) \ z,u)
    ]]></literal>
    <justification jstring="[para(4555(a,1),16172(a,2,1))].">
      <j1 rule="para" parents="4555 16172"/>
    </justification>
  </clause>

  <clause id="16174">
    <literal><![CDATA[
      K(T(x * y,x) \ z,u) = K((T(x,y) * y) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(11144,a,16173,a),flip(a)].">
      <j1 rule="hyper" parents="11144 16173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16175">
    <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(63,a,14091,a(flip),b,16173,a),flip(a)].">
      <j1 rule="hyper" parents="63 14091 16173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16176">
    <literal><![CDATA[
      K(T(x * y,y) \ z,u) = K((y * x) \ z,u)
    ]]></literal>
    <justification jstring="[para(11(a,1),16173(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="11 16173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16177">
    <literal><![CDATA[
      K(T(x \ y,y) \ z,u) = K((x \ T(y,x \ 1)) \ z,u)
    ]]></literal>
    <justification jstring="[para(3107(a,2),16173(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="3107 16173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16178">
    <literal><![CDATA[
      T(T(x,T(y * z,z) \ u),K((z * y) \ u,w)) = T(x,T(T(y * z,z) \ u,w))
    ]]></literal>
    <justification jstring="[para(16176(a,1),6191(a,1,2))].">
      <j1 rule="para" parents="16176 6191"/>
    </justification>
  </clause>

  <clause id="16179">
    <literal><![CDATA[
      K((T(x,y) * y) \ z,u) = K((y * x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,12617,a(flip),b,16174,a),flip(a)].">
      <j1 rule="hyper" parents="63 12617 16174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16180">
    <literal><![CDATA[
      K(x,T(y,z \ u) \ w) = K(x,T(y,z * u) \ w)
    ]]></literal>
    <justification jstring="[para(4555(a,1),16150(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4555 16150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16181">
    <literal><![CDATA[
      K(x,T(y,z \ 1) \ u) = K(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(8(a,1),16180(a,2,2,1,2))].">
      <j1 rule="para" parents="8 16180"/>
    </justification>
  </clause>

  <clause id="16182">
    <literal><![CDATA[
      K(x,T((1 / y) * z,y) \ u) = K(x,(z * (1 / y)) \ u)
    ]]></literal>
    <justification jstring="[hyper(12875,a,16181,a),flip(a)].">
      <j1 rule="hyper" parents="12875 16181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16183">
    <literal><![CDATA[
      K(x,T((y \ 1) * z,y) \ u) = K(x,(z * (y \ 1)) \ u)
    ]]></literal>
    <justification jstring="[hyper(12873,a,16181,a),flip(a)].">
      <j1 rule="hyper" parents="12873 16181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16184">
    <literal><![CDATA[
      K(x,T(T((y \ 1) \ z,u),y) \ w) = K(x,T(z / (y \ 1),u) \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,14966,a(flip),b,16181,a),flip(a)].">
      <j1 rule="hyper" parents="63 14966 16181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16185">
    <literal><![CDATA[
      K((x \ T(y,x \ 1)) \ z,u) = K((y / x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,15764,a(flip),b,16177,a),flip(a)].">
      <j1 rule="hyper" parents="63 15764 16177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16186">
    <literal><![CDATA[
      K((x / y) \ z,T(u,y)) = K(T(z,x) / (y \ x),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,14645,a(flip),b,16185,a),flip(a)].">
      <j1 rule="hyper" parents="63 14645 16185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16187">
    <literal><![CDATA[
      K(x,T((1 / y) * z,y) \ u) = K(x,(z * (y \ 1)) \ u)
    ]]></literal>
    <justification jstring="[hyper(333,a,5021,a(flip),b,16182,a),flip(a)].">
      <j1 rule="hyper" parents="333 5021 16182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16188">
    <literal><![CDATA[
      K(x,((y \ 1) * (y * z)) \ u) = K(x,((z * y) * (y \ 1)) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,14970,a(flip),b,16183,a)].">
      <j1 rule="hyper" parents="63 14970 16183"/>
    </justification>
  </clause>

  <clause id="16189">
    <literal><![CDATA[
      K(x,((y * z) * (z \ 1)) \ u) = K(x,L(y,z,z \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,15256,a(flip),b,16187,a),flip(a)].">
      <j1 rule="hyper" parents="63 15256 16187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16190">
    <literal><![CDATA[
      K(x,R(y,z,z \ 1) \ u) = K(x,L(y,z,z \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(385(a,1),16189(a,1,2,1))].">
      <j1 rule="para" parents="385 16189"/>
    </justification>
  </clause>

  <clause id="16191">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1) \ u) = K(x,R(y,z,z) \ u)
    ]]></literal>
    <justification jstring="[para(810(a,1),16189(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="810 16189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16192">
    <literal><![CDATA[
      K(x,y * (L(y,z,z \ 1) \ u)) = K(x,R(y,z,z) \ (y * u))
    ]]></literal>
    <justification jstring="[para(1258(a,1),16191(a,1,2))].">
      <j1 rule="para" parents="1258 16191"/>
    </justification>
  </clause>

  <clause id="16193">
    <literal><![CDATA[
      K(x,R(y,1 / z,1 / z) \ u) = K(x,L(y,z \ 1,z) \ u)
    ]]></literal>
    <justification jstring="[para(10101(a,1),16191(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10101 16191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16194">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1) \ (y * u)) = K(x,a(y,z,z \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,14093,a(flip),b,16190,a),flip(a)].">
      <j1 rule="hyper" parents="63 14093 16190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16195">
    <literal><![CDATA[
      K(x,y \ T(z,u \ w)) = K(x,y \ T(z,u * w))
    ]]></literal>
    <justification jstring="[hyper(6024,a,16161,a),flip(a)].">
      <j1 rule="hyper" parents="6024 16161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16196">
    <literal><![CDATA[
      K(x,y \ T(z,u \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ T(z,u * w)) = v5
    ]]></literal>
    <justification jstring="[para(16161(a,1),6024(a,1))].">
      <j1 rule="para" parents="16161 6024"/>
    </justification>
  </clause>

  <clause id="16197">
    <literal><![CDATA[
      K(x,(y \ 1) \ T(z,u * w)) = K(x,y * T(z,u \ w))
    ]]></literal>
    <justification jstring="[hyper(13421,a,16195,a),flip(a)].">
      <j1 rule="hyper" parents="13421 16195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16199">
    <literal><![CDATA[
      K(x,y * T(z,u \ w)) = K(x,y * T(z,u * w))
    ]]></literal>
    <justification jstring="[hyper(13421,a,16197,a),flip(a)].">
      <j1 rule="hyper" parents="13421 16197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16200">
    <literal><![CDATA[
      K(x,y * T(z,u \ 1)) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(8(a,1),16199(a,2,2,2,2))].">
      <j1 rule="para" parents="8 16199"/>
    </justification>
  </clause>

  <clause id="16201">
    <literal><![CDATA[
      K(x,(y \ z) * T(u,y * z)) = K(x,u * (y \ z))
    ]]></literal>
    <justification jstring="[para(111(a,1),16199(a,1,2)),flip(a)].">
      <j1 rule="para" parents="111 16199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16202">
    <literal><![CDATA[
      K(x,y * T(z,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(16199(a,2),12758(a,1))].">
      <j1 rule="para" parents="16199 12758"/>
    </justification>
  </clause>

  <clause id="16203">
    <literal><![CDATA[
      T(x,y * T(z,u \ 1)) = T(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(124,a,16200,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 16200 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16204">
    <literal><![CDATA[
      K(x,y * T((z \ 1) \ u,z)) = K(x,y * (u / (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(63,a,14987,a(flip),b,16200,a),flip(a)].">
      <j1 rule="hyper" parents="63 14987 16200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16205">
    <literal><![CDATA[
      T(x,(y * ((z \ 1) * K(u,z \ 1))) * u) = T(x,(y * (z \ 1)) * T(u,z))
    ]]></literal>
    <justification jstring="[para(6051(a,2),16203(a,1,2))].">
      <j1 rule="para" parents="6051 16203"/>
    </justification>
  </clause>

  <clause id="16206">
    <literal><![CDATA[
      T(x,(y \ z) * T(u,y * z)) = T(x,u * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(124,a,16201,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 16201 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16207">
    <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(63,a,14744,a(flip),b,16201,a)].">
      <j1 rule="hyper" parents="63 14744 16201"/>
    </justification>
  </clause>

  <clause id="16209">
    <literal><![CDATA[
      T(x,(y \ (1 / y)) * T(z * u,y * (1 / y))) = T(x,z * (u * (y \ (1 / y))))
    ]]></literal>
    <justification jstring="[para(553(a,1),16206(a,2,2))].">
      <j1 rule="para" parents="553 16206"/>
    </justification>
  </clause>

  <clause id="16210">
    <literal><![CDATA[
      K(x,y * (z / (z / u))) = K(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[hyper(16202,a,14989,a),flip(a)].">
      <j1 rule="hyper" parents="16202 14989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16211">
    <literal><![CDATA[
      K(x,T(y,z / (z / u)) * T(u,z)) = K(x,(z / (z / u)) * y)
    ]]></literal>
    <justification jstring="[hyper(12284,a,16210,a),flip(a)].">
      <j1 rule="hyper" parents="12284 16210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16212">
    <literal><![CDATA[
      K(x,y * T(z \ u,u)) = K(x,y * (u / z))
    ]]></literal>
    <justification jstring="[para(76(a,1),16210(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="76 16210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16213">
    <literal><![CDATA[
      K(x,L(y * T(z \ u,u),w,v5)) = K(L(x,w,v5),y * (u / z))
    ]]></literal>
    <justification jstring="[hyper(10963,a,16212,a)].">
      <j1 rule="hyper" parents="10963 16212"/>
    </justification>
  </clause>

  <clause id="16214">
    <literal><![CDATA[
      K(x,y * (z \ T((u \ (K(w,v5) * z)) * T(z,K(w,v5)),K(v5,w)))) = K(x,y * ((K(w,v5) * z) / u))
    ]]></literal>
    <justification jstring="[para(14916(a,2),16212(a,1,2,2))].">
      <j1 rule="para" parents="14916 16212"/>
    </justification>
  </clause>

  <clause id="16215">
    <literal><![CDATA[
      K(x,y * ((z \ K(z,u)) \ u)) = K(x,y * (u / (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(63,a,12743,a(flip),b,16204,a)].">
      <j1 rule="hyper" parents="63 12743 16204"/>
    </justification>
  </clause>

  <clause id="16216">
    <literal><![CDATA[
      K((x * (y / x)) / z,u) = K(T(y,x) / z,u)
    ]]></literal>
    <justification jstring="[hyper(333,a,15575,a(flip),b,16168,a),flip(a)].">
      <j1 rule="hyper" parents="333 15575 16168"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16217">
    <literal><![CDATA[
      K(T(x * y,y) / z,u) = K((y * x) / z,u)
    ]]></literal>
    <justification jstring="[para(11(a,1),16216(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="11 16216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16218">
    <literal><![CDATA[
      K(x,T(y * z,z) / u) = (w * K((z * y) / u,x)) \ w
    ]]></literal>
    <justification jstring="[para(16217(a,1),5990(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="16217 5990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16219">
    <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(13583(a,1),16217(a,2,1,1))].">
      <j1 rule="para" parents="13583 16217"/>
    </justification>
  </clause>

  <clause id="16220">
    <literal><![CDATA[
      K(x,T(y * z,z) / u) = K(x,(z * y) / u)
    ]]></literal>
    <justification jstring="[hyper(333,a,5990,a(flip),b,16218,a),flip(a)].">
      <j1 rule="hyper" parents="333 5990 16218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16221">
    <literal><![CDATA[
      K(x,T(y * z,z) / u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z * y) / u) = w
    ]]></literal>
    <justification jstring="[para(16218(a,2),6024(a,1))].">
      <j1 rule="para" parents="16218 6024"/>
    </justification>
  </clause>

  <clause id="16222">
    <literal><![CDATA[
      K(x,(y * (z / y)) / u) = K(x,T(z,y) / u)
    ]]></literal>
    <justification jstring="[para(12(a,1),16220(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="12 16220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16223">
    <literal><![CDATA[
      K(x,(y * ((y * z) / y)) / u) = K(x,(z * y) / u)
    ]]></literal>
    <justification jstring="[hyper(333,a,12674,a(flip),b,16222,a),flip(a)].">
      <j1 rule="hyper" parents="333 12674 16222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16224">
    <literal><![CDATA[
      K(x,T(y,z) / (u * (y / z))) = K(x,y / (u * (z \ y)))
    ]]></literal>
    <justification jstring="[para(14582(a,1),16222(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14582 16222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16225">
    <literal><![CDATA[
      K(x,(T(y,z) * z) / u) = K(x,(z * y) / u)
    ]]></literal>
    <justification jstring="[para(239(a,1),16223(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="239 16223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16226">
    <literal><![CDATA[
      K(x,L(T(y,z) / u,u,z)) = K(x,(z * y) / (u * z))
    ]]></literal>
    <justification jstring="[hyper(13923,a,16225,a)].">
      <j1 rule="hyper" parents="13923 16225"/>
    </justification>
  </clause>

  <clause id="16227">
    <literal><![CDATA[
      T(x,(T(y,z) * z) / u) = T(x,(z * y) / u)
    ]]></literal>
    <justification jstring="[hyper(124,a,16225,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 16225 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16228">
    <literal><![CDATA[
      T(x,(y * z) / T(y,u)) = T(x,K(y,u) \ T(z,y))
    ]]></literal>
    <justification jstring="[hyper(15776,a,16227,a),flip(a)].">
      <j1 rule="hyper" parents="15776 16227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16229">
    <literal><![CDATA[
      T(x,(y * z) / T(y,u)) = T(x,y \ (z * T(y,u)))
    ]]></literal>
    <justification jstring="[hyper(333,a,15711,a(flip),b,16228,a),flip(a)].">
      <j1 rule="hyper" parents="333 15711 16228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16230">
    <literal><![CDATA[
      T(x,y \ ((y \ z) * T(y,u))) = T(x,z / T(y,u))
    ]]></literal>
    <justification jstring="[para(10(a,1),16229(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 16229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16231">
    <literal><![CDATA[
      K(x,x * (y \ ((y \ z) * T(y,u)))) \ T(x,z / T(y,u)) = R(x,y \ ((y \ z) * T(y,u)),x)
    ]]></literal>
    <justification jstring="[para(16230(a,1),4737(a,1,2))].">
      <j1 rule="para" parents="16230 4737"/>
    </justification>
  </clause>

  <clause id="16232">
    <literal><![CDATA[
      K(x,((y \ 1) * (y * z)) \ u) = K(x,R(z,y,y) \ u)
    ]]></literal>
    <justification jstring="[para(810(a,1),16188(a,2,2,1))].">
      <j1 rule="para" parents="810 16188"/>
    </justification>
  </clause>

  <clause id="16233">
    <literal><![CDATA[
      K(x,R(y * z,K(u,L(w,y,z)),K(u,L(w,y,z))) \ v5) = K(x,((K(u,L(w,y,z)) \ 1) * ((K(u,w) * y) * z)) \ v5)
    ]]></literal>
    <justification jstring="[para(13872(a,1),16232(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="13872 16232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16234">
    <literal><![CDATA[
      K(x,R(y,1 / z,1 / z) \ u) = K(x,L(y,z,z) \ u)
    ]]></literal>
    <justification jstring="[para(2596(a,1),16193(a,2,2,1))].">
      <j1 rule="para" parents="2596 16193"/>
    </justification>
  </clause>

  <clause id="16235">
    <literal><![CDATA[
      K(x,R(y,z,z) \ u) = K(x,L(y,z,z) \ u)
    ]]></literal>
    <justification jstring="[para(1938(a,1),16234(a,1,2,1))].">
      <j1 rule="para" parents="1938 16234"/>
    </justification>
  </clause>

  <clause id="16236">
    <literal><![CDATA[
      T(x,R(y,z,z) \ u) = T(x,L(y,z,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(124,a,16235,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 16235 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16237">
    <literal><![CDATA[
      K(x,y * (L(y,z,z \ 1) \ u)) = K(x,L(y,z,z) \ (y * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,16192,a,b,16235,a)].">
      <j1 rule="hyper" parents="63 16192 16235"/>
    </justification>
  </clause>

  <clause id="16238">
    <literal><![CDATA[
      K(x,L(y,z,z) \ (y * u)) = K(x,a(y,z,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,14094,a(flip),b,16235,a),flip(a)].">
      <j1 rule="hyper" parents="63 14094 16235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16239">
    <literal><![CDATA[
      K(x,y) * T(x * K(y,x),L(z,u,u) \ w) = T(x,T(R(z,u,u) \ w,y))
    ]]></literal>
    <justification jstring="[hyper(126,a,16236,a(flip),b,8027,a)].">
      <j1 rule="hyper" parents="126 16236 8027"/>
    </justification>
  </clause>

  <clause id="16240">
    <literal><![CDATA[
      K(x,y * (L(y,z,z) \ u)) = K(x,a(y,z,z) \ u)
    ]]></literal>
    <justification jstring="[para(1258(a,1),16238(a,1,2))].">
      <j1 rule="para" parents="1258 16238"/>
    </justification>
  </clause>

  <clause id="16241">
    <literal><![CDATA[
      K(x,y * (L(y,z,z \ 1) \ u)) = K(x,a(y,z,z \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(1258(a,1),16194(a,1,2))].">
      <j1 rule="para" parents="1258 16194"/>
    </justification>
  </clause>

  <clause id="16242">
    <literal><![CDATA[
      K(x,T(y,T(z,u)) * T(z,u)) = K(x,(u / (u / z)) * y)
    ]]></literal>
    <justification jstring="[para(7030(a,1),16211(a,1,2,1))].">
      <j1 rule="para" parents="7030 16211"/>
    </justification>
  </clause>

  <clause id="16243">
    <literal><![CDATA[
      K(x,(y / (y / z)) * u) = K(x,T(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(12284,a,16242,a),flip(a)].">
      <j1 rule="hyper" parents="12284 16242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16244">
    <literal><![CDATA[
      K(x,T(y \ z,z) * u) = K(x,(z / y) * u)
    ]]></literal>
    <justification jstring="[para(76(a,1),16243(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="76 16243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16245">
    <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(16213(a,2),10963(a,1))].">
      <j1 rule="para" parents="16213 10963"/>
    </justification>
  </clause>

  <clause id="16246">
    <literal><![CDATA[
      K(x,y * (L(y,z,z \ 1) \ u)) = K(x,y * (L(y,z,z) \ u))
    ]]></literal>
    <justification jstring="[para(1258(a,1),16237(a,2,2))].">
      <j1 rule="para" parents="1258 16237"/>
    </justification>
  </clause>

  <clause id="16247">
    <literal><![CDATA[
      K(x,a(y \ 1,y,z) * u) = K(x,z * (L(z,y,y) \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,14455,a(flip),b,16246,a)].">
      <j1 rule="hyper" parents="63 14455 16246"/>
    </justification>
  </clause>

  <clause id="16248">
    <literal><![CDATA[
      K(x,a(y \ 1,y,z) * u) = K(x,a(z,y,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(333,a,16240,a(flip),b,16247,a),flip(a)].">
      <j1 rule="hyper" parents="333 16240 16247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16249">
    <literal><![CDATA[
      K(x,a(y,1 / z,1 / z) \ u) = K(x,a(z,1 / z,y) * u)
    ]]></literal>
    <justification jstring="[para(79(a,1),16248(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="79 16248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16251">
    <literal><![CDATA[
      K(x,a(y,1 / z,1 / z) \ u) = K(x,a(z,z,y) * u)
    ]]></literal>
    <justification jstring="[para(14334(a,1),16249(a,2,2,1))].">
      <j1 rule="para" parents="14334 16249"/>
    </justification>
  </clause>

  <clause id="16252">
    <literal><![CDATA[
      K(x,a(y,1 / z,z) \ u) = K(x,a(z,z,y) * u)
    ]]></literal>
    <justification jstring="[para(14324(a,1),16251(a,1,2,1))].">
      <j1 rule="para" parents="14324 16251"/>
    </justification>
  </clause>

  <clause id="16253">
    <literal><![CDATA[
      K(x,a(y,z,z) \ u) = K(x,a(z,z,y) * u)
    ]]></literal>
    <justification jstring="[para(14334(a,1),16252(a,1,2,1))].">
      <j1 rule="para" parents="14334 16252"/>
    </justification>
  </clause>

  <clause id="16254">
    <literal><![CDATA[
      K(x,a(y \ 1,y,z) * u) = K(x,a(y,y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,16248,a,b,16253,a)].">
      <j1 rule="hyper" parents="63 16248 16253"/>
    </justification>
  </clause>

  <clause id="16255">
    <literal><![CDATA[
      T(x,a(y \ 1,y,z) * u) = T(x,a(y,y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(124,a,16254,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 16254 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16257">
    <literal><![CDATA[
      (x \ T(y,a(z,z,u) * w)) \ (x \ y) = K(a(z \ 1,z,u) * w,y)
    ]]></literal>
    <justification jstring="[para(16255(a,1),13257(a,1,1,2))].">
      <j1 rule="para" parents="16255 13257"/>
    </justification>
  </clause>

  <clause id="16258">
    <literal><![CDATA[
      K(x,K(y * z,u) * T(w,K(u,y * z))) = K(x,w * K(y \ z,u))
    ]]></literal>
    <justification jstring="[para(15806(a,1),16151(a,1,2,2))].">
      <j1 rule="para" parents="15806 16151"/>
    </justification>
  </clause>

  <clause id="16259">
    <literal><![CDATA[
      K(a(x \ 1,x,y) * z,u) = K(a(x,x,y) * z,u)
    ]]></literal>
    <justification jstring="[hyper(13355,a,16257,a),flip(a)].">
      <j1 rule="hyper" parents="13355 16257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16260">
    <literal><![CDATA[
      K(x,y * K(z \ u,w)) = K(x,y * K(z * u,w))
    ]]></literal>
    <justification jstring="[para(6852(a,1),16258(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6852 16258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16261">
    <literal><![CDATA[
      K(x,(y * z) * K(u * w,L(v5,z,y))) = K(x,y * (z * K(u \ w,v5)))
    ]]></literal>
    <justification jstring="[para(10874(a,1),16260(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10874 16260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16262">
    <literal><![CDATA[
      K(x,(K(y \ z,u) * w) * v5) = K(x,(K(y * z,u) * w) * v5)
    ]]></literal>
    <justification jstring="[para(13872(a,1),16152(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13872 16152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16263">
    <literal><![CDATA[
      K(x,y * (z * K(u \ w,v5))) = K(x,y * (z * K(u * w,v5)))
    ]]></literal>
    <justification jstring="[para(10874(a,1),16261(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10874 16261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16264">
    <literal><![CDATA[
      T(x,y * (z * K(u \ w,v5))) = T(x,y * (z * K(u * w,v5)))
    ]]></literal>
    <justification jstring="[hyper(124,a,16263,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 16263 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16265">
    <literal><![CDATA[
      T(x,y * ((z * u) * K(w * u,w))) = T(x,y * (z * ((w \ u) * w)))
    ]]></literal>
    <justification jstring="[para(10318(a,1),16264(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10318 16264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16266">
    <literal><![CDATA[
      K(((T(x,y) * z) * y) / (z * T(x,y)),u) = K(z \ T(y * z,x),u)
    ]]></literal>
    <justification jstring="[hyper(13431,a,16122,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="13431 16122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16267">
    <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(10017,a,16266,a)].">
      <j1 rule="hyper" parents="10017 16266"/>
    </justification>
  </clause>

  <clause id="16268">
    <literal><![CDATA[
      K(x * K(y,z),T(u,z * T(y,x))) = K(z \ T(x * z,y),u)
    ]]></literal>
    <justification jstring="[para(6888(a,1),16267(a,1,1))].">
      <j1 rule="para" parents="6888 16267"/>
    </justification>
  </clause>

  <clause id="16269">
    <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(6365(a,2),16126(a,1,2))].">
      <j1 rule="para" parents="6365 16126"/>
    </justification>
  </clause>

  <clause id="16270">
    <literal><![CDATA[
      K(K(x,y) * ((z / (x * z)) \ u),w) = K(T(z / (x * z),y) \ u,w)
    ]]></literal>
    <justification jstring="[para(8(a,1),16144(a,1,1,1,1))].">
      <j1 rule="para" parents="8 16144"/>
    </justification>
  </clause>

  <clause id="16271">
    <literal><![CDATA[
      K(T(x,y) / (((z \ 1) / y) * y),u) = K(T(z,y) * x,T(u,y * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,15223,a(flip),b,16175,a),flip(a)].">
      <j1 rule="hyper" parents="63 15223 16175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16272">
    <literal><![CDATA[
      K(T(x,y) * z,T(u,y * x)) = K(T(z,y) / (x \ 1),u)
    ]]></literal>
    <justification jstring="[para(12(a,1),16271(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="12 16271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16273">
    <literal><![CDATA[
      K(T(x,y) * z,T(u,y * x)) = K(T(z,y) * x,u)
    ]]></literal>
    <justification jstring="[hyper(333,a,13275,a(flip),b,16272,a),flip(a)].">
      <j1 rule="hyper" parents="333 13275 16272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16275">
    <literal><![CDATA[
      K(x * T(y,z),T(u,z * y)) = K(T(x,z) * y,T(u,y))
    ]]></literal>
    <justification jstring="[hyper(15872,a,16273,a)].">
      <j1 rule="hyper" parents="15872 16273"/>
    </justification>
  </clause>

  <clause id="16276">
    <literal><![CDATA[
      K(x * T(y,z),T(u,z * y)) = K(y * T(x,z),u)
    ]]></literal>
    <justification jstring="[hyper(333,a,12201,a(flip),b,16275,a),flip(a)].">
      <j1 rule="hyper" parents="333 12201 16275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16277">
    <literal><![CDATA[
      K((x * y) * R(z,y,x),u) = K(x * T(z * y,y),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,15824,a(flip),b,16276,a)].">
      <j1 rule="hyper" parents="63 15824 16276"/>
    </justification>
  </clause>

  <clause id="16278">
    <literal><![CDATA[
      K((x * y) * R(z,y,x),u) = K(x * (y * z),u)
    ]]></literal>
    <justification jstring="[hyper(333,a,16043,a(flip),b,16277,a),flip(a)].">
      <j1 rule="hyper" parents="333 16043 16277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16279">
    <literal><![CDATA[
      K(x * (y * z),z * x) = K(x * (z * y),x * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,15841,a(flip),b,16278,a)].">
      <j1 rule="hyper" parents="63 15841 16278"/>
    </justification>
  </clause>

  <clause id="16280">
    <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(121,a,16278,a(flip),b,7080,a)].">
      <j1 rule="hyper" parents="121 16278 7080"/>
    </justification>
  </clause>

  <clause id="16281">
    <literal><![CDATA[
      K((((x * y) \ z) * y) * (z / (y * ((x * y) \ z))),u) = K(((x * y) \ z) * (y * x),u)
    ]]></literal>
    <justification jstring="[para(105(a,1),16278(a,1,1,2))].">
      <j1 rule="para" parents="105 16278"/>
    </justification>
  </clause>

  <clause id="16282">
    <literal><![CDATA[
      K(x * (((y \ z) * (z \ y)) * (1 / (z \ y))),(1 / (z \ y)) * x) = K(x * (y \ z),x * (1 / (z \ y)))
    ]]></literal>
    <justification jstring="[para(1480(a,1),16279(a,2,1,2))].">
      <j1 rule="para" parents="1480 16279"/>
    </justification>
  </clause>

  <clause id="16283">
    <literal><![CDATA[
      T(x,(y * (z \ K(u,z \ 1))) * u) = T(x,(y * (z \ 1)) * T(u,z))
    ]]></literal>
    <justification jstring="[para(4726(a,1),16205(a,1,2,1,2))].">
      <j1 rule="para" parents="4726 16205"/>
    </justification>
  </clause>

  <clause id="16284">
    <literal><![CDATA[
      T(x,T(R(y,z,z) \ u,w)) = T(x,T(L(y,z,z) \ u,w))
    ]]></literal>
    <justification jstring="[hyper(8028,a,16239,a),flip(a)].">
      <j1 rule="hyper" parents="8028 16239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16285">
    <literal><![CDATA[
      T(K(x,T(y,z)) * u,w) * K(y,x) != v5
    ]]></literal>
    <literal><![CDATA[
      T(K(x,y) * u,w) * K(y,T(x,z)) = v5
    ]]></literal>
    <justification jstring="[para(16269(a,1),6455(a,1))].">
      <j1 rule="para" parents="16269 6455"/>
    </justification>
  </clause>

  <clause id="16286">
    <literal><![CDATA[
      a((x \ y) \ 1,z,(x \ y) \ 1) = a(y \ x,z,y \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,12449,a(flip),b,15613,a),flip(a)].">
      <j1 rule="hyper" parents="63 12449 15613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16288">
    <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(16286(a,1),14878(a,1,1))].">
      <j1 rule="para" parents="16286 14878"/>
    </justification>
  </clause>

  <clause id="16289">
    <literal><![CDATA[
      T(x,L(K(y,z) * u,w,v5)) = T(x,L(u * K(y,z),w,v5))
    ]]></literal>
    <justification jstring="[hyper(10969,a,15640,a),flip(a)].">
      <j1 rule="hyper" parents="10969 15640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16290">
    <literal><![CDATA[
      T(x,L(K(y,z) * u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,L(u * K(y,z),w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(15640(a,1),10969(a,1))].">
      <j1 rule="para" parents="15640 10969"/>
    </justification>
  </clause>

  <clause id="16291">
    <literal><![CDATA[
      T(x,(y \ L(K(z,u) * w,v5,v6)) * T(y,L(K(z,u) * w,v5,v6))) != v7
    ]]></literal>
    <literal><![CDATA[
      T(x,L(w * K(z,u),v5,v6)) = v7
    ]]></literal>
    <justification jstring="[para(12629(a,2),16290(a,1))].">
      <j1 rule="para" parents="12629 16290"/>
    </justification>
  </clause>

  <clause id="16292">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * ((u * z) * (u \ 1))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,((u * z) * (u \ 1)) * y) = w
    ]]></literal>
    <justification jstring="[para(15813(a,1),15823(a,1,1))].">
      <j1 rule="para" parents="15813 15823"/>
    </justification>
  </clause>

  <clause id="16293">
    <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(6763(a,1),15991(a,1,1,1,2))].">
      <j1 rule="para" parents="6763 15991"/>
    </justification>
  </clause>

  <clause id="16294">
    <literal><![CDATA[
      K(K(L(x,y,z),u) * (z * (y * x)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(z * (y * T(x,u)),w) = v5
    ]]></literal>
    <justification jstring="[para(16056(a,2),6408(a,1))].">
      <j1 rule="para" parents="16056 6408"/>
    </justification>
  </clause>

  <clause id="16295">
    <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(15626(a,2),16293(a,1,1,1))].">
      <j1 rule="para" parents="15626 16293"/>
    </justification>
  </clause>

  <clause id="16296">
    <literal><![CDATA[
      T(K(x,K(y,z)) \ u,K(x,y) \ z) = z \ T(u * z,K(x,y))
    ]]></literal>
    <justification jstring="[para(534(a,1),16295(a,1,1))].">
      <j1 rule="para" parents="534 16295"/>
    </justification>
  </clause>

  <clause id="16297">
    <literal><![CDATA[
      K(x,K(y,z)) \ T(u,K(x,y) \ z) = z \ T(u * z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,15854,a(flip),b,16296,a)].">
      <j1 rule="hyper" parents="63 15854 16296"/>
    </justification>
  </clause>

  <clause id="16298">
    <literal><![CDATA[
      T(x,T(T(y,z) * (y \ u),(y \ u) \ u)) = T(x,(y \ u) * T(u / (y \ u),z))
    ]]></literal>
    <justification jstring="[hyper(333,a,12271,a(flip),b,15458,a),flip(a)].">
      <j1 rule="hyper" parents="333 12271 15458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16300">
    <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(4555(a,1),15636(a,2,2))].">
      <j1 rule="para" parents="4555 15636"/>
    </justification>
  </clause>

  <clause id="16301">
    <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(63,a,7489,a(flip),b,15837,a)].">
      <j1 rule="hyper" parents="63 7489 15837"/>
    </justification>
  </clause>

  <clause id="16302">
    <literal><![CDATA[
      T(x,K(y,K(z,u)) * w) = T(x,w)
    ]]></literal>
    <justification jstring="[para(15632(a,1),15898(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15632 15898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16303">
    <literal><![CDATA[
      T(x,K(K(y,z),u) * w) = T(x,w)
    ]]></literal>
    <justification jstring="[hyper(15769,a,16302,a)].">
      <j1 rule="hyper" parents="15769 16302"/>
    </justification>
  </clause>

  <clause id="16304">
    <literal><![CDATA[
      T(x,y * T(z,K(u,w))) = T(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(15597,a,16302,a)].">
      <j1 rule="hyper" parents="15597 16302"/>
    </justification>
  </clause>

  <clause id="16305">
    <literal><![CDATA[
      T(x,y * K(z,K(u,w))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(15486,a,16302,a)].">
      <j1 rule="hyper" parents="15486 16302"/>
    </justification>
  </clause>

  <clause id="16306">
    <literal><![CDATA[
      T(x,T(y,K(z,u)) \ w) = T(x,y \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,14925,a(flip),b,16302,a)].">
      <j1 rule="hyper" parents="63 14925 16302"/>
    </justification>
  </clause>

  <clause id="16307">
    <literal><![CDATA[
      K(x,K(y,K(z,u)) * w) = x \ T(x,w)
    ]]></literal>
    <justification jstring="[hyper(121,a,16302,a(flip),b,4222,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="121 16302 4222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16308">
    <literal><![CDATA[
      T(x,y \ T(z,K(u,w))) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(4963(a,1),16302(a,1,2))].">
      <j1 rule="para" parents="4963 16302"/>
    </justification>
  </clause>

  <clause id="16309">
    <literal><![CDATA[
      T(x,T(y,K(z,u)) / w) = T(x,y / w)
    ]]></literal>
    <justification jstring="[para(5220(a,1),16302(a,1,2))].">
      <j1 rule="para" parents="5220 16302"/>
    </justification>
  </clause>

  <clause id="16310">
    <literal><![CDATA[
      T(x,K(y,T(z,u)) * w) = T(x,K(y,z) * w)
    ]]></literal>
    <justification jstring="[para(6409(a,1),16302(a,1,2))].">
      <j1 rule="para" parents="6409 16302"/>
    </justification>
  </clause>

  <clause id="16311">
    <literal><![CDATA[
      T(x,y \ K(z,K(u,w))) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(15487(a,1),16302(a,1,2))].">
      <j1 rule="para" parents="15487 16302"/>
    </justification>
  </clause>

  <clause id="16312">
    <literal><![CDATA[
      T(x,y / T(z,K(u,w))) = T(x,y / z)
    ]]></literal>
    <justification jstring="[para(15628(a,1),16302(a,1,2))].">
      <j1 rule="para" parents="15628 16302"/>
    </justification>
  </clause>

  <clause id="16313">
    <literal><![CDATA[
      T(x,K(K(y,z),u) * w) = w \ (x * w)
    ]]></literal>
    <justification jstring="[hyper(333,a,22,a(flip),b,16303,a),flip(a)].">
      <j1 rule="hyper" parents="333 22 16303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16314">
    <literal><![CDATA[
      T(x,y * (K(z,K(u,w)) * v5)) = T(x,y * v5)
    ]]></literal>
    <justification jstring="[para(5354(a,1),16303(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5354 16303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16315">
    <literal><![CDATA[
      K(x * K(y,K(z,u)),w) = w / T(w,x)
    ]]></literal>
    <justification jstring="[hyper(197,a,16305,a(flip),b,4233,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="197 16305 4233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16317">
    <literal><![CDATA[
      T(x,y * T(z,T(u,w))) = T(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(6191(a,1),16304(a,1,2,2))].">
      <j1 rule="para" parents="6191 16304"/>
    </justification>
  </clause>

  <clause id="16319">
    <literal><![CDATA[
      T(x,y * (K(z,u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y * (w * K(z,u))) = v5
    ]]></literal>
    <justification jstring="[para(16304(a,1),12908(a,1))].">
      <j1 rule="para" parents="16304 12908"/>
    </justification>
  </clause>

  <clause id="16321">
    <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(63,a,13671,a(flip),b,16306,a),flip(a)].">
      <j1 rule="hyper" parents="63 13671 16306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16322">
    <literal><![CDATA[
      T(x,T(y,T(z,u)) \ w) = T(x,T(y,z) \ w)
    ]]></literal>
    <justification jstring="[para(6191(a,1),16306(a,1,2,1))].">
      <j1 rule="para" parents="6191 16306"/>
    </justification>
  </clause>

  <clause id="16323">
    <literal><![CDATA[
      K(x,K(y,K(z,u)) * w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(333,a,4215,a,b,16307,a),flip(a)].">
      <j1 rule="hyper" parents="333 4215 16307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16324">
    <literal><![CDATA[
      K(x,K(y,K(z,u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w) = v5
    ]]></literal>
    <justification jstring="[para(16307(a,2),4306(a,1))].">
      <j1 rule="para" parents="16307 4306"/>
    </justification>
  </clause>

  <clause id="16325">
    <literal><![CDATA[
      K(x,K(y,K(z,u)) \ w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(15779,a,16323,a)].">
      <j1 rule="hyper" parents="15779 16323"/>
    </justification>
  </clause>

  <clause id="16326">
    <literal><![CDATA[
      K(x,y \ T(z,K(u,w))) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(15609,a,16323,a)].">
      <j1 rule="hyper" parents="15609 16323"/>
    </justification>
  </clause>

  <clause id="16327">
    <literal><![CDATA[
      K(x,y * T(z,K(u,w))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(15605,a,16323,a)].">
      <j1 rule="hyper" parents="15605 16323"/>
    </justification>
  </clause>

  <clause id="16328">
    <literal><![CDATA[
      K(x,y * K(z,K(u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(15517,a,16323,a)].">
      <j1 rule="hyper" parents="15517 16323"/>
    </justification>
  </clause>

  <clause id="16329">
    <literal><![CDATA[
      K(x,y / T(z,K(u,w))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(63,a,15638,a(flip),b,16323,a)].">
      <j1 rule="hyper" parents="63 15638 16323"/>
    </justification>
  </clause>

  <clause id="16330">
    <literal><![CDATA[
      K(x,T(y,K(z,u)) \ w) = K(x,y \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,14930,a(flip),b,16323,a)].">
      <j1 rule="hyper" parents="63 14930 16323"/>
    </justification>
  </clause>

  <clause id="16331">
    <literal><![CDATA[
      K(x,K(K(y,z),u) \ w) = K(x,w)
    ]]></literal>
    <justification jstring="[para(4567(a,2),16323(a,1,2))].">
      <j1 rule="para" parents="4567 16323"/>
    </justification>
  </clause>

  <clause id="16332">
    <literal><![CDATA[
      K(x,T(y,K(z,u)) / w) = K(x,y / w)
    ]]></literal>
    <justification jstring="[para(5220(a,1),16323(a,1,2))].">
      <j1 rule="para" parents="5220 16323"/>
    </justification>
  </clause>

  <clause id="16333">
    <literal><![CDATA[
      K(x,T(y,T(z,u)) * w) = K(x,T(y,z) * w)
    ]]></literal>
    <justification jstring="[para(7775(a,1),16323(a,1,2))].">
      <j1 rule="para" parents="7775 16323"/>
    </justification>
  </clause>

  <clause id="16334">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ w) = K(x,(u * K(y,z)) \ w)
    ]]></literal>
    <justification jstring="[para(8434(a,1),16323(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8434 16323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16335">
    <literal><![CDATA[
      K(x,(K(y,z) * (u / K(y,z))) \ w) = K(x,u \ w)
    ]]></literal>
    <justification jstring="[para(10038(a,1),16323(a,1,2))].">
      <j1 rule="para" parents="10038 16323"/>
    </justification>
  </clause>

  <clause id="16336">
    <literal><![CDATA[
      K(x,(T(y,K(z,u)) * w) * v5) = K(x,(y * w) * v5)
    ]]></literal>
    <justification jstring="[para(13917(a,1),16323(a,1,2))].">
      <j1 rule="para" parents="13917 16323"/>
    </justification>
  </clause>

  <clause id="16337">
    <literal><![CDATA[
      K(x,y * K(z,T(u,w))) = K(x,y * K(z,u))
    ]]></literal>
    <justification jstring="[para(15835(a,1),16323(a,1,2))].">
      <j1 rule="para" parents="15835 16323"/>
    </justification>
  </clause>

  <clause id="16338">
    <literal><![CDATA[
      K(x,y * (z * T(u,K(w,v5)))) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(5996(a,1),16328(a,1,2))].">
      <j1 rule="para" parents="5996 16328"/>
    </justification>
  </clause>

  <clause id="16339">
    <literal><![CDATA[
      K(x,y / (K(z,u) * w)) = K(x,y / (w * K(z,u)))
    ]]></literal>
    <justification jstring="[para(10446(a,1),16328(a,1,2))].">
      <j1 rule="para" parents="10446 16328"/>
    </justification>
  </clause>

  <clause id="16340">
    <literal><![CDATA[
      K(x,y * (z * K(u,K(w,v5)))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(10975(a,1),16328(a,1,2))].">
      <j1 rule="para" parents="10975 16328"/>
    </justification>
  </clause>

  <clause id="16341">
    <literal><![CDATA[
      K(x,y \ (K(z,u) * w)) = K(x,y \ (w * K(z,u)))
    ]]></literal>
    <justification jstring="[para(14573(a,1),16328(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14573 16328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16342">
    <literal><![CDATA[
      T(x,y \ T(z,T(u,w))) = T(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(6191(a,1),16308(a,1,2,2))].">
      <j1 rule="para" parents="6191 16308"/>
    </justification>
  </clause>

  <clause id="16343">
    <literal><![CDATA[
      T(x,T(y,T(z,u)) / w) = T(x,T(y,z) / w)
    ]]></literal>
    <justification jstring="[para(6191(a,1),16309(a,1,2,1))].">
      <j1 rule="para" parents="6191 16309"/>
    </justification>
  </clause>

  <clause id="16344">
    <literal><![CDATA[
      T(x,y / T(z,T(u,w))) = T(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(6191(a,1),16312(a,1,2,2))].">
      <j1 rule="para" parents="6191 16312"/>
    </justification>
  </clause>

  <clause id="16345">
    <literal><![CDATA[
      T(x,y / T(T(z,T(u,w)),v5)) = T(x,y / T(T(z,u),v5))
    ]]></literal>
    <justification jstring="[para(6194(a,1),16312(a,1,2,2))].">
      <j1 rule="para" parents="6194 16312"/>
    </justification>
  </clause>

  <clause id="16346">
    <literal><![CDATA[
      T(x,K(K(y,z),u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,w) = v5
    ]]></literal>
    <justification jstring="[para(16313(a,2),347(a,1))].">
      <j1 rule="para" parents="16313 347"/>
    </justification>
  </clause>

  <clause id="16347">
    <literal><![CDATA[
      K(x * K(y,K(z,u)),w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(333,a,4212,a,b,16315,a),flip(a)].">
      <j1 rule="hyper" parents="333 4212 16315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16348">
    <literal><![CDATA[
      K(x * K(y,K(z,u)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w) = v5
    ]]></literal>
    <justification jstring="[para(16315(a,2),4313(a,1))].">
      <j1 rule="para" parents="16315 4313"/>
    </justification>
  </clause>

  <clause id="16350">
    <literal><![CDATA[
      K(K(x,K(y,z)) \ u,w) = K(u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,15702,a,b,16347,a)].">
      <j1 rule="hyper" parents="63 15702 16347"/>
    </justification>
  </clause>

  <clause id="16351">
    <literal><![CDATA[
      K(T(x,K(y,z)) \ u,w) = K(x \ u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,15703,a(flip),b,16347,a)].">
      <j1 rule="hyper" parents="63 15703 16347"/>
    </justification>
  </clause>

  <clause id="16352">
    <literal><![CDATA[
      K(x \ T(y,K(z,u)),w) = K(x \ y,w)
    ]]></literal>
    <justification jstring="[para(2086(a,1),16347(a,1,1))].">
      <j1 rule="para" parents="2086 16347"/>
    </justification>
  </clause>

  <clause id="16353">
    <literal><![CDATA[
      K(x / T(y,K(z,u)),w) = K(x / y,w)
    ]]></literal>
    <justification jstring="[para(5975(a,1),16347(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5975 16347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16354">
    <literal><![CDATA[
      (x * K(y,z)) * (y * K(u,K(w,v5))) = x * T(y * K(u,K(w,v5)),z)
    ]]></literal>
    <justification jstring="[para(16347(a,1),5982(a,1,1,2))].">
      <j1 rule="para" parents="16347 5982"/>
    </justification>
  </clause>

  <clause id="16355">
    <literal><![CDATA[
      K(x * (y * K(z,K(u,w))),v5) = K(x * y,v5)
    ]]></literal>
    <justification jstring="[para(10975(a,1),16347(a,1,1))].">
      <j1 rule="para" parents="10975 16347"/>
    </justification>
  </clause>

  <clause id="16356">
    <literal><![CDATA[
      K(K(x,T(y,z)) * u,w) = K(K(x,y) * u,w)
    ]]></literal>
    <justification jstring="[para(15624(a,1),16347(a,1,1))].">
      <j1 rule="para" parents="15624 16347"/>
    </justification>
  </clause>

  <clause id="16357">
    <literal><![CDATA[
      K(K(x,K(y,z)) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(u,w) = v5
    ]]></literal>
    <justification jstring="[para(16350(a,1),4614(a,1))].">
      <j1 rule="para" parents="16350 4614"/>
    </justification>
  </clause>

  <clause id="16358">
    <literal><![CDATA[
      K(x,y \ T(((z \ 1) \ 1) * u,K(w,v5))) = K(x,y \ (z * u))
    ]]></literal>
    <justification jstring="[hyper(333,a,5014,a(flip),b,16326,a),flip(a)].">
      <j1 rule="hyper" parents="333 5014 16326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16360">
    <literal><![CDATA[
      K(x,y * T(z,T(u,w))) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(6191(a,1),16327(a,1,2,2))].">
      <j1 rule="para" parents="6191 16327"/>
    </justification>
  </clause>

  <clause id="16361">
    <literal><![CDATA[
      K(x,y * (z * (u * K(z,w)))) = K(x,y * (T(z,w) * u))
    ]]></literal>
    <justification jstring="[para(6174(a,1),16327(a,1,2,2))].">
      <j1 rule="para" parents="6174 16327"/>
    </justification>
  </clause>

  <clause id="16362">
    <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(16327(a,1),12756(a,1))].">
      <j1 rule="para" parents="16327 12756"/>
    </justification>
  </clause>

  <clause id="16363">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (w \ z))) = K(x,y * (w \ T(z,u)))
    ]]></literal>
    <justification jstring="[para(13350(a,1),16327(a,1,2,2))].">
      <j1 rule="para" parents="13350 16327"/>
    </justification>
  </clause>

  <clause id="16364">
    <literal><![CDATA[
      K(x,y \ T(z,y)) = K(x,z / T(y,K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(333,a,15048,a,b,16329,a)].">
      <j1 rule="hyper" parents="333 15048 16329"/>
    </justification>
  </clause>

  <clause id="16365">
    <literal><![CDATA[
      K(x,y / T(z,u / w)) = K(x,y / T(z,w \ u))
    ]]></literal>
    <justification jstring="[para(6877(a,1),16329(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6877 16329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16366">
    <literal><![CDATA[
      K(x,y \ T(z * y,K(u,w))) = K(x,T(z,K(w,u) * y))
    ]]></literal>
    <justification jstring="[hyper(63,a,16080,a(flip),b,16330,a),flip(a)].">
      <j1 rule="hyper" parents="63 16080 16330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16367">
    <literal><![CDATA[
      K(x,T(y,z / u) / w) = K(x,T(y,u \ z) / w)
    ]]></literal>
    <justification jstring="[para(6877(a,1),16332(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6877 16332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16368">
    <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(16332(a,1),16221(a,1))].">
      <j1 rule="para" parents="16332 16221"/>
    </justification>
  </clause>

  <clause id="16369">
    <literal><![CDATA[
      K(T(x,T(y,z)) \ u,w) = K(T(x,y) \ u,w)
    ]]></literal>
    <justification jstring="[para(6191(a,1),16351(a,1,1,1))].">
      <j1 rule="para" parents="6191 16351"/>
    </justification>
  </clause>

  <clause id="16370">
    <literal><![CDATA[
      K(x \ (K(y,z) \ u),w) = K(x \ (u * K(z,y)),w)
    ]]></literal>
    <justification jstring="[para(6020(a,1),16352(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6020 16352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16371">
    <literal><![CDATA[
      K(x \ T(y,T(z,u)),w) = K(x \ T(y,z),w)
    ]]></literal>
    <justification jstring="[para(6191(a,1),16352(a,1,1,2))].">
      <j1 rule="para" parents="6191 16352"/>
    </justification>
  </clause>

  <clause id="16372">
    <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(16352(a,1),13298(a,1,1,1,2))].">
      <j1 rule="para" parents="16352 13298"/>
    </justification>
  </clause>

  <clause id="16373">
    <literal><![CDATA[
      K((x * y) \ z,T(u,y)) = K(((x \ z) * x) / T(y * x,K(w,v5)),u)
    ]]></literal>
    <justification jstring="[hyper(333,a,13981,a,b,16353,a)].">
      <j1 rule="hyper" parents="333 13981 16353"/>
    </justification>
  </clause>

  <clause id="16375">
    <literal><![CDATA[
      K(x,T(y,K(z,u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * w) = v5
    ]]></literal>
    <justification jstring="[para(4273(a,1),16324(a,1,2))].">
      <j1 rule="para" parents="4273 16324"/>
    </justification>
  </clause>

  <clause id="16376">
    <literal><![CDATA[
      K(x,y * T(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = v5
    ]]></literal>
    <justification jstring="[para(4967(a,1),16324(a,1,2))].">
      <j1 rule="para" parents="4967 16324"/>
    </justification>
  </clause>

  <clause id="16377">
    <literal><![CDATA[
      K(x,y \ T(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = v5
    ]]></literal>
    <justification jstring="[para(4963(a,1),16324(a,1,2))].">
      <j1 rule="para" parents="4963 16324"/>
    </justification>
  </clause>

  <clause id="16378">
    <literal><![CDATA[
      K(x,T(y,K(z,u)) / w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y / w) = v5
    ]]></literal>
    <justification jstring="[para(5220(a,1),16324(a,1,2))].">
      <j1 rule="para" parents="5220 16324"/>
    </justification>
  </clause>

  <clause id="16379">
    <literal><![CDATA[
      K(x,K(K(y,z),u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w) = v5
    ]]></literal>
    <justification jstring="[para(5296(a,2),16324(a,1,2,1))].">
      <j1 rule="para" parents="5296 16324"/>
    </justification>
  </clause>

  <clause id="16380">
    <literal><![CDATA[
      K(x,y * K(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(6888(a,1),16324(a,1,2))].">
      <j1 rule="para" parents="6888 16324"/>
    </justification>
  </clause>

  <clause id="16381">
    <literal><![CDATA[
      K(x,T(y,K(z,u)) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ w) = v5
    ]]></literal>
    <justification jstring="[para(6778(a,1),16324(a,1,2))].">
      <j1 rule="para" parents="6778 16324"/>
    </justification>
  </clause>

  <clause id="16382">
    <literal><![CDATA[
      K(x,y / T(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y / z) = v5
    ]]></literal>
    <justification jstring="[para(15628(a,1),16324(a,1,2))].">
      <j1 rule="para" parents="15628 16324"/>
    </justification>
  </clause>

  <clause id="16383">
    <literal><![CDATA[
      T(x,T(y,K(z,u)) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ w) = v5
    ]]></literal>
    <justification jstring="[para(4555(a,1),16346(a,1,2))].">
      <j1 rule="para" parents="4555 16346"/>
    </justification>
  </clause>

  <clause id="16384">
    <literal><![CDATA[
      T(x,T(y,K(z,u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y * w) = v5
    ]]></literal>
    <justification jstring="[para(14924(a,1),16346(a,1))].">
      <j1 rule="para" parents="14924 16346"/>
    </justification>
  </clause>

  <clause id="16385">
    <literal><![CDATA[
      T(x,y * K(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = v5
    ]]></literal>
    <justification jstring="[para(15616(a,1),16346(a,1))].">
      <j1 rule="para" parents="15616 16346"/>
    </justification>
  </clause>

  <clause id="16386">
    <literal><![CDATA[
      K(x \ T(y,K(z,u)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,w) = v5
    ]]></literal>
    <justification jstring="[para(2086(a,1),16348(a,1,1))].">
      <j1 rule="para" parents="2086 16348"/>
    </justification>
  </clause>

  <clause id="16387">
    <literal><![CDATA[
      K(T(x,K(y,z)) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x * u,w) = v5
    ]]></literal>
    <justification jstring="[para(4959(a,1),16348(a,1,1))].">
      <j1 rule="para" parents="4959 16348"/>
    </justification>
  </clause>

  <clause id="16388">
    <literal><![CDATA[
      K(x / T(y,K(z,u)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x / y,w) = v5
    ]]></literal>
    <justification jstring="[para(6828(a,1),16348(a,1,1))].">
      <j1 rule="para" parents="6828 16348"/>
    </justification>
  </clause>

  <clause id="16389">
    <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(12319(a,1),16348(a,1,1))].">
      <j1 rule="para" parents="12319 16348"/>
    </justification>
  </clause>

  <clause id="16390">
    <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(14573(a,1),16348(a,1,1))].">
      <j1 rule="para" parents="14573 16348"/>
    </justification>
  </clause>

  <clause id="16391">
    <literal><![CDATA[
      K(T(x,K(y,z)) \ u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x \ u,w) = v5
    ]]></literal>
    <justification jstring="[para(15625(a,1),16348(a,1,1))].">
      <j1 rule="para" parents="15625 16348"/>
    </justification>
  </clause>

  <clause id="16392">
    <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(10014(a,1),16357(a,1,1))].">
      <j1 rule="para" parents="10014 16357"/>
    </justification>
  </clause>

  <clause id="16393">
    <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(10080(a,1),16357(a,1,1))].">
      <j1 rule="para" parents="10080 16357"/>
    </justification>
  </clause>

  <clause id="16394">
    <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(10080(a,1),16379(a,1,2))].">
      <j1 rule="para" parents="10080 16379"/>
    </justification>
  </clause>

  <clause id="16396">
    <literal><![CDATA[
      K(x,y * (z * K(u,K(w,v5)))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = v6
    ]]></literal>
    <justification jstring="[para(10975(a,1),16380(a,1,2))].">
      <j1 rule="para" parents="10975 16380"/>
    </justification>
  </clause>

  <clause id="16397">
    <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(12319(a,1),16380(a,1,2))].">
      <j1 rule="para" parents="12319 16380"/>
    </justification>
  </clause>

  <clause id="16398">
    <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(14573(a,1),16380(a,1,2))].">
      <j1 rule="para" parents="14573 16380"/>
    </justification>
  </clause>

  <clause id="16399">
    <literal><![CDATA[
      T(x,y * T(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y * z) = v5
    ]]></literal>
    <justification jstring="[para(2087(a,1),16385(a,1,2))].">
      <j1 rule="para" parents="2087 16385"/>
    </justification>
  </clause>

  <clause id="16400">
    <literal><![CDATA[
      T(x,y * (z * K(u,K(w,v5)))) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,y * z) = v6
    ]]></literal>
    <justification jstring="[para(10975(a,1),16385(a,1,2))].">
      <j1 rule="para" parents="10975 16385"/>
    </justification>
  </clause>

  <clause id="16401">
    <literal><![CDATA[
      T(x,K(y,T(z,u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,K(z,y) * w) = v5
    ]]></literal>
    <justification jstring="[para(16310(a,2),15769(a,1))].">
      <j1 rule="para" parents="16310 15769"/>
    </justification>
  </clause>

  <clause id="16402">
    <literal><![CDATA[
      T(x,y * (T(K(z,u),w) * v5)) = T(x,y * (K(z,u) * v5))
    ]]></literal>
    <justification jstring="[para(4557(a,1),16314(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4557 16314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16403">
    <literal><![CDATA[
      T(x,y * K(z,u * w)) = T(x,y * K(z,w * u))
    ]]></literal>
    <justification jstring="[para(15858(a,1),16314(a,1,2,2))].">
      <j1 rule="para" parents="15858 16314"/>
    </justification>
  </clause>

  <clause id="16404">
    <literal><![CDATA[
      T(x,y * T(z * T(u,w),u)) = T(x,y * (T(u,w) * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,15904,a(flip),b,16317,a),flip(a)].">
      <j1 rule="hyper" parents="63 15904 16317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16405">
    <literal><![CDATA[
      R(T(x / y,y * T(z,u)),y,T(z,T(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      (y * T(z,T(u,w))) \ (x * T(z,T(u,w))) = v5
    ]]></literal>
    <justification jstring="[para(16317(a,1),952(a,1,1))].">
      <j1 rule="para" parents="16317 952"/>
    </justification>
  </clause>

  <clause id="16406">
    <literal><![CDATA[
      K(x,T(y,T(z,u)) * z) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(333,a,12267,a(flip),b,16333,a),flip(a)].">
      <j1 rule="hyper" parents="333 12267 16333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16407">
    <literal><![CDATA[
      K(x,T(T(y,z) / u,y) * w) = K(x,(u \ T(y,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,12775,a(flip),b,16333,a),flip(a)].">
      <j1 rule="hyper" parents="63 12775 16333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16408">
    <literal><![CDATA[
      K(x,T(y,z * u) * (u * z)) = K(x,(u * z) * y)
    ]]></literal>
    <justification jstring="[para(12225(a,1),16406(a,1,2,1))].">
      <j1 rule="para" parents="12225 16406"/>
    </justification>
  </clause>

  <clause id="16409">
    <literal><![CDATA[
      K(x,K(y,T(z,u)) * w) = K(x,w * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(15533,a,16337,a)].">
      <j1 rule="hyper" parents="15533 16337"/>
    </justification>
  </clause>

  <clause id="16410">
    <literal><![CDATA[
      K(x,y * K(z,T(u,w))) = K(x,K(u,z) \ y)
    ]]></literal>
    <justification jstring="[hyper(333,a,15524,a,b,16337,a),flip(a)].">
      <j1 rule="hyper" parents="333 15524 16337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16411">
    <literal><![CDATA[
      K(x,y * K(z,u / w)) = K(x,y * K(z,w \ u))
    ]]></literal>
    <justification jstring="[para(113(a,1),16337(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="113 16337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16412">
    <literal><![CDATA[
      K(x,y * K(z,u * w)) = K(x,y * K(z,w * u))
    ]]></literal>
    <justification jstring="[para(12229(a,1),16337(a,1,2,2))].">
      <j1 rule="para" parents="12229 16337"/>
    </justification>
  </clause>

  <clause id="16413">
    <literal><![CDATA[
      K(x,y * (z \ T(u,K(w,v5)))) = K(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[para(2086(a,1),16340(a,1,2,2))].">
      <j1 rule="para" parents="2086 16340"/>
    </justification>
  </clause>

  <clause id="16414">
    <literal><![CDATA[
      K(x,y * (T(z,K(u,w)) / v5)) = K(x,y * (z / v5))
    ]]></literal>
    <justification jstring="[para(2170(a,1),16340(a,1,2,2))].">
      <j1 rule="para" parents="2170 16340"/>
    </justification>
  </clause>

  <clause id="16416">
    <literal><![CDATA[
      K(x,y * (z * (u * K(w,K(v5,v6))))) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(10975(a,1),16340(a,1,2,2))].">
      <j1 rule="para" parents="10975 16340"/>
    </justification>
  </clause>

  <clause id="16417">
    <literal><![CDATA[
      T(x,T(y * K(y * z,u),z)) = T(x,z \ T(y * z,u))
    ]]></literal>
    <justification jstring="[para(13549(a,2),16342(a,1,2))].">
      <j1 rule="para" parents="13549 16342"/>
    </justification>
  </clause>

  <clause id="16418">
    <literal><![CDATA[
      T(x,T(T(y,z) \ u,y) / w) = T(x,(u / T(y,z)) / w)
    ]]></literal>
    <justification jstring="[hyper(63,a,15039,a(flip),b,16343,a),flip(a)].">
      <j1 rule="hyper" parents="63 15039 16343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16419">
    <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(16344(a,1),12685(a,1))].">
      <j1 rule="para" parents="16344 12685"/>
    </justification>
  </clause>

  <clause id="16421">
    <literal><![CDATA[
      K(x * (K(y,T(z,u)) * w),v5) = K(x * (K(y,z) * w),v5)
    ]]></literal>
    <justification jstring="[para(15624(a,1),16355(a,1,1,2))].">
      <j1 rule="para" parents="15624 16355"/>
    </justification>
  </clause>

  <clause id="16422">
    <literal><![CDATA[
      K(K(x,T(y,z)) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(u * K(y,x),w) = v5
    ]]></literal>
    <justification jstring="[para(16356(a,2),15660(a,1))].">
      <j1 rule="para" parents="16356 15660"/>
    </justification>
  </clause>

  <clause id="16423">
    <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(63,a,14841,a(flip),b,16360,a),flip(a)].">
      <j1 rule="hyper" parents="63 14841 16360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16424">
    <literal><![CDATA[
      K(T(x * y,x) \ ((x * T(y,K(x,z))) * u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(K(x * T(y,K(x,z)),x) \ u,w) = v5
    ]]></literal>
    <justification jstring="[para(16369(a,1),6211(a,1))].">
      <j1 rule="para" parents="16369 6211"/>
    </justification>
  </clause>

  <clause id="16425">
    <literal><![CDATA[
      K(T(x * y,y) \ ((x * T(y,K(x,z))) * u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(K(x * T(y,K(x,z)),y) \ u,w) = v5
    ]]></literal>
    <justification jstring="[para(16369(a,1),7259(a,1))].">
      <j1 rule="para" parents="16369 7259"/>
    </justification>
  </clause>

  <clause id="16426">
    <literal><![CDATA[
      K(T(x * K(x * y,z),y),u) = K(y \ T(x * y,z),u)
    ]]></literal>
    <justification jstring="[para(13549(a,2),16371(a,1,1))].">
      <j1 rule="para" parents="13549 16371"/>
    </justification>
  </clause>

  <clause id="16427">
    <literal><![CDATA[
      K(x,K(y,T(z,u)) * w) = K(x,K(z,y) * w)
    ]]></literal>
    <justification jstring="[hyper(333,a,15637,a,b,16409,a),flip(a)].">
      <j1 rule="hyper" parents="333 15637 16409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16428">
    <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(16409(a,2),15641(a,1))].">
      <j1 rule="para" parents="16409 15641"/>
    </justification>
  </clause>

  <clause id="16429">
    <literal><![CDATA[
      K(x,K(y,T(z,u)) \ w) = K(x,K(z,y) \ w)
    ]]></literal>
    <justification jstring="[hyper(15778,a,16410,a)].">
      <j1 rule="hyper" parents="15778 16410"/>
    </justification>
  </clause>

  <clause id="16430">
    <literal><![CDATA[
      K(x,K(y,z * u) \ w) = K(x,w * K(u * z,y))
    ]]></literal>
    <justification jstring="[para(12201(a,1),16410(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12201 16410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16431">
    <literal><![CDATA[
      K(x,K(y,T(z,u)) \ w) = K(x,K(y,z) \ w)
    ]]></literal>
    <justification jstring="[hyper(333,a,14934,a,b,16429,a),flip(a)].">
      <j1 rule="hyper" parents="333 14934 16429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16432">
    <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(16429(a,2),15780(a,1))].">
      <j1 rule="para" parents="16429 15780"/>
    </justification>
  </clause>

  <clause id="16433">
    <literal><![CDATA[
      K(x,K(y,z / u) \ w) = K(x,K(y,u \ z) \ w)
    ]]></literal>
    <justification jstring="[para(113(a,1),16431(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="113 16431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16434">
    <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(16431(a,2),15780(a,1))].">
      <j1 rule="para" parents="16431 15780"/>
    </justification>
  </clause>

  <clause id="16435">
    <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(6877(a,1),16375(a,1,2,1))].">
      <j1 rule="para" parents="6877 16375"/>
    </justification>
  </clause>

  <clause id="16436">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (w / u))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (w / T(u,z))) = v5
    ]]></literal>
    <justification jstring="[para(7096(a,1),16376(a,1,2,2))].">
      <j1 rule="para" parents="7096 16376"/>
    </justification>
  </clause>

  <clause id="16437">
    <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(7575(a,1),16376(a,1,2,2))].">
      <j1 rule="para" parents="7575 16376"/>
    </justification>
  </clause>

  <clause id="16438">
    <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(13303(a,1),16376(a,1,2,2))].">
      <j1 rule="para" parents="13303 16376"/>
    </justification>
  </clause>

  <clause id="16439">
    <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(13350(a,1),16376(a,1,2,2))].">
      <j1 rule="para" parents="13350 16376"/>
    </justification>
  </clause>

  <clause id="16440">
    <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(16212(a,1),16376(a,1))].">
      <j1 rule="para" parents="16212 16376"/>
    </justification>
  </clause>

  <clause id="16441">
    <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(6035(a,1),16377(a,1,2,2))].">
      <j1 rule="para" parents="6035 16377"/>
    </justification>
  </clause>

  <clause id="16442">
    <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(7575(a,1),16377(a,1,2,2))].">
      <j1 rule="para" parents="7575 16377"/>
    </justification>
  </clause>

  <clause id="16443">
    <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(12253(a,1),16377(a,1,2,2))].">
      <j1 rule="para" parents="12253 16377"/>
    </justification>
  </clause>

  <clause id="16444">
    <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(6191(a,1),16378(a,1,2,1))].">
      <j1 rule="para" parents="6191 16378"/>
    </justification>
  </clause>

  <clause id="16446">
    <literal><![CDATA[
      K(x,(L(K(y,z),u,w) * v5) / v6) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,(v5 * L(K(y,z),u,w)) / v6) = v7
    ]]></literal>
    <justification jstring="[para(11061(a,1),16378(a,1,2,1))].">
      <j1 rule="para" parents="11061 16378"/>
    </justification>
  </clause>

  <clause id="16447">
    <literal><![CDATA[
      K(x,(L(K(y,z),u,w) * v5) \ v6) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,(v5 * L(K(y,z),u,w)) \ v6) = v7
    ]]></literal>
    <justification jstring="[para(11061(a,1),16381(a,1,2,1))].">
      <j1 rule="para" parents="11061 16381"/>
    </justification>
  </clause>

  <clause id="16448">
    <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(25(a,2),16382(a,1,2,2))].">
      <j1 rule="para" parents="25 16382"/>
    </justification>
  </clause>

  <clause id="16449">
    <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(6019(a,1),16382(a,1,2,2))].">
      <j1 rule="para" parents="6019 16382"/>
    </justification>
  </clause>

  <clause id="16450">
    <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(13350(a,1),16382(a,1,2,2))].">
      <j1 rule="para" parents="13350 16382"/>
    </justification>
  </clause>

  <clause id="16451">
    <literal><![CDATA[
      T(x,T(y * K(z,u),w) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,T(K(z,u) * y,w) * v5) = v6
    ]]></literal>
    <justification jstring="[para(6104(a,1),16384(a,1,2,1))].">
      <j1 rule="para" parents="6104 16384"/>
    </justification>
  </clause>

  <clause id="16452">
    <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(6191(a,1),16386(a,1,1,2))].">
      <j1 rule="para" parents="6191 16386"/>
    </justification>
  </clause>

  <clause id="16453">
    <literal><![CDATA[
      K((K(x,y) / z) * u,w) = K((z \ K(x,y)) * u,w)
    ]]></literal>
    <justification jstring="[hyper(16387,a,12634,a)].">
      <j1 rule="hyper" parents="16387 12634"/>
    </justification>
  </clause>

  <clause id="16454">
    <literal><![CDATA[
      T(x,y * (z * K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y * (K(w,u) \ z)) = v5
    ]]></literal>
    <justification jstring="[para(6020(a,1),16399(a,1,2,2))].">
      <j1 rule="para" parents="6020 16399"/>
    </justification>
  </clause>

  <clause id="16455">
    <literal><![CDATA[
      T(x,y * T(z,T(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y * T(z,u)) = v5
    ]]></literal>
    <justification jstring="[para(6191(a,1),16399(a,1,2,2))].">
      <j1 rule="para" parents="6191 16399"/>
    </justification>
  </clause>

  <clause id="16456">
    <literal><![CDATA[
      T(x,y * T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y * T(z,T(u,v5))) = w
    ]]></literal>
    <justification jstring="[para(6863(a,1),16399(a,1,2,2))].">
      <j1 rule="para" parents="6863 16399"/>
    </justification>
  </clause>

  <clause id="16457">
    <literal><![CDATA[
      K(x,(y * K(z,u)) \ w) = K(x,(y \ K(u,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(13517,a,16334,a),flip(a)].">
      <j1 rule="hyper" parents="13517 16334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16459">
    <literal><![CDATA[
      K(x,((y / K(z,u)) * w) * v5) = K(x,((K(u,z) * y) * w) * v5)
    ]]></literal>
    <justification jstring="[para(5318(a,1),16336(a,1,2,1,1))].">
      <j1 rule="para" parents="5318 16336"/>
    </justification>
  </clause>

  <clause id="16460">
    <literal><![CDATA[
      K(x,((y \ z) * T(y,u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(T(y,u) * (z / y)) * w) = v5
    ]]></literal>
    <justification jstring="[para(16336(a,1),15154(a,1))].">
      <j1 rule="para" parents="16336 15154"/>
    </justification>
  </clause>

  <clause id="16461">
    <literal><![CDATA[
      K(x,y * (z * T(u,T(w,v5)))) = K(x,y * (z * T(u,w)))
    ]]></literal>
    <justification jstring="[para(6191(a,1),16338(a,1,2,2,2))].">
      <j1 rule="para" parents="6191 16338"/>
    </justification>
  </clause>

  <clause id="16462">
    <literal><![CDATA[
      K(x,y * (z * T(u,w / v5))) = K(x,y * (z * T(u,v5 \ w)))
    ]]></literal>
    <justification jstring="[para(6877(a,1),16338(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="6877 16338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16463">
    <literal><![CDATA[
      K(x,y / (z * K(u,w))) = K(x,y * (z \ K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(13519,a,16339,a),flip(a)].">
      <j1 rule="hyper" parents="13519 16339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16464">
    <literal><![CDATA[
      K(x,L(y / T(z / K(u,w),v5),T(z / K(u,w),v5),K(u,w))) = K(x,(y * K(u,w)) / (T(K(u,w) \ z,v5) * K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,13967,a,b,16339,a)].">
      <j1 rule="hyper" parents="63 13967 16339"/>
    </justification>
  </clause>

  <clause id="16465">
    <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(16339(a,1),13519(a,1))].">
      <j1 rule="para" parents="16339 13519"/>
    </justification>
  </clause>

  <clause id="16466">
    <literal><![CDATA[
      K(x,(y / z) / T(u,z \ y)) = K(x,u \ (y / z))
    ]]></literal>
    <justification jstring="[hyper(12670,a,16365,a),flip(a)].">
      <j1 rule="hyper" parents="12670 16365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16467">
    <literal><![CDATA[
      K(x,(y / z) / T(u,z \ y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u \ (y / z)) = w
    ]]></literal>
    <justification jstring="[para(16365(a,1),12670(a,1))].">
      <j1 rule="para" parents="16365 12670"/>
    </justification>
  </clause>

  <clause id="16468">
    <literal><![CDATA[
      K(x,T(y * K(z,u),y \ z) / w) = K(x,(T(z,u) / (z / y)) / w)
    ]]></literal>
    <justification jstring="[hyper(63,a,15044,a(flip),b,16367,a),flip(a)].">
      <j1 rule="hyper" parents="63 15044 16367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16469">
    <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(63,a,15043,a(flip),b,16367,a),flip(a)].">
      <j1 rule="hyper" parents="63 15043 16367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16470">
    <literal><![CDATA[
      K(x,T(y,z \ u) / (u / z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(u / z) \ y) = w
    ]]></literal>
    <justification jstring="[para(16367(a,1),12667(a,1))].">
      <j1 rule="para" parents="16367 12667"/>
    </justification>
  </clause>

  <clause id="16471">
    <literal><![CDATA[
      K(x \ (K(y,z) \ u),x) \ (u * K(z,y)) = x * ((u * K(z,y)) / x)
    ]]></literal>
    <justification jstring="[para(16370(a,2),4192(a,1,1))].">
      <j1 rule="para" parents="16370 4192"/>
    </justification>
  </clause>

  <clause id="16472">
    <literal><![CDATA[
      T(x,K(y,z * u) * w) = T(x,w * K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(15485,a,16403,a)].">
      <j1 rule="hyper" parents="15485 16403"/>
    </justification>
  </clause>

  <clause id="16473">
    <literal><![CDATA[
      K(x,T(y,(z / y) * u) * (u * (z / y))) = K(x,R(u,y \ z,y) * z)
    ]]></literal>
    <justification jstring="[para(10355(a,2),16408(a,2,2))].">
      <j1 rule="para" parents="10355 16408"/>
    </justification>
  </clause>

  <clause id="16474">
    <literal><![CDATA[
      K(x,(y * z) * K(u,z * y)) = K(x,T(y * z,u))
    ]]></literal>
    <justification jstring="[hyper(7013,a,16412,a),flip(a)].">
      <j1 rule="hyper" parents="7013 16412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16475">
    <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),16413(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14912 16413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16476">
    <literal><![CDATA[
      K(x,y * (T(z,u / w) / v5)) = K(x,y * (T(z,w \ u) / v5))
    ]]></literal>
    <justification jstring="[para(6877(a,1),16414(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="6877 16414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16477">
    <literal><![CDATA[
      K(x,K(y,z \ u) \ ((u / z) \ w)) = K(x,T(u / z,y) \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,14936,a(flip),b,16433,a),flip(a)].">
      <j1 rule="hyper" parents="63 14936 16433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16478">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,w) = K((x \ K(z,y)) * u,w)
    ]]></literal>
    <justification jstring="[hyper(13515,a,16453,a)].">
      <j1 rule="hyper" parents="13515 16453"/>
    </justification>
  </clause>

  <clause id="16479">
    <literal><![CDATA[
      K(x,y * (T(z \ (u \ w),x) \ K(u \ w,u))) = K(x,y / (z \ (w / u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,13564,a(flip),b,16463,a),flip(a)].">
      <j1 rule="hyper" parents="63 13564 16463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16480">
    <literal><![CDATA[
      K(x,y * ((z / u) \ K(u,w))) = K(x,y / (z / T(u,w)))
    ]]></literal>
    <justification jstring="[para(5450(a,1),16463(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5450 16463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16481">
    <literal><![CDATA[
      K(x,y * ((z * u) \ K(w,u))) = K(x,y / (z * T(u,w)))
    ]]></literal>
    <justification jstring="[para(5984(a,1),16463(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5984 16463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16482">
    <literal><![CDATA[
      K(x,y * (z \ K(y,u))) = K(x,T(y,u) / z)
    ]]></literal>
    <justification jstring="[para(13256(a,1),16463(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13256 16463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16483">
    <literal><![CDATA[
      K(x,y * ((z \ (u \ w)) \ K(u,w))) = K(x,y / (z \ (u \ T(w,u))))
    ]]></literal>
    <justification jstring="[para(14621(a,1),16463(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14621 16463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16484">
    <literal><![CDATA[
      T(x,y * (z \ K(y,u))) = T(x,T(y,u) / z)
    ]]></literal>
    <justification jstring="[hyper(124,a,16482,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 16482 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16485">
    <literal><![CDATA[
      K(x,(L(y,z,y) * u) * (w \ K(y * u,v5))) = K(x,T(L(y,z,y) * u,v5) / w)
    ]]></literal>
    <justification jstring="[para(12615(a,1),16482(a,1,2,2,2))].">
      <j1 rule="para" parents="12615 16482"/>
    </justification>
  </clause>

  <clause id="16486">
    <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(15076(a,1),16484(a,1,2,2,2))].">
      <j1 rule="para" parents="15076 16484"/>
    </justification>
  </clause>

  <clause id="16487">
    <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(12229(a,1),16389(a,1,1,2))].">
      <j1 rule="para" parents="12229 16389"/>
    </justification>
  </clause>

  <clause id="16488">
    <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(2086(a,1),16396(a,1,2,2))].">
      <j1 rule="para" parents="2086 16396"/>
    </justification>
  </clause>

  <clause id="16489">
    <literal><![CDATA[
      K(x,y * (K(z,K(u,w)) * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * v5) = v6
    ]]></literal>
    <justification jstring="[para(6357(a,1),16396(a,1,2,2))].">
      <j1 rule="para" parents="6357 16396"/>
    </justification>
  </clause>

  <clause id="16490">
    <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(6828(a,1),16396(a,1,2,2))].">
      <j1 rule="para" parents="6828 16396"/>
    </justification>
  </clause>

  <clause id="16491">
    <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(12319(a,1),16396(a,1,2,2))].">
      <j1 rule="para" parents="12319 16396"/>
    </justification>
  </clause>

  <clause id="16492">
    <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(15831(a,2),16396(a,1,2,2))].">
      <j1 rule="para" parents="15831 16396"/>
    </justification>
  </clause>

  <clause id="16493">
    <literal><![CDATA[
      K(x,(y \ (z * (u \ y))) \ K(z,u \ z)) = K(x,z \ ((y \ (z * (u \ y))) \ z))
    ]]></literal>
    <justification jstring="[hyper(16397,a,8356,a)].">
      <j1 rule="hyper" parents="16397 8356"/>
    </justification>
  </clause>

  <clause id="16494">
    <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(6902(a,1),16397(a,1,2,2))].">
      <j1 rule="para" parents="6902 16397"/>
    </justification>
  </clause>

  <clause id="16495">
    <literal><![CDATA[
      K(x,y \ K(z * u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ K(u * z,w)) = v5
    ]]></literal>
    <justification jstring="[para(12201(a,1),16397(a,1,2,2))].">
      <j1 rule="para" parents="12201 16397"/>
    </justification>
  </clause>

  <clause id="16496">
    <literal><![CDATA[
      T(x,y * K(z / u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y * K(u \ z,w)) = v5
    ]]></literal>
    <justification jstring="[para(7630(a,1),16400(a,1,2,2))].">
      <j1 rule="para" parents="7630 16400"/>
    </justification>
  </clause>

  <clause id="16497">
    <literal><![CDATA[
      T(x,K(y * z,T(u,w)) * v5) = T(x,K(u,y \ z) * v5)
    ]]></literal>
    <justification jstring="[hyper(16401,a,16128,a),flip(a)].">
      <j1 rule="hyper" parents="16401 16128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16499">
    <literal><![CDATA[
      T(x,y * K(z,T(u,w))) = T(x,K(u,z) * y)
    ]]></literal>
    <justification jstring="[hyper(16401,a,15470,a),flip(a)].">
      <j1 rule="hyper" parents="16401 15470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16500">
    <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(15470(a,1),16401(a,1))].">
      <j1 rule="para" parents="15470 16401"/>
    </justification>
  </clause>

  <clause id="16501">
    <literal><![CDATA[
      L((x \ (y * (x * K(z,T(u,w))))) / K(z,T(u,w)),K(z,T(u,w)),x) = T((K(z,T(u,w)) * y) / K(z,T(u,w)),K(u,z) * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1182,a,b,16499,a)].">
      <j1 rule="hyper" parents="63 1182 16499"/>
    </justification>
  </clause>

  <clause id="16502">
    <literal><![CDATA[
      T(x,K(y,z) * (u \ T(y,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,u \ T(T(y,w),z)) = v5
    ]]></literal>
    <justification jstring="[para(16499(a,1),15175(a,1))].">
      <j1 rule="para" parents="16499 15175"/>
    </justification>
  </clause>

  <clause id="16503">
    <literal><![CDATA[
      L(K(x,y * K(z,T(u,w))),x,v5) = (x * K(v6,v7)) \ (T(x,K(u,z) * y) * K(v6,v7))
    ]]></literal>
    <justification jstring="[para(16499(a,1),15528(a,2,2,1))].">
      <j1 rule="para" parents="16499 15528"/>
    </justification>
  </clause>

  <clause id="16504">
    <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(14993(a,1),16419(a,1,2,2))].">
      <j1 rule="para" parents="14993 16419"/>
    </justification>
  </clause>

  <clause id="16505">
    <literal><![CDATA[
      K(K(x * y,T(z,u)) * w,v5) = K(w * K(z,x \ y),v5)
    ]]></literal>
    <justification jstring="[hyper(16422,a,16142,a),flip(a)].">
      <j1 rule="hyper" parents="16422 16142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16506">
    <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(12201(a,1),16428(a,1,2,1))].">
      <j1 rule="para" parents="12201 16428"/>
    </justification>
  </clause>

  <clause id="16507">
    <literal><![CDATA[
      K(x,(T(y,z) * K(u,y)) / w) = K(x,T(T(y,u),z) / w)
    ]]></literal>
    <justification jstring="[hyper(16444,a,15176,a),flip(a)].">
      <j1 rule="hyper" parents="16444 15176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16508">
    <literal><![CDATA[
      K(x,T(T(y,z) / u,y) / w) = K(x,(u \ T(y,z)) / w)
    ]]></literal>
    <justification jstring="[hyper(16444,a,12663,a)].">
      <j1 rule="hyper" parents="16444 12663"/>
    </justification>
  </clause>

  <clause id="16509">
    <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(7775(a,1),16489(a,1,2,2))].">
      <j1 rule="para" parents="7775 16489"/>
    </justification>
  </clause>

  <clause id="16510">
    <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(63,a,12953,a(flip),b,16345,a),flip(a)].">
      <j1 rule="hyper" parents="63 12953 16345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16511">
    <literal><![CDATA[
      K(x,T(y * z,K(u,w)) / y) = K(x,T(z,K(w,u) * y))
    ]]></literal>
    <justification jstring="[hyper(7213,a,16366,a)].">
      <j1 rule="hyper" parents="7213 16366"/>
    </justification>
  </clause>

  <clause id="16513">
    <literal><![CDATA[
      T(x,y * T(z * T(u,w),T(u,v5))) = T(x,y * (T(u,w) * z))
    ]]></literal>
    <justification jstring="[hyper(16456,a,16404,a)].">
      <j1 rule="hyper" parents="16456 16404"/>
    </justification>
  </clause>

  <clause id="16514">
    <literal><![CDATA[
      K(x,y * (((z * K(u,K(w,v5))) * (v6 * K(z * K(u,K(w,v5)),v7))) * z)) = K(x,y * (((z * K(u,K(w,v5))) * v6) * T(z * K(u,K(w,v5)),v7)))
    ]]></literal>
    <justification jstring="[para(6144(a,1),16416(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6144 16416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16515">
    <literal><![CDATA[
      K(x,y * (((z * K(u,K(w,v5))) * v6) * ((v6 * (z * K(u,K(w,v5)))) / v6))) = K(x,y * ((v6 * (z * K(u,K(w,v5)))) * z))
    ]]></literal>
    <justification jstring="[para(7663(a,2),16416(a,1,2,2))].">
      <j1 rule="para" parents="7663 16416"/>
    </justification>
  </clause>

  <clause id="16516">
    <literal><![CDATA[
      K(x,y * (z * (u * (w * K(v5,K(v6,v7)))))) = K(x,y * (z * (u * w)))
    ]]></literal>
    <justification jstring="[para(10975(a,1),16416(a,1,2,2,2))].">
      <j1 rule="para" parents="10975 16416"/>
    </justification>
  </clause>

  <clause id="16517">
    <literal><![CDATA[
      K(x,y * (z * T(u * K(w,K(v5,v6)),v7))) = K(x,y * (z * T(u,v7)))
    ]]></literal>
    <justification jstring="[para(15831(a,2),16416(a,1,2,2,2))].">
      <j1 rule="para" parents="15831 16416"/>
    </justification>
  </clause>

  <clause id="16518">
    <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(16426(a,1),6695(a,1))].">
      <j1 rule="para" parents="16426 6695"/>
    </justification>
  </clause>

  <clause id="16519">
    <literal><![CDATA[
      T(x,K(y,z \ u) * w) = T(x,K(y,z * u) * w)
    ]]></literal>
    <justification jstring="[hyper(16401,a,16497,a),flip(a)].">
      <j1 rule="hyper" parents="16401 16497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16520">
    <literal><![CDATA[
      T(x,K(y,z * u) * T(w,K(y,z \ u))) = T(x,w * K(y,z \ u))
    ]]></literal>
    <justification jstring="[para(111(a,1),16519(a,1,2)),flip(a)].">
      <j1 rule="para" parents="111 16519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16521">
    <literal><![CDATA[
      K(x * K(y,z \ u),w) = K(x * K(y,z * u),w)
    ]]></literal>
    <justification jstring="[hyper(16422,a,16505,a),flip(a)].">
      <j1 rule="hyper" parents="16422 16505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16522">
    <literal><![CDATA[
      K(x * K(y,z * u),u \ z) = K(x,u \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,8623,a(flip),b,16521,a),flip(a)].">
      <j1 rule="hyper" parents="63 8623 16521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16523">
    <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(16411(a,1),16522(a,1,1,2))].">
      <j1 rule="para" parents="16411 16522"/>
    </justification>
  </clause>

  <clause id="16524">
    <literal><![CDATA[
      K(x,T(y * ((y / z) / y),y) / u) = K(x,(z \ T(y,z \ 1)) / u)
    ]]></literal>
    <justification jstring="[para(3093(a,1),16508(a,1,2,1,1))].">
      <j1 rule="para" parents="3093 16508"/>
    </justification>
  </clause>

  <clause id="16525">
    <literal><![CDATA[
      K(x,T(y,K(z,u) * w)) = K(x,(w * y) / w)
    ]]></literal>
    <justification jstring="[hyper(16378,a,16511,a),flip(a)].">
      <j1 rule="hyper" parents="16378 16511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16528">
    <literal><![CDATA[
      K(x,T(y,K(z,u) * w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(333,a,6924,a(flip),b,16525,a),flip(a)].">
      <j1 rule="hyper" parents="333 6924 16525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16529">
    <literal><![CDATA[
      K(x,T(y,K(z,u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,w)) = v5
    ]]></literal>
    <justification jstring="[para(16525(a,2),7011(a,1))].">
      <j1 rule="para" parents="16525 7011"/>
    </justification>
  </clause>

  <clause id="16530">
    <literal><![CDATA[
      K(x,T(y,z * K(u,w))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(15608,a,16528,a)].">
      <j1 rule="hyper" parents="15608 16528"/>
    </justification>
  </clause>

  <clause id="16533">
    <literal><![CDATA[
      T(x,T(y,K(z,u) * w)) = T(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(124,a,16528,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 16528 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16534">
    <literal><![CDATA[
      K(x,T(y,K(z,u) \ w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,15396,a,b,16528,a)].">
      <j1 rule="hyper" parents="63 15396 16528"/>
    </justification>
  </clause>

  <clause id="16535">
    <literal><![CDATA[
      K(x,T(T(((y \ z) * y) \ u,w),u)) = K(x,T((K(y,y \ z) * u) / z,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,10054,a(flip),b,16528,a),flip(a)].">
      <j1 rule="hyper" parents="63 10054 16528"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16536">
    <literal><![CDATA[
      K(x,T(y,T(z,u) * w)) = K(x,T(y,z * w))
    ]]></literal>
    <justification jstring="[para(4273(a,1),16528(a,1,2,2))].">
      <j1 rule="para" parents="4273 16528"/>
    </justification>
  </clause>

  <clause id="16537">
    <literal><![CDATA[
      K(x,T(y,(z / u) * w)) = K(x,T(y,(u \ z) * w))
    ]]></literal>
    <justification jstring="[para(4875(a,1),16528(a,1,2,2))].">
      <j1 rule="para" parents="4875 16528"/>
    </justification>
  </clause>

  <clause id="16538">
    <literal><![CDATA[
      K(x,T(y,z \ T(u,w))) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[para(4840(a,1),16528(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4840 16528"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16540">
    <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(16528(a,1),6397(a,1,2))].">
      <j1 rule="para" parents="16528 6397"/>
    </justification>
  </clause>

  <clause id="16545">
    <literal><![CDATA[
      T(K(x,y),z * K(u,w)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(6552,a,16530,a)].">
      <j1 rule="hyper" parents="6552 16530"/>
    </justification>
  </clause>

  <clause id="16546">
    <literal><![CDATA[
      K(x,T(y,z)) * (z * K(u,w)) = (z * K(u,w)) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(125,a,16530,a(flip),b,6884,a)].">
      <j1 rule="hyper" parents="125 16530 6884"/>
    </justification>
  </clause>

  <clause id="16547">
    <literal><![CDATA[
      K(x,T(y,z / K(u,w))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(12(a,1),16530(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 16530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16548">
    <literal><![CDATA[
      K(x,T(y,z / (u / w))) = K(x,T(y,z / (w \ u)))
    ]]></literal>
    <justification jstring="[para(5520(a,1),16530(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5520 16530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16549">
    <literal><![CDATA[
      K(x,T(y,z * (u / w))) = K(x,T(y,z * (w \ u)))
    ]]></literal>
    <justification jstring="[para(5523(a,1),16530(a,1,2,2))].">
      <j1 rule="para" parents="5523 16530"/>
    </justification>
  </clause>

  <clause id="16552">
    <literal><![CDATA[
      K(x,T(y,(z * K(u,w)) * v5)) = K(x,T(y,z * v5))
    ]]></literal>
    <justification jstring="[para(7980(a,1),16530(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7980 16530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16554">
    <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(16530(a,1),13919(a,1))].">
      <j1 rule="para" parents="16530 13919"/>
    </justification>
  </clause>

  <clause id="16555">
    <literal><![CDATA[
      K(x,T(y,K(z,u) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,w)) = v5
    ]]></literal>
    <justification jstring="[para(16530(a,1),15723(a,1))].">
      <j1 rule="para" parents="16530 15723"/>
    </justification>
  </clause>

  <clause id="16556">
    <literal><![CDATA[
      T(x,T(y,K(z,u) \ w)) = T(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,15399,a,b,16533,a)].">
      <j1 rule="hyper" parents="63 15399 16533"/>
    </justification>
  </clause>

  <clause id="16557">
    <literal><![CDATA[
      T(x,T(y,T(z,u) * w)) = T(x,T(y,z * w))
    ]]></literal>
    <justification jstring="[para(4273(a,1),16533(a,1,2,2))].">
      <j1 rule="para" parents="4273 16533"/>
    </justification>
  </clause>

  <clause id="16558">
    <literal><![CDATA[
      T(x,T(y,(z * u) * w)) = T(x,T(y,(u * z) * w))
    ]]></literal>
    <justification jstring="[para(10080(a,1),16533(a,1,2,2))].">
      <j1 rule="para" parents="10080 16533"/>
    </justification>
  </clause>

  <clause id="16559">
    <literal><![CDATA[
      T(x,T(y,(T(z,u) * w) * v5)) = T(x,T(y,(z * w) * v5))
    ]]></literal>
    <justification jstring="[para(13917(a,1),16533(a,1,2,2))].">
      <j1 rule="para" parents="13917 16533"/>
    </justification>
  </clause>

  <clause id="16561">
    <literal><![CDATA[
      (K(x,T(y,z)) * z) * K(x,y) = (x * y) * ((y * x) \ (K(x,y) * z))
    ]]></literal>
    <justification jstring="[para(16545(a,1),10117(a,1,1,1))].">
      <j1 rule="para" parents="16545 10117"/>
    </justification>
  </clause>

  <clause id="16564">
    <literal><![CDATA[
      (K(x,T(y,z)) * u) \ (z * K(x,y)) = (K(x,y) * u) \ (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(16545(a,1),13437(a,1,1,1))].">
      <j1 rule="para" parents="16545 13437"/>
    </justification>
  </clause>

  <clause id="16565">
    <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(16545(a,1),14812(a,1,2,2))].">
      <j1 rule="para" parents="16545 14812"/>
    </justification>
  </clause>

  <clause id="16566">
    <literal><![CDATA[
      K(x,T(y,K(z,u) / w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(7285,a,16547,a)].">
      <j1 rule="hyper" parents="7285 16547"/>
    </justification>
  </clause>

  <clause id="16567">
    <literal><![CDATA[
      T(x,T((K(y,z) \ u) \ w,u)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,w / (K(y,z) \ u)) = v5
    ]]></literal>
    <justification jstring="[para(16556(a,1),13513(a,1))].">
      <j1 rule="para" parents="16556 13513"/>
    </justification>
  </clause>

  <clause id="16568">
    <literal><![CDATA[
      K(x,T(y,z)) * (K(u,w) / z) = (K(u,w) / z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(125,a,16566,a(flip),b,6884,a)].">
      <j1 rule="hyper" parents="125 16566 6884"/>
    </justification>
  </clause>

  <clause id="16569">
    <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(2064(a,1),16529(a,1,2,2))].">
      <j1 rule="para" parents="2064 16529"/>
    </justification>
  </clause>

  <clause id="16570">
    <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(4273(a,1),16529(a,1,2,2))].">
      <j1 rule="para" parents="4273 16529"/>
    </justification>
  </clause>

  <clause id="16571">
    <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(4967(a,1),16529(a,1,2,2))].">
      <j1 rule="para" parents="4967 16529"/>
    </justification>
  </clause>

  <clause id="16572">
    <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(4963(a,1),16529(a,1,2,2))].">
      <j1 rule="para" parents="4963 16529"/>
    </justification>
  </clause>

  <clause id="16573">
    <literal><![CDATA[
      T(K(x,y),K(z,u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,w)) = v5
    ]]></literal>
    <justification jstring="[para(6365(a,1),16529(a,1))].">
      <j1 rule="para" parents="6365 16529"/>
    </justification>
  </clause>

  <clause id="16574">
    <literal><![CDATA[
      K(x,T(y,z * K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = v5
    ]]></literal>
    <justification jstring="[para(6887(a,1),16529(a,1,2,2))].">
      <j1 rule="para" parents="6887 16529"/>
    </justification>
  </clause>

  <clause id="16575">
    <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(10080(a,1),16529(a,1,2,2))].">
      <j1 rule="para" parents="10080 16529"/>
    </justification>
  </clause>

  <clause id="16576">
    <literal><![CDATA[
      T(K(x,y),z * K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = v5
    ]]></literal>
    <justification jstring="[para(6887(a,1),16573(a,1,2))].">
      <j1 rule="para" parents="6887 16573"/>
    </justification>
  </clause>

  <clause id="16577">
    <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(6012(a,1),16574(a,1,2,2))].">
      <j1 rule="para" parents="6012 16574"/>
    </justification>
  </clause>

  <clause id="16578">
    <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(13414(a,1),16574(a,1,2,2))].">
      <j1 rule="para" parents="13414 16574"/>
    </justification>
  </clause>

  <clause id="16579">
    <literal><![CDATA[
      K(x,T(y,L(z,u,u \ w) * w)) = K(x,T(y,(u \ w) * (u * z)))
    ]]></literal>
    <justification jstring="[hyper(15781,a,16537,a)].">
      <j1 rule="hyper" parents="15781 16537"/>
    </justification>
  </clause>

  <clause id="16580">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z / (u / w))) = K(x,T(y,z / (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(7083,a,16548,a)].">
      <j1 rule="hyper" parents="7083 16548"/>
    </justification>
  </clause>

  <clause id="16581">
    <literal><![CDATA[
      K(L(x,y,z),T(u,w * (v5 \ v6))) = K(x,L(T(u,w * (v6 / v5)),y,z))
    ]]></literal>
    <justification jstring="[hyper(10963,a,16549,a),flip(a)].">
      <j1 rule="hyper" parents="10963 16549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16582">
    <literal><![CDATA[
      K(x * K(y,z),T(u,z * y)) = K(z \ T(x * z,y),u)
    ]]></literal>
    <justification jstring="[hyper(16571,a,16268,a)].">
      <j1 rule="hyper" parents="16571 16268"/>
    </justification>
  </clause>

  <clause id="16583">
    <literal><![CDATA[
      K(x,T(y,z)) * (z * K(u,y)) = z * (K(u,y) * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(333,a,8165,a(flip),b,16546,a),flip(a)].">
      <j1 rule="hyper" parents="333 8165 16546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16584">
    <literal><![CDATA[
      K(x,K(y,z)) * (z * K(u,w)) = T(z * K(u,w),K(x,y))
    ]]></literal>
    <justification jstring="[hyper(253,a,16546,a(flip),b,8087,a),flip(a)].">
      <j1 rule="hyper" parents="253 16546 8087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16585">
    <literal><![CDATA[
      K(x,y) * ((1 / y) * K(z,u)) = ((1 / y) * K(z,u)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(4622(a,1),16546(a,1,1))].">
      <j1 rule="para" parents="4622 16546"/>
    </justification>
  </clause>

  <clause id="16586">
    <literal><![CDATA[
      T(x,T(y,(z * T(u,w)) * v5)) = T(x,T(y,(u * z) * v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,16558,a,b,16559,a)].">
      <j1 rule="hyper" parents="63 16558 16559"/>
    </justification>
  </clause>

  <clause id="16587">
    <literal><![CDATA[
      K(x,T(y,z)) / T(z,u) = (K(u,z) / z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,13304,a(flip),b,16568,a)].">
      <j1 rule="hyper" parents="63 13304 16568"/>
    </justification>
  </clause>

  <clause id="16588">
    <literal><![CDATA[
      ((1 / x) * K(y,z)) * K(u,x) = (K(u,x) / x) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,13553,a,b,16587,a)].">
      <j1 rule="hyper" parents="63 13553 16587"/>
    </justification>
  </clause>

  <clause id="16589">
    <literal><![CDATA[
      K(T(K(x,y) * z,x * y),u) = K(y \ T(z * y,x),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,12311,a,b,16582,a)].">
      <j1 rule="hyper" parents="63 12311 16582"/>
    </justification>
  </clause>

  <clause id="16590">
    <literal><![CDATA[
      x * (y * (K(x,z) * K(x,z))) = T(x,z) * (K(x,z) * y)
    ]]></literal>
    <justification jstring="[para(16583(a,1),6406(a,1,2))].">
      <j1 rule="para" parents="16583 6406"/>
    </justification>
  </clause>

  <clause id="16591">
    <literal><![CDATA[
      (x * (T(T(x,y),y) \ z)) * u = (z * (K(y,x) * K(y,x))) * u
    ]]></literal>
    <justification jstring="[para(16583(a,1),6411(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16583 6411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16592">
    <literal><![CDATA[
      T(x * K(y,z),K(u,w)) = T(x,K(u,w)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(6813,a,16584,a),flip(a)].">
      <j1 rule="hyper" parents="6813 16584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16593">
    <literal><![CDATA[
      K(x,K(y,z * K(u,w))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(35,a,6795,a,b,16584,a)].">
      <j1 rule="hyper" parents="35 6795 16584"/>
    </justification>
  </clause>

  <clause id="16594">
    <literal><![CDATA[
      K(x,K(y,K(z,u) * w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(15681,a,16593,a)].">
      <j1 rule="hyper" parents="15681 16593"/>
    </justification>
  </clause>

  <clause id="16596">
    <literal><![CDATA[
      K(x,K(y,z * K(u,w))) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(333,a,6800,a,b,16593,a),flip(a)].">
      <j1 rule="hyper" parents="333 6800 16593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16597">
    <literal><![CDATA[
      T(x,K(y,z * K(u,w))) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(124,a,16593,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 16593 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16598">
    <literal><![CDATA[
      K(x,K(y,K(z,u) \ w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,15805,a,b,16593,a)].">
      <j1 rule="hyper" parents="63 15805 16593"/>
    </justification>
  </clause>

  <clause id="16600">
    <literal><![CDATA[
      K(x,K(y,z * T(u,w))) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[para(2087(a,1),16593(a,1,2,2))].">
      <j1 rule="para" parents="2087 16593"/>
    </justification>
  </clause>

  <clause id="16602">
    <literal><![CDATA[
      K(x,K(y,z / T(u,w))) = K(x,K(y,z / u))
    ]]></literal>
    <justification jstring="[para(5450(a,1),16593(a,1,2,2))].">
      <j1 rule="para" parents="5450 16593"/>
    </justification>
  </clause>

  <clause id="16603">
    <literal><![CDATA[
      K(x,K(y,z / (u / w))) = K(x,K(y,z / (w \ u)))
    ]]></literal>
    <justification jstring="[para(5520(a,1),16593(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5520 16593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16604">
    <literal><![CDATA[
      K(x,K(y,z * (u * w))) = K(x,K(y,z * (w * u)))
    ]]></literal>
    <justification jstring="[para(6305(a,1),16593(a,1,2,2))].">
      <j1 rule="para" parents="6305 16593"/>
    </justification>
  </clause>

  <clause id="16605">
    <literal><![CDATA[
      K(x,K(y,T(z,u) \ w)) = K(x,K(y,z \ w))
    ]]></literal>
    <justification jstring="[para(7339(a,1),16593(a,1,2,2))].">
      <j1 rule="para" parents="7339 16593"/>
    </justification>
  </clause>

  <clause id="16606">
    <literal><![CDATA[
      K(x,K(y,z / ((u * w) / u))) = K(x,K(y,z / w))
    ]]></literal>
    <justification jstring="[para(7664(a,2),16593(a,1,2,2))].">
      <j1 rule="para" parents="7664 16593"/>
    </justification>
  </clause>

  <clause id="16607">
    <literal><![CDATA[
      K(x,K(y,z / (u / (u / w)))) = K(x,K(y,z / w))
    ]]></literal>
    <justification jstring="[para(7672(a,2),16593(a,1,2,2))].">
      <j1 rule="para" parents="7672 16593"/>
    </justification>
  </clause>

  <clause id="16608">
    <literal><![CDATA[
      K(x,K(y,(z * K(u,w)) * v5)) = K(x,K(y,z * v5))
    ]]></literal>
    <justification jstring="[para(7980(a,1),16593(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7980 16593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16609">
    <literal><![CDATA[
      K(x,K(y,z / (u * w))) = K(x,K(y,z / (w * u)))
    ]]></literal>
    <justification jstring="[para(10446(a,1),16593(a,1,2,2))].">
      <j1 rule="para" parents="10446 16593"/>
    </justification>
  </clause>

  <clause id="16610">
    <literal><![CDATA[
      K(x,K(y,z \ (u / w))) = K(x,K(y,z \ (w \ u)))
    ]]></literal>
    <justification jstring="[para(13414(a,1),16593(a,1,2,2))].">
      <j1 rule="para" parents="13414 16593"/>
    </justification>
  </clause>

  <clause id="16611">
    <literal><![CDATA[
      T(x,K(y,K(z,u) * w)) = T(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(124,a,16594,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 16594 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16612">
    <literal><![CDATA[
      K(x,K(y,((z * u) / z) * w)) = K(x,K(y,u * w))
    ]]></literal>
    <justification jstring="[para(4817(a,1),16594(a,1,2,2))].">
      <j1 rule="para" parents="4817 16594"/>
    </justification>
  </clause>

  <clause id="16616">
    <literal><![CDATA[
      K(x,K(y,(z * u) * w)) = K(x,K(y,(u * z) * w))
    ]]></literal>
    <justification jstring="[para(10080(a,1),16594(a,1,2,2))].">
      <j1 rule="para" parents="10080 16594"/>
    </justification>
  </clause>

  <clause id="16617">
    <literal><![CDATA[
      K(x,K(y,(z * u) / w)) = K(x,K(y,(u * z) / w))
    ]]></literal>
    <justification jstring="[para(13471(a,1),16594(a,1,2,2))].">
      <j1 rule="para" parents="13471 16594"/>
    </justification>
  </clause>

  <clause id="16618">
    <literal><![CDATA[
      K(x,K(y,(K(z,u) * w) / v5)) = K(x,K(y,w / v5))
    ]]></literal>
    <justification jstring="[para(14186(a,1),16594(a,1,2,2))].">
      <j1 rule="para" parents="14186 16594"/>
    </justification>
  </clause>

  <clause id="16619">
    <literal><![CDATA[
      K(x,K(y,K(z,u) / w)) = K(x,K(w,y))
    ]]></literal>
    <justification jstring="[hyper(15808,a,16596,a)].">
      <j1 rule="hyper" parents="15808 16596"/>
    </justification>
  </clause>

  <clause id="16620">
    <literal><![CDATA[
      K(x,K(y * K(z,u),w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(6836,a,16596,a)].">
      <j1 rule="hyper" parents="6836 16596"/>
    </justification>
  </clause>

  <clause id="16621">
    <literal><![CDATA[
      T(x,K(y,z \ K(u,w))) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(15820,a,16597,a)].">
      <j1 rule="hyper" parents="15820 16597"/>
    </justification>
  </clause>

  <clause id="16622">
    <literal><![CDATA[
      T(x,K(y,T(z,u) * w)) = T(x,K(y,z * w))
    ]]></literal>
    <justification jstring="[para(4959(a,1),16597(a,1,2,2))].">
      <j1 rule="para" parents="4959 16597"/>
    </justification>
  </clause>

  <clause id="16623">
    <literal><![CDATA[
      T(x,K(y,z * (u * K(w,v5)))) = T(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[para(10874(a,1),16597(a,1,2,2))].">
      <j1 rule="para" parents="10874 16597"/>
    </justification>
  </clause>

  <clause id="16624">
    <literal><![CDATA[
      T(T(x,K(y,z)),(z * K(u,w)) * y) = T(x,y * (z * K(u,w)))
    ]]></literal>
    <justification jstring="[para(16597(a,1),12228(a,1,1))].">
      <j1 rule="para" parents="16597 12228"/>
    </justification>
  </clause>

  <clause id="16625">
    <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(16597(a,1),14912(a,1,2,1,2))].">
      <j1 rule="para" parents="16597 14912"/>
    </justification>
  </clause>

  <clause id="16626">
    <literal><![CDATA[
      K(x,K(y,K(z,u) \ w)) = K(w,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(333,a,6788,a(flip),b,16598,a),flip(a)].">
      <j1 rule="hyper" parents="333 6788 16598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16628">
    <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(16598(a,1),15839(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16598 15839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16629">
    <literal><![CDATA[
      T(x,K(y,K(z,u) * w)) = T(x,K(w,y))
    ]]></literal>
    <justification jstring="[hyper(333,a,6840,a,b,16611,a),flip(a)].">
      <j1 rule="hyper" parents="333 6840 16611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16630">
    <literal><![CDATA[
      T(x,K(y,K(z,u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,K(w,y)) = v5
    ]]></literal>
    <justification jstring="[para(16611(a,2),6868(a,1))].">
      <j1 rule="para" parents="16611 6868"/>
    </justification>
  </clause>

  <clause id="16631">
    <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(11001,a,16619,a)].">
      <j1 rule="hyper" parents="11001 16619"/>
    </justification>
  </clause>

  <clause id="16632">
    <literal><![CDATA[
      K(x,K(K(y,z) / u,w)) = K(x,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(6836,a,16619,a)].">
      <j1 rule="hyper" parents="6836 16619"/>
    </justification>
  </clause>

  <clause id="16633">
    <literal><![CDATA[
      K(x,K(K(y,z) * u,w)) = K(x,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(15722,a,16620,a)].">
      <j1 rule="hyper" parents="15722 16620"/>
    </justification>
  </clause>

  <clause id="16634">
    <literal><![CDATA[
      K(x,K(T(y,z) / u,w)) = K(x,K(y / u,w))
    ]]></literal>
    <justification jstring="[para(2170(a,1),16620(a,1,2,1))].">
      <j1 rule="para" parents="2170 16620"/>
    </justification>
  </clause>

  <clause id="16636">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,(K(u,w) * y) * z) = K(x,z * (K(u,w) * y))
    ]]></literal>
    <justification jstring="[para(16620(a,1),15863(a,1,1))].">
      <j1 rule="para" parents="16620 15863"/>
    </justification>
  </clause>

  <clause id="16637">
    <literal><![CDATA[
      T(x,K(y,z \ K(u,w))) = T(x,K(y,K(v5,v6) * z))
    ]]></literal>
    <justification jstring="[hyper(333,a,16611,a,b,16621,a),flip(a)].">
      <j1 rule="hyper" parents="333 16611 16621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16638">
    <literal><![CDATA[
      K(x,K(K(y,z) \ u,w)) = K(u,K(x,w))
    ]]></literal>
    <justification jstring="[hyper(6836,a,16626,a)].">
      <j1 rule="hyper" parents="6836 16626"/>
    </justification>
  </clause>

  <clause id="16639">
    <literal><![CDATA[
      T(T(K(x,y) * z,K(x,y)) \ u,K(K(x,y) * z,w)) = (z * K(x,y)) \ T(u,K(z,w))
    ]]></literal>
    <justification jstring="[para(16629(a,1),11706(a,2,2))].">
      <j1 rule="para" parents="16629 11706"/>
    </justification>
  </clause>

  <clause id="16640">
    <literal><![CDATA[
      T(T(K(x,y) * z,K(x,y)) / u,K(K(x,y) * z,w)) = (z * K(x,y)) / T(u,K(z,w))
    ]]></literal>
    <justification jstring="[para(16629(a,1),12387(a,2,2))].">
      <j1 rule="para" parents="16629 12387"/>
    </justification>
  </clause>

  <clause id="16641">
    <literal><![CDATA[
      K(x,K(K(y,z) / u,w)) = K(x,K(u * K(v5,v6),w))
    ]]></literal>
    <justification jstring="[hyper(333,a,16620,a,b,16632,a),flip(a)].">
      <j1 rule="hyper" parents="333 16620 16632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16642">
    <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(10917,a,16633,a)].">
      <j1 rule="hyper" parents="10917 16633"/>
    </justification>
  </clause>

  <clause id="16643">
    <literal><![CDATA[
      K(x,T(K(y,z) * u,w)) * K(x,K(u,w)) = K(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(126,a,16633,a(flip),b,7124,a)].">
      <j1 rule="hyper" parents="126 16633 7124"/>
    </justification>
  </clause>

  <clause id="16644">
    <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(16600(a,2),15681(a,1))].">
      <j1 rule="para" parents="16600 15681"/>
    </justification>
  </clause>

  <clause id="16645">
    <literal><![CDATA[
      T(x,K(y \ ((z * u) / z),w)) = K(x,K(w,y * u)) * x
    ]]></literal>
    <justification jstring="[para(16600(a,1),15807(a,2,1))].">
      <j1 rule="para" parents="16600 15807"/>
    </justification>
  </clause>

  <clause id="16648">
    <literal><![CDATA[
      K(x,K(y / z,L(u,z,w))) = K(x,K(u,(y * w) / (w * z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,16015,a(flip),b,16634,a),flip(a)].">
      <j1 rule="hyper" parents="63 16015 16634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16649">
    <literal><![CDATA[
      T((x \ 1) * K(y,z),K(u,w)) = K(x,K(u,w)) * (x \ K(y,z))
    ]]></literal>
    <justification jstring="[hyper(333,a,13696,a(flip),b,16592,a),flip(a)].">
      <j1 rule="hyper" parents="333 13696 16592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16651">
    <literal><![CDATA[
      T(K(x,y) * z,K(u,w)) = K(x,y) * T(z,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(35,a,5367,a(flip),b,16592,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="35 5367 16592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16652">
    <literal><![CDATA[
      T(K(x,y) \ z,K(u,w)) = K(x,y) \ T(z,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(35,a,4105,a(flip),b,16592,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="35 4105 16592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16654">
    <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(16603(a,2),10896(a,1,1))].">
      <j1 rule="para" parents="16603 10896"/>
    </justification>
  </clause>

  <clause id="16655">
    <literal><![CDATA[
      K(x,K(y,(T(z,u) / w) * v5)) = K(x,K(y,(z / w) * v5))
    ]]></literal>
    <justification jstring="[para(2170(a,1),16608(a,1,2,2,1))].">
      <j1 rule="para" parents="2170 16608"/>
    </justification>
  </clause>

  <clause id="16656">
    <literal><![CDATA[
      K(x,K(y,((z / u) * w) * v5)) = K(x,K(y,((u \ z) * w) * v5))
    ]]></literal>
    <justification jstring="[para(5966(a,1),16608(a,1,2,2,1))].">
      <j1 rule="para" parents="5966 16608"/>
    </justification>
  </clause>

  <clause id="16657">
    <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(16608(a,2),15681(a,1))].">
      <j1 rule="para" parents="16608 15681"/>
    </justification>
  </clause>

  <clause id="16658">
    <literal><![CDATA[
      K(x,K(y,(z * u) / w)) = K(x,K(y,w / (u * z)))
    ]]></literal>
    <justification jstring="[hyper(7214,a,16609,a)].">
      <j1 rule="hyper" parents="7214 16609"/>
    </justification>
  </clause>

  <clause id="16662">
    <literal><![CDATA[
      K(x,K(y,((z * u) * w) / (w * u))) = K(x,K(y,L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(333,a,16014,a(flip),b,16617,a),flip(a)].">
      <j1 rule="hyper" parents="333 16014 16617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16663">
    <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(980(a,1),16617(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="980 16617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16664">
    <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(16617(a,1),7214(a,1))].">
      <j1 rule="para" parents="16617 7214"/>
    </justification>
  </clause>

  <clause id="16665">
    <literal><![CDATA[
      K(x,K(y,z / (K(u,w) * v5))) = K(x,K(y,v5 / z))
    ]]></literal>
    <justification jstring="[hyper(7214,a,16618,a)].">
      <j1 rule="hyper" parents="7214 16618"/>
    </justification>
  </clause>

  <clause id="16667">
    <literal><![CDATA[
      K(x,K(y,(z * T(u,w)) / v5)) = K(x,K(y,(z * u) / v5))
    ]]></literal>
    <justification jstring="[para(4967(a,1),16618(a,1,2,2,1))].">
      <j1 rule="para" parents="4967 16618"/>
    </justification>
  </clause>

  <clause id="16668">
    <literal><![CDATA[
      T(x,K(y,z * (u \ T(w,v5)))) = T(x,K(y,z * (u \ w)))
    ]]></literal>
    <justification jstring="[para(2086(a,1),16623(a,1,2,2,2))].">
      <j1 rule="para" parents="2086 16623"/>
    </justification>
  </clause>

  <clause id="16669">
    <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(121,a,16637,a(flip),b,7316,a),flip(a)].">
      <j1 rule="hyper" parents="121 16637 7316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16670">
    <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(16637(a,1),6883(a,1))].">
      <j1 rule="para" parents="16637 6883"/>
    </justification>
  </clause>

  <clause id="16671">
    <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(63,a,10944,a(flip),b,16641,a),flip(a)].">
      <j1 rule="hyper" parents="63 10944 16641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16676">
    <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(16658(a,2),7214(a,1))].">
      <j1 rule="para" parents="16658 7214"/>
    </justification>
  </clause>

  <clause id="16677">
    <literal><![CDATA[
      K(x,K(y,(z * K(u,w)) / v5)) = K(x,K(y,v5 / z))
    ]]></literal>
    <justification jstring="[para(6943(a,1),16665(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="6943 16665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16678">
    <literal><![CDATA[
      K(x,K(y,z / ((K(u,w) * v5) * v6))) = K(x,K(y,(v5 * v6) / z))
    ]]></literal>
    <justification jstring="[para(11580(a,1),16665(a,1,2,2,2))].">
      <j1 rule="para" parents="11580 16665"/>
    </justification>
  </clause>

  <clause id="16680">
    <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(16677(a,1),15835(a,1,1))].">
      <j1 rule="para" parents="16677 15835"/>
    </justification>
  </clause>

  <clause id="16681">
    <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(63,a,6757,a(flip),b,16586,a),flip(a)].">
      <j1 rule="hyper" parents="63 6757 16586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16682">
    <literal><![CDATA[
      K(K(x,y) * z,T(u,x * y)) = K(y \ T(z * y,x),u)
    ]]></literal>
    <justification jstring="[hyper(6695,a,16589,a)].">
      <j1 rule="hyper" parents="6695 16589"/>
    </justification>
  </clause>

  <clause id="16683">
    <literal><![CDATA[
      x * (y * (K(x,z) * K(x,z))) = T(T(x,z),z) * y
    ]]></literal>
    <justification jstring="[hyper(333,a,4412,a(flip),b,16590,a),flip(a)].">
      <j1 rule="hyper" parents="333 4412 16590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16684">
    <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(16683(a,1),11279(a,2,2,1))].">
      <j1 rule="para" parents="16683 11279"/>
    </justification>
  </clause>

  <clause id="16685">
    <literal><![CDATA[
      T(x,T(T(y,z),z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y * u) = w
    ]]></literal>
    <justification jstring="[para(16683(a,1),15788(a,1,2))].">
      <j1 rule="para" parents="16683 15788"/>
    </justification>
  </clause>

  <clause id="16686">
    <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(333,a,10914,a,b,16631,a),flip(a)].">
      <j1 rule="hyper" parents="333 10914 16631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16687">
    <literal><![CDATA[
      T(x,K(y \ ((z * u) / z),w)) = T(x,K(w,y * u))
    ]]></literal>
    <justification jstring="[hyper(333,a,4274,a,b,16645,a),flip(a)].">
      <j1 rule="hyper" parents="333 4274 16645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16689">
    <literal><![CDATA[
      T(x,K(y \ T(z,u),w)) = T(x,K(w,y * z))
    ]]></literal>
    <justification jstring="[para(15064(a,1),16687(a,1,2))].">
      <j1 rule="para" parents="15064 16687"/>
    </justification>
  </clause>

  <clause id="16690">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),z \ T(u,w)) = T(x,T(z \ T(u,w),y))
    ]]></literal>
    <justification jstring="[para(16689(a,1),6190(a,1,1))].">
      <j1 rule="para" parents="16689 6190"/>
    </justification>
  </clause>

  <clause id="16691">
    <literal><![CDATA[
      K(x,K(y,((z / (z / u)) / w) * v5)) = K(x,K(y,(u / w) * v5))
    ]]></literal>
    <justification jstring="[para(258(a,1),16655(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="258 16655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16692">
    <literal><![CDATA[
      K(x,K(y,z / (T(u,w) * v5))) = K(x,K(y,(v5 * u) / z))
    ]]></literal>
    <justification jstring="[hyper(63,a,16658,a(flip),b,16667,a)].">
      <j1 rule="hyper" parents="63 16658 16667"/>
    </justification>
  </clause>

  <clause id="16693">
    <literal><![CDATA[
      K(x,K(y,(z * (u / w)) / v5)) = K(x,K(y,v5 / ((w \ u) * z)))
    ]]></literal>
    <justification jstring="[para(113(a,1),16692(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="113 16692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16694">
    <literal><![CDATA[
      K(x,y * (z * K(u,u \ w))) = K(x,y * (K(u,w) * z))
    ]]></literal>
    <justification jstring="[hyper(16362,a,12798,a)].">
      <j1 rule="hyper" parents="16362 12798"/>
    </justification>
  </clause>

  <clause id="16695">
    <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(63,a,15288,a,b,16694,a)].">
      <j1 rule="hyper" parents="63 15288 16694"/>
    </justification>
  </clause>

  <clause id="16696">
    <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(63,a,13209,a,b,16694,a)].">
      <j1 rule="hyper" parents="63 13209 16694"/>
    </justification>
  </clause>

  <clause id="16697">
    <literal><![CDATA[
      K(x,y * (z / (u / (u / w)))) = K(x,y * (K(w,u) * (z / w)))
    ]]></literal>
    <justification jstring="[para(7672(a,2),16694(a,1,2,2))].">
      <j1 rule="para" parents="7672 16694"/>
    </justification>
  </clause>

  <clause id="16698">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (w * u))) = K(x,y * (w * (z * (u / z))))
    ]]></literal>
    <justification jstring="[para(10324(a,1),16694(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10324 16694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16699">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (w \ (z \ u)))) = K(x,y * (w \ (u / z)))
    ]]></literal>
    <justification jstring="[para(13414(a,1),16694(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13414 16694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16700">
    <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(16322(a,1),16467(a,1,2,2))].">
      <j1 rule="para" parents="16322 16467"/>
    </justification>
  </clause>

  <clause id="16701">
    <literal><![CDATA[
      K(x \ K(y,z * (u * y)),w) = K(x \ K(y,u * z),w)
    ]]></literal>
    <justification jstring="[hyper(16487,a,12718,a)].">
      <j1 rule="hyper" parents="16487 12718"/>
    </justification>
  </clause>

  <clause id="16702">
    <literal><![CDATA[
      K(x \ K(y,z * u),w) = K(x \ K(y,u * z),w)
    ]]></literal>
    <justification jstring="[hyper(16487,a,xx)].">
      <j1 rule="hyper" parents="16487"/>
    </justification>
  </clause>

  <clause id="16703">
    <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(8012(a,2),16487(a,1))].">
      <j1 rule="para" parents="8012 16487"/>
    </justification>
  </clause>

  <clause id="16704">
    <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(6035(a,1),16488(a,1,2,2,2))].">
      <j1 rule="para" parents="6035 16488"/>
    </justification>
  </clause>

  <clause id="16705">
    <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(13199(a,1),16488(a,1,2,2,2))].">
      <j1 rule="para" parents="13199 16488"/>
    </justification>
  </clause>

  <clause id="16706">
    <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(6191(a,1),16490(a,1,2,2,2))].">
      <j1 rule="para" parents="6191 16490"/>
    </justification>
  </clause>

  <clause id="16707">
    <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(13199(a,1),16490(a,1,2,2,2))].">
      <j1 rule="para" parents="13199 16490"/>
    </justification>
  </clause>

  <clause id="16708">
    <literal><![CDATA[
      K(x,y \ K(z * (u \ w),u)) = K(x,y \ K(w * z,u))
    ]]></literal>
    <justification jstring="[hyper(16495,a,13664,a)].">
      <j1 rule="hyper" parents="16495 13664"/>
    </justification>
  </clause>

  <clause id="16709">
    <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(15233(a,1),16495(a,1))].">
      <j1 rule="para" parents="15233 16495"/>
    </justification>
  </clause>

  <clause id="16710">
    <literal><![CDATA[
      T(x,((y / z) \ u) * K(z \ y,w)) = T(x,T(y / z,w) \ u)
    ]]></literal>
    <justification jstring="[hyper(16496,a,15618,a)].">
      <j1 rule="hyper" parents="16496 15618"/>
    </justification>
  </clause>

  <clause id="16711">
    <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(16496,a,15008,a)].">
      <j1 rule="hyper" parents="16496 15008"/>
    </justification>
  </clause>

  <clause id="16712">
    <literal><![CDATA[
      K(x,T(y,T(z * u,w) * v5)) = K(x,T(y,(u * z) * v5))
    ]]></literal>
    <justification jstring="[hyper(16575,a,16536,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="16575 16536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16713">
    <literal><![CDATA[
      K(x,T(y,K(z,u) * (w \ (v5 / v6)))) = K(x,T(y,w \ (v6 \ v5)))
    ]]></literal>
    <justification jstring="[hyper(16578,a,16528,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="16578 16528"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16715">
    <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(63,a,14363,a(flip),b,16648,a)].">
      <j1 rule="hyper" parents="63 14363 16648"/>
    </justification>
  </clause>

  <clause id="16716">
    <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(6861(a,1),16648(a,1,2,1))].">
      <j1 rule="para" parents="6861 16648"/>
    </justification>
  </clause>

  <clause id="16717">
    <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(2086(a,1),16657(a,1,2,2,1))].">
      <j1 rule="para" parents="2086 16657"/>
    </justification>
  </clause>

  <clause id="16718">
    <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(5450(a,1),16657(a,1,2,2,1))].">
      <j1 rule="para" parents="5450 16657"/>
    </justification>
  </clause>

  <clause id="16719">
    <literal><![CDATA[
      K(x,y \ T(((z \ 1) \ 1) * ((z \ 1) * u),K(w,v5))) = K(x,y \ L(u,z,z))
    ]]></literal>
    <justification jstring="[para(2599(a,1),16358(a,2,2,2))].">
      <j1 rule="para" parents="2599 16358"/>
    </justification>
  </clause>

  <clause id="16720">
    <literal><![CDATA[
      T(x,y * (z * T(u,w / v5))) = T(x,y * (z * T(u,v5 \ w)))
    ]]></literal>
    <justification jstring="[hyper(124,a,16462,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 16462 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16721">
    <literal><![CDATA[
      K(x,K(y,z * u) \ ((u / (z \ 1)) \ w)) = K(x,T(u / (z \ 1),y) \ w)
    ]]></literal>
    <justification jstring="[para(13141(a,1),16477(a,1,2,1))].">
      <j1 rule="para" parents="13141 16477"/>
    </justification>
  </clause>

  <clause id="16722">
    <literal><![CDATA[
      T(x,y * (T(z,z \ u) * w)) = T(x,y * (T(z,u) * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,16127,a(flip),b,16513,a),flip(a)].">
      <j1 rule="hyper" parents="63 16127 16513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16724">
    <literal><![CDATA[
      T(x,y * (T(z / u,z) * w)) = T(x,y * ((u \ z) * w))
    ]]></literal>
    <justification jstring="[para(332(a,1),16722(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="332 16722"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16725">
    <literal><![CDATA[
      ((1 / x) * K(y,z)) * K(u,x) = K(u,x) / (K(z,y) * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,13646,a(flip),b,16585,a),flip(a)].">
      <j1 rule="hyper" parents="63 13646 16585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16726">
    <literal><![CDATA[
      K(x,y) / (K(z,u) * y) = (K(x,y) / y) * K(u,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,16588,a(flip),b,16725,a),flip(a)].">
      <j1 rule="hyper" parents="63 16588 16725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16727">
    <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(16726(a,2),9745(a,2,2))].">
      <j1 rule="para" parents="16726 9745"/>
    </justification>
  </clause>

  <clause id="16728">
    <literal><![CDATA[
      (x * (T(T(x,y),y) \ z)) * u = z * ((K(y,x) * K(y,x)) * u)
    ]]></literal>
    <justification jstring="[hyper(333,a,32,a(flip),b,16591,a),flip(a)].">
      <j1 rule="hyper" parents="333 32 16591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16729">
    <literal><![CDATA[
      T(T(x,K(y,z)),(y * K(u,w)) * z) = T(x,z * (y * K(u,w)))
    ]]></literal>
    <justification jstring="[para(6840(a,1),16624(a,1,1))].">
      <j1 rule="para" parents="6840 16624"/>
    </justification>
  </clause>

  <clause id="16730">
    <literal><![CDATA[
      K(x,K(y,y \ z) * u) = K(x,T(K(y,z) * u,w)) * K(x,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(333,a,14947,a,b,16643,a)].">
      <j1 rule="hyper" parents="333 14947 16643"/>
    </justification>
  </clause>

  <clause id="16732">
    <literal><![CDATA[
      K(x,K(y,z)) * (x \ K(u,w)) = T(x \ K(u,w),K(y,z))
    ]]></literal>
    <justification jstring="[para(13126(a,1),16649(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13126 16649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16733">
    <literal><![CDATA[
      T(x \ K(y,z),K(u,w)) = T(x,K(u,w)) \ K(y,z)
    ]]></literal>
    <justification jstring="[hyper(6834,a,16732,a),flip(a)].">
      <j1 rule="hyper" parents="6834 16732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16734">
    <literal><![CDATA[
      T(x \ K(y,z),K(z,y)) = (x * K(z,y)) \ 1
    ]]></literal>
    <justification jstring="[hyper(333,a,13263,a(flip),b,16733,a),flip(a)].">
      <j1 rule="hyper" parents="333 13263 16733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16735">
    <literal><![CDATA[
      (x * K(y,z)) \ 1 = K(z,y) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(13201,a,16734,a),flip(a)].">
      <j1 rule="hyper" parents="13201 16734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16736">
    <literal><![CDATA[
      (x * K(y,z)) \ 1 != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) * (x \ 1) = u
    ]]></literal>
    <justification jstring="[para(16734(a,1),13201(a,1))].">
      <j1 rule="para" parents="16734 13201"/>
    </justification>
  </clause>

  <clause id="16737">
    <literal><![CDATA[
      T(K(x,y) / z,z * K(y,x)) = K(x,y) * (z \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,13338,a,b,16735,a)].">
      <j1 rule="hyper" parents="63 13338 16735"/>
    </justification>
  </clause>

  <clause id="16738">
    <literal><![CDATA[
      (x * K(y,z)) * L(K(z,y) * (x \ 1),u,w) = x * (K(y,z) * L(K(y,z) \ (x \ 1),u,w))
    ]]></literal>
    <justification jstring="[para(16735(a,1),1024(a,1,2,1))].">
      <j1 rule="para" parents="16735 1024"/>
    </justification>
  </clause>

  <clause id="16739">
    <literal><![CDATA[
      ((x * K(y,z)) * L(K(z,y) * (x \ 1),u,w)) / 1 = ((x * K(y,z)) / 1) \ L((x * K(y,z)) / 1,u,w)
    ]]></literal>
    <justification jstring="[para(16735(a,1),2585(a,1,1,2,1))].">
      <j1 rule="para" parents="16735 2585"/>
    </justification>
  </clause>

  <clause id="16740">
    <literal><![CDATA[
      K(x,x \ y) * ((z * y) \ 1) = (z * ((x \ y) * x)) \ 1
    ]]></literal>
    <justification jstring="[para(10318(a,1),16735(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10318 16735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16741">
    <literal><![CDATA[
      K(x,y) * ((z \ 1) \ 1) = (z \ K(y,x)) \ 1
    ]]></literal>
    <justification jstring="[para(13126(a,1),16735(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13126 16735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16742">
    <literal><![CDATA[
      ((x * K(y,z)) \ 1) \ 1 = (x \ 1) \ K(y,z)
    ]]></literal>
    <justification jstring="[para(16735(a,2),13162(a,1,1))].">
      <j1 rule="para" parents="16735 13162"/>
    </justification>
  </clause>

  <clause id="16743">
    <literal><![CDATA[
      K(x,y * (z / (K(u,w) * (v5 \ 1)))) = K(x,y * (z / (K(u,w) / v5)))
    ]]></literal>
    <justification jstring="[para(16735(a,1),13343(a,1,2,2,2))].">
      <j1 rule="para" parents="16735 13343"/>
    </justification>
  </clause>

  <clause id="16744">
    <literal><![CDATA[
      ((x \ K(y,z)) \ 1) / T(T(K(z,y),(x \ 1) \ 1),u) = K(u,K(z,y)) * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(16741(a,1),6490(a,1,1))].">
      <j1 rule="para" parents="16741 6490"/>
    </justification>
  </clause>

  <clause id="16745">
    <literal><![CDATA[
      K(((x \ 1) \ K(y,z)) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K((x * K(y,z)) * u,w) = v5
    ]]></literal>
    <justification jstring="[para(16742(a,1),13512(a,1,1,1))].">
      <j1 rule="para" parents="16742 13512"/>
    </justification>
  </clause>

  <clause id="16746">
    <literal><![CDATA[
      (T(x,y) / z) \ K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * ((x / z) \ 1) = u
    ]]></literal>
    <justification jstring="[para(13721(a,2),16736(a,1))].">
      <j1 rule="para" parents="13721 16736"/>
    </justification>
  </clause>

  <clause id="16747">
    <literal><![CDATA[
      L(x,(y * ((z \ u) * z)) \ 1,w) = L(x,(z * (u / z)) * T(y,u),w)
    ]]></literal>
    <justification jstring="[para(16740(a,1),10135(a,1,2))].">
      <j1 rule="para" parents="16740 10135"/>
    </justification>
  </clause>

  <clause id="16748">
    <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(899(a,1),16656(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="899 16656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16749">
    <literal><![CDATA[
      K(x,K(y,z / ((K(u,w) * v5) * v6))) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z / (v5 * v6))) = v7
    ]]></literal>
    <justification jstring="[para(16678(a,2),7214(a,1))].">
      <j1 rule="para" parents="16678 7214"/>
    </justification>
  </clause>

  <clause id="16750">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),u \ T(z,w)) = T(x,T(u \ T(z,w),y))
    ]]></literal>
    <justification jstring="[para(15590(a,1),16690(a,1,1))].">
      <j1 rule="para" parents="15590 16690"/>
    </justification>
  </clause>

  <clause id="16751">
    <literal><![CDATA[
      K(x,K(y,z * ((u / (u / w)) / v5))) = K(x,K(y,(w / v5) * z))
    ]]></literal>
    <justification jstring="[hyper(15681,a,16691,a)].">
      <j1 rule="hyper" parents="15681 16691"/>
    </justification>
  </clause>

  <clause id="16752">
    <literal><![CDATA[
      K(x,y * ((z \ (u \ w)) * K(u,w))) = K(x,y * (z \ (w / u)))
    ]]></literal>
    <justification jstring="[hyper(16362,a,16699,a)].">
      <j1 rule="hyper" parents="16362 16699"/>
    </justification>
  </clause>

  <clause id="16753">
    <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(16699(a,1),16489(a,1))].">
      <j1 rule="para" parents="16699 16489"/>
    </justification>
  </clause>

  <clause id="16754">
    <literal><![CDATA[
      (x * (T(T(x,y),y) \ z)) * u = z * (K(y,x) * (K(y,x) * u))
    ]]></literal>
    <justification jstring="[para(8084(a,1),16728(a,2,2))].">
      <j1 rule="para" parents="8084 16728"/>
    </justification>
  </clause>

  <clause id="16755">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),T(u \ T(z,w),y)) = T(x,u \ T(z,w))
    ]]></literal>
    <justification jstring="[para(6848(a,1),16750(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6848 16750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16756">
    <literal><![CDATA[
      K(x,K(y,((z \ u) / w) * v5)) = K(x,K(y,v5 * ((u / z) / w)))
    ]]></literal>
    <justification jstring="[para(76(a,1),16751(a,1,2,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="76 16751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16757">
    <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(16751(a,1),15681(a,1))].">
      <j1 rule="para" parents="16751 15681"/>
    </justification>
  </clause>

  <clause id="16758">
    <literal><![CDATA[
      (x * (T(T(x,y),y) \ z)) * u = z * (x * (T(T(x,y),y) \ u))
    ]]></literal>
    <justification jstring="[para(5205(a,1),16754(a,2,2))].">
      <j1 rule="para" parents="5205 16754"/>
    </justification>
  </clause>

  <clause id="16759">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (w / T(u,z)))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (w / T(T(u,z),z))) = v5
    ]]></literal>
    <justification jstring="[para(4370(a,1),16436(a,1,2,2,1))].">
      <j1 rule="para" parents="4370 16436"/>
    </justification>
  </clause>

  <clause id="16760">
    <literal><![CDATA[
      K(x,y * (T(z,u) * T(u,w))) = K(x,y * (T(u,w) * z))
    ]]></literal>
    <justification jstring="[hyper(16509,a,16034,a)].">
      <j1 rule="hyper" parents="16509 16034"/>
    </justification>
  </clause>

  <clause id="16761">
    <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="[para(6946(a,1),16760(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="6946 16760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16762">
    <literal><![CDATA[
      K(x,y * (z / T(u,T(w,v5)))) = K(x,y * (z / T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(16706,a,xx),flip(a)].">
      <j1 rule="hyper" parents="16706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16763">
    <literal><![CDATA[
      K(x * (y / T(z,T(u,w))),v5) = K(v5,x * (y / T(z,u))) \ 1
    ]]></literal>
    <justification jstring="[para(16762(a,1),4367(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16762 4367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16764">
    <literal><![CDATA[
      K(x * (y / T(z,T(u,w))),v5) = K(x * (y / T(z,u)),v5)
    ]]></literal>
    <justification jstring="[hyper(333,a,4367,a(flip),b,16763,a),flip(a)].">
      <j1 rule="hyper" parents="333 4367 16763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16765">
    <literal><![CDATA[
      K(((x \ y) * x) / T(L(K(z,u),w,v5) * x,K(v6,v7)),v8) = K((x * L(K(z,u),w,v5)) \ y,v8)
    ]]></literal>
    <justification jstring="[hyper(15600,a,16373,a),flip(a)].">
      <j1 rule="hyper" parents="15600 16373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16766">
    <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(6054(a,2),16475(a,1,2,2))].">
      <j1 rule="para" parents="6054 16475"/>
    </justification>
  </clause>

  <clause id="16767">
    <literal><![CDATA[
      K(x,y * (z * (u * (K(w,K(v5,v6)) * v7)))) = K(x,y * (z * (u * v7)))
    ]]></literal>
    <justification jstring="[para(6357(a,1),16516(a,1,2,2,2,2))].">
      <j1 rule="para" parents="6357 16516"/>
    </justification>
  </clause>

  <clause id="16768">
    <literal><![CDATA[
      T(x,K(y,z * u) * T(w,K(y,z * u))) = T(x,w * K(y,z \ u))
    ]]></literal>
    <justification jstring="[para(15806(a,1),16520(a,1,2,2))].">
      <j1 rule="para" parents="15806 16520"/>
    </justification>
  </clause>

  <clause id="16769">
    <literal><![CDATA[
      K(x,(y \ T(z,y \ 1)) / u) = K(x,(((z / y) / z) * z) / u)
    ]]></literal>
    <justification jstring="[hyper(63,a,12674,a(flip),b,16524,a),flip(a)].">
      <j1 rule="hyper" parents="63 12674 16524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16770">
    <literal><![CDATA[
      K(x,(y \ T(z,y \ 1)) / u) = K(x,(z / y) / u)
    ]]></literal>
    <justification jstring="[para(12(a,1),16769(a,2,2,1))].">
      <j1 rule="para" parents="12 16769"/>
    </justification>
  </clause>

  <clause id="16772">
    <literal><![CDATA[
      (x * y) * ((y * x) \ (K(x,y) * z)) = (z * K(x,y)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(6887(a,1),16561(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6887 16561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16774">
    <literal><![CDATA[
      (x * y) * ((y * x) \ (K(x,y) * z)) = z * (K(x,y) * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(333,a,8165,a(flip),b,16772,a),flip(a)].">
      <j1 rule="hyper" parents="333 8165 16772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16775">
    <literal><![CDATA[
      (x * y) * ((T(y,x) * x) \ z) = z * (K(x,y) * K(x,y))
    ]]></literal>
    <justification jstring="[para(14545(a,1),16774(a,1,2))].">
      <j1 rule="para" parents="14545 16774"/>
    </justification>
  </clause>

  <clause id="16776">
    <literal><![CDATA[
      (x * (K(y,z) * K(y,z))) / (y * z) = x / (T(z,y) * y)
    ]]></literal>
    <justification jstring="[para(16775(a,1),12362(a,1,1))].">
      <j1 rule="para" parents="16775 12362"/>
    </justification>
  </clause>

  <clause id="16778">
    <literal><![CDATA[
      K(x,L(T(y,z * (u / w)),v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,L(T(y,z * (w \ u)),v5,v6)) = v7
    ]]></literal>
    <justification jstring="[para(16581(a,1),10963(a,1))].">
      <j1 rule="para" parents="16581 10963"/>
    </justification>
  </clause>

  <clause id="16779">
    <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(6788(a,1),16636(a,1,1))].">
      <j1 rule="para" parents="6788 16636"/>
    </justification>
  </clause>

  <clause id="16780">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,(K(u * w,v5) * y) * z) = K(x,z * (K(u \ w,v5) * y))
    ]]></literal>
    <justification jstring="[para(16262(a,1),16636(a,1,2))].">
      <j1 rule="para" parents="16262 16636"/>
    </justification>
  </clause>

  <clause id="16782">
    <literal><![CDATA[
      K(x,T(K(y,y \ z) * u,w)) = K(x,T(K(y,z) * u,w))
    ]]></literal>
    <justification jstring="[hyper(35,a,16643,a,b,16730,a(flip))].">
      <j1 rule="hyper" parents="35 16643 16730"/>
    </justification>
  </clause>

  <clause id="16783">
    <literal><![CDATA[
      L(x,(y * (z / y)) * T(u,z),w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,u * ((y \ z) * y),w) = v5
    ]]></literal>
    <justification jstring="[para(16747(a,1),2631(a,1))].">
      <j1 rule="para" parents="16747 2631"/>
    </justification>
  </clause>

  <clause id="16784">
    <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(16766(a,1),16492(a,1))].">
      <j1 rule="para" parents="16766 16492"/>
    </justification>
  </clause>

  <clause id="16785">
    <literal><![CDATA[
      K(x,y * T((K(z,u) * w) \ v5,w)) = K(x,y * (v5 / (K(z,u) * w)))
    ]]></literal>
    <justification jstring="[hyper(16784,a,14987,a)].">
      <j1 rule="hyper" parents="16784 14987"/>
    </justification>
  </clause>

  <clause id="16786">
    <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(4967(a,1),16784(a,1,2,2,2))].">
      <j1 rule="para" parents="4967 16784"/>
    </justification>
  </clause>

  <clause id="16787">
    <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(6887(a,1),16784(a,1,2,2,2))].">
      <j1 rule="para" parents="6887 16784"/>
    </justification>
  </clause>

  <clause id="16788">
    <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(13414(a,1),16787(a,1,2,2,2))].">
      <j1 rule="para" parents="13414 16787"/>
    </justification>
  </clause>

  <clause id="16789">
    <literal><![CDATA[
      T(x,y * K(z,u \ w)) = T(x,y * K(z,u * w))
    ]]></literal>
    <justification jstring="[para(111(a,1),16768(a,1,2)),flip(a)].">
      <j1 rule="para" parents="111 16768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16790">
    <literal><![CDATA[
      x \ T(x,y * K(z,u * w)) = K(x,y * K(z,u \ w))
    ]]></literal>
    <justification jstring="[hyper(121,a,16789,a(flip),b,4222,a(flip))].">
      <j1 rule="hyper" parents="121 16789 4222"/>
    </justification>
  </clause>

  <clause id="16791">
    <literal><![CDATA[
      T(x,(y * (z * u)) * K(L(u,z,y),w * v5)) = T(x,y * (z * T(u,w \ v5)))
    ]]></literal>
    <justification jstring="[para(5996(a,1),16789(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5996 16789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16792">
    <literal><![CDATA[
      K(x,y * K(z,u \ w)) = K(x,y * K(z,u * w))
    ]]></literal>
    <justification jstring="[hyper(4306,a,16790,a),flip(a)].">
      <j1 rule="hyper" parents="4306 16790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16793">
    <literal><![CDATA[
      K(x,y * K(z,u \ w)) = K(x,y * K(z,w * u))
    ]]></literal>
    <justification jstring="[hyper(333,a,16412,a,b,16792,a),flip(a)].">
      <j1 rule="hyper" parents="333 16412 16792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16794">
    <literal><![CDATA[
      K(x,(y * z) * K(L(u,z,y) \ 1,w * v5)) = K(x,y * (z * K(u \ 1,w \ v5)))
    ]]></literal>
    <justification jstring="[para(5368(a,1),16792(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5368 16792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16795">
    <literal><![CDATA[
      K(x,(y * (z * u)) * K(L(u,z,y),w * v5)) = K(x,y * (z * T(u,w \ v5)))
    ]]></literal>
    <justification jstring="[para(5996(a,1),16792(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5996 16792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16797">
    <literal><![CDATA[
      K(x,T(y,z * (y \ u)) * (u * (z / y))) = K(x,R(u,y \ z,y) * z)
    ]]></literal>
    <justification jstring="[para(10669(a,1),16473(a,1,2,1))].">
      <j1 rule="para" parents="10669 16473"/>
    </justification>
  </clause>

  <clause id="16798">
    <literal><![CDATA[
      K(x,K(y,z / (u * (K(w,v5) * v6)))) = K(x,K(y,z / (v6 * u)))
    ]]></literal>
    <justification jstring="[hyper(16749,a,16609,a),flip(a)].">
      <j1 rule="hyper" parents="16749 16609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16799">
    <literal><![CDATA[
      K(x,K(y,z / (u * (K(w,v5) * v6)))) = K(x,K(y,z / (u * v6)))
    ]]></literal>
    <justification jstring="[hyper(333,a,16609,a,b,16798,a),flip(a)].">
      <j1 rule="hyper" parents="333 16609 16798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16800">
    <literal><![CDATA[
      K(x,T(y,z * u) * (u * (z / y))) = K(x,R(u,y \ z,y) * z)
    ]]></literal>
    <justification jstring="[hyper(14197,a,16797,a)].">
      <j1 rule="hyper" parents="14197 16797"/>
    </justification>
  </clause>

  <clause id="16801">
    <literal><![CDATA[
      K(x,T(y,z * u) * (u * (z / y))) = K(x,(u * (z / y)) * y)
    ]]></literal>
    <justification jstring="[para(10355(a,1),16800(a,2,2))].">
      <j1 rule="para" parents="10355 16800"/>
    </justification>
  </clause>

  <clause id="16803">
    <literal><![CDATA[
      T((x * T(y,z)) \ T(y,z),(x * y) \ y) = T(x * y,K(y,z)) \ y
    ]]></literal>
    <justification jstring="[para(6075(a,1),16321(a,2,1))].">
      <j1 rule="para" parents="6075 16321"/>
    </justification>
  </clause>

  <clause id="16804">
    <literal><![CDATA[
      T((x * T(y,z)) \ T(y,z),(x * y) \ y) = T((x * y) \ y,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(333,a,7290,a,b,16803,a),flip(a)].">
      <j1 rule="hyper" parents="333 7290 16803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16805">
    <literal><![CDATA[
      K(x,((K(y,z) * u) / (y \ z)) / w) = K(x,(u / (T(y,z) \ z)) / w)
    ]]></literal>
    <justification jstring="[hyper(63,a,15042,a(flip),b,16469,a)].">
      <j1 rule="hyper" parents="63 15042 16469"/>
    </justification>
  </clause>

  <clause id="16806">
    <literal><![CDATA[
      K(x,(K(y,z) * (u / (y \ z))) / w) = K(x,(u / (T(y,z) \ z)) / w)
    ]]></literal>
    <justification jstring="[para(11851(a,1),16805(a,1,2,1))].">
      <j1 rule="para" parents="11851 16805"/>
    </justification>
  </clause>

  <clause id="16808">
    <literal><![CDATA[
      K(x,T((K(y,y \ z) * u) / z,w)) = K(x,T(u / ((y \ z) * y),w))
    ]]></literal>
    <justification jstring="[hyper(63,a,7656,a(flip),b,16535,a),flip(a)].">
      <j1 rule="hyper" parents="63 7656 16535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16809">
    <literal><![CDATA[
      K(x,T(K(y,y \ z) * (u / z),w)) = K(x,T(u / ((y \ z) * y),w))
    ]]></literal>
    <justification jstring="[para(14613(a,1),16808(a,1,2,1))].">
      <j1 rule="para" parents="14613 16808"/>
    </justification>
  </clause>

  <clause id="16810">
    <literal><![CDATA[
      K(x,T(y / ((z \ u) * z),w)) = K(x,T(K(z,u) * (y / u),w))
    ]]></literal>
    <justification jstring="[hyper(63,a,16782,a(flip),b,16809,a),flip(a)].">
      <j1 rule="hyper" parents="63 16782 16809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16811">
    <literal><![CDATA[
      K(x,T(y / ((z \ u) * z),w)) = K(x,T(y / T(u,z),w))
    ]]></literal>
    <justification jstring="[hyper(333,a,16060,a(flip),b,16810,a),flip(a)].">
      <j1 rule="hyper" parents="333 16060 16810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16812">
    <literal><![CDATA[
      K(x,T(y / T(z,u),z * u)) = K(x,z \ T(y,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,15413,a(flip),b,16811,a),flip(a)].">
      <j1 rule="hyper" parents="63 15413 16811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16813">
    <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(333,a,16686,a(flip),b,16671,a),flip(a)].">
      <j1 rule="hyper" parents="333 16686 16671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16815">
    <literal><![CDATA[
      K(x,K(y * K(z,u),L(w,K(v5,v6),v7))) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(333,a,6843,a(flip),b,16813,a),flip(a)].">
      <j1 rule="hyper" parents="333 6843 16813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16817">
    <literal><![CDATA[
      K(x,K(y,L(z,K(u,w),v5))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,16620,a(flip),b,16815,a)].">
      <j1 rule="hyper" parents="63 16620 16815"/>
    </justification>
  </clause>

  <clause id="16818">
    <literal><![CDATA[
      K(x,T(y,(z * K(u,w)) / v5)) = K(x,T(y,v5 / z))
    ]]></literal>
    <justification jstring="[hyper(15857,a,16680,a),flip(a)].">
      <j1 rule="hyper" parents="15857 16680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16819">
    <literal><![CDATA[
      K(x,T(y,(z / T(u,w)) / v5)) = K(x,T(y,v5 / (z / u)))
    ]]></literal>
    <justification jstring="[para(5450(a,1),16818(a,1,2,2,1))].">
      <j1 rule="para" parents="5450 16818"/>
    </justification>
  </clause>

  <clause id="16820">
    <literal><![CDATA[
      K(x,T(y,z / (u / T(w,v5)))) = K(x,T(y,z / (u / w)))
    ]]></literal>
    <justification jstring="[hyper(7285,a,16819,a)].">
      <j1 rule="hyper" parents="7285 16819"/>
    </justification>
  </clause>

  <clause id="16821">
    <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(333,a,9493,a(flip),b,16820,a),flip(a)].">
      <j1 rule="hyper" parents="333 9493 16820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16822">
    <literal><![CDATA[
      K(x,T(y,z / (u / (w / v5)))) = K(x,T(y,z / (u / (v5 \ w))))
    ]]></literal>
    <justification jstring="[para(113(a,1),16820(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="113 16820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16823">
    <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(16820(a,1),4447(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16820 4447"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16824">
    <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(12793(a,1),16681(a,1,2))].">
      <j1 rule="para" parents="12793 16681"/>
    </justification>
  </clause>

  <clause id="16825">
    <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(16629(a,1),16670(a,1))].">
      <j1 rule="para" parents="16629 16670"/>
    </justification>
  </clause>

  <clause id="16826">
    <literal><![CDATA[
      K(x,y * (z / (K(u,w) / v5))) = K(x,y * (z / (v5 \ K(u,w))))
    ]]></literal>
    <justification jstring="[hyper(16707,a,16743,a),flip(a)].">
      <j1 rule="hyper" parents="16707 16743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16827">
    <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(2512(a,2),16826(a,1,2))].">
      <j1 rule="para" parents="2512 16826"/>
    </justification>
  </clause>

  <clause id="16828">
    <literal><![CDATA[
      K(x,y \ (z * ((1 / z) * u))) = K(x,y \ L(u,z,z))
    ]]></literal>
    <justification jstring="[para(7871(a,1),16719(a,1,2,2))].">
      <j1 rule="para" parents="7871 16719"/>
    </justification>
  </clause>

  <clause id="16829">
    <literal><![CDATA[
      K(x,y \ R(z,u,u)) = K(x,y \ L(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,15348,a(flip),b,16828,a)].">
      <j1 rule="hyper" parents="63 15348 16828"/>
    </justification>
  </clause>

  <clause id="16830">
    <literal><![CDATA[
      K(x,(1 / y) \ L(z,u,u)) = K(x,y * R(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(13505,a,16829,a),flip(a)].">
      <j1 rule="hyper" parents="13505 16829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16831">
    <literal><![CDATA[
      K(x,y * R(z,u,u)) = K(x,y * L(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(13505,a,16830,a),flip(a)].">
      <j1 rule="hyper" parents="13505 16830"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16832">
    <literal><![CDATA[
      T(x,y * R(z,u,u)) = T(x,y * L(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(124,a,16831,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 16831 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16833">
    <literal><![CDATA[
      x * K(x,y * L(z,u,u)) = T(x,y * R(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(126,a,16831,a(flip),b,4215,a(flip))].">
      <j1 rule="hyper" parents="126 16831 4215"/>
    </justification>
  </clause>

  <clause id="16834">
    <literal><![CDATA[
      T(x,R(y,R(z,u,u),u * u) * ((z * u) * u)) = T(T(x,u * u),y * L(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,1644,a,b,16832,a)].">
      <j1 rule="hyper" parents="63 1644 16832"/>
    </justification>
  </clause>

  <clause id="16835">
    <literal><![CDATA[
      T(x,y * L(T(z,u \ 1),u,u)) = T(x,y * ((u \ 1) * (z * u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,16062,a(flip),b,16832,a),flip(a)].">
      <j1 rule="hyper" parents="63 16062 16832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16836">
    <literal><![CDATA[
      T(x,(y * z) * R(L(u,z,y),w,w)) = T(x,y * (z * L(u,w,w)))
    ]]></literal>
    <justification jstring="[para(461(a,1),16832(a,2,2))].">
      <j1 rule="para" parents="461 16832"/>
    </justification>
  </clause>

  <clause id="16837">
    <literal><![CDATA[
      T(x,y * L(z,1 / u,1 / u)) = T(x,y * R(z,u,u))
    ]]></literal>
    <justification jstring="[para(1938(a,1),16832(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1938 16832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16838">
    <literal><![CDATA[
      T(x,y * R(z,u,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y * L(z,u,u)) = w
    ]]></literal>
    <justification jstring="[para(16833(a,1),4285(a,1))].">
      <j1 rule="para" parents="16833 4285"/>
    </justification>
  </clause>

  <clause id="16839">
    <literal><![CDATA[
      T(x,y * L(z,1 / u,1 / u)) = T(x,y * L(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(333,a,16832,a(flip),b,16837,a),flip(a)].">
      <j1 rule="hyper" parents="333 16832 16837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16840">
    <literal><![CDATA[
      T(x,y * L(z,1 / u,1 / u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y * L(z,u,u)) = w
    ]]></literal>
    <justification jstring="[para(16837(a,2),16838(a,1))].">
      <j1 rule="para" parents="16837 16838"/>
    </justification>
  </clause>

  <clause id="16841">
    <literal><![CDATA[
      T(x,y * L(z,u,u \ 1)) = T(x,y * L(z,u,u))
    ]]></literal>
    <justification jstring="[para(3148(a,1),16839(a,1,2,2))].">
      <j1 rule="para" parents="3148 16839"/>
    </justification>
  </clause>

  <clause id="16842">
    <literal><![CDATA[
      T(x,y * L(T(z,u \ 1),u,u)) = T(x,y * ((u * z) * (u \ 1)))
    ]]></literal>
    <justification jstring="[hyper(63,a,12981,a(flip),b,16841,a),flip(a)].">
      <j1 rule="hyper" parents="63 12981 16841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16843">
    <literal><![CDATA[
      T(x,y * ((z \ 1) * (u * z))) = T(x,y * (z * (u * (z \ 1))))
    ]]></literal>
    <justification jstring="[para(2600(a,1),16835(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2600 16835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16844">
    <literal><![CDATA[
      T(x,y * (z * R(u,w,w))) = T(x,y * (z * L(u,w,w)))
    ]]></literal>
    <justification jstring="[para(462(a,1),16836(a,1,2))].">
      <j1 rule="para" parents="462 16836"/>
    </justification>
  </clause>

  <clause id="16845">
    <literal><![CDATA[
      T(x,y * ((1 / z) * R(z,u,u))) = T(x,y * (z \ L(z,u,u)))
    ]]></literal>
    <justification jstring="[para(2521(a,1),16844(a,2,2,2))].">
      <j1 rule="para" parents="2521 16844"/>
    </justification>
  </clause>

  <clause id="16846">
    <literal><![CDATA[
      T(x,y * (z \ L(z,u,u))) = T(x,y * a(z,u,u))
    ]]></literal>
    <justification jstring="[para(13604(a,1),16845(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13604 16845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16847">
    <literal><![CDATA[
      T(x,y * ((z * u) * (z \ 1))) = T(x,y * (z * (u * (z \ 1))))
    ]]></literal>
    <justification jstring="[para(2600(a,1),16842(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2600 16842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16848">
    <literal><![CDATA[
      K(x,L(T(y \ z,y * (z \ u)),y,z \ u)) = K(x,u / ((u / z) * y))
    ]]></literal>
    <justification jstring="[hyper(16778,a,16095,a)].">
      <j1 rule="hyper" parents="16778 16095"/>
    </justification>
  </clause>

  <clause id="16849">
    <literal><![CDATA[
      K(x,L(T(y \ z,z * (y \ u)),y,y \ u)) = K(x,((u / y) * z) / u)
    ]]></literal>
    <justification jstring="[hyper(16778,a,16094,a)].">
      <j1 rule="hyper" parents="16778 16094"/>
    </justification>
  </clause>

  <clause id="16850">
    <literal><![CDATA[
      K(x,T((y * (y \ z)) \ (u * (y \ z)),y)) = K(x,((z / y) * u) / z)
    ]]></literal>
    <justification jstring="[hyper(63,a,13880,a(flip),b,16849,a)].">
      <j1 rule="hyper" parents="63 13880 16849"/>
    </justification>
  </clause>

  <clause id="16851">
    <literal><![CDATA[
      K(x,T(y \ (z * (u \ y)),u)) = K(x,((y / u) * z) / y)
    ]]></literal>
    <justification jstring="[para(10(a,1),16850(a,1,2,1,1))].">
      <j1 rule="para" parents="10 16850"/>
    </justification>
  </clause>

  <clause id="16853">
    <literal><![CDATA[
      T(x,y * (z * T(u,w \ v5))) = T(x,y * (z * T(u,w * v5)))
    ]]></literal>
    <justification jstring="[para(5996(a,1),16791(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5996 16791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16854">
    <literal><![CDATA[
      T(x,y * (z * T(u,u * w))) = T(x,y * (z * (w / (w / u))))
    ]]></literal>
    <justification jstring="[hyper(63,a,16107,a(flip),b,16853,a),flip(a)].">
      <j1 rule="hyper" parents="63 16107 16853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16855">
    <literal><![CDATA[
      T(x,y * ((z \ u) * T(w,z * u))) = T(x,y * (w * (z \ u)))
    ]]></literal>
    <justification jstring="[para(111(a,1),16853(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="111 16853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16856">
    <literal><![CDATA[
      T(x,y * (z * T(u,u * w))) = T(x,y * (z * ((u \ w) \ w)))
    ]]></literal>
    <justification jstring="[para(112(a,1),16853(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="112 16853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16857">
    <literal><![CDATA[
      T(x,y * ((z \ 1) * T(u,z))) = T(x,y * (u * (z \ 1)))
    ]]></literal>
    <justification jstring="[para(8(a,1),16855(a,1,2,2,2,2))].">
      <j1 rule="para" parents="8 16855"/>
    </justification>
  </clause>

  <clause id="16859">
    <literal><![CDATA[
      T(x,y * ((z \ 1) * T(R(u,z,z),z))) = T(x,y * R(u * (1 / z),z,z))
    ]]></literal>
    <justification jstring="[para(1192(a,2),16857(a,2,2,2))].">
      <j1 rule="para" parents="1192 16857"/>
    </justification>
  </clause>

  <clause id="16860">
    <literal><![CDATA[
      T(x,y * (z * T(u,u * w))) = T(x,y * (z * T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(333,a,13698,a(flip),b,16856,a),flip(a)].">
      <j1 rule="hyper" parents="333 13698 16856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16861">
    <literal><![CDATA[
      T(x,y * (z * (u / (u / w)))) = T(x,y * (z * T(w,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,16854,a(flip),b,16860,a)].">
      <j1 rule="hyper" parents="63 16854 16860"/>
    </justification>
  </clause>

  <clause id="16862">
    <literal><![CDATA[
      T(x,y * (z * (u / (u / w)))) = x * K(x,y * (z * T(w,u)))
    ]]></literal>
    <justification jstring="[hyper(333,a,4222,a(flip),b,16861,a),flip(a)].">
      <j1 rule="hyper" parents="333 4222 16861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16863">
    <literal><![CDATA[
      K(x,y * (z * (u / (u / w)))) = K(x,y * (z * T(w,u)))
    ]]></literal>
    <justification jstring="[hyper(4305,a,16862,a)].">
      <j1 rule="hyper" parents="4305 16862"/>
    </justification>
  </clause>

  <clause id="16864">
    <literal><![CDATA[
      K(x,y * (z * T(u \ w,w))) = K(x,y * (z * (w / u)))
    ]]></literal>
    <justification jstring="[para(76(a,1),16863(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="76 16863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16865">
    <literal><![CDATA[
      K(x,y * (z * (K(u,w) / v5))) = K(x,y * (z * (v5 \ K(u,w))))
    ]]></literal>
    <justification jstring="[hyper(63,a,16338,a(flip),b,16864,a),flip(a)].">
      <j1 rule="hyper" parents="63 16338 16864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16866">
    <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(63,a,13310,a,b,16865,a)].">
      <j1 rule="hyper" parents="63 13310 16865"/>
    </justification>
  </clause>

  <clause id="16867">
    <literal><![CDATA[
      T(x,y * ((z \ 1) * R(T(u,z),z,z))) = T(x,y * R(u * (1 / z),z,z))
    ]]></literal>
    <justification jstring="[para(27(a,2),16859(a,1,2,2,2))].">
      <j1 rule="para" parents="27 16859"/>
    </justification>
  </clause>

  <clause id="16868">
    <literal><![CDATA[
      T(x,y * R((1 / z) * T(u,z),z,z)) = T(x,y * R(u * (1 / z),z,z))
    ]]></literal>
    <justification jstring="[para(2999(a,2),16867(a,1,2,2))].">
      <j1 rule="para" parents="2999 16867"/>
    </justification>
  </clause>

  <clause id="16869">
    <literal><![CDATA[
      T(x,y * L((1 / z) * T(u,z),z,z)) = T(x,y * R(u * (1 / z),z,z))
    ]]></literal>
    <justification jstring="[hyper(16838,a,16868,a)].">
      <j1 rule="hyper" parents="16838 16868"/>
    </justification>
  </clause>

  <clause id="16870">
    <literal><![CDATA[
      K(x,y * (z * T(u,w \ v5))) = K(x,y * (z * T(u,w * v5)))
    ]]></literal>
    <justification jstring="[para(5996(a,1),16795(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5996 16795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16871">
    <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(6201(a,1),16020(a,1,2,2))].">
      <j1 rule="para" parents="6201 16020"/>
    </justification>
  </clause>

  <clause id="16872">
    <literal><![CDATA[
      K(x,y \ (z / T(z / u,w))) = K(x,y \ (T(u \ z,w) \ z))
    ]]></literal>
    <justification jstring="[para(6634(a,1),16871(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6634 16871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16873">
    <literal><![CDATA[
      K(x,y * (T(z,T(u,w * v5)) * T(u,w * v5))) = K(x,y * (T(u,w \ v5) * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,16870,a(flip),b,16037,a)].">
      <j1 rule="hyper" parents="63 16870 16037"/>
    </justification>
  </clause>

  <clause id="16874">
    <literal><![CDATA[
      T(T(x,(y * z) \ u),K((y * z) \ u,w)) = T(x,T(T(z * y,y) \ u,w))
    ]]></literal>
    <justification jstring="[para(15093(a,1),16178(a,1,1))].">
      <j1 rule="para" parents="15093 16178"/>
    </justification>
  </clause>

  <clause id="16875">
    <literal><![CDATA[
      T(x,T(T(y * z,z) \ u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,T((z * y) \ u,w)) = v5
    ]]></literal>
    <justification jstring="[para(16874(a,1),7056(a,1))].">
      <j1 rule="para" parents="16874 7056"/>
    </justification>
  </clause>

  <clause id="16876">
    <literal><![CDATA[
      T(x,T(T(y * (1 / z),z \ 1) \ u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,T(((1 / z) * y) \ u,w)) = v5
    ]]></literal>
    <justification jstring="[para(2986(a,1),16875(a,1,2,1,1))].">
      <j1 rule="para" parents="2986 16875"/>
    </justification>
  </clause>

  <clause id="16877">
    <literal><![CDATA[
      T(x,(y \ (1 / y)) * (z * u)) = T(x,z * (u * (y \ (1 / y))))
    ]]></literal>
    <justification jstring="[para(2405(a,1),16209(a,1,2,2))].">
      <j1 rule="para" parents="2405 16209"/>
    </justification>
  </clause>

  <clause id="16878">
    <literal><![CDATA[
      T(x,y * (z * (u \ (1 / u)))) = T(x,u \ (u \ (y * z)))
    ]]></literal>
    <justification jstring="[hyper(16024,a,16877,a),flip(a)].">
      <j1 rule="hyper" parents="16024 16877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16880">
    <literal><![CDATA[
      T(x,y \ (y \ (z * u))) = T(x,z * (u / (y * y)))
    ]]></literal>
    <justification jstring="[hyper(63,a,3192,a(flip),b,16878,a),flip(a)].">
      <j1 rule="hyper" parents="63 3192 16878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16881">
    <literal><![CDATA[
      T(x,y \ (y \ (z * u))) = T(x,z * ((y * y) \ u))
    ]]></literal>
    <justification jstring="[hyper(333,a,15890,a(flip),b,16880,a),flip(a)].">
      <j1 rule="hyper" parents="333 15890 16880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16882">
    <literal><![CDATA[
      T(T(x,y * ((z * z) \ u)),w) = T(T(x,y * u),z \ (z \ w))
    ]]></literal>
    <justification jstring="[para(16881(a,1),15988(a,1,1))].">
      <j1 rule="para" parents="16881 15988"/>
    </justification>
  </clause>

  <clause id="16883">
    <literal><![CDATA[
      T(T(x,y * (z * ((u * u) \ w))),v5) = T(T(x,y * (z * w)),u \ (u \ v5))
    ]]></literal>
    <justification jstring="[para(16026(a,1),16882(a,1,1))].">
      <j1 rule="para" parents="16026 16882"/>
    </justification>
  </clause>

  <clause id="16884">
    <literal><![CDATA[
      T(x,T(T(y,z) * (y \ u),(y \ u) \ u)) = T(x,(y \ u) * T(y,z))
    ]]></literal>
    <justification jstring="[para(76(a,1),16298(a,2,2,2,1))].">
      <j1 rule="para" parents="76 16298"/>
    </justification>
  </clause>

  <clause id="16886">
    <literal><![CDATA[
      T(x,T(K(y,z) * u,(y \ u) \ u)) = T(x,(y \ u) * T(y,z))
    ]]></literal>
    <justification jstring="[para(4242(a,1),16884(a,1,2,1))].">
      <j1 rule="para" parents="4242 16884"/>
    </justification>
  </clause>

  <clause id="16887">
    <literal><![CDATA[
      T(x,T(K(y,z) * u,T(y,u))) = T(x,(y \ u) * T(y,z))
    ]]></literal>
    <justification jstring="[para(6465(a,1),16886(a,1,2))].">
      <j1 rule="para" parents="6465 16886"/>
    </justification>
  </clause>

  <clause id="16888">
    <literal><![CDATA[
      T(x,T(K(y,z) * u,y)) = T(x,(y \ u) * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(15595,a,16887,a)].">
      <j1 rule="hyper" parents="15595 16887"/>
    </justification>
  </clause>

  <clause id="16889">
    <literal><![CDATA[
      T(x,(y \ z) * T(y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T(K(y,u) * z,y)) = w
    ]]></literal>
    <justification jstring="[para(16887(a,1),15595(a,1))].">
      <j1 rule="para" parents="16887 15595"/>
    </justification>
  </clause>

  <clause id="16891">
    <literal><![CDATA[
      K(x,T(L(y,z,y) * u,w) / v5) = K(x,(y * u) * (v5 \ K(y * u,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,12812,a(flip),b,16485,a),flip(a)].">
      <j1 rule="hyper" parents="63 12812 16485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16893">
    <literal><![CDATA[
      K(x,T(L(y,z,y) * u,w) / v5) = K(x,T(y * u,w) / v5)
    ]]></literal>
    <justification jstring="[hyper(333,a,16482,a(flip),b,16891,a),flip(a)].">
      <j1 rule="hyper" parents="333 16482 16891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16894">
    <literal><![CDATA[
      K(x,(y * L(z,u,z)) / w) = K(x,T(z * y,z) / w)
    ]]></literal>
    <justification jstring="[hyper(63,a,12720,a(flip),b,16893,a)].">
      <j1 rule="hyper" parents="63 12720 16893"/>
    </justification>
  </clause>

  <clause id="16896">
    <literal><![CDATA[
      K(x,(y * L(z,u,z)) / w) = K(x,(y * z) / w)
    ]]></literal>
    <justification jstring="[hyper(333,a,12674,a(flip),b,16894,a),flip(a)].">
      <j1 rule="hyper" parents="333 12674 16894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16897">
    <literal><![CDATA[
      K(x,(y * T(z,z * u)) / w) = K(x,(y * T(z,u)) / w)
    ]]></literal>
    <justification jstring="[para(3742(a,1),16896(a,1,2,1,2))].">
      <j1 rule="para" parents="3742 16896"/>
    </justification>
  </clause>

  <clause id="16898">
    <literal><![CDATA[
      K(x,(y * T(z,z \ u)) / w) = K(x,(y * T(z,u)) / w)
    ]]></literal>
    <justification jstring="[para(10(a,1),16897(a,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 16897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16899">
    <literal><![CDATA[
      K(x,(y \ (z * (u \ y))) \ K(z,u)) = K(x,z \ ((y \ (z * (u \ y))) \ z))
    ]]></literal>
    <justification jstring="[hyper(63,a,15340,a(flip),b,16493,a)].">
      <j1 rule="hyper" parents="63 15340 16493"/>
    </justification>
  </clause>

  <clause id="16900">
    <literal><![CDATA[
      K(x,(y \ (z * (u \ y))) \ K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T((z * (u \ y)) \ y,z)) = w
    ]]></literal>
    <justification jstring="[para(16899(a,2),7976(a,1))].">
      <j1 rule="para" parents="16899 7976"/>
    </justification>
  </clause>

  <clause id="16902">
    <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(63,a,15194,a(flip),b,16510,a)].">
      <j1 rule="hyper" parents="63 15194 16510"/>
    </justification>
  </clause>

  <clause id="16903">
    <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(16793(a,1),16523(a,1,1,2))].">
      <j1 rule="para" parents="16793 16523"/>
    </justification>
  </clause>

  <clause id="16904">
    <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(16597(a,1),16625(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16597 16625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16905">
    <literal><![CDATA[
      T(x,K(y * K(z,u),w) * v5) = T(x,K(y,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(333,a,14912,a(flip),b,16904,a),flip(a)].">
      <j1 rule="hyper" parents="333 14912 16904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16906">
    <literal><![CDATA[
      T(x,K(K(y,z) * u,w) * v5) = v5 \ T(x * T(v5,K(w,u)),K(w,u))
    ]]></literal>
    <justification jstring="[para(6357(a,1),16904(a,1,2,1,1))].">
      <j1 rule="para" parents="6357 16904"/>
    </justification>
  </clause>

  <clause id="16908">
    <literal><![CDATA[
      T(x,y * K(z \ K(u,w),v5)) = T(x,K(z,v5) * y)
    ]]></literal>
    <justification jstring="[hyper(16134,a,16905,a)].">
      <j1 rule="hyper" parents="16134 16905"/>
    </justification>
  </clause>

  <clause id="16909">
    <literal><![CDATA[
      T(x,K(K(y,z) * u,w) * v5) = T(x,K(u,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,16154,a(flip),b,16905,a),flip(a)].">
      <j1 rule="hyper" parents="63 16154 16905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16911">
    <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(63,a,16710,a(flip),b,16908,a),flip(a)].">
      <j1 rule="hyper" parents="63 16710 16908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16912">
    <literal><![CDATA[
      T(x,y * K(K(z,u) * w,v5)) = T(x,K(w,v5) * y)
    ]]></literal>
    <justification jstring="[hyper(15486,a,16909,a)].">
      <j1 rule="hyper" parents="15486 16909"/>
    </justification>
  </clause>

  <clause id="16913">
    <literal><![CDATA[
      T(x,K(K(y,z) * u,w) * v5) = T(x,v5 * K(u \ K(v6,v7),w))
    ]]></literal>
    <justification jstring="[hyper(333,a,16908,a,b,16909,a),flip(a)].">
      <j1 rule="hyper" parents="333 16908 16909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16914">
    <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(63,a,14925,a(flip),b,16909,a),flip(a)].">
      <j1 rule="hyper" parents="63 14925 16909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16915">
    <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(126,a,16912,a(flip),b,13991,a(flip))].">
      <j1 rule="hyper" parents="126 16912 13991"/>
    </justification>
  </clause>

  <clause id="16916">
    <literal><![CDATA[
      T(x,K(y \ K(z,u),w) * v5) = T(x,K(K(v6,v7) * y,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(333,a,15470,a,b,16913,a)].">
      <j1 rule="hyper" parents="333 15470 16913"/>
    </justification>
  </clause>

  <clause id="16917">
    <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(63,a,15689,a(flip),b,16916,a),flip(a)].">
      <j1 rule="hyper" parents="63 15689 16916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16918">
    <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(16906(a,2),15794(a,1))].">
      <j1 rule="para" parents="16906 15794"/>
    </justification>
  </clause>

  <clause id="16920">
    <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(16917(a,1),16918(a,1))].">
      <j1 rule="para" parents="16917 16918"/>
    </justification>
  </clause>

  <clause id="16921">
    <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(13229(a,1),16695(a,2,2,2))].">
      <j1 rule="para" parents="13229 16695"/>
    </justification>
  </clause>

  <clause id="16922">
    <literal><![CDATA[
      K(x,y * (((z \ u) \ u) / w)) = K(x,y * (T(z,u) / w))
    ]]></literal>
    <justification jstring="[hyper(16376,a,16921,a)].">
      <j1 rule="hyper" parents="16376 16921"/>
    </justification>
  </clause>

  <clause id="16923">
    <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(12736,a,16922,a),flip(a)].">
      <j1 rule="hyper" parents="12736 16922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16925">
    <literal><![CDATA[
      K(x,(((y \ z) \ z) / u) * w) = K(x,(T(y,z) / u) * w)
    ]]></literal>
    <justification jstring="[hyper(12284,a,16923,a),flip(a)].">
      <j1 rule="hyper" parents="12284 16923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16926">
    <literal><![CDATA[
      K(x,y * (K(z \ u,w) * v5)) = K(x,y * (K(z * u,w) * v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,16636,a(flip),b,16780,a),flip(a)].">
      <j1 rule="hyper" parents="63 16636 16780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16927">
    <literal><![CDATA[
      K(x,y * (K(z * u,y) * w)) = K(x,T(y,z \ u) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,14984,a(flip),b,16926,a),flip(a)].">
      <j1 rule="hyper" parents="63 14984 16926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16928">
    <literal><![CDATA[
      K(x,y * (K(z * u,w) * (w \ v5))) = K(x,y * (T(w,z \ u) \ v5))
    ]]></literal>
    <justification jstring="[para(4555(a,1),16926(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4555 16926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16929">
    <literal><![CDATA[
      K(x,T(y,z \ u) * w) = K(x,T(y,z * u) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,14984,a(flip),b,16927,a),flip(a)].">
      <j1 rule="hyper" parents="63 14984 16927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16930">
    <literal><![CDATA[
      K(x,T(y,z \ 1) * u) = K(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[para(8(a,1),16929(a,2,2,1,2))].">
      <j1 rule="para" parents="8 16929"/>
    </justification>
  </clause>

  <clause id="16931">
    <literal><![CDATA[
      K(x,T(y,z * (z * u)) * w) = K(x,T(y,u) * w)
    ]]></literal>
    <justification jstring="[para(9(a,1),16929(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="9 16929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16932">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ 1)) * w) = K(x,T(y,u * z) * w)
    ]]></literal>
    <justification jstring="[para(13409(a,1),16930(a,1,2,1))].">
      <j1 rule="para" parents="13409 16930"/>
    </justification>
  </clause>

  <clause id="16933">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,T(u,w * (w * v5)) * v6)),K(T(u,w * (w * v5)) * v6,z)) = T(y,K(z,T(u,v5) * v6) * x)
    ]]></literal>
    <justification jstring="[para(16931(a,1),14916(a,2,2,1))].">
      <j1 rule="para" parents="16931 14916"/>
    </justification>
  </clause>

  <clause id="16934">
    <literal><![CDATA[
      K(x,y * (T(z,u \ w) \ v5)) = K(x,y * (T(z,u * w) \ v5))
    ]]></literal>
    <justification jstring="[para(4555(a,1),16928(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4555 16928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16935">
    <literal><![CDATA[
      T(x,y * (T(z,u \ w) \ v5)) = T(x,y * (T(z,u * w) \ v5))
    ]]></literal>
    <justification jstring="[hyper(124,a,16934,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 16934 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16936">
    <literal><![CDATA[
      T(x,K(T(y,z \ u) \ w,v5) * (T(y,z * u) \ w)) = T(x,T(T(y,z \ u) \ w,v5))
    ]]></literal>
    <justification jstring="[para(4274(a,2),16935(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4274 16935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16937">
    <literal><![CDATA[
      K(x,y * (T(z,u \ w) * v5)) = K(x,y * (T(z,u * w) * v5))
    ]]></literal>
    <justification jstring="[hyper(16044,a,16873,a),flip(a)].">
      <j1 rule="hyper" parents="16044 16873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16938">
    <literal><![CDATA[
      T(x,y * (T(z,u \ w) * v5)) = T(x,y * (T(z,u * w) * v5))
    ]]></literal>
    <justification jstring="[hyper(124,a,16937,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 16937 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16939">
    <literal><![CDATA[
      x * K(x,y * (T(z,u * w) * v5)) = T(x,y * (T(z,u \ w) * v5))
    ]]></literal>
    <justification jstring="[hyper(126,a,16937,a(flip),b,4215,a(flip))].">
      <j1 rule="hyper" parents="126 16937 4215"/>
    </justification>
  </clause>

  <clause id="16940">
    <literal><![CDATA[
      T(x,y * (T(z,u \ w) * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,y * (T(z,u * w) * v5)) = v6
    ]]></literal>
    <justification jstring="[para(16939(a,1),4285(a,1))].">
      <j1 rule="para" parents="16939 4285"/>
    </justification>
  </clause>

  <clause id="16942">
    <literal><![CDATA[
      K(x,K(y \ (1 / z),L(y / u,u,z))) = K(x,K(y / u,1 / (z * y)))
    ]]></literal>
    <justification jstring="[para(4809(a,1),15643(a,2,2))].">
      <j1 rule="para" parents="4809 15643"/>
    </justification>
  </clause>

  <clause id="16944">
    <literal><![CDATA[
      K(x,K(y \ (1 / z),L(y / u,u,z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z * y,y / u)) = w
    ]]></literal>
    <justification jstring="[para(16942(a,2),7190(a,1))].">
      <j1 rule="para" parents="16942 7190"/>
    </justification>
  </clause>

  <clause id="16945">
    <literal><![CDATA[
      K(x,K((1 / y) / z,L(z / u,u,y))) = K(x,K(y * z,z / u))
    ]]></literal>
    <justification jstring="[hyper(16944,a,15555,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="16944 15555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16946">
    <literal><![CDATA[
      K(x,K((y \ z) * u,u / y)) = K(x,K(z,(1 / (y \ z)) / u))
    ]]></literal>
    <justification jstring="[hyper(63,a,13886,a(flip),b,16945,a),flip(a)].">
      <j1 rule="hyper" parents="63 13886 16945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16947">
    <literal><![CDATA[
      K(x,K(y / z,(z \ u) * y)) = K(x,K(u,(1 / (z \ u)) / y))
    ]]></literal>
    <justification jstring="[hyper(6836,a,16946,a)].">
      <j1 rule="hyper" parents="6836 16946"/>
    </justification>
  </clause>

  <clause id="16948">
    <literal><![CDATA[
      K(x,K(y,(1 / (z \ y)) / u)) = K(x,K(y,u / z))
    ]]></literal>
    <justification jstring="[hyper(63,a,15683,a(flip),b,16947,a),flip(a)].">
      <j1 rule="hyper" parents="63 15683 16947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16949">
    <literal><![CDATA[
      K(x,K(y,(1 / z) / u)) = K(x,K(y,u / (y / z)))
    ]]></literal>
    <justification jstring="[para(79(a,1),16948(a,1,2,2,1,2))].">
      <j1 rule="para" parents="79 16948"/>
    </justification>
  </clause>

  <clause id="16950">
    <literal><![CDATA[
      K(x,K(y,z / (y / u))) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,11449,a(flip),b,16949,a),flip(a)].">
      <j1 rule="hyper" parents="63 11449 16949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16951">
    <literal><![CDATA[
      K(x,K(y,z * (y / u))) = K(x,K(y,z / u))
    ]]></literal>
    <justification jstring="[hyper(63,a,16607,a(flip),b,16950,a),flip(a)].">
      <j1 rule="hyper" parents="63 16607 16950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16952">
    <literal><![CDATA[
      K(x,K(y,z * x)) * K(y / x,(y / x) \ z) = K(x \ y,z / (y / x))
    ]]></literal>
    <justification jstring="[para(16950(a,1),7299(a,1,1))].">
      <j1 rule="para" parents="16950 7299"/>
    </justification>
  </clause>

  <clause id="16953">
    <literal><![CDATA[
      K(x,K(y,z * (x / u))) = K(y,K(x,z / u))
    ]]></literal>
    <justification jstring="[hyper(6798,a,16951,a)].">
      <j1 rule="hyper" parents="6798 16951"/>
    </justification>
  </clause>

  <clause id="16954">
    <literal><![CDATA[
      K(x,K(y,z * (x / u))) = K(x,K(y,z / u))
    ]]></literal>
    <justification jstring="[hyper(333,a,6785,a,b,16953,a),flip(a)].">
      <j1 rule="hyper" parents="333 6785 16953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16955">
    <literal><![CDATA[
      K(x,K(y,z / y)) * K(y / x,(x / y) * z) = K(x \ y,z * (x / y))
    ]]></literal>
    <justification jstring="[para(16954(a,1),12358(a,1,1))].">
      <j1 rule="para" parents="16954 12358"/>
    </justification>
  </clause>

  <clause id="16956">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z / x,(z / x) \ y) = K(x \ z,y / (z / x))
    ]]></literal>
    <justification jstring="[para(7022(a,1),16952(a,1,1))].">
      <j1 rule="para" parents="7022 16952"/>
    </justification>
  </clause>

  <clause id="16957">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z / x,y / (z / x)) = K(x \ z,y / (z / x))
    ]]></literal>
    <justification jstring="[para(4368(a,2),16956(a,1,2))].">
      <j1 rule="para" parents="4368 16956"/>
    </justification>
  </clause>

  <clause id="16958">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y / x,(x / y) * z) = K(x \ y,z * (x / y))
    ]]></literal>
    <justification jstring="[para(6872(a,1),16955(a,1,1))].">
      <j1 rule="para" parents="6872 16955"/>
    </justification>
  </clause>

  <clause id="16959">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z / x,(x / z) * y) = K(x \ z,y * (x / z))
    ]]></literal>
    <justification jstring="[para(6800(a,1),16958(a,1,1))].">
      <j1 rule="para" parents="6800 16958"/>
    </justification>
  </clause>

  <clause id="16960">
    <literal><![CDATA[
      K(x,K(y,z) \ (x * (u * y))) \ T(x,u * T(y,z)) = R(x,K(y,z) \ (u * y),x)
    ]]></literal>
    <justification jstring="[para(10651(a,2),15754(a,1,1))].">
      <j1 rule="para" parents="10651 15754"/>
    </justification>
  </clause>

  <clause id="16961">
    <literal><![CDATA[
      K(x,(y * z) * (u * K(y * z,w))) = K(x,T(T(z,y) * y,w) * u)
    ]]></literal>
    <justification jstring="[hyper(15877,a,15149,a),flip(a)].">
      <j1 rule="hyper" parents="15877 15149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16962">
    <literal><![CDATA[
      K(x,T(T(y,z) * z,u) * w) = K(x,T(z * y,u) * w)
    ]]></literal>
    <justification jstring="[hyper(15603,a,16961,a),flip(a)].">
      <j1 rule="hyper" parents="15603 16961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16963">
    <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(13306(a,1),16219(a,1,1,1,1))].">
      <j1 rule="para" parents="13306 16219"/>
    </justification>
  </clause>

  <clause id="16964">
    <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="[para(4989(a,1),16963(a,1,1,1))].">
      <j1 rule="para" parents="4989 16963"/>
    </justification>
  </clause>

  <clause id="16965">
    <literal><![CDATA[
      K(x,y) \ T((K(x,K(y,z)) * u) * K(x,y),w) = T(K(x,y) * u,w) * K(y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(16285,a,9042,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="16285 9042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16966">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * (u * (z * (u \ 1)))) = T(x,((u * z) * (u \ 1)) * y)
    ]]></literal>
    <justification jstring="[hyper(16292,a,16847,a),flip(a)].">
      <j1 rule="hyper" parents="16292 16847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16967">
    <literal><![CDATA[
      T(x,((y * z) * (y \ 1)) * u) = T(x,(y * (z * (y \ 1))) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,15915,a(flip),b,16966,a),flip(a)].">
      <j1 rule="hyper" parents="63 15915 16966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16968">
    <literal><![CDATA[
      T(x,(((1 / y) * z) * ((1 / y) \ 1)) * u) = T(x,((y \ 1) * (z * ((1 / y) \ 1))) * u)
    ]]></literal>
    <justification jstring="[hyper(333,a,3182,a(flip),b,16967,a),flip(a)].">
      <j1 rule="hyper" parents="333 3182 16967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16969">
    <literal><![CDATA[
      T(x,(y * ((((y \ 1) * (y \ z)) / (y \ 1)) * (y \ 1))) * u) = T(x,(y * ((y \ 1) * ((y \ (z * (y \ 1))) / (y \ 1)))) * u)
    ]]></literal>
    <justification jstring="[para(2022(a,1),16967(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2022 16967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16970">
    <literal><![CDATA[
      L(K(x,y * K(z,T(u * K(w,v5),v6))),x,v7) = (x * K(v8,v9)) \ (T(x,K(u,z) * y) * K(v8,v9))
    ]]></literal>
    <justification jstring="[para(16905(a,1),16503(a,2,2,1))].">
      <j1 rule="para" parents="16905 16503"/>
    </justification>
  </clause>

  <clause id="16971">
    <literal><![CDATA[
      K(x,(y * z) * K(L(u,z,y) \ 1,w * v5)) = K(x,y * (z * K(u * 1,w \ v5)))
    ]]></literal>
    <justification jstring="[hyper(333,a,16263,a(flip),b,16794,a),flip(a)].">
      <j1 rule="hyper" parents="333 16263 16794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16972">
    <literal><![CDATA[
      T(x,R(y,R(z,u,u),u * u) * ((z * u) * u)) = T(x,(y * L(z,u,u)) * (u * u))
    ]]></literal>
    <justification jstring="[hyper(333,a,1124,a(flip),b,16834,a),flip(a)].">
      <j1 rule="hyper" parents="333 1124 16834"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16973">
    <literal><![CDATA[
      K(x,(y * z) * K(L(u,z,y) \ 1,w * v5)) = K(x,y * (z * K(u,w \ v5)))
    ]]></literal>
    <justification jstring="[para(8(a,1),16971(a,2,2,2,2,1))].">
      <j1 rule="para" parents="8 16971"/>
    </justification>
  </clause>

  <clause id="16974">
    <literal><![CDATA[
      K(x,y * (z * K(u \ 1,w * v5))) = K(x,y * (z * K(u,w \ v5)))
    ]]></literal>
    <justification jstring="[para(5368(a,1),16973(a,1,2))].">
      <j1 rule="para" parents="5368 16973"/>
    </justification>
  </clause>

  <clause id="16975">
    <literal><![CDATA[
      K(x,y * (z * K(u * 1,w * v5))) = K(x,y * (z * K(u,w \ v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,16263,a(flip),b,16974,a)].">
      <j1 rule="hyper" parents="63 16263 16974"/>
    </justification>
  </clause>

  <clause id="16976">
    <literal><![CDATA[
      K(x,y * (z * K(u,w \ v5))) = K(x,y * (z * K(u,w * v5)))
    ]]></literal>
    <justification jstring="[para(8(a,1),16975(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="8 16975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16977">
    <literal><![CDATA[
      K(x,y * ((T(z,T(u,w)) / u) * K(u,u * w))) = K(x,y * ((w / (w / u)) \ z))
    ]]></literal>
    <justification jstring="[hyper(63,a,13011,a(flip),b,16976,a),flip(a)].">
      <j1 rule="hyper" parents="63 13011 16976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16978">
    <literal><![CDATA[
      K(x,y * ((T(z,T(u,w)) / u) * K(u,w * u))) = K(x,y * ((w / (w / u)) \ z))
    ]]></literal>
    <justification jstring="[para(4636(a,2),16977(a,1,2,2,2))].">
      <j1 rule="para" parents="4636 16977"/>
    </justification>
  </clause>

  <clause id="16979">
    <literal><![CDATA[
      T(x,R(y,R(z,u,u),u * u) * ((z * u) * u)) = T(x,y * (L(z,u,u) * (u * u)))
    ]]></literal>
    <justification jstring="[para(33(a,1),16972(a,2,2))].">
      <j1 rule="para" parents="33 16972"/>
    </justification>
  </clause>

  <clause id="16980">
    <literal><![CDATA[
      T(x,R(y,R(z,u,u),u * u) * ((z * u) * u)) = T(x,y * L(z * (u * u),u,u))
    ]]></literal>
    <justification jstring="[para(1216(a,2),16979(a,2,2,2))].">
      <j1 rule="para" parents="1216 16979"/>
    </justification>
  </clause>

  <clause id="16981">
    <literal><![CDATA[
      T(x,y * L(z * (u * u),u,u)) = T(x,y * ((z * u) * u))
    ]]></literal>
    <justification jstring="[para(534(a,1),16980(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="534 16980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16982">
    <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(5908(a,1),15615(a,1,2,2))].">
      <j1 rule="para" parents="5908 15615"/>
    </justification>
  </clause>

  <clause id="16983">
    <literal><![CDATA[
      (K(x,y) \ z) \ (u * (z * K(y,x))) = (z * K(y,x)) \ (u * (K(x,y) \ z))
    ]]></literal>
    <justification jstring="[para(6847(a,1),15849(a,1,2,2))].">
      <j1 rule="para" parents="6847 15849"/>
    </justification>
  </clause>

  <clause id="16984">
    <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(333,a,6946,a(flip),b,15873,a),flip(a)].">
      <j1 rule="hyper" parents="333 6946 15873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16985">
    <literal><![CDATA[
      T(((x \ 1) * y) \ z,K(y * (x \ 1),x)) = T(z / ((x \ 1) * y),y / x)
    ]]></literal>
    <justification jstring="[para(12201(a,1),16984(a,1,2))].">
      <j1 rule="para" parents="12201 16984"/>
    </justification>
  </clause>

  <clause id="16986">
    <literal><![CDATA[
      T(((x \ 1) * y) \ z,K(x \ y,x)) = T(z / ((x \ 1) * y),y / x)
    ]]></literal>
    <justification jstring="[para(8574(a,1),16985(a,1,2))].">
      <j1 rule="para" parents="8574 16985"/>
    </justification>
  </clause>

  <clause id="16987">
    <literal><![CDATA[
      T(x / ((y \ 1) * z),z / y) = T(((y \ 1) * z) \ x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(7216,a,16986,a),flip(a)].">
      <j1 rule="hyper" parents="7216 16986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16988">
    <literal><![CDATA[
      K(x,K(y,z * u)) * K(y,T(z * u,w) * x) = K(y,x * T(T(u,z) * z,w))
    ]]></literal>
    <justification jstring="[para(16962(a,1),15980(a,1,2))].">
      <j1 rule="para" parents="16962 15980"/>
    </justification>
  </clause>

  <clause id="16989">
    <literal><![CDATA[
      K(x,y * T(T(z,u) * u,w)) = K(x,y * T(u * z,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,15865,a(flip),b,16988,a),flip(a)].">
      <j1 rule="hyper" parents="63 15865 16988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16990">
    <literal><![CDATA[
      K(x,y * T(z * ((z * u) / z),w)) = K(x,y * T(u * z,w))
    ]]></literal>
    <justification jstring="[para(238(a,1),16989(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="238 16989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16991">
    <literal><![CDATA[
      K(x,y * T(T(z * u,z),w)) = K(x,y * T(u * z,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,16041,a(flip),b,16990,a)].">
      <j1 rule="hyper" parents="63 16041 16990"/>
    </justification>
  </clause>

  <clause id="16992">
    <literal><![CDATA[
      K(x,K(y,z * u)) * K(y,T(z * u,w) * x) = K(y,x * T(T(u * z,u),w))
    ]]></literal>
    <justification jstring="[hyper(333,a,15865,a,b,16991,a)].">
      <j1 rule="hyper" parents="333 15865 16991"/>
    </justification>
  </clause>

  <clause id="16993">
    <literal><![CDATA[
      K(x,T(T(y * z,y),u) * w) = K(x,T(z * y,u) * w)
    ]]></literal>
    <justification jstring="[hyper(34,a,15979,a,b,16992,a)].">
      <j1 rule="hyper" parents="34 15979 16992"/>
    </justification>
  </clause>

  <clause id="16994">
    <literal><![CDATA[
      K(x,T(y * z,z) * u) = K(x,(z * y) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,14975,a(flip),b,16993,a),flip(a)].">
      <j1 rule="hyper" parents="63 14975 16993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16995">
    <literal><![CDATA[
      T(x,y * (T(z,u \ w) * (w / T(u,w)))) = T(x,y * (K(w,u) * ((w / u) * z)))
    ]]></literal>
    <justification jstring="[para(12631(a,1),16040(a,1,2,2,1))].">
      <j1 rule="para" parents="12631 16040"/>
    </justification>
  </clause>

  <clause id="16996">
    <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(16156(a,1),14377(a,1))].">
      <j1 rule="para" parents="16156 14377"/>
    </justification>
  </clause>

  <clause id="16998">
    <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(63,a,12211,a(flip),b,16281,a)].">
      <j1 rule="hyper" parents="63 12211 16281"/>
    </justification>
  </clause>

  <clause id="16999">
    <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(6847(a,1),16628(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6847 16628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17000">
    <literal><![CDATA[
      (K(x,y) \ z) \ (u * (z * K(y,x))) = z \ T(u * z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,16297,a(flip),b,16999,a),flip(a)].">
      <j1 rule="hyper" parents="63 16297 16999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17001">
    <literal><![CDATA[
      (x * K(y,z)) \ (u * (K(z,y) \ x)) = x \ T(u * x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,16983,a(flip),b,17000,a)].">
      <j1 rule="hyper" parents="63 16983 17000"/>
    </justification>
  </clause>

  <clause id="17002">
    <literal><![CDATA[
      (x * K(y,z)) \ (u * (K(z,y) \ x)) = x \ T(u * x,K(y,z))
    ]]></literal>
    <justification jstring="[para(6840(a,1),17001(a,2,2))].">
      <j1 rule="para" parents="6840 17001"/>
    </justification>
  </clause>

  <clause id="17003">
    <literal><![CDATA[
      T((x * K(y,z)) \ u,K(K(y,z) * x,w)) = (x * K(y,z)) \ T(u,K(x,w))
    ]]></literal>
    <justification jstring="[para(6019(a,1),16639(a,1,1,1))].">
      <j1 rule="para" parents="6019 16639"/>
    </justification>
  </clause>

  <clause id="17005">
    <literal><![CDATA[
      T((x * K(y,z)) \ u,K(w,K(y,z) * x)) = (x * K(y,z)) \ T(u,K(x,w))
    ]]></literal>
    <justification jstring="[hyper(6868,a,17003,a)].">
      <j1 rule="hyper" parents="6868 17003"/>
    </justification>
  </clause>

  <clause id="17006">
    <literal><![CDATA[
      T((x * K(y,z)) \ u,K(x,w)) = (x * K(y,z)) \ T(u,K(x,w))
    ]]></literal>
    <justification jstring="[hyper(16630,a,17005,a)].">
      <j1 rule="hyper" parents="16630 17005"/>
    </justification>
  </clause>

  <clause id="17008">
    <literal><![CDATA[
      K(x,T((y * K(z,u)) / T(w,K(y,v5)),T((y * K(z,u)) \ w,K(y,v5)))) = K(x,(y * K(z,u)) / T(w,K(y,v5)))
    ]]></literal>
    <justification jstring="[para(17006(a,2),4623(a,1,2,2))].">
      <j1 rule="para" parents="17006 4623"/>
    </justification>
  </clause>

  <clause id="17009">
    <literal><![CDATA[
      T((x * K(y,z)) / u,K(K(y,z) * x,w)) = (x * K(y,z)) / T(u,K(x,w))
    ]]></literal>
    <justification jstring="[para(6019(a,1),16640(a,1,1,1))].">
      <j1 rule="para" parents="6019 16640"/>
    </justification>
  </clause>

  <clause id="17011">
    <literal><![CDATA[
      T((x * K(y,z)) / u,K(w,K(y,z) * x)) = (x * K(y,z)) / T(u,K(x,w))
    ]]></literal>
    <justification jstring="[hyper(6868,a,17009,a)].">
      <j1 rule="hyper" parents="6868 17009"/>
    </justification>
  </clause>

  <clause id="17012">
    <literal><![CDATA[
      (x * K(y,z)) / T(u,K(x,w)) = T((x * K(y,z)) / u,K(x,w))
    ]]></literal>
    <justification jstring="[hyper(16630,a,17011,a),flip(a)].">
      <j1 rule="hyper" parents="16630 17011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17014">
    <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(63,a,16637,a(flip),b,16669,a)].">
      <j1 rule="hyper" parents="63 16637 16669"/>
    </justification>
  </clause>

  <clause id="17015">
    <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(5981(a,2),16696(a,1,2))].">
      <j1 rule="para" parents="5981 16696"/>
    </justification>
  </clause>

  <clause id="17016">
    <literal><![CDATA[
      ((x \ K(y,z)) \ 1) / T(T(K(z,y),x),u) = K(u,K(z,y)) * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(2983(a,1),16744(a,1,2,1))].">
      <j1 rule="para" parents="2983 16744"/>
    </justification>
  </clause>

  <clause id="17017">
    <literal><![CDATA[
      ((x \ K(y,z)) \ 1) / T(K(z,T(y,x)),u) = K(u,K(z,y)) * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(6365(a,2),17016(a,1,2,1))].">
      <j1 rule="para" parents="6365 17016"/>
    </justification>
  </clause>

  <clause id="17018">
    <literal><![CDATA[
      ((x \ K(y,z)) \ 1) / K(z,T(T(y,x),u)) = K(u,K(z,y)) * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(6365(a,2),17017(a,1,2))].">
      <j1 rule="para" parents="6365 17017"/>
    </justification>
  </clause>

  <clause id="17019">
    <literal><![CDATA[
      ((x \ K(y,z)) \ 1) * K(T(T(y,x),u),z) = K(u,K(z,y)) * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(5999,a,17018,a)].">
      <j1 rule="hyper" parents="5999 17018"/>
    </justification>
  </clause>

  <clause id="17020">
    <literal><![CDATA[
      ((x \ K(y,z)) \ 1) * K(y,T(T(z,u),x)) = K(u,K(z,y)) * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(6417(a,1),17019(a,1,2))].">
      <j1 rule="para" parents="6417 17019"/>
    </justification>
  </clause>

  <clause id="17021">
    <literal><![CDATA[
      (x \ K(y,z)) \ K(y,T(T(z,u),x)) = K(u,K(z,y)) * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(13279,a,17020,a)].">
      <j1 rule="hyper" parents="13279 17020"/>
    </justification>
  </clause>

  <clause id="17022">
    <literal><![CDATA[
      (x \ K(y,z)) \ K(y,T(T(z,u),x)) = K(y,K(z,u)) * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(6762(a,1),17021(a,2,1))].">
      <j1 rule="para" parents="6762 17021"/>
    </justification>
  </clause>

  <clause id="17023">
    <literal><![CDATA[
      (x \ K(y,z)) \ K(y,T(T(z,u),x)) = (x \ 1) \ K(y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(333,a,15487,a(flip),b,17022,a),flip(a)].">
      <j1 rule="hyper" parents="333 15487 17022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17024">
    <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(63,a,16557,a(flip),b,16824,a)].">
      <j1 rule="hyper" parents="63 16557 16824"/>
    </justification>
  </clause>

  <clause id="17026">
    <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(63,a,12301,a(flip),b,17024,a),flip(a)].">
      <j1 rule="hyper" parents="63 12301 17024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17027">
    <literal><![CDATA[
      T(x,T(y * T(z / y,u),z * w)) = T(x,T(y * T(z / y,u),w))
    ]]></literal>
    <justification jstring="[hyper(63,a,12301,a(flip),b,17026,a),flip(a)].">
      <j1 rule="hyper" parents="63 12301 17026"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17028">
    <literal><![CDATA[
      K(x,y * (((z * (u / z)) / z) * (w \ 1))) = K(x,y * ((u / z) * (w \ K(z,u))))
    ]]></literal>
    <justification jstring="[hyper(333,a,12769,a(flip),b,16866,a),flip(a)].">
      <j1 rule="hyper" parents="333 12769 16866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17029">
    <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(14460(a,1),16915(a,1,2,1,2))].">
      <j1 rule="para" parents="14460 16915"/>
    </justification>
  </clause>

  <clause id="17030">
    <literal><![CDATA[
      T(x,K(T(y,z * u) \ w,v5) * (T(y,z * u) \ w)) = T(x,T(T(y,z \ u) \ w,v5))
    ]]></literal>
    <justification jstring="[para(16170(a,1),16936(a,1,2,1))].">
      <j1 rule="para" parents="16170 16936"/>
    </justification>
  </clause>

  <clause id="17031">
    <literal><![CDATA[
      K(x,y) \ T(K(x,K(y,z)) * (u * K(x,y)),w) = T(K(x,y) * u,w) * K(y,T(x,z))
    ]]></literal>
    <justification jstring="[para(6591(a,1),16965(a,1,2,1))].">
      <j1 rule="para" parents="6591 16965"/>
    </justification>
  </clause>

  <clause id="17032">
    <literal><![CDATA[
      T(x,((y \ 1) * (z * ((1 / y) \ 1))) * u) = T(x,(((1 / y) * z) * y) * u)
    ]]></literal>
    <justification jstring="[para(79(a,1),16968(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="79 16968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17033">
    <literal><![CDATA[
      T(x,((y \ 1) * (z * ((1 / y) \ 1))) * u) = T(x,(((y \ 1) * z) * y) * u)
    ]]></literal>
    <justification jstring="[hyper(333,a,12385,a(flip),b,17032,a),flip(a)].">
      <j1 rule="hyper" parents="333 12385 17032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17034">
    <literal><![CDATA[
      T(x,(((y \ 1) * z) * y) * u) = T(x,((y \ 1) * (z * y)) * u)
    ]]></literal>
    <justification jstring="[para(79(a,1),17033(a,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="79 17033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17035">
    <literal><![CDATA[
      K(((x \ y) * x) / z,T(u,y / x)) = y \ (y * K((x * (z / x)) \ y,u))
    ]]></literal>
    <justification jstring="[para(7682(a,1),16982(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7682 16982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17036">
    <literal><![CDATA[
      K(((x \ y) * x) / z,T(u,y / x)) = K((x * (z / x)) \ y,u)
    ]]></literal>
    <justification jstring="[hyper(333,a,9,a(flip),b,17035,a),flip(a)].">
      <j1 rule="hyper" parents="333 9 17035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17037">
    <literal><![CDATA[
      K((x * ((y * ((x \ z) * x)) / x)) \ z,u) = K(1 / y,T(u,z / x))
    ]]></literal>
    <justification jstring="[hyper(4976,a,17036,a),flip(a)].">
      <j1 rule="hyper" parents="4976 17036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17039">
    <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(17036(a,1),4976(a,1))].">
      <j1 rule="para" parents="17036 4976"/>
    </justification>
  </clause>

  <clause id="17040">
    <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(10315(a,1),16998(a,1,1,2))].">
      <j1 rule="para" parents="10315 16998"/>
    </justification>
  </clause>

  <clause id="17042">
    <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(16629(a,1),17014(a,2,2))].">
      <j1 rule="para" parents="16629 17014"/>
    </justification>
  </clause>

  <clause id="17043">
    <literal><![CDATA[
      (x \ K(y,z)) \ T(u,K(x,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T((x \ K(y,z)) \ u,K(x,w)) = v5
    ]]></literal>
    <justification jstring="[para(17042(a,1),16630(a,1))].">
      <j1 rule="para" parents="17042 16630"/>
    </justification>
  </clause>

  <clause id="17044">
    <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(17043,a,16300,a)].">
      <j1 rule="hyper" parents="17043 16300"/>
    </justification>
  </clause>

  <clause id="17045">
    <literal><![CDATA[
      T(T(x,y \ K(z,u)),K(y,w)) = T(x,T(y,w) \ K(z,u))
    ]]></literal>
    <justification jstring="[para(22(a,2),17044(a,1,1))].">
      <j1 rule="para" parents="22 17044"/>
    </justification>
  </clause>

  <clause id="17046">
    <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(17045(a,1),16825(a,1))].">
      <j1 rule="para" parents="17045 16825"/>
    </justification>
  </clause>

  <clause id="17047">
    <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(14491(a,1),17029(a,1,2,1))].">
      <j1 rule="para" parents="14491 17029"/>
    </justification>
  </clause>

  <clause id="17048">
    <literal><![CDATA[
      T(x,T(T(y,z \ u) \ w,v5)) = T(x,T(T(y,z * u) \ w,v5))
    ]]></literal>
    <justification jstring="[para(4274(a,2),17030(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4274 17030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17049">
    <literal><![CDATA[
      T(x,T(T(y * (1 / z),z * 1) \ u,w)) = T(x,T(((1 / z) * y) \ u,w))
    ]]></literal>
    <justification jstring="[hyper(16876,a,17048,a),flip(a)].">
      <j1 rule="hyper" parents="16876 17048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17050">
    <literal><![CDATA[
      T(x,T(T(((1 / y) * z) * y,y * 1) \ u,w)) = T(x,T(R(z,y,y) \ u,w))
    ]]></literal>
    <justification jstring="[para(2997(a,1),17048(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="2997 17048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17051">
    <literal><![CDATA[
      T(x,T(T(y * (1 / z),z) \ u,w)) = T(x,T(((1 / z) * y) \ u,w))
    ]]></literal>
    <justification jstring="[para(8(a,1),17049(a,1,2,1,1,2))].">
      <j1 rule="para" parents="8 17049"/>
    </justification>
  </clause>

  <clause id="17052">
    <literal><![CDATA[
      T(x,T(T(((1 / y) * z) * y,y * 1) \ u,w)) = T(x,T(L(z,y,y) \ u,w))
    ]]></literal>
    <justification jstring="[hyper(333,a,16284,a(flip),b,17050,a),flip(a)].">
      <j1 rule="hyper" parents="333 16284 17050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17053">
    <literal><![CDATA[
      T(x,T(T(((1 / y) * z) * y,y) \ u,w)) = T(x,T(L(z,y,y) \ u,w))
    ]]></literal>
    <justification jstring="[para(8(a,1),17052(a,1,2,1,1,2))].">
      <j1 rule="para" parents="8 17052"/>
    </justification>
  </clause>

  <clause id="17054">
    <literal><![CDATA[
      T(x,T((y * ((1 / y) * z)) \ u,w)) = T(x,T(L(z,y,y) \ u,w))
    ]]></literal>
    <justification jstring="[hyper(16875,a,17053,a)].">
      <j1 rule="hyper" parents="16875 17053"/>
    </justification>
  </clause>

  <clause id="17055">
    <literal><![CDATA[
      T(x,T(L(T((1 / y) \ (y \ (z * (1 / y))),u),y,y) \ w,v5)) = T(x,T(((y * T(y \ z,u)) * (1 / y)) \ w,v5))
    ]]></literal>
    <justification jstring="[para(1358(a,1),17054(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="1358 17054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17056">
    <literal><![CDATA[
      K(x,y) \ T(z * K(x,T(y,u)),w) = T(K(x,y) * z,w) * K(y,T(x,u))
    ]]></literal>
    <justification jstring="[para(15835(a,1),17031(a,1,2,1))].">
      <j1 rule="para" parents="15835 17031"/>
    </justification>
  </clause>

  <clause id="17057">
    <literal><![CDATA[
      T(K(x,y) * z,u) * K(y,T(x,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * T(z * K(x,T(y,w)),u) = v5
    ]]></literal>
    <justification jstring="[para(17056(a,1),4580(a,1))].">
      <j1 rule="para" parents="17056 4580"/>
    </justification>
  </clause>

  <clause id="17058">
    <literal><![CDATA[
      K(x,T(y,z)) * T(u * K(y,x),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * T(u * K(y,T(x,z)),w) = v5
    ]]></literal>
    <justification jstring="[para(15454(a,1),17057(a,1))].">
      <j1 rule="para" parents="15454 17057"/>
    </justification>
  </clause>

  <clause id="17059">
    <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(7649(a,1),15623(a,1,2,2,1))].">
      <j1 rule="para" parents="7649 15623"/>
    </justification>
  </clause>

  <clause id="17061">
    <literal><![CDATA[
      K(x * ((x * y) \ (z * (x * y))),y) = K(z / (1 / x),L(y,x,x \ 1))
    ]]></literal>
    <justification jstring="[hyper(14429,a,15718,a)].">
      <j1 rule="hyper" parents="14429 15718"/>
    </justification>
  </clause>

  <clause id="17062">
    <literal><![CDATA[
      K(x / (1 / y),L(z,y,y \ 1)) = K(y * T(x,y * z),z)
    ]]></literal>
    <justification jstring="[para(22(a,2),17061(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="22 17061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17063">
    <literal><![CDATA[
      K(x * T(y,x * z),z) = K(y / (1 / x),z)
    ]]></literal>
    <justification jstring="[hyper(13527,a,17062,a),flip(a)].">
      <j1 rule="hyper" parents="13527 17062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17065">
    <literal><![CDATA[
      K(x * T(y,x * z),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y * x,z) = u
    ]]></literal>
    <justification jstring="[para(17063(a,2),13509(a,1))].">
      <j1 rule="para" parents="17063 13509"/>
    </justification>
  </clause>

  <clause id="17066">
    <literal><![CDATA[
      K(((x \ y) \ z) * K(y,x),u) = K((y / x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(17065,a,16113,a)].">
      <j1 rule="hyper" parents="17065 16113"/>
    </justification>
  </clause>

  <clause id="17067">
    <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(260(a,1),15753(a,2,2,2))].">
      <j1 rule="para" parents="260 15753"/>
    </justification>
  </clause>

  <clause id="17068">
    <literal><![CDATA[
      T(x,K(y / z,u) * T(T(y,z),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,(z * K(y,w)) * T(y / z,u)) = v5
    ]]></literal>
    <justification jstring="[para(16045(a,1),15875(a,1))].">
      <j1 rule="para" parents="16045 15875"/>
    </justification>
  </clause>

  <clause id="17069">
    <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(13670(a,1),15739(a,1,2,1))].">
      <j1 rule="para" parents="13670 15739"/>
    </justification>
  </clause>

  <clause id="17070">
    <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(15748(a,1),15749(a,1,2,2))].">
      <j1 rule="para" parents="15748 15749"/>
    </justification>
  </clause>

  <clause id="17072">
    <literal><![CDATA[
      (x * T(y,z)) / T(x,K(u,w)) = T((x * y) / T(x,K(u,w)),z)
    ]]></literal>
    <justification jstring="[para(4513(a,1),15870(a,1,1))].">
      <j1 rule="para" parents="4513 15870"/>
    </justification>
  </clause>

  <clause id="17073">
    <literal><![CDATA[
      (x * T(x \ y,z)) / T(x,K(u,w)) = T(y / T(x,K(u,w)),z)
    ]]></literal>
    <justification jstring="[para(10(a,1),17072(a,2,1,1))].">
      <j1 rule="para" parents="10 17072"/>
    </justification>
  </clause>

  <clause id="17075">
    <literal><![CDATA[
      T(x,K(y,z)) * T(u / T(x,K(y,z)),w) = x * T(u / x,w)
    ]]></literal>
    <justification jstring="[para(17073(a,1),15844(a,1,2))].">
      <j1 rule="para" parents="17073 15844"/>
    </justification>
  </clause>

  <clause id="17076">
    <literal><![CDATA[
      T((x / T(y,K(z,u))) * T(T(y,K(z,u)),K(w,v5) \ (x / T(y,K(z,u)))),K(w,v5)) = y * T(x / y,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,15987,a,b,17075,a)].">
      <j1 rule="hyper" parents="63 15987 17075"/>
    </justification>
  </clause>

  <clause id="17077">
    <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(15343(a,1),16163(a,1,1))].">
      <j1 rule="para" parents="15343 16163"/>
    </justification>
  </clause>

  <clause id="17078">
    <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(17077(a,1),10933(a,1))].">
      <j1 rule="para" parents="17077 10933"/>
    </justification>
  </clause>

  <clause id="17079">
    <literal><![CDATA[
      K(x,L(((y * z) \ y) \ T(u,z),w,v5)) = K(x,L(u / ((y * z) \ y),w,v5))
    ]]></literal>
    <justification jstring="[hyper(17078,a,15088,a)].">
      <j1 rule="hyper" parents="17078 15088"/>
    </justification>
  </clause>

  <clause id="17080">
    <literal><![CDATA[
      K(x,L((y / (z * y)) \ T(u,z),w,v5)) = K(x,L(u / (y / (z * y)),w,v5))
    ]]></literal>
    <justification jstring="[hyper(17078,a,15087,a)].">
      <j1 rule="hyper" parents="17078 15087"/>
    </justification>
  </clause>

  <clause id="17081">
    <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(15180(a,1),16166(a,1,1))].">
      <j1 rule="para" parents="15180 16166"/>
    </justification>
  </clause>

  <clause id="17082">
    <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(17081(a,1),10933(a,1))].">
      <j1 rule="para" parents="17081 10933"/>
    </justification>
  </clause>

  <clause id="17083">
    <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(16278(a,1),16280(a,1,1))].">
      <j1 rule="para" parents="16278 16280"/>
    </justification>
  </clause>

  <clause id="17084">
    <literal><![CDATA[
      K(x,(y * z) * R(u,z,y)) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[hyper(7084,a,17083,a),flip(a)].">
      <j1 rule="hyper" parents="7084 17083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17085">
    <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(782(a,1),17084(a,2,2))].">
      <j1 rule="para" parents="782 17084"/>
    </justification>
  </clause>

  <clause id="17086">
    <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(10104(a,1),17084(a,2,2))].">
      <j1 rule="para" parents="10104 17084"/>
    </justification>
  </clause>

  <clause id="17087">
    <literal><![CDATA[
      K(x,y * R(T(z,y),u \ y,u)) = K(x,L(z,u \ y,u) * y)
    ]]></literal>
    <justification jstring="[para(10(a,1),17085(a,1,2,1))].">
      <j1 rule="para" parents="10 17085"/>
    </justification>
  </clause>

  <clause id="17089">
    <literal><![CDATA[
      K(x,R(y,z \ u,z) * u) = K(x,L(y,z \ u,z) * u)
    ]]></literal>
    <justification jstring="[para(252(a,1),17087(a,1,2))].">
      <j1 rule="para" parents="252 17087"/>
    </justification>
  </clause>

  <clause id="17090">
    <literal><![CDATA[
      K(x,L(y,z \ u,z) * u) = K(x,(y * (u / z)) * z)
    ]]></literal>
    <justification jstring="[para(10355(a,1),17089(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10355 17089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17091">
    <literal><![CDATA[
      K(x,y * ((y \ T(z,u)) * u)) = K(x,(u * (z / y)) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,13695,a(flip),b,17090,a)].">
      <j1 rule="hyper" parents="63 13695 17090"/>
    </justification>
  </clause>

  <clause id="17092">
    <literal><![CDATA[
      K(x,y * R(T(z,y),u,y / u)) = K(x,L(z,u,u \ y) * y)
    ]]></literal>
    <justification jstring="[para(12(a,1),17086(a,1,2,1))].">
      <j1 rule="para" parents="12 17086"/>
    </justification>
  </clause>

  <clause id="17094">
    <literal><![CDATA[
      K(x,y * R(T(z,y),u,u \ y)) = K(x,L(z,u,u \ y) * y)
    ]]></literal>
    <justification jstring="[para(10344(a,1),17092(a,1,2,2))].">
      <j1 rule="para" parents="10344 17092"/>
    </justification>
  </clause>

  <clause id="17095">
    <literal><![CDATA[
      K(x,L(y,z,z \ u) * u) = K(x,(y * z) * (z \ u))
    ]]></literal>
    <justification jstring="[para(776(a,1),17094(a,1,2)),flip(a)].">
      <j1 rule="para" parents="776 17094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17096">
    <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(333,a,13786,a,b,16663,a),flip(a)].">
      <j1 rule="hyper" parents="333 13786 16663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17097">
    <literal><![CDATA[
      (x * K(y,z)) * L(K(z,y) * (x \ 1),u,w) = x * (K(y,z) * L(K(z,y) * (x \ 1),u,w))
    ]]></literal>
    <justification jstring="[para(4567(a,1),16738(a,2,2,2,1))].">
      <j1 rule="para" parents="4567 16738"/>
    </justification>
  </clause>

  <clause id="17100">
    <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(15581(a,1),17096(a,2,3))].">
      <j1 rule="para" parents="15581 17096"/>
    </justification>
  </clause>

  <clause id="17101">
    <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(63,a,16602,a(flip),b,17100,a)].">
      <j1 rule="hyper" parents="63 16602 17100"/>
    </justification>
  </clause>

  <clause id="17103">
    <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(25(a,2),15853(a,1,1))].">
      <j1 rule="para" parents="25 15853"/>
    </justification>
  </clause>

  <clause id="17104">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * (L(z,u,u) * (u * u))) = T(x,(u * (u * T(z,u * u))) * y)
    ]]></literal>
    <justification jstring="[para(15401(a,1),16021(a,1,1,2))].">
      <j1 rule="para" parents="15401 16021"/>
    </justification>
  </clause>

  <clause id="17105">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * L(z * (u * u),u,u)) = T(x,(u * (u * T(z,u * u))) * y)
    ]]></literal>
    <justification jstring="[para(1216(a,2),17104(a,1,2,2))].">
      <j1 rule="para" parents="1216 17104"/>
    </justification>
  </clause>

  <clause id="17108">
    <literal><![CDATA[
      x * a(y \ 1,y \ 1,(y \ 1) * ((y \ 1) \ x)) = y \ ((1 / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(582,a,16104,a)].">
      <j1 rule="hyper" parents="582 16104"/>
    </justification>
  </clause>

  <clause id="17110">
    <literal><![CDATA[
      x * a(y \ 1,y \ 1,x) = y \ ((1 / y) \ x)
    ]]></literal>
    <justification jstring="[para(10(a,1),17108(a,1,2,3))].">
      <j1 rule="para" parents="10 17108"/>
    </justification>
  </clause>

  <clause id="17111">
    <literal><![CDATA[
      x * a(y \ 1,y,x) = y \ ((1 / y) \ x)
    ]]></literal>
    <justification jstring="[para(14331(a,1),17110(a,1,2))].">
      <j1 rule="para" parents="14331 17110"/>
    </justification>
  </clause>

  <clause id="17112">
    <literal><![CDATA[
      L(x * a((y \ 1) \ 1,y \ 1,x),y,y) = y * ((1 / (y \ 1)) \ x)
    ]]></literal>
    <justification jstring="[para(17111(a,2),2601(a,1,1))].">
      <j1 rule="para" parents="17111 2601"/>
    </justification>
  </clause>

  <clause id="17113">
    <literal><![CDATA[
      T(x,y * (z * a((1 / u) \ 1,1 / u,z))) = T(x,y * ((u \ 1) \ ((1 / (1 / u)) \ z)))
    ]]></literal>
    <justification jstring="[para(17111(a,2),3181(a,1,2,2))].">
      <j1 rule="para" parents="17111 3181"/>
    </justification>
  </clause>

  <clause id="17115">
    <literal><![CDATA[
      L(x * a((y \ 1) \ 1,y,x),y,y) = y * ((1 / (y \ 1)) \ x)
    ]]></literal>
    <justification jstring="[para(14331(a,1),17112(a,1,1,2))].">
      <j1 rule="para" parents="14331 17112"/>
    </justification>
  </clause>

  <clause id="17117">
    <literal><![CDATA[
      L(x * a(y,y,x),y,y) = y * ((1 / (y \ 1)) \ x)
    ]]></literal>
    <justification jstring="[para(3202(a,1),17115(a,1,1,2))].">
      <j1 rule="para" parents="3202 17115"/>
    </justification>
  </clause>

  <clause id="17118">
    <literal><![CDATA[
      L(x * a(y,y,x),y,y) = y * (y \ x)
    ]]></literal>
    <justification jstring="[para(76(a,1),17117(a,2,2,1))].">
      <j1 rule="para" parents="76 17117"/>
    </justification>
  </clause>

  <clause id="17120">
    <literal><![CDATA[
      (x \ 1) \ (x \ y) = y * a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(2612,a,17118,a)].">
      <j1 rule="hyper" parents="2612 17118"/>
    </justification>
  </clause>

  <clause id="17121">
    <literal><![CDATA[
      (x \ 1) * (y * a(x,x,y)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(2603,a,17118,a)].">
      <j1 rule="hyper" parents="2603 17118"/>
    </justification>
  </clause>

  <clause id="17122">
    <literal><![CDATA[
      ((x \ 1) \ (x \ y)) / y = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(123,a,17120,a,b,13101,a)].">
      <j1 rule="hyper" parents="123 17120 13101"/>
    </justification>
  </clause>

  <clause id="17123">
    <literal><![CDATA[
      x \ ((y \ 1) \ (y \ x)) = a(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(121,a,17120,a,b,xx)].">
      <j1 rule="hyper" parents="121 17120"/>
    </justification>
  </clause>

  <clause id="17124">
    <literal><![CDATA[
      L(a(x,x,y),y,x \ 1) = ((x \ 1) * y) \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(121,a,17121,a(flip),b,97,a),flip(a)].">
      <j1 rule="hyper" parents="121 17121 97"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17126">
    <literal><![CDATA[
      ((x \ 1) * (y * a(x,x,y))) / T((x \ 1) * y,a(x,x,y)) = ((x \ 1) * y) \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,13403,a(flip),b,17124,a)].">
      <j1 rule="hyper" parents="63 13403 17124"/>
    </justification>
  </clause>

  <clause id="17127">
    <literal><![CDATA[
      (x \ y) / T((x \ 1) * y,a(x,x,y)) = ((x \ 1) * y) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(17121(a,1),17126(a,1,1))].">
      <j1 rule="para" parents="17121 17126"/>
    </justification>
  </clause>

  <clause id="17128">
    <literal><![CDATA[
      (x \ y) / ((x \ 1) * y) = ((x \ 1) * y) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(13826(a,1),17127(a,1,2))].">
      <j1 rule="para" parents="13826 17127"/>
    </justification>
  </clause>

  <clause id="17129">
    <literal><![CDATA[
      R(x * ((x \ y) / y),x,y) = ((x \ 1) * y) \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(2195,a,17128,a)].">
      <j1 rule="hyper" parents="2195 17128"/>
    </justification>
  </clause>

  <clause id="17131">
    <literal><![CDATA[
      T(x,y * ((z \ 1) \ ((1 / (1 / z)) \ u))) = T(x,y * (u * a(z,1 / z,u)))
    ]]></literal>
    <justification jstring="[para(79(a,1),17113(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="79 17113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17132">
    <literal><![CDATA[
      T(x,y * ((z \ 1) \ ((1 / (1 / z)) \ u))) = T(x,y * (u * a(z,z,u)))
    ]]></literal>
    <justification jstring="[para(14334(a,1),17131(a,2,2,2,2))].">
      <j1 rule="para" parents="14334 17131"/>
    </justification>
  </clause>

  <clause id="17133">
    <literal><![CDATA[
      K((x * y) \ ((y * T(x,K(y,z))) * u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(K(y * T(x,K(y,z)),y) \ u,w) = v5
    ]]></literal>
    <justification jstring="[para(12617(a,1),16424(a,1))].">
      <j1 rule="para" parents="12617 16424"/>
    </justification>
  </clause>

  <clause id="17135">
    <literal><![CDATA[
      K((x * y) \ ((y * T(x,K(y,z))) * u),w) = K(K(y * T(x,K(y,z)),x) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(16425,a,16176,a),flip(a)].">
      <j1 rule="hyper" parents="16425 16176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17137">
    <literal><![CDATA[
      K((x * y) \ ((y * T(x,K(y,z))) * u),w) = K(K(y * x,x) \ u,w)
    ]]></literal>
    <justification jstring="[para(7400(a,1),17135(a,2,1,1))].">
      <j1 rule="para" parents="7400 17135"/>
    </justification>
  </clause>

  <clause id="17138">
    <literal><![CDATA[
      K(K(x * T(y,K(x,z)),x) \ u,w) = K(K(x * y,y) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(17133,a,17137,a)].">
      <j1 rule="hyper" parents="17133 17137"/>
    </justification>
  </clause>

  <clause id="17140">
    <literal><![CDATA[
      K(K(x * y,y) \ z,u) = K(K(y,x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,12828,a(flip),b,17138,a),flip(a)].">
      <j1 rule="hyper" parents="63 12828 17138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17141">
    <literal><![CDATA[
      K(K(x \ 1,y) \ z,u) = K(K(y,x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,15955,a,b,17140,a)].">
      <j1 rule="hyper" parents="63 15955 17140"/>
    </justification>
  </clause>

  <clause id="17142">
    <literal><![CDATA[
      K(K(x,y) \ (z / u),w) \ K((K(y \ 1,x) \ (z / u)) * w,w) = a(w,u \ (K(y \ 1,x) \ z),w)
    ]]></literal>
    <justification jstring="[para(17141(a,1),12893(a,1,1))].">
      <j1 rule="para" parents="17141 12893"/>
    </justification>
  </clause>

  <clause id="17143">
    <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(9(a,1),16748(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="9 16748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17144">
    <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(15786,a,17143,a)].">
      <j1 rule="hyper" parents="15786 17143"/>
    </justification>
  </clause>

  <clause id="17146">
    <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(29(a,1),17144(a,1,2,2,2))].">
      <j1 rule="para" parents="29 17144"/>
    </justification>
  </clause>

  <clause id="17147">
    <literal><![CDATA[
      L(K(x,y * K(z,T(u * K(w,v5),v6))),x,v7) = L(K(x,y * K(u,z)),x,v8)
    ]]></literal>
    <justification jstring="[hyper(333,a,15874,a,b,16970,a),flip(a)].">
      <j1 rule="hyper" parents="333 15874 16970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17148">
    <literal><![CDATA[
      L(K(x,y * K(z,T(u * K(w,v5),v6))),x,v7) = K(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(333,a,16066,a(flip),b,17147,a),flip(a)].">
      <j1 rule="hyper" parents="333 16066 17147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17149">
    <literal><![CDATA[
      L(K(x,y * K(z,u * K(w,v5))),x,v6) = K(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[para(110(a,1),17148(a,1,1,2,2,2))].">
      <j1 rule="para" parents="110 17148"/>
    </justification>
  </clause>

  <clause id="17150">
    <literal><![CDATA[
      K(x,y * K(z,u * K(w,v5))) = K(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(16067,a,17149,a)].">
      <j1 rule="hyper" parents="16067 17149"/>
    </justification>
  </clause>

  <clause id="17151">
    <literal><![CDATA[
      K(x,K(y,z * K(u,w)) * v5) = K(x,v5 * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(15533,a,17150,a)].">
      <j1 rule="hyper" parents="15533 17150"/>
    </justification>
  </clause>

  <clause id="17152">
    <literal><![CDATA[
      K(x,(y * K(z,u)) * K(y,w)) = K(x,T(y * K(z,u),w))
    ]]></literal>
    <justification jstring="[hyper(7013,a,17150,a),flip(a)].">
      <j1 rule="hyper" parents="7013 17150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17153">
    <literal><![CDATA[
      K(x,K(y,z * K(u,w)) * v5) = K(x,K(z,y) * v5)
    ]]></literal>
    <justification jstring="[hyper(333,a,15489,a,b,17151,a),flip(a)].">
      <j1 rule="hyper" parents="333 15489 17151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17154">
    <literal><![CDATA[
      K(x,K(K(y,z) * u,w) * v5) = K(x,K(w,u) * v5)
    ]]></literal>
    <justification jstring="[para(6355(a,1),17153(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="6355 17153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17155">
    <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(17154(a,2),14927(a,1))].">
      <j1 rule="para" parents="17154 14927"/>
    </justification>
  </clause>

  <clause id="17157">
    <literal><![CDATA[
      K(x,T(y * K(z,u),w)) = K(x,T(y,w) * K(z,u))
    ]]></literal>
    <justification jstring="[para(15513(a,1),17152(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15513 17152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17158">
    <literal><![CDATA[
      K(x,T(y * K(z,u),w)) = K(x,K(u,z) * T(y,w))
    ]]></literal>
    <justification jstring="[hyper(333,a,15637,a,b,17157,a),flip(a)].">
      <j1 rule="hyper" parents="333 15637 17157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17159">
    <literal><![CDATA[
      T(x,T(y * K(z,u),w)) = T(x,K(u,z) * T(y,w))
    ]]></literal>
    <justification jstring="[hyper(124,a,17158,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 17158 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17160">
    <literal><![CDATA[
      T(x,T(K(y,z) * u,w)) = T(x,K(y,z) * T(u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,16084,a,b,17159,a)].">
      <j1 rule="hyper" parents="63 16084 17159"/>
    </justification>
  </clause>

  <clause id="17161">
    <literal><![CDATA[
      T(x,T(K(y,z) * u,w)) = T(x,T(u,w) * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(333,a,15616,a(flip),b,17160,a),flip(a)].">
      <j1 rule="hyper" parents="333 15616 17160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17162">
    <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(17068,a,17160,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="17068 17160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17163">
    <literal><![CDATA[
      T(x,((y \ z) * y) * K(u,w)) = T(x,T(K(u,w) * z,y))
    ]]></literal>
    <justification jstring="[hyper(15770,a,17160,a(flip))].">
      <j1 rule="hyper" parents="15770 17160"/>
    </justification>
  </clause>

  <clause id="17164">
    <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(333,a,16711,a(flip),b,17161,a),flip(a)].">
      <j1 rule="hyper" parents="333 16711 17161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17165">
    <literal><![CDATA[
      K(x,y * K(K(z,u) * w,v5)) = K(x,K(w,v5) * y)
    ]]></literal>
    <justification jstring="[hyper(17155,a,15489,a),flip(a)].">
      <j1 rule="hyper" parents="17155 15489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17166">
    <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(4312(a,1),17155(a,1,2,1,1))].">
      <j1 rule="para" parents="4312 17155"/>
    </justification>
  </clause>

  <clause id="17167">
    <literal><![CDATA[
      K(x,K(y / z,u) * w) = K(x,K(z \ y,u) * w)
    ]]></literal>
    <justification jstring="[hyper(17166,a,xx),flip(a)].">
      <j1 rule="hyper" parents="17166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17168">
    <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(4567(a,2),17166(a,1,2))].">
      <j1 rule="para" parents="4567 17166"/>
    </justification>
  </clause>

  <clause id="17169">
    <literal><![CDATA[
      K(x,K(y * (z \ u),u) * w) = K(x,K(z \ y,u) * w)
    ]]></literal>
    <justification jstring="[hyper(15719,a,17167,a)].">
      <j1 rule="hyper" parents="15719 17167"/>
    </justification>
  </clause>

  <clause id="17170">
    <literal><![CDATA[
      K(x,K(y \ z,u) * (w * ((y / z) \ 1))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w * T((y / z) \ 1,u)) = v5
    ]]></literal>
    <justification jstring="[para(17167(a,1),15878(a,1))].">
      <j1 rule="para" parents="17167 15878"/>
    </justification>
  </clause>

  <clause id="17171">
    <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(17168,a,16903,a)].">
      <j1 rule="hyper" parents="17168 16903"/>
    </justification>
  </clause>

  <clause id="17172">
    <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(16052(a,2),17162(a,1,2,1))].">
      <j1 rule="para" parents="16052 17162"/>
    </justification>
  </clause>

  <clause id="17173">
    <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(63,a,16088,a(flip),b,17172,a),flip(a)].">
      <j1 rule="hyper" parents="63 16088 17172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17174">
    <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(7890(a,1),17164(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7890 17164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17175">
    <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(333,a,9033,a(flip),b,17174,a),flip(a)].">
      <j1 rule="hyper" parents="333 9033 17174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17176">
    <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(16996,a,17171,a)].">
      <j1 rule="hyper" parents="16996 17171"/>
    </justification>
  </clause>

  <clause id="17177">
    <literal><![CDATA[
      K(x,K(y,z / u) \ w) = K(x,K(z * u,y) * w)
    ]]></literal>
    <justification jstring="[hyper(7453,a,17176,a),flip(a)].">
      <j1 rule="hyper" parents="7453 17176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17178">
    <literal><![CDATA[
      K(x,K(y \ z,u) * w) = K(x,K(z * y,u) * w)
    ]]></literal>
    <justification jstring="[hyper(17168,a,17177,a)].">
      <j1 rule="hyper" parents="17168 17177"/>
    </justification>
  </clause>

  <clause id="17179">
    <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(14486(a,1),17103(a,1,1))].">
      <j1 rule="para" parents="14486 17103"/>
    </justification>
  </clause>

  <clause id="17180">
    <literal><![CDATA[
      T(T(x,K(y,R(z,u,u))),y * T((u \ 1) * (u * z),u)) = T(x,((u \ 1) * (z * u)) * y)
    ]]></literal>
    <justification jstring="[para(810(a,1),15914(a,1,1,2,2))].">
      <j1 rule="para" parents="810 15914"/>
    </justification>
  </clause>

  <clause id="17181">
    <literal><![CDATA[
      K(x,y * (z \ T((u \ (z * K(w,v5))) * z,K(v5,w)))) = K(x,y * ((K(w,v5) * z) / u))
    ]]></literal>
    <justification jstring="[para(14577(a,1),16214(a,1,2,2,2,1))].">
      <j1 rule="para" parents="14577 16214"/>
    </justification>
  </clause>

  <clause id="17182">
    <literal><![CDATA[
      K(x,y * (z \ ((u \ (z * K(w,v5))) * z))) = K(x,y * ((K(w,v5) * z) / u))
    ]]></literal>
    <justification jstring="[hyper(16488,a,17181,a)].">
      <j1 rule="hyper" parents="16488 17181"/>
    </justification>
  </clause>

  <clause id="17184">
    <literal><![CDATA[
      K(x,y * T(z \ (u * K(w,v5)),u)) = K(x,y * ((K(w,v5) * u) / z))
    ]]></literal>
    <justification jstring="[para(22(a,2),17182(a,1,2,2))].">
      <j1 rule="para" parents="22 17182"/>
    </justification>
  </clause>

  <clause id="17186">
    <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(63,a,7585,a(flip),b,16423,a),flip(a)].">
      <j1 rule="hyper" parents="63 7585 16423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17188">
    <literal><![CDATA[
      K((x * y) / x,z * ((x / y) / T(x,y))) = K(y,((x / y) / x) * T(z,x))
    ]]></literal>
    <justification jstring="[hyper(333,a,7892,a(flip),b,17186,a),flip(a)].">
      <j1 rule="hyper" parents="333 7892 17186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17189">
    <literal><![CDATA[
      K(x,T(y * ((z / x) / T(z,x)),z)) = K(x,((z / x) / z) * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(7001,a,17188,a)].">
      <j1 rule="hyper" parents="7001 17188"/>
    </justification>
  </clause>

  <clause id="17190">
    <literal><![CDATA[
      K(x,T(y * ((z / x) / z),z)) = K(x,((z / x) / z) * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,9654,a(flip),b,17189,a)].">
      <j1 rule="hyper" parents="63 9654 17189"/>
    </justification>
  </clause>

  <clause id="17191">
    <literal><![CDATA[
      K(x,T(((y / x) / y) * z,y)) = K(x,((y / x) / y) * T(z,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,16087,a,b,17190,a)].">
      <j1 rule="hyper" parents="63 16087 17190"/>
    </justification>
  </clause>

  <clause id="17192">
    <literal><![CDATA[
      K(x,((y / x) / y) * T(T(z,y),y)) = K(x,z * ((y / x) / y))
    ]]></literal>
    <justification jstring="[hyper(63,a,14842,a(flip),b,17191,a),flip(a)].">
      <j1 rule="hyper" parents="63 14842 17191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17193">
    <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(3311(a,1),17192(a,2,2))].">
      <j1 rule="para" parents="3311 17192"/>
    </justification>
  </clause>

  <clause id="17194">
    <literal><![CDATA[
      K(x,T(T(y,z),z) * ((z / x) / z)) = K(x,y * ((y * ((z / x) / z)) / y))
    ]]></literal>
    <justification jstring="[para(470(a,1),17193(a,1,2))].">
      <j1 rule="para" parents="470 17193"/>
    </justification>
  </clause>

  <clause id="17195">
    <literal><![CDATA[
      K(x,T(y * ((z / x) / z),y)) = K(x,T(T(y,z),z) * ((z / x) / z))
    ]]></literal>
    <justification jstring="[hyper(333,a,12249,a(flip),b,17194,a)].">
      <j1 rule="hyper" parents="333 12249 17194"/>
    </justification>
  </clause>

  <clause id="17196">
    <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(17195(a,1),12278(a,1))].">
      <j1 rule="para" parents="17195 12278"/>
    </justification>
  </clause>

  <clause id="17197">
    <literal><![CDATA[
      K(x,T(T(y,z),z) / x) = K(x,((z / x) / z) * y)
    ]]></literal>
    <justification jstring="[hyper(17196,a,16078,a),flip(a)].">
      <j1 rule="hyper" parents="17196 16078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17198">
    <literal><![CDATA[
      K(x,((y / x) / y) * z) = K(x,z / x)
    ]]></literal>
    <justification jstring="[hyper(63,a,15045,a(flip),b,17197,a),flip(a)].">
      <j1 rule="hyper" parents="63 15045 17197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17200">
    <literal><![CDATA[
      K(x / y,z / (x / y)) = K(x / y,(y / x) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,7511,a(flip),b,17198,a),flip(a)].">
      <j1 rule="hyper" parents="63 7511 17198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17201">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z / x,(x / z) * y) = K(x \ z,y / (z / x))
    ]]></literal>
    <justification jstring="[para(17200(a,1),16957(a,1,2))].">
      <j1 rule="para" parents="17200 16957"/>
    </justification>
  </clause>

  <clause id="17202">
    <literal><![CDATA[
      K(x \ y,z / (y / x)) = K(x \ y,z * (x / y))
    ]]></literal>
    <justification jstring="[hyper(63,a,16959,a(flip),b,17201,a),flip(a)].">
      <j1 rule="hyper" parents="63 16959 17201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17203">
    <literal><![CDATA[
      x * K(y \ z,x * (y / z)) = (y \ z) * (x / (y \ z))
    ]]></literal>
    <justification jstring="[para(17202(a,1),7595(a,1,2))].">
      <j1 rule="para" parents="17202 7595"/>
    </justification>
  </clause>

  <clause id="17204">
    <literal><![CDATA[
      (1 / (x \ y)) * (z / (1 / (x \ y))) = (y \ x) * (z / (y \ x))
    ]]></literal>
    <justification jstring="[hyper(63,a,8643,a,b,17203,a)].">
      <j1 rule="hyper" parents="63 8643 17203"/>
    </justification>
  </clause>

  <clause id="17205">
    <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(10901(a,1),16727(a,1,1))].">
      <j1 rule="para" parents="10901 16727"/>
    </justification>
  </clause>

  <clause id="17206">
    <literal><![CDATA[
      K(x / T(y,z),u) \ K((K(y \ 1,z) \ (x / y)) * u,u) = a(u,y \ (K(y \ 1,z) \ x),u)
    ]]></literal>
    <justification jstring="[para(15716(a,1),17142(a,1,1))].">
      <j1 rule="para" parents="15716 17142"/>
    </justification>
  </clause>

  <clause id="17207">
    <literal><![CDATA[
      K(x / T(y,z),u) \ K(u * (K(y \ 1,z) \ (x / y)),u) = a(u,y \ (K(y \ 1,z) \ x),u)
    ]]></literal>
    <justification jstring="[para(4543(a,1),17206(a,1,2))].">
      <j1 rule="para" parents="4543 17206"/>
    </justification>
  </clause>

  <clause id="17208">
    <literal><![CDATA[
      K(x / T(y,z),u) \ K(K(y \ 1,z) \ (u * (x / y)),u) = a(u,y \ (K(y \ 1,z) \ x),u)
    ]]></literal>
    <justification jstring="[para(10676(a,2),17207(a,1,2))].">
      <j1 rule="para" parents="10676 17207"/>
    </justification>
  </clause>

  <clause id="17209">
    <literal><![CDATA[
      K(x / T(y,z),u) \ K(K(z,y) \ (u * (x / y)),u) = a(u,y \ (K(y \ 1,z) \ x),u)
    ]]></literal>
    <justification jstring="[para(17141(a,1),17208(a,1,2))].">
      <j1 rule="para" parents="17141 17208"/>
    </justification>
  </clause>

  <clause id="17210">
    <literal><![CDATA[
      K(x,y * T(T(z / u,T(w,u)) * v5,v5)) = K(x,y * ((K(u \ z,w) * v5) * (z / u)))
    ]]></literal>
    <justification jstring="[hyper(16784,a,16033,a)].">
      <j1 rule="hyper" parents="16784 16033"/>
    </justification>
  </clause>

  <clause id="17211">
    <literal><![CDATA[
      K(x,y * ((K(z \ u,w) * v5) * (u / z))) = K(x,y * (v5 * T(u / z,T(w,z))))
    ]]></literal>
    <justification jstring="[hyper(63,a,16029,a(flip),b,17210,a),flip(a)].">
      <j1 rule="hyper" parents="63 16029 17210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17212">
    <literal><![CDATA[
      K(x,y * ((K(z \ u,w) * v5) * (u / z))) = K(x,y * (v5 * T(u / z,w)))
    ]]></literal>
    <justification jstring="[hyper(333,a,16461,a(flip),b,17211,a),flip(a)].">
      <j1 rule="hyper" parents="333 16461 17211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17214">
    <literal><![CDATA[
      K(x,y * (K(z \ u,w) * (v5 * (u / z)))) = K(x,y * (v5 * T(u / z,w)))
    ]]></literal>
    <justification jstring="[para(6593(a,1),17212(a,1,2,2))].">
      <j1 rule="para" parents="6593 17212"/>
    </justification>
  </clause>

  <clause id="17215">
    <literal><![CDATA[
      K(x * (y \ z),(1 / (z \ y)) * x) = K(x * (y \ z),x * (1 / (z \ y)))
    ]]></literal>
    <justification jstring="[para(1617(a,1),16282(a,1,1,2))].">
      <j1 rule="para" parents="1617 16282"/>
    </justification>
  </clause>

  <clause id="17216">
    <literal><![CDATA[
      K(x * (y \ z),x * (1 / (z \ y))) = K(x * (y \ z),(z \ y) \ x)
    ]]></literal>
    <justification jstring="[hyper(13530,a,17215,a),flip(a)].">
      <j1 rule="hyper" parents="13530 17215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17217">
    <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(17216(a,1),13533(a,1))].">
      <j1 rule="para" parents="17216 13533"/>
    </justification>
  </clause>

  <clause id="17218">
    <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(6424(a,1),16565(a,1,2))].">
      <j1 rule="para" parents="6424 16565"/>
    </justification>
  </clause>

  <clause id="17220">
    <literal><![CDATA[
      (x * (K(y,z) * L(K(z,y) * (x \ 1),u,w))) / 1 = ((x * K(y,z)) / 1) \ L((x * K(y,z)) / 1,u,w)
    ]]></literal>
    <justification jstring="[para(17097(a,1),16739(a,1,1))].">
      <j1 rule="para" parents="17097 16739"/>
    </justification>
  </clause>

  <clause id="17221">
    <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(16500,a,17218,a)].">
      <j1 rule="hyper" parents="16500 17218"/>
    </justification>
  </clause>

  <clause id="17222">
    <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(15688,a,17221,a),flip(a)].">
      <j1 rule="hyper" parents="15688 17221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17224">
    <literal><![CDATA[
      (x / K(y,T(z,u))) \ (K(z,y) * u) = (x * K(z,y)) \ (u * K(z,y))
    ]]></literal>
    <justification jstring="[para(16545(a,1),17222(a,1,1,2))].">
      <j1 rule="para" parents="16545 17222"/>
    </justification>
  </clause>

  <clause id="17225">
    <literal><![CDATA[
      (x * K(y,T(z,u))) \ (K(y,z) * u) = (x * K(y,z)) \ (u * K(y,z))
    ]]></literal>
    <justification jstring="[para(6424(a,1),17224(a,1,1))].">
      <j1 rule="para" parents="6424 17224"/>
    </justification>
  </clause>

  <clause id="17227">
    <literal><![CDATA[
      ((x * K(y,z)) / 1) \ L((x * K(y,z)) / 1,u,w) = x * (K(y,z) * L(K(z,y) * (x \ 1),u,w))
    ]]></literal>
    <justification jstring="[hyper(176,a,17220,a),flip(a)].">
      <j1 rule="hyper" parents="176 17220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17228">
    <literal><![CDATA[
      (x * K(y,z)) \ L((x * K(y,z)) / 1,u,w) = x * (K(y,z) * L(K(z,y) * (x \ 1),u,w))
    ]]></literal>
    <justification jstring="[para(74(a,1),17227(a,1,1))].">
      <j1 rule="para" parents="74 17227"/>
    </justification>
  </clause>

  <clause id="17229">
    <literal><![CDATA[
      x * (K(y,z) * L(K(z,y) * (x \ 1),u,w)) = (x * K(y,z)) \ L(x * K(y,z),u,w)
    ]]></literal>
    <justification jstring="[para(74(a,1),17228(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="74 17228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17230">
    <literal><![CDATA[
      x * (K(y,z) * L(K(z,y) * (x \ 1),u,w)) = (K(z,y) / x) * L(x * K(y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(333,a,13340,a(flip),b,17229,a),flip(a)].">
      <j1 rule="hyper" parents="333 13340 17229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17231">
    <literal><![CDATA[
      (K(x,y) / z) * L(z * K(y,x),u,w) = z * (L(z \ K(y,x),u,w) * K(x,y))
    ]]></literal>
    <justification jstring="[para(14248(a,1),17230(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14248 17230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17232">
    <literal><![CDATA[
      K(x,K(y * K(z,u),w)) * K(x,(y * K(z,T(u,w))) * w) = K(x,T(w,K(z,u)) * (y * K(z,u)))
    ]]></literal>
    <justification jstring="[para(15472(a,1),15861(a,1,1,2))].">
      <j1 rule="para" parents="15472 15861"/>
    </justification>
  </clause>

  <clause id="17235">
    <literal><![CDATA[
      K(x,T(y,K(z,u)) * (w * K(z,u))) = K(x,K(w,y)) * K(x,(w * K(z,T(u,y))) * y)
    ]]></literal>
    <justification jstring="[para(16620(a,1),17232(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16620 17232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17237">
    <literal><![CDATA[
      K(x,K(y,z) \ (u * w)) \ K(x,K(L(u,w,K(z,y)),w * K(z,y))) = K((w * K(z,y)) * L(u,w,K(z,y)),x)
    ]]></literal>
    <justification jstring="[para(15524(a,2),15869(a,1,1))].">
      <j1 rule="para" parents="15524 15869"/>
    </justification>
  </clause>

  <clause id="17238">
    <literal><![CDATA[
      T(x,K(K(y,z) * u,w) * (v5 / (w * K(u,K(y,z))))) = T(x,v5 / (u \ T(w * u,K(y,z))))
    ]]></literal>
    <justification jstring="[para(16328(a,1),16054(a,1,2,1))].">
      <j1 rule="para" parents="16328 16054"/>
    </justification>
  </clause>

  <clause id="17239">
    <literal><![CDATA[
      T(x,K(K(y,z) * u,w) * (v5 / (w * K(y,K(z,u))))) = T(x,v5 / (u \ T(w * u,K(y,z))))
    ]]></literal>
    <justification jstring="[para(6788(a,2),17238(a,1,2,2,2,2))].">
      <j1 rule="para" parents="6788 17238"/>
    </justification>
  </clause>

  <clause id="17241">
    <literal><![CDATA[
      K(x,T(T((y * K(z,u)) / w,K(y,v5)),T((y * K(z,u)) \ w,K(y,v5)))) = K(x,(y * K(z,u)) / T(w,K(y,v5)))
    ]]></literal>
    <justification jstring="[para(17012(a,1),17008(a,1,2,1))].">
      <j1 rule="para" parents="17012 17008"/>
    </justification>
  </clause>

  <clause id="17242">
    <literal><![CDATA[
      T((x / T(y,K(z,u))) * T(T(y,K(z,u)),K(w,v5) \ (T(y,K(z,u)) \ x)),K(w,v5)) = y * T(x / y,K(w,v5))
    ]]></literal>
    <justification jstring="[para(7405(a,1),17076(a,1,1,2))].">
      <j1 rule="para" parents="7405 17076"/>
    </justification>
  </clause>

  <clause id="17243">
    <literal><![CDATA[
      K(x,K(y,z) \ (u * w)) \ K(x,K(L(u,w,K(z,y)),K(y,z) \ w)) = K((w * K(z,y)) * L(u,w,K(z,y)),x)
    ]]></literal>
    <justification jstring="[para(15524(a,2),17237(a,1,2,2))].">
      <j1 rule="para" parents="15524 17237"/>
    </justification>
  </clause>

  <clause id="17244">
    <literal><![CDATA[
      K(x,T(T((y * K(z,u)) / w,K(y,v5)),(y * K(z,u)) \ w)) = K(x,(y * K(z,u)) / T(w,K(y,v5)))
    ]]></literal>
    <justification jstring="[hyper(15602,a,17241,a)].">
      <j1 rule="hyper" parents="15602 17241"/>
    </justification>
  </clause>

  <clause id="17247">
    <literal><![CDATA[
      T(x,T(L((y \ 1) * z,y \ 1,y),y) * u) = T(x,(((y \ 1) * ((1 / (y \ 1)) * z)) * (y \ 1)) * u)
    ]]></literal>
    <justification jstring="[para(3144(a,1),16157(a,1,2,1,1))].">
      <j1 rule="para" parents="3144 16157"/>
    </justification>
  </clause>

  <clause id="17249">
    <literal><![CDATA[
      T(x,T(L((y \ 1) * z,y,y),y) * u) = T(x,(((y \ 1) * ((1 / (y \ 1)) * z)) * (y \ 1)) * u)
    ]]></literal>
    <justification jstring="[para(2596(a,1),17247(a,1,2,1,1))].">
      <j1 rule="para" parents="2596 17247"/>
    </justification>
  </clause>

  <clause id="17250">
    <literal><![CDATA[
      T(x,L(T((y \ 1) * z,y),y,y) * u) = T(x,(((y \ 1) * ((1 / (y \ 1)) * z)) * (y \ 1)) * u)
    ]]></literal>
    <justification jstring="[para(25(a,2),17249(a,1,2,1))].">
      <j1 rule="para" parents="25 17249"/>
    </justification>
  </clause>

  <clause id="17253">
    <literal><![CDATA[
      T(x,T(L(T((1 / y) \ (y \ (z * (1 / y))),u),y,y) \ w,v5)) = T(x,T(T((y * (y \ z)) * (1 / y),u) \ w,v5))
    ]]></literal>
    <justification jstring="[para(5595(a,2),17055(a,2,2,1,1))].">
      <j1 rule="para" parents="5595 17055"/>
    </justification>
  </clause>

  <clause id="17254">
    <literal><![CDATA[
      T(x,T(L(T((1 / y) \ (y \ (z * (1 / y))),u),y,y) \ w,v5)) = T(x,T(T(z * (1 / y),u) \ w,v5))
    ]]></literal>
    <justification jstring="[para(10(a,1),17253(a,2,2,1,1,1,1))].">
      <j1 rule="para" parents="10 17253"/>
    </justification>
  </clause>

  <clause id="17256">
    <literal><![CDATA[
      T(x,T(T(L(y,y,y) * (y \ (z * (1 / y))),u) \ w,v5)) = T(x,T(T(z * (1 / y),u) \ w,v5))
    ]]></literal>
    <justification jstring="[para(11899(a,1),17254(a,1,2,1,1))].">
      <j1 rule="para" parents="11899 17254"/>
    </justification>
  </clause>

  <clause id="17257">
    <literal><![CDATA[
      T(x,T(T(a(y,y,y) \ (z * (1 / y)),u) \ w,v5)) = T(x,T(T(z * (1 / y),u) \ w,v5))
    ]]></literal>
    <justification jstring="[para(9273(a,1),17256(a,1,2,1,1,1))].">
      <j1 rule="para" parents="9273 17256"/>
    </justification>
  </clause>

  <clause id="17258">
    <literal><![CDATA[
      T(x,T(T(y * (a(z,z,z) \ (1 / z)),u) \ w,v5)) = T(x,T(T(y * (1 / z),u) \ w,v5))
    ]]></literal>
    <justification jstring="[para(12800(a,1),17257(a,1,2,1,1,1))].">
      <j1 rule="para" parents="12800 17257"/>
    </justification>
  </clause>

  <clause id="17259">
    <literal><![CDATA[
      T(x,T(T(y * (1 / z),u) \ w,v5)) = T(x,T(T(y * (z \ 1),u) \ w,v5))
    ]]></literal>
    <justification jstring="[para(9255(a,1),17258(a,1,2,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9255 17258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17260">
    <literal><![CDATA[
      T(x,T(T(y * (z \ 1),z) \ u,w)) = T(x,T(((1 / z) * y) \ u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,17051,a(flip),b,17259,a),flip(a)].">
      <j1 rule="hyper" parents="63 17051 17259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17261">
    <literal><![CDATA[
      T(x,T(T(y * (z \ 1),z) \ u,w)) = T(x,T(((z \ 1) * y) \ u,w))
    ]]></literal>
    <justification jstring="[hyper(333,a,8928,a(flip),b,17260,a),flip(a)].">
      <j1 rule="hyper" parents="333 8928 17260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17262">
    <literal><![CDATA[
      T(x,T(((y \ 1) * z) \ u,w * w)) = T(x,T(z * (y \ 1),y) \ u)
    ]]></literal>
    <justification jstring="[hyper(15410,a,17261,a),flip(a)].">
      <j1 rule="hyper" parents="15410 17261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17263">
    <literal><![CDATA[
      T(x,T(y * (z \ 1),z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,((z \ 1) * y) \ u) = w
    ]]></literal>
    <justification jstring="[para(17262(a,1),15410(a,1))].">
      <j1 rule="para" parents="17262 15410"/>
    </justification>
  </clause>

  <clause id="17264">
    <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(16452,a,16022,a)].">
      <j1 rule="hyper" parents="16452 16022"/>
    </justification>
  </clause>

  <clause id="17266">
    <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(16304(a,1),17264(a,1,1,2))].">
      <j1 rule="para" parents="16304 17264"/>
    </justification>
  </clause>

  <clause id="17268">
    <literal><![CDATA[
      K(x,R(y * z,K(u,L(w,y,z)),K(u,L(w,y,z))) \ v5) = K(x,((K(L(w,y,z),u) * 1) * ((K(u,w) * y) * z)) \ v5)
    ]]></literal>
    <justification jstring="[para(4567(a,1),16233(a,2,2,1,1))].">
      <j1 rule="para" parents="4567 16233"/>
    </justification>
  </clause>

  <clause id="17269">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u * w)),K(T(u,v5 * (v5 * v6)) * w,z)) = T(y,K(z,T(u,v6) * w) * x)
    ]]></literal>
    <justification jstring="[para(16622(a,1),16933(a,1,2,1,2))].">
      <j1 rule="para" parents="16622 16933"/>
    </justification>
  </clause>

  <clause id="17270">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u * w)),K(z,T(u,v5 * (v5 * v6)) * w)) = T(y,K(z,T(u,v6) * w) * x)
    ]]></literal>
    <justification jstring="[para(6840(a,1),17269(a,1,2))].">
      <j1 rule="para" parents="6840 17269"/>
    </justification>
  </clause>

  <clause id="17272">
    <literal><![CDATA[
      T(x,K(y,T(z,u) * w) * v5) = v5 \ T(x * T(v5,K(y,z * w)),K(y,z * w))
    ]]></literal>
    <justification jstring="[para(16622(a,1),17270(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16622 17270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17273">
    <literal><![CDATA[
      T(x,K(y,T(z,u) * w) * v5) = T(x,K(z * w,y) * v5)
    ]]></literal>
    <justification jstring="[hyper(333,a,14912,a(flip),b,17272,a),flip(a)].">
      <j1 rule="hyper" parents="333 14912 17272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17275">
    <literal><![CDATA[
      T(x,y * K(z,T(u,w) * v5)) = T(x,K(u * v5,z) * y)
    ]]></literal>
    <justification jstring="[hyper(15486,a,17273,a)].">
      <j1 rule="hyper" parents="15486 17273"/>
    </justification>
  </clause>

  <clause id="17276">
    <literal><![CDATA[
      T(x,y * K(z,u * T(w,v5))) = T(x,K(w * u,z) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,16472,a(flip),b,17273,a)].">
      <j1 rule="hyper" parents="63 16472 17273"/>
    </justification>
  </clause>

  <clause id="17277">
    <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(63,a,17070,a(flip),b,17275,a),flip(a)].">
      <j1 rule="hyper" parents="63 17070 17275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17278">
    <literal><![CDATA[
      T(x,T(y,K(z,u) * (w * z)) \ v5) = T(x,K(z * w,y) * (y \ v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,15743,a,b,17276,a)].">
      <j1 rule="hyper" parents="63 15743 17276"/>
    </justification>
  </clause>

  <clause id="17280">
    <literal><![CDATA[
      T(x,T(y,K(z,u) * (w * z)) \ v5) = T(x,T(y,z * w) \ v5)
    ]]></literal>
    <justification jstring="[para(4555(a,1),17278(a,2,2))].">
      <j1 rule="para" parents="4555 17278"/>
    </justification>
  </clause>

  <clause id="17281">
    <literal><![CDATA[
      T(x,T(y,z * T(u,w)) \ v5) = T(x,T(y,u * z) \ v5)
    ]]></literal>
    <justification jstring="[para(7717(a,1),17280(a,1,2,1,2))].">
      <j1 rule="para" parents="7717 17280"/>
    </justification>
  </clause>

  <clause id="17283">
    <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(13229(a,1),17277(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13229 17277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17284">
    <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(333,a,15729,a(flip),b,17283,a),flip(a)].">
      <j1 rule="hyper" parents="333 15729 17283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17285">
    <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(63,a,7015,a(flip),b,17284,a)].">
      <j1 rule="hyper" parents="63 7015 17284"/>
    </justification>
  </clause>

  <clause id="17286">
    <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(5417(a,1),17285(a,1,2,2,1))].">
      <j1 rule="para" parents="5417 17285"/>
    </justification>
  </clause>

  <clause id="17287">
    <literal><![CDATA[
      K(x,R(y * z,K(u,L(w,y,z)),K(u,L(w,y,z))) \ v5) = K(x,((K(w,L(u,y,z)) * 1) * ((K(u,w) * y) * z)) \ v5)
    ]]></literal>
    <justification jstring="[para(10898(a,1),17268(a,2,2,1,1,1))].">
      <j1 rule="para" parents="10898 17268"/>
    </justification>
  </clause>

  <clause id="17288">
    <literal><![CDATA[
      K(x,R(y * z,K(u,L(w,y,z)),K(u,L(w,y,z))) \ v5) = K(x,(K(w,L(u,y,z)) * ((K(u,w) * y) * z)) \ v5)
    ]]></literal>
    <justification jstring="[para(8(a,1),17287(a,2,2,1,1))].">
      <j1 rule="para" parents="8 17287"/>
    </justification>
  </clause>

  <clause id="17289">
    <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(9(a,1),16288(a,1,1,1))].">
      <j1 rule="para" parents="9 16288"/>
    </justification>
  </clause>

  <clause id="17290">
    <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(9(a,1),17289(a,1,1,3)),flip(a)].">
      <j1 rule="para" parents="9 17289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17291">
    <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(5768(a,1),17290(a,2,2))].">
      <j1 rule="para" parents="5768 17290"/>
    </justification>
  </clause>

  <clause id="17292">
    <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(9(a,1),17291(a,2,2,2))].">
      <j1 rule="para" parents="9 17291"/>
    </justification>
  </clause>

  <clause id="17293">
    <literal><![CDATA[
      K(x * (1 / ((y * z) \ y)),1 / ((y * z) \ y)) = a(z,x,z) * K(x,z)
    ]]></literal>
    <justification jstring="[para(4365(a,1),17292(a,2,2))].">
      <j1 rule="para" parents="4365 17292"/>
    </justification>
  </clause>

  <clause id="17294">
    <literal><![CDATA[
      K(x * (1 / ((y * z) \ y)),1 / ((y * z) \ y)) = K(z * x,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,8249,a(flip),b,17293,a),flip(a)].">
      <j1 rule="hyper" parents="333 8249 17293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17295">
    <literal><![CDATA[
      K(x * (1 / ((y * z) \ y)),y \ (y * z)) = K(z * x,z)
    ]]></literal>
    <justification jstring="[hyper(5953,a,17294,a)].">
      <j1 rule="hyper" parents="5953 17294"/>
    </justification>
  </clause>

  <clause id="17296">
    <literal><![CDATA[
      K(x * (1 / ((y * z) \ y)),z) = K(z * x,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),17295(a,1,2))].">
      <j1 rule="para" parents="9 17295"/>
    </justification>
  </clause>

  <clause id="17297">
    <literal><![CDATA[
      K(x * (((y * z) \ y) \ 1),z) = K(z * x,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,4757,a(flip),b,17296,a)].">
      <j1 rule="hyper" parents="63 4757 17296"/>
    </justification>
  </clause>

  <clause id="17298">
    <literal><![CDATA[
      K(((x * y) \ x) \ z,y) = K(y * z,y)
    ]]></literal>
    <justification jstring="[hyper(8457,a,17297,a)].">
      <j1 rule="hyper" parents="8457 17297"/>
    </justification>
  </clause>

  <clause id="17299">
    <literal><![CDATA[
      K(((x * y) \ x) \ (y \ z),y) = K(z,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),17298(a,2,1))].">
      <j1 rule="para" parents="10 17298"/>
    </justification>
  </clause>

  <clause id="17300">
    <literal><![CDATA[
      K((1 / ((x * y) \ x)) \ z,y) = K(y \ z,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,9135,a(flip),b,17299,a),flip(a)].">
      <j1 rule="hyper" parents="63 9135 17299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17302">
    <literal><![CDATA[
      K((((x * y) \ x) \ 1) \ z,y) = K(y \ z,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,4763,a(flip),b,17300,a)].">
      <j1 rule="hyper" parents="63 4763 17300"/>
    </justification>
  </clause>

  <clause id="17303">
    <literal><![CDATA[
      K(x * ((y * z) \ y),z) = K(z \ x,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,8713,a(flip),b,17302,a)].">
      <j1 rule="hyper" parents="63 8713 17302"/>
    </justification>
  </clause>

  <clause id="17305">
    <literal><![CDATA[
      K((x \ y) \ z,x \ y) = K(z * (y \ x),x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),17303(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 17303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17306">
    <literal><![CDATA[
      K((x \ y) \ z,x \ y) = K(z * (x / y),x \ y)
    ]]></literal>
    <justification jstring="[hyper(333,a,8629,a,b,17305,a),flip(a)].">
      <j1 rule="hyper" parents="333 8629 17305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17307">
    <literal><![CDATA[
      x * K(x * (y / z),y \ z) = ((y \ z) \ x) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(126,a,17306,a(flip),b,89,a)].">
      <j1 rule="hyper" parents="126 17306 89"/>
    </justification>
  </clause>

  <clause id="17308">
    <literal><![CDATA[
      ((1 / (x \ y)) \ z) * (1 / (x \ y)) = ((y \ x) \ z) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,8644,a,b,17307,a)].">
      <j1 rule="hyper" parents="63 8644 17307"/>
    </justification>
  </clause>

  <clause id="17309">
    <literal><![CDATA[
      (((x \ y) \ 1) \ z) * ((x \ y) \ 1) = ((y \ x) \ z) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,2670,a(flip),b,17308,a)].">
      <j1 rule="hyper" parents="63 2670 17308"/>
    </justification>
  </clause>

  <clause id="17310">
    <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(17308(a,1),17037(a,1,1,1,2,1,2))].">
      <j1 rule="para" parents="17308 17037"/>
    </justification>
  </clause>

  <clause id="17311">
    <literal><![CDATA[
      ((x * y) \ x) \ T(((x * y) \ x) * z,y) = ((x \ (x * y)) \ z) * (x \ (x * y))
    ]]></literal>
    <justification jstring="[hyper(63,a,5831,a,b,17309,a)].">
      <j1 rule="hyper" parents="63 5831 17309"/>
    </justification>
  </clause>

  <clause id="17312">
    <literal><![CDATA[
      ((x \ y) * z) * (z / ((x \ y) * z)) = ((y \ x) \ z) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,3115,a(flip),b,17309,a)].">
      <j1 rule="hyper" parents="63 3115 17309"/>
    </justification>
  </clause>

  <clause id="17313">
    <literal><![CDATA[
      ((x * y) \ x) \ T(((x * y) \ x) * z,y) = (y \ z) * (x \ (x * y))
    ]]></literal>
    <justification jstring="[para(9(a,1),17311(a,2,1,1))].">
      <j1 rule="para" parents="9 17311"/>
    </justification>
  </clause>

  <clause id="17314">
    <literal><![CDATA[
      ((x * y) \ x) \ T(((x * y) \ x) * z,y) = (y \ z) * y
    ]]></literal>
    <justification jstring="[hyper(333,a,155,a(flip),b,17313,a),flip(a)].">
      <j1 rule="hyper" parents="333 155 17313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17316">
    <literal><![CDATA[
      K(x,y * ((z * x) \ z)) = (((x \ y) * x) \ u) * ((y \ u) \ 1)
    ]]></literal>
    <justification jstring="[para(17314(a,1),14814(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="17314 14814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17317">
    <literal><![CDATA[
      K(x,y * ((z * x) \ z)) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(333,a,13390,a(flip),b,17316,a),flip(a)].">
      <j1 rule="hyper" parents="333 13390 17316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17319">
    <literal><![CDATA[
      K(x / y,(x / y) \ z) = K(x / y,(x \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,9049,a(flip),b,17317,a),flip(a)].">
      <j1 rule="hyper" parents="63 9049 17317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17320">
    <literal><![CDATA[
      K(x / y,(x \ y) * z) = K(y \ x,(x \ z) * y)
    ]]></literal>
    <justification jstring="[hyper(14175,a,17319,a),flip(a)].">
      <j1 rule="hyper" parents="14175 17319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17322">
    <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(17204(a,1),17310(a,1,1,1))].">
      <j1 rule="para" parents="17204 17310"/>
    </justification>
  </clause>

  <clause id="17323">
    <literal><![CDATA[
      K(1 / x,T(y,z / (1 / (u \ w)))) = K(1 / x,T(y,z / (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(17039,a,17322,a),flip(a)].">
      <j1 rule="hyper" parents="17039 17322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17324">
    <literal><![CDATA[
      K(1 / x,T(y,z / (1 / (u \ w)))) = K(1 / x,T(y,z / (u / w)))
    ]]></literal>
    <justification jstring="[hyper(333,a,16548,a,b,17323,a),flip(a)].">
      <j1 rule="hyper" parents="333 16548 17323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17325">
    <literal><![CDATA[
      K(1 / x,T(y,z / (1 / (u / w)))) = K(1 / x,T(y,z / (w / u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,16822,a,b,17324,a)].">
      <j1 rule="hyper" parents="63 16822 17324"/>
    </justification>
  </clause>

  <clause id="17326">
    <literal><![CDATA[
      K(1 / x,T(y,z / (u / w))) = K(1 / x,T(y,(w / u) * z))
    ]]></literal>
    <justification jstring="[hyper(15782,a,17325,a),flip(a)].">
      <j1 rule="hyper" parents="15782 17325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17327">
    <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(17326(a,1),16823(a,2,1))].">
      <j1 rule="para" parents="17326 16823"/>
    </justification>
  </clause>

  <clause id="17328">
    <literal><![CDATA[
      T(1 / x,T(y,z / (u / T(w,v5)))) = T(1 / x,T(y,(w / u) * z))
    ]]></literal>
    <justification jstring="[hyper(333,a,4447,a(flip),b,17327,a),flip(a)].">
      <j1 rule="hyper" parents="333 4447 17327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17329">
    <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(17328(a,1),11082(a,1,1))].">
      <j1 rule="para" parents="17328 11082"/>
    </justification>
  </clause>

  <clause id="17330">
    <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(63,a,11082,a(flip),b,17329,a),flip(a)].">
      <j1 rule="hyper" parents="63 11082 17329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17332">
    <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(17330(a,1),13460(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="17330 13460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17333">
    <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(333,a,13460,a(flip),b,17332,a),flip(a)].">
      <j1 rule="hyper" parents="333 13460 17332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17334">
    <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(333,a,6370,a(flip),b,17333,a),flip(a)].">
      <j1 rule="hyper" parents="333 6370 17333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17335">
    <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(6695,a,17334,a)].">
      <j1 rule="hyper" parents="6695 17334"/>
    </justification>
  </clause>

  <clause id="17336">
    <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(63,a,16820,a(flip),b,17335,a)].">
      <j1 rule="hyper" parents="63 16820 17335"/>
    </justification>
  </clause>

  <clause id="17337">
    <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(63,a,16821,a(flip),b,17336,a),flip(a)].">
      <j1 rule="hyper" parents="63 16821 17336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17338">
    <literal><![CDATA[
      K(x,T(y,(T(z,u) / w) * v5)) = K(x,T(y,v5 / (w / z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,9493,a(flip),b,17337,a)].">
      <j1 rule="hyper" parents="63 9493 17337"/>
    </justification>
  </clause>

  <clause id="17339">
    <literal><![CDATA[
      K(x,T(y,z / (u / w))) = K(x,T(y,(w / u) * z))
    ]]></literal>
    <justification jstring="[para(110(a,1),17338(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="110 17338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17340">
    <literal><![CDATA[
      K(x,T(y,z / (u \ w))) = K(x,T(y,(u / w) * z))
    ]]></literal>
    <justification jstring="[hyper(16577,a,17339,a)].">
      <j1 rule="hyper" parents="16577 17339"/>
    </justification>
  </clause>

  <clause id="17342">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,(z / u) * w)) = K(x,T(y,w / (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(333,a,6761,a,b,17340,a)].">
      <j1 rule="hyper" parents="333 6761 17340"/>
    </justification>
  </clause>

  <clause id="17343">
    <literal><![CDATA[
      K(x,K(y,z / (u / w))) = K(x,K(y,(w / u) * z))
    ]]></literal>
    <justification jstring="[hyper(34,a,16580,a,b,17342,a)].">
      <j1 rule="hyper" parents="34 16580 17342"/>
    </justification>
  </clause>

  <clause id="17344">
    <literal><![CDATA[
      K(x,K(y,(z / u) / w)) = K(x,K(y,(u / z) * w))
    ]]></literal>
    <justification jstring="[hyper(7214,a,17343,a)].">
      <j1 rule="hyper" parents="7214 17343"/>
    </justification>
  </clause>

  <clause id="17345">
    <literal><![CDATA[
      K(x,K(y,((z / u) / z) * w)) = K(x,K(y,w / u))
    ]]></literal>
    <justification jstring="[hyper(63,a,16607,a(flip),b,17343,a),flip(a)].">
      <j1 rule="hyper" parents="63 16607 17343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17346">
    <literal><![CDATA[
      K(x,K(y,(z / (z * u)) * w)) = K(x,K(y,w / u))
    ]]></literal>
    <justification jstring="[hyper(63,a,16606,a(flip),b,17343,a),flip(a)].">
      <j1 rule="hyper" parents="63 16606 17343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17347">
    <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(17343(a,1),16654(a,1,1))].">
      <j1 rule="para" parents="17343 16654"/>
    </justification>
  </clause>

  <clause id="17348">
    <literal><![CDATA[
      K(x,K(y,z * (u / (u * w)))) = K(x,K(y,z / w))
    ]]></literal>
    <justification jstring="[hyper(15681,a,17346,a)].">
      <j1 rule="hyper" parents="15681 17346"/>
    </justification>
  </clause>

  <clause id="17349">
    <literal><![CDATA[
      K(x,K(y,z / (u \ w))) = K(x,K(y,z * (u / w)))
    ]]></literal>
    <justification jstring="[para(10(a,1),17348(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="10 17348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17350">
    <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(10902,a,17347,a),flip(a)].">
      <j1 rule="hyper" parents="10902 17347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17351">
    <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(63,a,16715,a(flip),b,17350,a),flip(a)].">
      <j1 rule="hyper" parents="63 16715 17350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17352">
    <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(79(a,1),17350(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="79 17350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17353">
    <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(15722,a,17352,a)].">
      <j1 rule="hyper" parents="15722 17352"/>
    </justification>
  </clause>

  <clause id="17354">
    <literal><![CDATA[
      K(x,K((y / z) * u,L(w,z,y))) = K(x,K(w,(u * y) / z))
    ]]></literal>
    <justification jstring="[para(10(a,1),17351(a,2,2,2,2))].">
      <j1 rule="para" parents="10 17351"/>
    </justification>
  </clause>

  <clause id="17355">
    <literal><![CDATA[
      K(x,K((y / z) * u,L(w,z,y))) = K(x,K(w,(y * u) / z))
    ]]></literal>
    <justification jstring="[hyper(333,a,16617,a,b,17354,a),flip(a)].">
      <j1 rule="hyper" parents="333 16617 17354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17356">
    <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(17354(a,2),16676(a,1))].">
      <j1 rule="para" parents="17354 16676"/>
    </justification>
  </clause>

  <clause id="17357">
    <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(63,a,17353,a(flip),b,17355,a)].">
      <j1 rule="hyper" parents="63 17353 17355"/>
    </justification>
  </clause>

  <clause id="17358">
    <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(17355(a,2),16676(a,1))].">
      <j1 rule="para" parents="17355 16676"/>
    </justification>
  </clause>

  <clause id="17359">
    <literal><![CDATA[
      K(x,K((y / z) / u,L(w,z,y))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(w,(y * (1 / u)) / z)) = v5
    ]]></literal>
    <justification jstring="[para(13274(a,1),17356(a,1,2))].">
      <j1 rule="para" parents="13274 17356"/>
    </justification>
  </clause>

  <clause id="17360">
    <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(3097(a,2),17357(a,2,2,2,1))].">
      <j1 rule="para" parents="3097 17357"/>
    </justification>
  </clause>

  <clause id="17361">
    <literal><![CDATA[
      K(x,K(y,(z * ((u / w) / u)) / v5)) = K(x,K(y,(z * (1 / w)) / v5))
    ]]></literal>
    <justification jstring="[hyper(17359,a,17357,a),flip(a)].">
      <j1 rule="hyper" parents="17359 17357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17362">
    <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(13276(a,1),17360(a,1,2))].">
      <j1 rule="para" parents="13276 17360"/>
    </justification>
  </clause>

  <clause id="17363">
    <literal><![CDATA[
      K(x,K(y,(T(z,u) / (1 / u)) / w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,(z * u) / w)) = v5
    ]]></literal>
    <justification jstring="[para(17362(a,1),17356(a,1))].">
      <j1 rule="para" parents="17362 17356"/>
    </justification>
  </clause>

  <clause id="17364">
    <literal><![CDATA[
      K(x,K(y,((1 / z) / T(u,z)) * w)) = K(x,K(y,(u * z) / w))
    ]]></literal>
    <justification jstring="[hyper(17363,a,17344,a),flip(a)].">
      <j1 rule="hyper" parents="17363 17344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17365">
    <literal><![CDATA[
      K(x,K(y,z * ((1 / u) / w))) = K(x,K(y,(w * u) / z))
    ]]></literal>
    <justification jstring="[hyper(16718,a,17364,a)].">
      <j1 rule="hyper" parents="16718 17364"/>
    </justification>
  </clause>

  <clause id="17366">
    <literal><![CDATA[
      K(x,K(y,((z \ 1) / u) * w)) = K(x,K(y,(u * z) / w))
    ]]></literal>
    <justification jstring="[hyper(63,a,16756,a,b,17365,a)].">
      <j1 rule="hyper" parents="63 16756 17365"/>
    </justification>
  </clause>

  <clause id="17367">
    <literal><![CDATA[
      K(x,K(y,(z * (1 / u)) / w)) = K(x,K(y,(u / z) * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,16751,a(flip),b,17365,a),flip(a)].">
      <j1 rule="hyper" parents="63 16751 17365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17368">
    <literal><![CDATA[
      K(x,K(y,((z / (z / (u \ 1))) / w) * v5)) = K(x,K(y,(w * u) / v5))
    ]]></literal>
    <justification jstring="[hyper(16757,a,17366,a)].">
      <j1 rule="hyper" parents="16757 17366"/>
    </justification>
  </clause>

  <clause id="17369">
    <literal><![CDATA[
      K(x,K(y,z / ((1 / u) * w))) = K(x,K(y,(u / w) * z))
    ]]></literal>
    <justification jstring="[hyper(16664,a,17367,a)].">
      <j1 rule="hyper" parents="16664 17367"/>
    </justification>
  </clause>

  <clause id="17370">
    <literal><![CDATA[
      K(x,K(y,(z * ((u / w) / u)) / v5)) = K(x,K(y,(w / z) * v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,17361,a,b,17367,a)].">
      <j1 rule="hyper" parents="63 17361 17367"/>
    </justification>
  </clause>

  <clause id="17371">
    <literal><![CDATA[
      K(x,K((y / z) * u,L(w,y / z,z))) = K(x,K(w,(u / z) * y))
    ]]></literal>
    <justification jstring="[hyper(63,a,14154,a,b,17369,a)].">
      <j1 rule="hyper" parents="63 14154 17369"/>
    </justification>
  </clause>

  <clause id="17372">
    <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(7853(a,1),17369(a,1,2))].">
      <j1 rule="para" parents="7853 17369"/>
    </justification>
  </clause>

  <clause id="17373">
    <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(14448(a,1),17369(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="14448 17369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17374">
    <literal><![CDATA[
      K(x,K(y,z / (((u / w) / u) * v5))) = K(x,K(y,(w / v5) * z))
    ]]></literal>
    <justification jstring="[hyper(16664,a,17370,a)].">
      <j1 rule="hyper" parents="16664 17370"/>
    </justification>
  </clause>

  <clause id="17375">
    <literal><![CDATA[
      K(x,K((y / z) * u,L(w,y,z))) = K(x,K(w,(u / z) * y))
    ]]></literal>
    <justification jstring="[hyper(63,a,14364,a(flip),b,17371,a)].">
      <j1 rule="hyper" parents="63 14364 17371"/>
    </justification>
  </clause>

  <clause id="17376">
    <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(15910(a,1),17372(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15910 17372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17377">
    <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(333,a,17374,a(flip),b,17373,a),flip(a)].">
      <j1 rule="hyper" parents="333 17374 17373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17379">
    <literal><![CDATA[
      K(x,K(y,(z * (u / w)) / v5)) = K(x,K(y,((w / u) / z) * v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,17368,a(flip),b,17377,a)].">
      <j1 rule="hyper" parents="63 17368 17377"/>
    </justification>
  </clause>

  <clause id="17380">
    <literal><![CDATA[
      K(x,K(y,((z / u) * w) / v5)) = K(x,K(y,((u / z) / w) * v5))
    ]]></literal>
    <justification jstring="[hyper(16676,a,17379,a)].">
      <j1 rule="hyper" parents="16676 17379"/>
    </justification>
  </clause>

  <clause id="17382">
    <literal><![CDATA[
      K(x,K(y,z / ((u \ w) * v5))) = K(x,K(y,((u / w) / v5) * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,16693,a(flip),b,17379,a)].">
      <j1 rule="hyper" parents="63 16693 17379"/>
    </justification>
  </clause>

  <clause id="17383">
    <literal><![CDATA[
      K(x,K(y,((z \ u) * w) / v5)) = K(x,K(y,((z / u) / w) * v5))
    ]]></literal>
    <justification jstring="[hyper(7214,a,17382,a)].">
      <j1 rule="hyper" parents="7214 17382"/>
    </justification>
  </clause>

  <clause id="17384">
    <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(63,a,17101,a(flip),b,17383,a),flip(a)].">
      <j1 rule="hyper" parents="63 17101 17383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17385">
    <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(15671,a,17384,a)].">
      <j1 rule="hyper" parents="15671 17384"/>
    </justification>
  </clause>

  <clause id="17386">
    <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(333,a,14141,a,b,17384,a),flip(a)].">
      <j1 rule="hyper" parents="333 14141 17384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17387">
    <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(17384(a,1),6798(a,1))].">
      <j1 rule="para" parents="17384 6798"/>
    </justification>
  </clause>

  <clause id="17388">
    <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(12(a,1),17385(a,1,2,2,2,2))].">
      <j1 rule="para" parents="12 17385"/>
    </justification>
  </clause>

  <clause id="17389">
    <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(12(a,1),17386(a,2,2))].">
      <j1 rule="para" parents="12 17386"/>
    </justification>
  </clause>

  <clause id="17390">
    <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(333,a,7165,a(flip),b,17376,a),flip(a)].">
      <j1 rule="hyper" parents="333 7165 17376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17391">
    <literal><![CDATA[
      K(x,K(y,z * ((1 / u) * w))) = K(x,K(y,(u / w) / z))
    ]]></literal>
    <justification jstring="[hyper(63,a,17348,a(flip),b,17390,a),flip(a)].">
      <j1 rule="hyper" parents="63 17348 17390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17393">
    <literal><![CDATA[
      K(x,K(y,z * ((1 / u) * w))) = K(x,K(y,(w / u) * z))
    ]]></literal>
    <justification jstring="[hyper(333,a,17344,a(flip),b,17391,a),flip(a)].">
      <j1 rule="hyper" parents="333 17344 17391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17394">
    <literal><![CDATA[
      K(x,K(y,z * L(u,w,1 / w))) = K(x,K(y,((w * u) / w) * z))
    ]]></literal>
    <justification jstring="[para(277(a,1),17393(a,1,2,2,2))].">
      <j1 rule="para" parents="277 17393"/>
    </justification>
  </clause>

  <clause id="17395">
    <literal><![CDATA[
      K(x,K(y,z * L(u,w,1 / w))) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(333,a,16612,a(flip),b,17394,a),flip(a)].">
      <j1 rule="hyper" parents="333 16612 17394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17397">
    <literal><![CDATA[
      K(x,K(y,R(z / u,w,v5) * (w * v5))) = K(x,K(y,(((1 / u) * z) * w) * v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,17146,a(flip),b,17395,a),flip(a)].">
      <j1 rule="hyper" parents="63 17146 17395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17399">
    <literal><![CDATA[
      K(x,K(y,(((1 / z) * u) * w) * v5)) = K(x,K(y,((u / z) * w) * v5))
    ]]></literal>
    <justification jstring="[para(107(a,1),17397(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="107 17397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17400">
    <literal><![CDATA[
      K(x,K(y,(z * ((1 / u) * w)) * v5)) = K(x,K(y,((w / u) * z) * v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,16616,a,b,17399,a)].">
      <j1 rule="hyper" parents="63 16616 17399"/>
    </justification>
  </clause>

  <clause id="17401">
    <literal><![CDATA[
      K(x,K(y,((z / u) * w) * T(v5,v6))) = K(x,K(y,v5 * (w * ((1 / u) * z))))
    ]]></literal>
    <justification jstring="[hyper(16644,a,17400,a),flip(a)].">
      <j1 rule="hyper" parents="16644 17400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17402">
    <literal><![CDATA[
      K(x,K(y,(z * ((1 / u) * w)) / v5)) = K(x,K(y,((w / u) * z) * (1 / v5)))
    ]]></literal>
    <justification jstring="[hyper(13653,a,17400,a)].">
      <j1 rule="hyper" parents="13653 17400"/>
    </justification>
  </clause>

  <clause id="17403">
    <literal><![CDATA[
      K(x,K(y,z * (u * ((1 / w) * v5)))) = K(x,K(y,z * ((v5 / w) * u)))
    ]]></literal>
    <justification jstring="[hyper(16644,a,17401,a),flip(a)].">
      <j1 rule="hyper" parents="16644 17401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17404">
    <literal><![CDATA[
      K(x,K(y,z * (((1 / u) * w) * v5))) = K(x,K(y,z * ((w / u) * v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,16604,a,b,17403,a)].">
      <j1 rule="hyper" parents="63 16604 17403"/>
    </justification>
  </clause>

  <clause id="17405">
    <literal><![CDATA[
      K(x,K(y,(z * ((1 / u) * w)) / v5)) = K(x,K(y,((w / u) * z) / v5))
    ]]></literal>
    <justification jstring="[hyper(333,a,11438,a(flip),b,17402,a),flip(a)].">
      <j1 rule="hyper" parents="333 11438 17402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17406">
    <literal><![CDATA[
      K(x,K(y,(z * ((1 / u) * w)) / v5)) = K(x,K(y,((u / w) / z) * v5))
    ]]></literal>
    <justification jstring="[hyper(333,a,17380,a(flip),b,17405,a),flip(a)].">
      <j1 rule="hyper" parents="333 17380 17405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17407">
    <literal><![CDATA[
      K(x,K(y,z / (u * ((1 / w) * v5)))) = K(x,K(y,((w / v5) / u) * z))
    ]]></literal>
    <justification jstring="[hyper(7214,a,17406,a)].">
      <j1 rule="hyper" parents="7214 17406"/>
    </justification>
  </clause>

  <clause id="17408">
    <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(12418(a,1),17407(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12418 17407"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17409">
    <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(333,a,13951,a,b,17408,a),flip(a)].">
      <j1 rule="hyper" parents="333 13951 17408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17410">
    <literal><![CDATA[
      K(x,L(y / T(z * K(u,K(w,v5)),v6),T(z / K(u,K(w,v5)),v6),K(u,K(w,v5)))) = K(x,(y * K(u,K(w,v5))) / (T(K(u,K(w,v5)) \ z,v6) * K(u,K(w,v5))))
    ]]></literal>
    <justification jstring="[para(6827(a,1),16464(a,1,2,1,2,1))].">
      <j1 rule="para" parents="6827 16464"/>
    </justification>
  </clause>

  <clause id="17411">
    <literal><![CDATA[
      K(x,K(y,(((K(z,u) * w) * v5) * v6) / (v6 * (K(z,u) * v5)))) = K(x,K(R(w,K(z,u),v5),L(y,K(z,u) * v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(15721,a,16716,a),flip(a)].">
      <j1 rule="hyper" parents="15721 16716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17413">
    <literal><![CDATA[
      K(x,K(y,(((K(z,u) * w) * v5) * v6) / (v6 * (K(z,u) * v5)))) = K(x,K(w,L(L(y,K(z,u) * v5,v6),K(z,u),v5)))
    ]]></literal>
    <justification jstring="[para(13867(a,1),17411(a,2,2))].">
      <j1 rule="para" parents="13867 17411"/>
    </justification>
  </clause>

  <clause id="17414">
    <literal><![CDATA[
      K(x,K(y,(((K(z,u) * w) * v5) * v6) / (v6 * (K(z,u) * v5)))) = K(x,K(w,L(y,K(z,u) * v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(333,a,16817,a(flip),b,17413,a),flip(a)].">
      <j1 rule="hyper" parents="333 16817 17413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17416">
    <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(63,a,16799,a(flip),b,17414,a)].">
      <j1 rule="hyper" parents="63 16799 17414"/>
    </justification>
  </clause>

  <clause id="17418">
    <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(63,a,16662,a(flip),b,17416,a)].">
      <j1 rule="hyper" parents="63 16662 17416"/>
    </justification>
  </clause>

  <clause id="17419">
    <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(63,a,16642,a(flip),b,17418,a),flip(a)].">
      <j1 rule="hyper" parents="63 16642 17418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17420">
    <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(10926,a,17419,a)].">
      <j1 rule="hyper" parents="10926 17419"/>
    </justification>
  </clause>

  <clause id="17422">
    <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(13230(a,1),17419(a,1,2,2,2))].">
      <j1 rule="para" parents="13230 17419"/>
    </justification>
  </clause>

  <clause id="17423">
    <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(333,a,13948,a,b,17420,a),flip(a)].">
      <j1 rule="hyper" parents="333 13948 17420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17424">
    <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(333,a,10952,a(flip),b,17422,a),flip(a)].">
      <j1 rule="hyper" parents="333 10952 17422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17425">
    <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(17424(a,1),17205(a,1,1)),flip(a)].">
      <j1 rule="para" parents="17424 17205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17426">
    <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(13949,a,17423,a)].">
      <j1 rule="hyper" parents="13949 17423"/>
    </justification>
  </clause>

  <clause id="17427">
    <literal><![CDATA[
      a(x,y * (z / y),K(u,K(w,v5))) = a(x,z,K(u,K(w,v5)))
    ]]></literal>
    <justification jstring="[para(4185(a,1),17426(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4185 17426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17428">
    <literal><![CDATA[
      a(x,y / z,K(u,K(w,v5))) = a(x,z \ y,K(u,K(w,v5)))
    ]]></literal>
    <justification jstring="[para(4312(a,1),17426(a,1,2))].">
      <j1 rule="para" parents="4312 17426"/>
    </justification>
  </clause>

  <clause id="17429">
    <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(63,a,11454,a(flip),b,17427,a),flip(a)].">
      <j1 rule="hyper" parents="63 11454 17427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17430">
    <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(6788(a,2),17429(a,2,3))].">
      <j1 rule="para" parents="6788 17429"/>
    </justification>
  </clause>

  <clause id="17431">
    <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(11449(a,1),17430(a,2,3))].">
      <j1 rule="para" parents="11449 17430"/>
    </justification>
  </clause>

  <clause id="17432">
    <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(10(a,1),17431(a,1,3,2,2))].">
      <j1 rule="para" parents="10 17431"/>
    </justification>
  </clause>

  <clause id="17433">
    <literal><![CDATA[
      a(x,1 / (y \ z),K(z,K(u,w))) = a(x,y,K(u,K(w,y * (y \ z))))
    ]]></literal>
    <justification jstring="[para(6788(a,1),17432(a,1,3))].">
      <j1 rule="para" parents="6788 17432"/>
    </justification>
  </clause>

  <clause id="17434">
    <literal><![CDATA[
      a(x,1 / (y \ z),K(z,K(u,w))) = a(x,y,K(u,K(w,z)))
    ]]></literal>
    <justification jstring="[para(10(a,1),17433(a,2,3,2,2))].">
      <j1 rule="para" parents="10 17433"/>
    </justification>
  </clause>

  <clause id="17435">
    <literal><![CDATA[
      a(x,1 / (y \ z),K(z,K(u,w))) = a(x,y,K(z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(6788(a,1),17434(a,2,3))].">
      <j1 rule="para" parents="6788 17434"/>
    </justification>
  </clause>

  <clause id="17436">
    <literal><![CDATA[
      a(x,1 / y,K(z,K(u,w))) = a(x,z / y,K(z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(79(a,1),17435(a,1,2,2))].">
      <j1 rule="para" parents="79 17435"/>
    </justification>
  </clause>

  <clause id="17437">
    <literal><![CDATA[
      a(x,1 / y,K(z,K(u,w))) = a(x,w / y,K(w,K(z,u)))
    ]]></literal>
    <justification jstring="[para(6788(a,2),17436(a,1,3))].">
      <j1 rule="para" parents="6788 17436"/>
    </justification>
  </clause>

  <clause id="17438">
    <literal><![CDATA[
      a(x,1 / y,K(z,K(u,w))) = a(x,w / y,K(z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(6788(a,2),17437(a,2,3))].">
      <j1 rule="para" parents="6788 17437"/>
    </justification>
  </clause>

  <clause id="17439">
    <literal><![CDATA[
      a(x,1 / y,K(z,K(u,w))) = a(w,u / y,K(z,K(x,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,13851,a,b,17438,a)].">
      <j1 rule="hyper" parents="63 13851 17438"/>
    </justification>
  </clause>

  <clause id="17440">
    <literal><![CDATA[
      a(x,1 / y,K(z,K(u,w))) = a(w,u / y,K(z,K(u,x)))
    ]]></literal>
    <justification jstring="[para(6800(a,1),17439(a,2,3))].">
      <j1 rule="para" parents="6800 17439"/>
    </justification>
  </clause>

  <clause id="17441">
    <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(6799(a,1),17425(a,2,2))].">
      <j1 rule="para" parents="6799 17425"/>
    </justification>
  </clause>

  <clause id="17443">
    <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(333,a,11678,a(flip),b,17441,a),flip(a)].">
      <j1 rule="hyper" parents="333 11678 17441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17444">
    <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(9745(a,1),17443(a,2,1))].">
      <j1 rule="para" parents="9745 17443"/>
    </justification>
  </clause>

  <clause id="17445">
    <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(333,a,14150,a(flip),b,17444,a),flip(a)].">
      <j1 rule="hyper" parents="333 14150 17444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17446">
    <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(16726(a,1),17445(a,1,2))].">
      <j1 rule="para" parents="16726 17445"/>
    </justification>
  </clause>

  <clause id="17447">
    <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(6799(a,1),17446(a,1,3))].">
      <j1 rule="para" parents="6799 17446"/>
    </justification>
  </clause>

  <clause id="17448">
    <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(11005,a,17447,a)].">
      <j1 rule="hyper" parents="11005 17447"/>
    </justification>
  </clause>

  <clause id="17449">
    <literal><![CDATA[
      a(x,1 / y,K(z,K(u,w))) = a(w,y,K(z,K(u,x)))
    ]]></literal>
    <justification jstring="[para(171(a,1),17448(a,1,2,1))].">
      <j1 rule="para" parents="171 17448"/>
    </justification>
  </clause>

  <clause id="17450">
    <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(63,a,17409,a,b,17449,a)].">
      <j1 rule="hyper" parents="63 17409 17449"/>
    </justification>
  </clause>

  <clause id="17451">
    <literal><![CDATA[
      a(x,y / z,K(u,K(y,w))) = a(x,z,K(u,K(y,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,17440,a(flip),b,17449,a)].">
      <j1 rule="hyper" parents="63 17440 17449"/>
    </justification>
  </clause>

  <clause id="17452">
    <literal><![CDATA[
      a(x,y / z,K(u,K(y,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      a(y,z,K(u,K(x,w))) = v5
    ]]></literal>
    <justification jstring="[para(17451(a,2),14059(a,1))].">
      <j1 rule="para" parents="17451 14059"/>
    </justification>
  </clause>

  <clause id="17453">
    <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(6788(a,1),17450(a,2,3))].">
      <j1 rule="para" parents="6788 17450"/>
    </justification>
  </clause>

  <clause id="17454">
    <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(4945(a,1),17453(a,1,2,2,2,1))].">
      <j1 rule="para" parents="4945 17453"/>
    </justification>
  </clause>

  <clause id="17455">
    <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(13252(a,1),16827(a,1,2,2,1,2))].">
      <j1 rule="para" parents="13252 16827"/>
    </justification>
  </clause>

  <clause id="17456">
    <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(16737(a,1),17455(a,1,2,2,1))].">
      <j1 rule="para" parents="16737 17455"/>
    </justification>
  </clause>

  <clause id="17457">
    <literal><![CDATA[
      T(x,(y * ((((y \ 1) * (y \ z)) / (y \ 1)) * (y \ 1))) * u) = T(x,(((1 / y) * (z / y)) * y) * u)
    ]]></literal>
    <justification jstring="[para(5534(a,1),16969(a,2,2,1))].">
      <j1 rule="para" parents="5534 16969"/>
    </justification>
  </clause>

  <clause id="17458">
    <literal><![CDATA[
      T(x,(y * ((((y \ 1) * (y \ z)) / (y \ 1)) * (y \ 1))) * u) = T(x,(((y \ 1) * (z / y)) * y) * u)
    ]]></literal>
    <justification jstring="[hyper(333,a,12385,a(flip),b,17457,a),flip(a)].">
      <j1 rule="hyper" parents="333 12385 17457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17459">
    <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(5713(a,1),17454(a,1,2))].">
      <j1 rule="para" parents="5713 17454"/>
    </justification>
  </clause>

  <clause id="17460">
    <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(13344(a,1),17459(a,1,2))].">
      <j1 rule="para" parents="13344 17459"/>
    </justification>
  </clause>

  <clause id="17461">
    <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(7673(a,1),17460(a,1,2,2,1))].">
      <j1 rule="para" parents="7673 17460"/>
    </justification>
  </clause>

  <clause id="17462">
    <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(63,a,17404,a(flip),b,17461,a)].">
      <j1 rule="hyper" parents="63 17404 17461"/>
    </justification>
  </clause>

  <clause id="17463">
    <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(16657,a,17462,a)].">
      <j1 rule="hyper" parents="16657 17462"/>
    </justification>
  </clause>

  <clause id="17464">
    <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(6032(a,1),17463(a,2,3,2))].">
      <j1 rule="para" parents="6032 17463"/>
    </justification>
  </clause>

  <clause id="17465">
    <literal><![CDATA[
      K(x,K(y,((z / u) * w) * ((u / w) / z))) = a(w,u,K(x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(16593(a,1),17464(a,2,3))].">
      <j1 rule="para" parents="16593 17464"/>
    </justification>
  </clause>

  <clause id="17466">
    <literal><![CDATA[
      a(x,y,K(z,K(u / y,w / y))) = a(w,y,K(x,K(z,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,17388,a(flip),b,17465,a)].">
      <j1 rule="hyper" parents="63 17388 17465"/>
    </justification>
  </clause>

  <clause id="17468">
    <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(76(a,1),17466(a,1,3,2,1))].">
      <j1 rule="para" parents="76 17466"/>
    </justification>
  </clause>

  <clause id="17469">
    <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(17349(a,1),17468(a,1,3))].">
      <j1 rule="para" parents="17349 17468"/>
    </justification>
  </clause>

  <clause id="17470">
    <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(6785(a,1),17469(a,1,3))].">
      <j1 rule="para" parents="6785 17469"/>
    </justification>
  </clause>

  <clause id="17471">
    <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(16954(a,1),17470(a,1,3))].">
      <j1 rule="para" parents="16954 17470"/>
    </justification>
  </clause>

  <clause id="17472">
    <literal><![CDATA[
      a(x,y \ z,K(u,K(w,z))) = a(u,z,K(y,K(w,x / z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,14139,a(flip),b,17471,a),flip(a)].">
      <j1 rule="hyper" parents="63 14139 17471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17473">
    <literal><![CDATA[
      a(x,y \ z,K(u,K(z,w))) = a(u,z,K(y,K(w,x / z)))
    ]]></literal>
    <justification jstring="[para(6800(a,1),17472(a,1,3))].">
      <j1 rule="para" parents="6800 17472"/>
    </justification>
  </clause>

  <clause id="17474">
    <literal><![CDATA[
      a(x,y / z,K(u,K(y,w))) = a(u,y,K(z,K(w,x / y)))
    ]]></literal>
    <justification jstring="[hyper(63,a,17428,a,b,17473,a)].">
      <j1 rule="hyper" parents="63 17428 17473"/>
    </justification>
  </clause>

  <clause id="17475">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w / y))) = a(y,z,K(x,K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(17452,a,17474,a),flip(a)].">
      <j1 rule="hyper" parents="17452 17474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17476">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w / y))) = a(y,z,K(w,K(x,u)))
    ]]></literal>
    <justification jstring="[para(6785(a,1),17475(a,2,3))].">
      <j1 rule="para" parents="6785 17475"/>
    </justification>
  </clause>

  <clause id="17477">
    <literal><![CDATA[
      K(x,K(y,((z / u) / (w * z)) * (w * u))) = a(z,y,K(u,K(x,w)))
    ]]></literal>
    <justification jstring="[hyper(17387,a,17476,a)].">
      <j1 rule="hyper" parents="17387 17476"/>
    </justification>
  </clause>

  <clause id="17478">
    <literal><![CDATA[
      K(x,K(y,((z / u) / (w * z)) * (w * u))) = a(z,y,K(x,K(w,u)))
    ]]></literal>
    <justification jstring="[para(6788(a,2),17477(a,2,3))].">
      <j1 rule="para" parents="6788 17477"/>
    </justification>
  </clause>

  <clause id="17479">
    <literal><![CDATA[
      a(x,y,K(z,K(u,y / w))) = a(w,x,K(z,K(u,y)))
    ]]></literal>
    <justification jstring="[hyper(63,a,17389,a(flip),b,17478,a)].">
      <j1 rule="hyper" parents="63 17389 17478"/>
    </justification>
  </clause>

  <clause id="17480">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w / y))) = a(w,x,K(z,K(u,y)))
    ]]></literal>
    <justification jstring="[para(7166(a,1),17479(a,1,3))].">
      <j1 rule="para" parents="7166 17479"/>
    </justification>
  </clause>

  <clause id="17481">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w / y))) = a(w,x,K(z,K(y,u)))
    ]]></literal>
    <justification jstring="[para(6800(a,1),17480(a,2,3))].">
      <j1 rule="para" parents="6800 17480"/>
    </justification>
  </clause>

  <clause id="17482">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = a(u,z,K(x,K(y,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,17476,a(flip),b,17481,a),flip(a)].">
      <j1 rule="hyper" parents="63 17476 17481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17483">
    <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(17482(a,1),13937(a,1,1))].">
      <j1 rule="para" parents="17482 13937"/>
    </justification>
  </clause>

  <clause id="17484">
    <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(6785(a,1),17483(a,1,2))].">
      <j1 rule="para" parents="6785 17483"/>
    </justification>
  </clause>

  <clause id="17485">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) = K(x,K(z,L(y,w,u)))
    ]]></literal>
    <justification jstring="[hyper(14206,a,17484,a),flip(a)].">
      <j1 rule="hyper" parents="14206 17484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17486">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) = K(x,K(y,L(z,w,u)))
    ]]></literal>
    <justification jstring="[hyper(10998,a,17485,a)].">
      <j1 rule="hyper" parents="10998 17485"/>
    </justification>
  </clause>

  <clause id="17487">
    <literal><![CDATA[
      K(x,K((y / z) * u,L(w,z,y))) = K(x,K(w,(u / z) * y))
    ]]></literal>
    <justification jstring="[hyper(333,a,17375,a(flip),b,17486,a),flip(a)].">
      <j1 rule="hyper" parents="333 17375 17486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17488">
    <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(757(a,1),17486(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="757 17486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17489">
    <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(11085(a,1),17486(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11085 17486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17490">
    <literal><![CDATA[
      K(x,K(y,(z * u) / w)) = K(x,K(y,(z / w) * u))
    ]]></literal>
    <justification jstring="[hyper(17358,a,17487,a)].">
      <j1 rule="hyper" parents="17358 17487"/>
    </justification>
  </clause>

  <clause id="17491">
    <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(17489(a,2),7180(a,1))].">
      <j1 rule="para" parents="17489 7180"/>
    </justification>
  </clause>

  <clause id="17492">
    <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(333,a,15554,a,b,17488,a),flip(a)].">
      <j1 rule="hyper" parents="333 15554 17488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17493">
    <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(333,a,17490,a(flip),b,17492,a),flip(a)].">
      <j1 rule="hyper" parents="333 17490 17492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17494">
    <literal><![CDATA[
      K(x,K(y,L(L(z,u,w),v5 / (w * u),w * u))) = K(x,K(y,(w * (u * z)) / (w * u)))
    ]]></literal>
    <justification jstring="[hyper(333,a,17345,a(flip),b,17493,a),flip(a)].">
      <j1 rule="hyper" parents="333 17345 17493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17497">
    <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(7004(a,1),17494(a,2,2))].">
      <j1 rule="para" parents="7004 17494"/>
    </justification>
  </clause>

  <clause id="17498">
    <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(333,a,15550,a(flip),b,17497,a),flip(a)].">
      <j1 rule="hyper" parents="333 15550 17497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17501">
    <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(63,a,14364,a(flip),b,17498,a)].">
      <j1 rule="hyper" parents="63 14364 17498"/>
    </justification>
  </clause>

  <clause id="17502">
    <literal><![CDATA[
      K(x,K(y,L(1 / z,z,u))) = K(x,K(y,L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(17491,a,17501,a),flip(a)].">
      <j1 rule="hyper" parents="17491 17501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17504">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) = K(x,K(y,1 / z))
    ]]></literal>
    <justification jstring="[para(5829(a,1),17502(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5829 17502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17506">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(333,a,7165,a(flip),b,17504,a),flip(a)].">
      <j1 rule="hyper" parents="333 7165 17504"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17509">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(10924,a,17506,a)].">
      <j1 rule="hyper" parents="10924 17506"/>
    </justification>
  </clause>

  <clause id="17510">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(6798,a,17506,a)].">
      <j1 rule="hyper" parents="6798 17506"/>
    </justification>
  </clause>

  <clause id="17516">
    <literal><![CDATA[
      T(x,K(y,L(z,u,w))) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(124,a,17506,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 17506 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17517">
    <literal><![CDATA[
      T(x,K(y,L(z,u,w))) = x * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(126,a,17506,a(flip),b,4215,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="126 17506 4215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17518">
    <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(17506(a,1),7622(a,1,1))].">
      <j1 rule="para" parents="17506 7622"/>
    </justification>
  </clause>

  <clause id="17519">
    <literal><![CDATA[
      (x * y) * K(z,K(u,w)) = x * (y * K(z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(17506(a,1),10975(a,1,2))].">
      <j1 rule="para" parents="17506 10975"/>
    </justification>
  </clause>

  <clause id="17523">
    <literal><![CDATA[
      K(x * K(y,z),L(x,u,w)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(12969,a,17509,a)].">
      <j1 rule="hyper" parents="12969 17509"/>
    </justification>
  </clause>

  <clause id="17526">
    <literal><![CDATA[
      a(K(x,y),z,K(u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(120,a,17509,a(flip),b,13761,a),flip(a)].">
      <j1 rule="hyper" parents="120 17509 13761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17527">
    <literal><![CDATA[
      x \ (y * K(z,K(u,w))) = (x \ y) * K(z,K(u,w))
    ]]></literal>
    <justification jstring="[para(17509(a,1),495(a,1,2,2))].">
      <j1 rule="para" parents="17509 495"/>
    </justification>
  </clause>

  <clause id="17529">
    <literal><![CDATA[
      K(x,K(y,z)) \ ((K(y,z) \ u) * (u \ x)) = L(K(z,T(y,x)),u,u \ x) * x
    ]]></literal>
    <justification jstring="[para(17509(a,1),14761(a,1,1))].">
      <j1 rule="para" parents="17509 14761"/>
    </justification>
  </clause>

  <clause id="17530">
    <literal><![CDATA[
      K(x,K(y,z)) \ (K(x,y) * (z * u)) = (z * K(x,y)) * L(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(17509(a,1),14212(a,1,1))].">
      <j1 rule="para" parents="17509 14212"/>
    </justification>
  </clause>

  <clause id="17537">
    <literal><![CDATA[
      L(K(x,y),z,K(u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(52,a,17526,a)].">
      <j1 rule="hyper" parents="52 17526"/>
    </justification>
  </clause>

  <clause id="17538">
    <literal><![CDATA[
      T(K(x,y),a(z,u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(14477,a,17537,a)].">
      <j1 rule="hyper" parents="14477 17537"/>
    </justification>
  </clause>

  <clause id="17539">
    <literal><![CDATA[
      K(x,L(y,z,K(u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(10960,a,17537,a)].">
      <j1 rule="hyper" parents="10960 17537"/>
    </justification>
  </clause>

  <clause id="17540">
    <literal><![CDATA[
      K(L(x,y,K(z,u)),w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(9539,a,17537,a)].">
      <j1 rule="hyper" parents="9539 17537"/>
    </justification>
  </clause>

  <clause id="17542">
    <literal><![CDATA[
      K(x,(K(y,z) \ u) \ w) = K(x,u \ (K(y,z) * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,10876,a(flip),b,17537,a),flip(a)].">
      <j1 rule="hyper" parents="63 10876 17537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17543">
    <literal><![CDATA[
      K((K(x,y) * z) \ u,w) = K(z \ (K(y,x) * u),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,6287,a(flip),b,17537,a),flip(a)].">
      <j1 rule="hyper" parents="63 6287 17537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17544">
    <literal><![CDATA[
      K(x,y) \ (z * K(u,w)) = (K(x,y) \ z) * K(u,w)
    ]]></literal>
    <justification jstring="[hyper(126,a,17537,a(flip),b,5160,a),flip(a)].">
      <j1 rule="hyper" parents="126 17537 5160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17545">
    <literal><![CDATA[
      (K(x,y) * z) * K(u,w) = K(x,y) * (z * K(u,w))
    ]]></literal>
    <justification jstring="[hyper(126,a,17537,a(flip),b,3220,a(flip))].">
      <j1 rule="hyper" parents="126 17537 3220"/>
    </justification>
  </clause>

  <clause id="17546">
    <literal><![CDATA[
      (K(x,y) * z) * K(u,T(w,z)) = K(x,y) * (K(u,w) * z)
    ]]></literal>
    <justification jstring="[hyper(125,a,17537,a(flip),b,14467,a),flip(a)].">
      <j1 rule="hyper" parents="125 17537 14467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17548">
    <literal><![CDATA[
      (K(x,y) * z) * L(K(u,w),v5,v6) = K(x,y) * (z * L(K(u,w),v5,v6))
    ]]></literal>
    <justification jstring="[para(17537(a,1),461(a,1,2,1))].">
      <j1 rule="para" parents="17537 461"/>
    </justification>
  </clause>

  <clause id="17550">
    <literal><![CDATA[
      (L(K(x,y),z,u) * w) * K(v5,v6) = L(K(x,y),z,u) * (w * K(v5,v6))
    ]]></literal>
    <justification jstring="[para(17537(a,1),13893(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="17537 13893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17553">
    <literal><![CDATA[
      K(x,T(y,a(z,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6960,a,17538,a),flip(a)].">
      <j1 rule="hyper" parents="6960 17538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17557">
    <literal><![CDATA[
      K(x,T(y,a(z,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(17538(a,1),6960(a,1))].">
      <j1 rule="para" parents="17538 6960"/>
    </justification>
  </clause>

  <clause id="17558">
    <literal><![CDATA[
      T(x,L(y,z,K(u,w))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(124,a,17539,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 17539 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17560">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ w) = K(x,u \ (K(z,y) * w))
    ]]></literal>
    <justification jstring="[para(4581(a,1),17539(a,1,2))].">
      <j1 rule="para" parents="4581 17539"/>
    </justification>
  </clause>

  <clause id="17561">
    <literal><![CDATA[
      K(x,L(y,z,T(u,w))) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(5600(a,1),17539(a,1,2))].">
      <j1 rule="para" parents="5600 17539"/>
    </justification>
  </clause>

  <clause id="17562">
    <literal><![CDATA[
      K(x,T(y,L(z,u,w) \ z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(14482(a,2),17539(a,1,2))].">
      <j1 rule="para" parents="14482 17539"/>
    </justification>
  </clause>

  <clause id="17563">
    <literal><![CDATA[
      K(x,T(y,L(z,u,w))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(14486(a,1),17539(a,1,2))].">
      <j1 rule="para" parents="14486 17539"/>
    </justification>
  </clause>

  <clause id="17564">
    <literal><![CDATA[
      K(x,(y * K(z,u)) / w) = K(x,y / (w * K(u,z)))
    ]]></literal>
    <justification jstring="[para(14463(a,1),17539(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14463 17539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17565">
    <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(16554,a,17540,a)].">
      <j1 rule="hyper" parents="16554 17540"/>
    </justification>
  </clause>

  <clause id="17566">
    <literal><![CDATA[
      K(x,K(y,z) \ (u * w)) \ K(x,K(u,K(y,z) \ w)) = K((w * K(z,y)) * L(u,w,K(z,y)),x)
    ]]></literal>
    <justification jstring="[para(17540(a,1),17243(a,1,2,2))].">
      <j1 rule="para" parents="17540 17243"/>
    </justification>
  </clause>

  <clause id="17567">
    <literal><![CDATA[
      T(x,T(y,a(z,u,w))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(124,a,17553,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 17553 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17568">
    <literal><![CDATA[
      T(K(x,y),a(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(17553(a,1),6960(a,1,1))].">
      <j1 rule="para" parents="17553 6960"/>
    </justification>
  </clause>

  <clause id="17569">
    <literal><![CDATA[
      K(x,a(y,z,u) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w / a(y,z,u)) = v5
    ]]></literal>
    <justification jstring="[para(17553(a,1),7076(a,1))].">
      <j1 rule="para" parents="17553 7076"/>
    </justification>
  </clause>

  <clause id="17570">
    <literal><![CDATA[
      T(x / L(y,z,K(u,w)),y) = L(y,z,K(u,w)) \ x
    ]]></literal>
    <justification jstring="[hyper(423,a,17558,a),flip(a)].">
      <j1 rule="hyper" parents="423 17558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17571">
    <literal><![CDATA[
      T(x,(y * K(z,K(u,w))) / (v5 \ T(z,K(u,w)))) = T(x,y / (v5 \ z))
    ]]></literal>
    <justification jstring="[hyper(63,a,13979,a(flip),b,17558,a)].">
      <j1 rule="hyper" parents="63 13979 17558"/>
    </justification>
  </clause>

  <clause id="17572">
    <literal><![CDATA[
      T(x,a(K(y,z),u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(40,a,13828,a,b,17558,a)].">
      <j1 rule="hyper" parents="40 13828 17558"/>
    </justification>
  </clause>

  <clause id="17573">
    <literal><![CDATA[
      T(x,a(y,z,K(u,w))) = x
    ]]></literal>
    <justification jstring="[hyper(40,a,13808,a(flip),b,17558,a),flip(a)].">
      <j1 rule="hyper" parents="40 13808 17558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17574">
    <literal><![CDATA[
      L(x,y,K(z,u)) * T(w,x) != v5
    ]]></literal>
    <literal><![CDATA[
      w * L(x,y,K(z,u)) = v5
    ]]></literal>
    <justification jstring="[para(17558(a,1),300(a,1,2))].">
      <j1 rule="para" parents="17558 300"/>
    </justification>
  </clause>

  <clause id="17575">
    <literal><![CDATA[
      T(x,T((K(y,z) * u) \ w,v5)) = T(x,T(u \ (K(y,z) \ w),v5))
    ]]></literal>
    <justification jstring="[para(576(a,1),17558(a,1,2))].">
      <j1 rule="para" parents="576 17558"/>
    </justification>
  </clause>

  <clause id="17576">
    <literal><![CDATA[
      T(x,L(K(y,z),u,w)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(14537,a,17572,a)].">
      <j1 rule="hyper" parents="14537 17572"/>
    </justification>
  </clause>

  <clause id="17577">
    <literal><![CDATA[
      L(x,y,K(z,K(u,w))) = x
    ]]></literal>
    <justification jstring="[hyper(14530,a,17572,a)].">
      <j1 rule="hyper" parents="14530 17572"/>
    </justification>
  </clause>

  <clause id="17579">
    <literal><![CDATA[
      (a(K(x,y),z,u) \ w) * a(K(x,y),z,u) = w
    ]]></literal>
    <justification jstring="[hyper(2260,a,17572,a)].">
      <j1 rule="hyper" parents="2260 17572"/>
    </justification>
  </clause>

  <clause id="17582">
    <literal><![CDATA[
      T(x,K(y,a(z,u,w))) = x
    ]]></literal>
    <justification jstring="[para(12422(a,1),17572(a,1,2))].">
      <j1 rule="para" parents="12422 17572"/>
    </justification>
  </clause>

  <clause id="17583">
    <literal><![CDATA[
      T(x,K(a(y,z,u),w)) = x
    ]]></literal>
    <justification jstring="[para(13790(a,1),17572(a,1,2))].">
      <j1 rule="para" parents="13790 17572"/>
    </justification>
  </clause>

  <clause id="17584">
    <literal><![CDATA[
      a(x,y,K(z,u)) * w = w * a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(2261,a,17573,a),flip(a)].">
      <j1 rule="hyper" parents="2261 17573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17585">
    <literal><![CDATA[
      T(a(x,y,K(z,u)),w) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(54,a,17573,a)].">
      <j1 rule="hyper" parents="54 17573"/>
    </justification>
  </clause>

  <clause id="17586">
    <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(17573(a,1),300(a,1,2))].">
      <j1 rule="para" parents="17573 300"/>
    </justification>
  </clause>

  <clause id="17587">
    <literal><![CDATA[
      R(x,y,T(z,K(u,w))) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(14475,a,17577,a)].">
      <j1 rule="hyper" parents="14475 17577"/>
    </justification>
  </clause>

  <clause id="17588">
    <literal><![CDATA[
      L(x,y,T(z,K(u,w))) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(5601,a,17577,a)].">
      <j1 rule="hyper" parents="5601 17577"/>
    </justification>
  </clause>

  <clause id="17589">
    <literal><![CDATA[
      (K(x,K(y,z)) \ u) \ w = u \ (K(x,K(y,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(597,a,17577,a),flip(a)].">
      <j1 rule="hyper" parents="597 17577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17591">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) / w = K(x,K(y,z)) * (u / w)
    ]]></literal>
    <justification jstring="[hyper(197,a,17577,a(flip),b,10409,a(flip))].">
      <j1 rule="hyper" parents="197 17577 10409"/>
    </justification>
  </clause>

  <clause id="17592">
    <literal><![CDATA[
      L(x,y,K(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      x = v5
    ]]></literal>
    <justification jstring="[para(17577(a,1),50(a,2))].">
      <j1 rule="para" parents="17577 50"/>
    </justification>
  </clause>

  <clause id="17593">
    <literal><![CDATA[
      K(x,K(y,z)) \ (u * w) = (K(x,K(y,z)) \ u) * w
    ]]></literal>
    <justification jstring="[para(17577(a,1),495(a,1,2,2))].">
      <j1 rule="para" parents="17577 495"/>
    </justification>
  </clause>

  <clause id="17594">
    <literal><![CDATA[
      (K(x,K(y,z)) * (u * w)) \ ((K(x,K(y,z)) * u) * (w * v5)) = L(v5,L(w,u,K(x,K(y,z))),K(x,K(y,z)) * u)
    ]]></literal>
    <justification jstring="[para(17577(a,1),497(a,1,2,2,1))].">
      <j1 rule="para" parents="17577 497"/>
    </justification>
  </clause>

  <clause id="17595">
    <literal><![CDATA[
      (x * (K(y,K(z,u)) * (w * v5))) \ ((x * (K(y,K(z,u)) * w)) * v5) = a(x,K(y,K(z,u)) * w,L(v5,w,K(y,K(z,u))))
    ]]></literal>
    <justification jstring="[para(17577(a,1),496(a,1,2,2))].">
      <j1 rule="para" parents="17577 496"/>
    </justification>
  </clause>

  <clause id="17596">
    <literal><![CDATA[
      L(x,y,K(z,u) * w) = L(x,y,w * K(z,u))
    ]]></literal>
    <justification jstring="[para(17577(a,1),14564(a,1,1))].">
      <j1 rule="para" parents="17577 14564"/>
    </justification>
  </clause>

  <clause id="17597">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) / w = (u / w) * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(17577(a,1),15631(a,1,2))].">
      <j1 rule="para" parents="17577 15631"/>
    </justification>
  </clause>

  <clause id="17598">
    <literal><![CDATA[
      T(x,a(y,z,u) * w) = T(x,w * a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(12264,a,17582,a)].">
      <j1 rule="hyper" parents="12264 17582"/>
    </justification>
  </clause>

  <clause id="17600">
    <literal><![CDATA[
      T(x,T(y,a(z,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = v5
    ]]></literal>
    <justification jstring="[para(17582(a,1),6192(a,2))].">
      <j1 rule="para" parents="17582 6192"/>
    </justification>
  </clause>

  <clause id="17601">
    <literal><![CDATA[
      T(x,a(y,z,u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,w * a(y,z,u)) = v5
    ]]></literal>
    <justification jstring="[para(17582(a,1),12277(a,1,1))].">
      <j1 rule="para" parents="17582 12277"/>
    </justification>
  </clause>

  <clause id="17602">
    <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(17582(a,1),14916(a,1,2,1,2))].">
      <j1 rule="para" parents="17582 14916"/>
    </justification>
  </clause>

  <clause id="17603">
    <literal><![CDATA[
      K(a(x,y,z),T(u,w)) = K(a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(7257,a,17583,a)].">
      <j1 rule="hyper" parents="7257 17583"/>
    </justification>
  </clause>

  <clause id="17604">
    <literal><![CDATA[
      T(K(x,T(y,a(z,u,w))) * (v5 / T(y,a(z,u,w))),y) = T(T(y,a(z,u,w)),x) \ v5
    ]]></literal>
    <justification jstring="[hyper(63,a,6635,a(flip),b,17567,a),flip(a)].">
      <j1 rule="hyper" parents="63 6635 17567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17606">
    <literal><![CDATA[
      R(x,y,T(z,T(u,w))) = R(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[para(6191(a,1),17587(a,1,3))].">
      <j1 rule="para" parents="6191 17587"/>
    </justification>
  </clause>

  <clause id="17607">
    <literal><![CDATA[
      L(x,y,K(z,u) / w) = L(x,y,w \ K(z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,11834,a(flip),b,17588,a),flip(a)].">
      <j1 rule="hyper" parents="63 11834 17588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17608">
    <literal><![CDATA[
      L(x,y,(y * x) \ z) = L(x,y,(x * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,11035,a(flip),b,17588,a),flip(a)].">
      <j1 rule="hyper" parents="63 11035 17588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17609">
    <literal><![CDATA[
      L(x,y,T(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = v5
    ]]></literal>
    <justification jstring="[para(5600(a,1),17592(a,1))].">
      <j1 rule="para" parents="5600 17592"/>
    </justification>
  </clause>

  <clause id="17610">
    <literal><![CDATA[
      R(x,y,T(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = v5
    ]]></literal>
    <justification jstring="[para(14462(a,1),17592(a,1))].">
      <j1 rule="para" parents="14462 17592"/>
    </justification>
  </clause>

  <clause id="17613">
    <literal><![CDATA[
      K(x,y) * (T(K(y,L(x,z,u)) * K(y,K(w,x)),w) * v5) = a(y,z,K(u,x)) * v5
    ]]></literal>
    <justification jstring="[para(17510(a,1),14083(a,1,2,1,1,2))].">
      <j1 rule="para" parents="17510 14083"/>
    </justification>
  </clause>

  <clause id="17614">
    <literal><![CDATA[
      T(x * (T(y,x) * K(z,u)),K(z,u)) = K(z,L(u,y,x)) * (y * x)
    ]]></literal>
    <justification jstring="[hyper(10995,a,17516,a),flip(a)].">
      <j1 rule="hyper" parents="10995 17516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17616">
    <literal><![CDATA[
      T(x,K(y,L(z / u,w,v5))) = T(x,K(y,u \ z))
    ]]></literal>
    <justification jstring="[hyper(333,a,15587,a(flip),b,17516,a),flip(a)].">
      <j1 rule="hyper" parents="333 15587 17516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17617">
    <literal><![CDATA[
      T(K(x,y) * z,K(y,L(x,u,w))) = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,6846,a(flip),b,17516,a),flip(a)].">
      <j1 rule="hyper" parents="333 6846 17516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17618">
    <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(17516(a,1),300(a,1,2))].">
      <j1 rule="para" parents="17516 300"/>
    </justification>
  </clause>

  <clause id="17619">
    <literal><![CDATA[
      T(x,K(y,(z \ u) \ w)) = T(x,K(y,u \ (z * w)))
    ]]></literal>
    <justification jstring="[para(515(a,1),17516(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="515 17516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17622">
    <literal><![CDATA[
      T(x,K(y,R(z,u,w))) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(13864(a,2),17516(a,1,2))].">
      <j1 rule="para" parents="13864 17516"/>
    </justification>
  </clause>

  <clause id="17623">
    <literal><![CDATA[
      K(x,T(y,z \ L(z,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(7286,a,17562,a)].">
      <j1 rule="hyper" parents="7286 17562"/>
    </justification>
  </clause>

  <clause id="17624">
    <literal><![CDATA[
      K(x,T(y \ R(z,u,w),z)) = K(x,R(z,u,w) / y)
    ]]></literal>
    <justification jstring="[hyper(13913,a,17563,a),flip(a)].">
      <j1 rule="hyper" parents="13913 17563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17625">
    <literal><![CDATA[
      K(x,T(y * (L(y,z,u) \ w),y)) = K(x,(y * w) / L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(7212,a,17563,a),flip(a)].">
      <j1 rule="hyper" parents="7212 17563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17627">
    <literal><![CDATA[
      K(x * K(y,L(x,z,u)),w) = K(x,T(w,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,10916,a,b,17563,a)].">
      <j1 rule="hyper" parents="63 10916 17563"/>
    </justification>
  </clause>

  <clause id="17628">
    <literal><![CDATA[
      K(x,T(y,(z * u) \ w)) = K(x,T(y,u \ (z \ w)))
    ]]></literal>
    <justification jstring="[para(311(a,1),17563(a,1,2,2))].">
      <j1 rule="para" parents="311 17563"/>
    </justification>
  </clause>

  <clause id="17629">
    <literal><![CDATA[
      K(x,T(y,(z * u) \ (w * z))) = K(x,T(y,u \ T(w,z)))
    ]]></literal>
    <justification jstring="[para(468(a,1),17563(a,1,2,2))].">
      <j1 rule="para" parents="468 17563"/>
    </justification>
  </clause>

  <clause id="17631">
    <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(17563(a,1),12283(a,1))].">
      <j1 rule="para" parents="17563 12283"/>
    </justification>
  </clause>

  <clause id="17632">
    <literal><![CDATA[
      K(x,T(y,(z / u) / w)) = K(x,T(y,z / (w * u)))
    ]]></literal>
    <justification jstring="[para(13912(a,1),17563(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13912 17563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17633">
    <literal><![CDATA[
      (T(x,K(y,z)) * K(u,z)) * (K(z,u) * L(K(y,z),w,v5)) = x * ((x * L(K(y,z),w,v5)) / x)
    ]]></literal>
    <justification jstring="[para(17576(a,1),8462(a,1,1,1))].">
      <j1 rule="para" parents="17576 8462"/>
    </justification>
  </clause>

  <clause id="17636">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * T((u \ 1) * (u * z),u)) = T(x,((u \ 1) * (z * u)) * y)
    ]]></literal>
    <justification jstring="[para(17622(a,1),17180(a,1,1))].">
      <j1 rule="para" parents="17622 17180"/>
    </justification>
  </clause>

  <clause id="17637">
    <literal><![CDATA[
      K(x,(y \ L(y,z,u)) * w) = K(x,w * (y \ L(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(12281,a,17623,a)].">
      <j1 rule="hyper" parents="12281 17623"/>
    </justification>
  </clause>

  <clause id="17638">
    <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(6923(a,1),17557(a,1))].">
      <j1 rule="para" parents="6923 17557"/>
    </justification>
  </clause>

  <clause id="17639">
    <literal><![CDATA[
      K(x,T(y,L(z,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = v5
    ]]></literal>
    <justification jstring="[para(13824(a,1),17557(a,1,2))].">
      <j1 rule="para" parents="13824 17557"/>
    </justification>
  </clause>

  <clause id="17640">
    <literal><![CDATA[
      K(x,L(y,z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(14461(a,2),17557(a,1,2))].">
      <j1 rule="para" parents="14461 17557"/>
    </justification>
  </clause>

  <clause id="17641">
    <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(63,a,14793,a(flip),b,17561,a),flip(a)].">
      <j1 rule="hyper" parents="63 14793 17561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17642">
    <literal><![CDATA[
      K(x,L(y,z * u,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,14016,a(flip),b,17561,a),flip(a)].">
      <j1 rule="hyper" parents="63 14016 17561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17643">
    <literal><![CDATA[
      K(x,L((y / T(z,u)) / w,w,z)) = K(x,y / (w * T(z,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,13882,a(flip),b,17561,a),flip(a)].">
      <j1 rule="hyper" parents="63 13882 17561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17644">
    <literal><![CDATA[
      K(x,L(y,z,u / w)) = K(x,L(y,z,w \ u))
    ]]></literal>
    <justification jstring="[para(113(a,1),17561(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="113 17561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17645">
    <literal><![CDATA[
      K(x,L(y,z,(u * w) * (u \ 1))) = K(x,L(y,z,R(w,u,u \ 1)))
    ]]></literal>
    <justification jstring="[para(833(a,1),17561(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="833 17561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17646">
    <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(17561(a,1),14766(a,1,1,1))].">
      <j1 rule="para" parents="17561 14766"/>
    </justification>
  </clause>

  <clause id="17647">
    <literal><![CDATA[
      L(K(x,y),z,K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(14461(a,2),17568(a,1))].">
      <j1 rule="para" parents="14461 17568"/>
    </justification>
  </clause>

  <clause id="17649">
    <literal><![CDATA[
      T(K(a(x,y,z),u),w) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(13539(a,1),17585(a,1,1))].">
      <j1 rule="para" parents="13539 17585"/>
    </justification>
  </clause>

  <clause id="17650">
    <literal><![CDATA[
      T(x,L(y,z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = v5
    ]]></literal>
    <justification jstring="[para(14461(a,2),17600(a,1,2))].">
      <j1 rule="para" parents="14461 17600"/>
    </justification>
  </clause>

  <clause id="17655">
    <literal><![CDATA[
      R(T(x / y,y * T(z,u)),y,T(z,u)) = (y * T(z,T(u,w))) \ (x * T(z,T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(16405,a,17606,a),flip(a)].">
      <j1 rule="hyper" parents="16405 17606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17657">
    <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(5600(a,1),17640(a,1,2))].">
      <j1 rule="para" parents="5600 17640"/>
    </justification>
  </clause>

  <clause id="17658">
    <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(5716(a,1),17640(a,1,2))].">
      <j1 rule="para" parents="5716 17640"/>
    </justification>
  </clause>

  <clause id="17660">
    <literal><![CDATA[
      K(x,L(y,z * u,u \ 1)) = K(x,L(y,z,u \ 1))
    ]]></literal>
    <justification jstring="[para(2634(a,1),17642(a,1,2))].">
      <j1 rule="para" parents="2634 17642"/>
    </justification>
  </clause>

  <clause id="17661">
    <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(17642(a,1),14879(a,2,2,2,1))].">
      <j1 rule="para" parents="17642 14879"/>
    </justification>
  </clause>

  <clause id="17662">
    <literal><![CDATA[
      L(K(x,y),z,L(K(u,w),v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v7
    ]]></literal>
    <justification jstring="[para(5372(a,1),17647(a,1,3))].">
      <j1 rule="para" parents="5372 17647"/>
    </justification>
  </clause>

  <clause id="17663">
    <literal><![CDATA[
      T(K(a(x,y,z),u),w) = a(x,y,K(z,T(u,v5)))
    ]]></literal>
    <justification jstring="[para(17603(a,1),17649(a,1,1))].">
      <j1 rule="para" parents="17603 17649"/>
    </justification>
  </clause>

  <clause id="17664">
    <literal><![CDATA[
      T(x,K(y,L(z / u,w,v5))) = x * K(x,K(y,u \ z))
    ]]></literal>
    <justification jstring="[para(15554(a,1),17517(a,2,2))].">
      <j1 rule="para" parents="15554 17517"/>
    </justification>
  </clause>

  <clause id="17665">
    <literal><![CDATA[
      (x \ T(L(y,z,u),y * K(w,v5))) * K(y,K(w,v5)) = x \ L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(126,a,17523,a(flip),b,13257,a)].">
      <j1 rule="hyper" parents="126 17523 13257"/>
    </justification>
  </clause>

  <clause id="17666">
    <literal><![CDATA[
      L(x,y,T(T(z,K(u,w)),v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,y,T(z,v5)) = v6
    ]]></literal>
    <justification jstring="[para(23(a,1),17609(a,1,3))].">
      <j1 rule="para" parents="23 17609"/>
    </justification>
  </clause>

  <clause id="17667">
    <literal><![CDATA[
      L(x,y,z * K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,K(u,w) * z) = v5
    ]]></literal>
    <justification jstring="[para(6019(a,1),17609(a,1,3))].">
      <j1 rule="para" parents="6019 17609"/>
    </justification>
  </clause>

  <clause id="17668">
    <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(6035(a,1),17609(a,1,3))].">
      <j1 rule="para" parents="6035 17609"/>
    </justification>
  </clause>

  <clause id="17670">
    <literal><![CDATA[
      K(L(x,y,z) * K(u,x),w) = K(L(x,y,z),T(w,u))
    ]]></literal>
    <justification jstring="[para(14180(a,1),17627(a,1,1,2))].">
      <j1 rule="para" parents="14180 17627"/>
    </justification>
  </clause>

  <clause id="17671">
    <literal><![CDATA[
      a(K(x,y),z,u) \ (w * a(u,z,K(y,x))) = w
    ]]></literal>
    <justification jstring="[hyper(13940,a,17579,a),flip(a)].">
      <j1 rule="hyper" parents="13940 17579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17672">
    <literal><![CDATA[
      (x \ y) * a(z,u,K(w,x)) = L(x,u,K(w,z)) \ y
    ]]></literal>
    <justification jstring="[hyper(14540,a,17584,a),flip(a)].">
      <j1 rule="hyper" parents="14540 17584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17673">
    <literal><![CDATA[
      a(x,y,K(z,u)) * w = w * a(z,y,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(333,a,13742,a,b,17584,a),flip(a)].">
      <j1 rule="hyper" parents="333 13742 17584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17674">
    <literal><![CDATA[
      x / a(y,z,K(u,w)) = a(w,z,K(u,y)) * x
    ]]></literal>
    <justification jstring="[hyper(333,a,13740,a,b,17584,a)].">
      <j1 rule="hyper" parents="333 13740 17584"/>
    </justification>
  </clause>

  <clause id="17675">
    <literal><![CDATA[
      (a(x,y,K(z,u)) * w) * a(u,y,K(z,x)) = w
    ]]></literal>
    <justification jstring="[hyper(125,a,17584,a,b,13740,a)].">
      <j1 rule="hyper" parents="125 17584 13740"/>
    </justification>
  </clause>

  <clause id="17677">
    <literal><![CDATA[
      x \ (L(y,a(z,u,K(w,v5)),x) * (x * a(z,u,K(w,v5)))) = T(y,x * a(z,u,K(w,v5))) * a(z,u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,665,a,b,17584,a)].">
      <j1 rule="hyper" parents="63 665 17584"/>
    </justification>
  </clause>

  <clause id="17678">
    <literal><![CDATA[
      K(x,a(y,z,u)) * w = w * a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[para(13732(a,1),17584(a,1,1))].">
      <j1 rule="para" parents="13732 17584"/>
    </justification>
  </clause>

  <clause id="17679">
    <literal><![CDATA[
      a(x,y,K(z,u)) * u != w
    ]]></literal>
    <literal><![CDATA[
      T(u,a(z,y,x)) = w
    ]]></literal>
    <justification jstring="[para(17584(a,2),13773(a,1))].">
      <j1 rule="para" parents="17584 13773"/>
    </justification>
  </clause>

  <clause id="17680">
    <literal><![CDATA[
      (x \ y) * a(z,u,K(w,x)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,u,K(w,z)) \ y = v5
    ]]></literal>
    <justification jstring="[para(17584(a,1),14540(a,1))].">
      <j1 rule="para" parents="17584 14540"/>
    </justification>
  </clause>

  <clause id="17681">
    <literal><![CDATA[
      x * L(y,K(z,u),K(u,z) * x) = (x * K(u,z)) * (K(z,u) * y)
    ]]></literal>
    <justification jstring="[para(17596(a,2),6036(a,1,2))].">
      <j1 rule="para" parents="17596 6036"/>
    </justification>
  </clause>

  <clause id="17682">
    <literal><![CDATA[
      T(x,(K(a(y,z,u),w) * v5) * a(y,z,u)) = T(x,T(a(y,z,u),w) * v5)
    ]]></literal>
    <justification jstring="[para(4241(a,1),17598(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4241 17598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17683">
    <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(17598(a,1),16812(a,1,2,1,2))].">
      <j1 rule="para" parents="17598 16812"/>
    </justification>
  </clause>

  <clause id="17684">
    <literal><![CDATA[
      L(x,y,z \ K(z,z \ u)) = L(x,y,K(u,z \ 1) / z)
    ]]></literal>
    <justification jstring="[hyper(63,a,14441,a,b,17607,a),flip(a)].">
      <j1 rule="hyper" parents="63 14441 17607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17686">
    <literal><![CDATA[
      L(x,y,(x * y) \ (y * (x * z))) = L(x,y,L(z,x,y))
    ]]></literal>
    <justification jstring="[para(18(a,2),17608(a,1,3)),flip(a)].">
      <j1 rule="para" parents="18 17608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17687">
    <literal><![CDATA[
      x / L(y,z,(y * z) \ x) = (x / (z * y)) * z
    ]]></literal>
    <justification jstring="[para(17608(a,1),13622(a,1,2))].">
      <j1 rule="para" parents="17608 13622"/>
    </justification>
  </clause>

  <clause id="17688">
    <literal><![CDATA[
      K(x,T(y,(z * u) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u \ (z \ w))) = v5
    ]]></literal>
    <justification jstring="[para(311(a,1),17639(a,1,2,2))].">
      <j1 rule="para" parents="311 17639"/>
    </justification>
  </clause>

  <clause id="17689">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(u \ w,y)) = K(x,L(y,z,w / u))
    ]]></literal>
    <justification jstring="[hyper(333,a,13764,a,b,17644,a)].">
      <j1 rule="hyper" parents="333 13764 17644"/>
    </justification>
  </clause>

  <clause id="17690">
    <literal><![CDATA[
      a(x,y,K(z,T(u,w))) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,17649,a(flip),b,17663,a),flip(a)].">
      <j1 rule="hyper" parents="63 17649 17663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17691">
    <literal><![CDATA[
      a(T(x,y),z,K(u,w)) = a(u,z,K(w,x))
    ]]></literal>
    <justification jstring="[hyper(13837,a,17690,a)].">
      <j1 rule="hyper" parents="13837 17690"/>
    </justification>
  </clause>

  <clause id="17692">
    <literal><![CDATA[
      a(x,y,K(z,T(u,w))) = a(z,y,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(333,a,13731,a,b,17690,a),flip(a)].">
      <j1 rule="hyper" parents="333 13731 17690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17693">
    <literal><![CDATA[
      a(x,y,K(z,u / w)) = a(x,y,K(z,w \ u))
    ]]></literal>
    <justification jstring="[para(113(a,1),17690(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="113 17690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17694">
    <literal><![CDATA[
      a(x,y,K(z / u,w)) = a(x,y,K(u \ z,w))
    ]]></literal>
    <justification jstring="[para(6382(a,1),17690(a,1,3)),flip(a)].">
      <j1 rule="para" parents="6382 17690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17695">
    <literal><![CDATA[
      a(x,y,K(z * u,w)) = a(x,y,K(u * z,w))
    ]]></literal>
    <justification jstring="[para(12201(a,1),17690(a,1,3))].">
      <j1 rule="para" parents="12201 17690"/>
    </justification>
  </clause>

  <clause id="17697">
    <literal><![CDATA[
      L(x,y,K(z,T(u,w))) = a(x,y,K(z,u)) * x
    ]]></literal>
    <justification jstring="[para(17690(a,1),14479(a,1,1)),flip(a)].">
      <j1 rule="para" parents="17690 14479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17698">
    <literal><![CDATA[
      a(T(x,y),z,K(u,w)) = a(x,z,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(333,a,13731,a(flip),b,17691,a),flip(a)].">
      <j1 rule="hyper" parents="333 13731 17691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17699">
    <literal><![CDATA[
      a(x * y,z,K(u,w)) = a(u,z,K(w,y * x))
    ]]></literal>
    <justification jstring="[hyper(63,a,11943,a(flip),b,17691,a)].">
      <j1 rule="hyper" parents="63 11943 17691"/>
    </justification>
  </clause>

  <clause id="17700">
    <literal><![CDATA[
      T(x,a(y,z,T(u,w))) = x * a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(126,a,17692,a(flip),b,13178,a),flip(a)].">
      <j1 rule="hyper" parents="126 17692 13178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17703">
    <literal><![CDATA[
      a(x * y,z,K(u,w)) = a(w,z,K(y * x,u))
    ]]></literal>
    <justification jstring="[para(12201(a,1),17692(a,1,3)),flip(a)].">
      <j1 rule="para" parents="12201 17692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17707">
    <literal><![CDATA[
      K(L(x,y,z) * u,x * u) = a(x,y,K(z,x * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,14147,a(flip),b,17698,a)].">
      <j1 rule="hyper" parents="63 14147 17698"/>
    </justification>
  </clause>

  <clause id="17708">
    <literal><![CDATA[
      a(x / y,z,K(u,w)) = a(y \ x,z,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,11952,a(flip),b,17698,a),flip(a)].">
      <j1 rule="hyper" parents="63 11952 17698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17709">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(K(u,z),y,x) = w
    ]]></literal>
    <justification jstring="[para(17671(a,1),144(a,1)),flip(a),flip(b)].">
      <j1 rule="para" parents="17671 144"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17710">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(K(x,u),y,z) = w
    ]]></literal>
    <justification jstring="[para(13731(a,1),17709(a,1))].">
      <j1 rule="para" parents="13731 17709"/>
    </justification>
  </clause>

  <clause id="17711">
    <literal><![CDATA[
      L(x,y,z) * a(u,w,K(x,z)) = L(T(x,a(u,w,z)),y,z)
    ]]></literal>
    <justification jstring="[hyper(14080,a,17673,a),flip(a)].">
      <j1 rule="hyper" parents="14080 17673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17712">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (w * K(x,u)) = w * L(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,9737,a(flip),b,17673,a),flip(a)].">
      <j1 rule="hyper" parents="333 9737 17673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17713">
    <literal><![CDATA[
      (x * y) * a(z,u,K(x,w)) = T(x,a(z,u,w)) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,13834,a(flip),b,17673,a),flip(a)].">
      <j1 rule="hyper" parents="63 13834 17673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17714">
    <literal><![CDATA[
      (L(x,y,z) * (u / L(x,y,z))) / K(x,L(x,y,z) \ u) = a(x,y,K(z,u)) * u
    ]]></literal>
    <justification jstring="[hyper(63,a,14675,a,b,17674,a)].">
      <j1 rule="hyper" parents="63 14675 17674"/>
    </justification>
  </clause>

  <clause id="17716">
    <literal><![CDATA[
      (x / y) * a(x,z,K(u,w)) = T(x,a(w,z,u)) / y
    ]]></literal>
    <justification jstring="[hyper(13389,a,17678,a),flip(a)].">
      <j1 rule="hyper" parents="13389 17678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17717">
    <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(17693(a,1),14073(a,1,1))].">
      <j1 rule="para" parents="17693 14073"/>
    </justification>
  </clause>

  <clause id="17718">
    <literal><![CDATA[
      a(x,y,K(z,y \ u)) \ K(z,(y * x) / u) = K(z,y / (u / x))
    ]]></literal>
    <justification jstring="[para(17693(a,1),14218(a,1,1))].">
      <j1 rule="para" parents="17693 14218"/>
    </justification>
  </clause>

  <clause id="17719">
    <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(17693(a,1),13930(a,1,2))].">
      <j1 rule="para" parents="17693 13930"/>
    </justification>
  </clause>

  <clause id="17720">
    <literal><![CDATA[
      a(x,y,K(z,x \ (u * (x / w)))) = a(z,y,K(w \ u,x))
    ]]></literal>
    <justification jstring="[hyper(15072,a,17694,a)].">
      <j1 rule="hyper" parents="15072 17694"/>
    </justification>
  </clause>

  <clause id="17721">
    <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(17694(a,1),13797(a,1,2))].">
      <j1 rule="para" parents="17694 13797"/>
    </justification>
  </clause>

  <clause id="17722">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(u \ w,y)) = K(x,L(y,z,w / (y * u)))
    ]]></literal>
    <justification jstring="[para(17694(a,1),14179(a,1,2))].">
      <j1 rule="para" parents="17694 14179"/>
    </justification>
  </clause>

  <clause id="17723">
    <literal><![CDATA[
      a(x,y,K((z / (u / w)) * K(w,z),v5)) = a(x,y,K(z / (u / T(w,z)),v5))
    ]]></literal>
    <justification jstring="[para(13449(a,1),17695(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="13449 17695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17724">
    <literal><![CDATA[
      L(x,y,K(z,T(u,w))) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(333,a,14479,a(flip),b,17697,a),flip(a)].">
      <j1 rule="hyper" parents="333 14479 17697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17725">
    <literal><![CDATA[
      L(x,y,K(z,T(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,K(z,u)) = v5
    ]]></literal>
    <justification jstring="[para(17697(a,2),14505(a,1))].">
      <j1 rule="para" parents="17697 14505"/>
    </justification>
  </clause>

  <clause id="17726">
    <literal><![CDATA[
      T(x,a(T(y,z),u,w)) = L(x,u,K(w,y))
    ]]></literal>
    <justification jstring="[hyper(14477,a,17724,a)].">
      <j1 rule="hyper" parents="14477 17724"/>
    </justification>
  </clause>

  <clause id="17727">
    <literal><![CDATA[
      T(x,a(T(y,z),u,w)) = T(x,a(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(333,a,14461,a(flip),b,17726,a),flip(a)].">
      <j1 rule="hyper" parents="333 14461 17726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17728">
    <literal><![CDATA[
      T(x,a(y / z,u,w)) = T(x,a(z \ y,u,w))
    ]]></literal>
    <justification jstring="[para(113(a,1),17727(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="113 17727"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17729">
    <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(17699(a,1),13803(a,1))].">
      <j1 rule="para" parents="17699 13803"/>
    </justification>
  </clause>

  <clause id="17730">
    <literal><![CDATA[
      T(x,a(y,z,T(u,w))) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(333,a,13741,a(flip),b,17700,a),flip(a)].">
      <j1 rule="hyper" parents="333 13741 17700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17731">
    <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(17700(a,2),13774(a,1))].">
      <j1 rule="para" parents="17700 13774"/>
    </justification>
  </clause>

  <clause id="17732">
    <literal><![CDATA[
      T(x,a(y,T(z,u),u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(7679(a,1),17730(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7679 17730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17733">
    <literal><![CDATA[
      T(x,a(y,z * u,u)) = T(x,a(y,u * z,u))
    ]]></literal>
    <justification jstring="[para(13018(a,1),17732(a,1,2))].">
      <j1 rule="para" parents="13018 17732"/>
    </justification>
  </clause>

  <clause id="17734">
    <literal><![CDATA[
      a(K(x,y),z,u \ w) = a(w / u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(333,a,13737,a,b,17708,a)].">
      <j1 rule="hyper" parents="333 13737 17708"/>
    </justification>
  </clause>

  <clause id="17735">
    <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(17708(a,1),13192(a,1,2))].">
      <j1 rule="para" parents="17708 13192"/>
    </justification>
  </clause>

  <clause id="17736">
    <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(17708(a,1),14425(a,1,2))].">
      <j1 rule="para" parents="17708 14425"/>
    </justification>
  </clause>

  <clause id="17737">
    <literal><![CDATA[
      T(T(x,x * y),a(x \ (x * (x * y)),z,u)) = T(T(x,x * y),a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,13944,a(flip),b,17728,a),flip(a)].">
      <j1 rule="hyper" parents="63 13944 17728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17738">
    <literal><![CDATA[
      T(x,a(y,z * u,u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(333,a,14000,a(flip),b,17733,a),flip(a)].">
      <j1 rule="hyper" parents="333 14000 17733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17739">
    <literal><![CDATA[
      L(x,y * z,K(z,u)) = T(x,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(14528,a,17738,a)].">
      <j1 rule="hyper" parents="14528 17738"/>
    </justification>
  </clause>

  <clause id="17740">
    <literal><![CDATA[
      L(x,y * z,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(17739(a,2),14528(a,1))].">
      <j1 rule="para" parents="17739 14528"/>
    </justification>
  </clause>

  <clause id="17742">
    <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(17734(a,1),13839(a,1))].">
      <j1 rule="para" parents="17734 13839"/>
    </justification>
  </clause>

  <clause id="17743">
    <literal><![CDATA[
      T(x,K(y,z / (u * w))) = T(x,K(y,u \ (z / w)))
    ]]></literal>
    <justification jstring="[para(13882(a,1),17616(a,1,2))].">
      <j1 rule="para" parents="13882 17616"/>
    </justification>
  </clause>

  <clause id="17744">
    <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(11824(a,1),17657(a,1,2))].">
      <j1 rule="para" parents="11824 17657"/>
    </justification>
  </clause>

  <clause id="17745">
    <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(10865(a,2),17658(a,1))].">
      <j1 rule="para" parents="10865 17658"/>
    </justification>
  </clause>

  <clause id="17746">
    <literal><![CDATA[
      K(x,(L(K(y,z),u,w) \ v5) \ v6) = K(x,v5 \ (L(K(y,z),u,w) * v6))
    ]]></literal>
    <justification jstring="[hyper(17662,a,10876,a)].">
      <j1 rule="hyper" parents="17662 10876"/>
    </justification>
  </clause>

  <clause id="17747">
    <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(11159(a,1),17679(a,1,1))].">
      <j1 rule="para" parents="11159 17679"/>
    </justification>
  </clause>

  <clause id="17748">
    <literal><![CDATA[
      L(x,y,K(z,u / w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,K(z,w \ u)) = v5
    ]]></literal>
    <justification jstring="[para(6902(a,1),17725(a,1,3))].">
      <j1 rule="para" parents="6902 17725"/>
    </justification>
  </clause>

  <clause id="17749">
    <literal><![CDATA[
      L(a(x,y,z),y * z,K(x,y)) = a(x,y,K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(17740,a,14741,a)].">
      <j1 rule="hyper" parents="17740 14741"/>
    </justification>
  </clause>

  <clause id="17750">
    <literal><![CDATA[
      (x * T(y,T(z,x))) \ (K(y,z) * u) = L((x * y) \ u,x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(17740,a,7716,a),flip(a)].">
      <j1 rule="hyper" parents="17740 7716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17751">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * w) = u * (w * K(x,K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(15484,a,17519,a)].">
      <j1 rule="hyper" parents="15484 17519"/>
    </justification>
  </clause>

  <clause id="17752">
    <literal><![CDATA[
      L(K(K(x,y),z) * ((u * w) \ v5),K(z,K(x,y)),u * w) = (u * (w * K(z,K(x,y)))) \ v5
    ]]></literal>
    <justification jstring="[para(17519(a,1),4591(a,2,1))].">
      <j1 rule="para" parents="17519 4591"/>
    </justification>
  </clause>

  <clause id="17753">
    <literal><![CDATA[
      T(x,y * (T(z,(u * w) \ K(v5,K(v6,v7))) * v8)) = T(x,y * (T(z,u * (w * K(v5,K(v6,v7)))) * v8))
    ]]></literal>
    <justification jstring="[para(17519(a,1),16938(a,2,2,2,1,2))].">
      <j1 rule="para" parents="17519 16938"/>
    </justification>
  </clause>

  <clause id="17755">
    <literal><![CDATA[
      x \ (y * K(z,K(u,w))) = K(z,K(u,w)) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(333,a,15475,a,b,17527,a),flip(a)].">
      <j1 rule="hyper" parents="333 15475 17527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17756">
    <literal><![CDATA[
      (x \ (y * z)) * K(z,K(u,w)) = x \ (y * T(z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(5984(a,1),17527(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5984 17527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17757">
    <literal><![CDATA[
      (x \ (y * z)) * K(y,K(u,w)) = x \ (T(y,K(u,w)) * z)
    ]]></literal>
    <justification jstring="[para(15478(a,1),17527(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15478 17527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17758">
    <literal><![CDATA[
      x \ T(K(y,K(z,u)) * w,v5) = (x \ T(w,v5)) * K(y,K(z,u))
    ]]></literal>
    <justification jstring="[para(15559(a,2),17527(a,1,2))].">
      <j1 rule="para" parents="15559 17527"/>
    </justification>
  </clause>

  <clause id="17759">
    <literal><![CDATA[
      x \ (y * (z * K(u,K(w,v5)))) = (x \ (y * z)) * K(u,K(w,v5))
    ]]></literal>
    <justification jstring="[para(17519(a,1),17527(a,1,2))].">
      <j1 rule="para" parents="17519 17527"/>
    </justification>
  </clause>

  <clause id="17760">
    <literal><![CDATA[
      K(x,(K(y,z) \ u) \ w) = K(x,u \ (K(z,y) \ w))
    ]]></literal>
    <justification jstring="[para(4567(a,2),17542(a,2,2,2))].">
      <j1 rule="para" parents="4567 17542"/>
    </justification>
  </clause>

  <clause id="17761">
    <literal><![CDATA[
      K(x,(y * z) \ (K(u,y) * w)) = K(x,(T(y,u) * z) \ w)
    ]]></literal>
    <justification jstring="[para(4598(a,1),17542(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4598 17542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17762">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,w) = K(x \ (K(z,y) * u),w)
    ]]></literal>
    <justification jstring="[hyper(16392,a,17543,a)].">
      <j1 rule="hyper" parents="16392 17543"/>
    </justification>
  </clause>

  <clause id="17764">
    <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(17543(a,1),16392(a,1))].">
      <j1 rule="para" parents="17543 16392"/>
    </justification>
  </clause>

  <clause id="17765">
    <literal><![CDATA[
      ((K(x,y) * (z * K(u,w))) * v5) / (K(u,w) * v5) = R(K(x,y) * z,K(u,w),v5)
    ]]></literal>
    <justification jstring="[para(17545(a,1),20(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="17545 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17769">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ w) = K(x,u \ (w * K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(333,a,16341,a(flip),b,17560,a),flip(a)].">
      <j1 rule="hyper" parents="333 16341 17560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17770">
    <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(17560(a,2),16441(a,1))].">
      <j1 rule="para" parents="17560 16441"/>
    </justification>
  </clause>

  <clause id="17771">
    <literal><![CDATA[
      K(x,(K(y,z) * u) / w) = K(x,u / (w * K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(16368,a,17564,a)].">
      <j1 rule="hyper" parents="16368 17564"/>
    </justification>
  </clause>

  <clause id="17772">
    <literal><![CDATA[
      K(x,(y / (z * K(u,w))) \ 1) = K(x,z / (y * K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(5066,a,17564,a)].">
      <j1 rule="hyper" parents="5066 17564"/>
    </justification>
  </clause>

  <clause id="17773">
    <literal><![CDATA[
      K(x,(y * K(z,u)) / w) = K(x,y * (w \ K(z,u)))
    ]]></literal>
    <justification jstring="[hyper(333,a,16463,a(flip),b,17564,a),flip(a)].">
      <j1 rule="hyper" parents="333 16463 17564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17774">
    <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(17564(a,2),16465(a,1))].">
      <j1 rule="para" parents="17564 16465"/>
    </justification>
  </clause>

  <clause id="17775">
    <literal><![CDATA[
      L(x,y,K(z,u)) \ (K(u,z) \ (y * x)) = T(K(u,z) \ y,x)
    ]]></literal>
    <justification jstring="[para(5159(a,1),17570(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5159 17570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17776">
    <literal><![CDATA[
      (K(x,K(y,z)) \ u) \ (K(x,K(y,z)) \ w) = u \ w
    ]]></literal>
    <justification jstring="[para(10(a,1),17589(a,2,2))].">
      <j1 rule="para" parents="10 17589"/>
    </justification>
  </clause>

  <clause id="17777">
    <literal><![CDATA[
      (K(x,K(y,z)) \ u) \ w = u \ (K(x,K(y,z)) \ w)
    ]]></literal>
    <justification jstring="[para(6829(a,2),17589(a,2,2))].">
      <j1 rule="para" parents="6829 17589"/>
    </justification>
  </clause>

  <clause id="17778">
    <literal><![CDATA[
      K(x,K(y,z)) * (T(x,y) / u) = T(x,T(y,z)) / u
    ]]></literal>
    <justification jstring="[para(6728(a,1),17591(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6728 17591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17779">
    <literal><![CDATA[
      (K(x,K(y,z)) \ u) / w = K(x,K(y,z)) * (u / w)
    ]]></literal>
    <justification jstring="[para(6829(a,2),17591(a,1,1))].">
      <j1 rule="para" parents="6829 17591"/>
    </justification>
  </clause>

  <clause id="17780">
    <literal><![CDATA[
      K(x,K(y,z)) \ (u * w) = (K(y,K(x,z)) \ u) * w
    ]]></literal>
    <justification jstring="[para(6785(a,1),17593(a,1,1))].">
      <j1 rule="para" parents="6785 17593"/>
    </justification>
  </clause>

  <clause id="17782">
    <literal><![CDATA[
      (x * K(y,K(z,u))) / w = (x / w) * K(y,K(z,u))
    ]]></literal>
    <justification jstring="[para(15475(a,1),17597(a,1,1))].">
      <j1 rule="para" parents="15475 17597"/>
    </justification>
  </clause>

  <clause id="17783">
    <literal><![CDATA[
      T(T(x,(y \ z) \ u),K(w,z \ (y * u))) = T(x,T((y \ z) \ u,w))
    ]]></literal>
    <justification jstring="[hyper(6883,a,17619,a),flip(a)].">
      <j1 rule="hyper" parents="6883 17619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17784">
    <literal><![CDATA[
      K(x,T(T((y * K(z,u)) / w,K(y,v5)),K(z,u) \ (y \ w))) = K(x,(y * K(z,u)) / T(w,K(y,v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,17244,a(flip),b,17628,a),flip(a)].">
      <j1 rule="hyper" parents="63 17244 17628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17785">
    <literal><![CDATA[
      K(x,T(y,z / (u * w))) = K(x,T(y,u \ (z / w)))
    ]]></literal>
    <justification jstring="[hyper(15606,a,17632,a),flip(a)].">
      <j1 rule="hyper" parents="15606 17632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17786">
    <literal><![CDATA[
      K(x,L(y,z * u,(w * u) \ w)) = K(x,L(y,z,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,14132,a,b,17660,a)].">
      <j1 rule="hyper" parents="63 14132 17660"/>
    </justification>
  </clause>

  <clause id="17787">
    <literal><![CDATA[
      K(x,L((y * z) / u,y,z \ 1)) = K(x,((y * z) * (z \ 1)) / (u * (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(63,a,13869,a(flip),b,17660,a),flip(a)].">
      <j1 rule="hyper" parents="63 13869 17660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17788">
    <literal><![CDATA[
      K(L(x,y,z) * K(u,x),w) = K(x,L(T(w,u),y,z))
    ]]></literal>
    <justification jstring="[hyper(333,a,10898,a(flip),b,17670,a),flip(a)].">
      <j1 rule="hyper" parents="333 10898 17670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17789">
    <literal><![CDATA[
      L(x,y,K(z,u)) \ R(x,y,z) = (u * (x \ R(x,y,z))) / u
    ]]></literal>
    <justification jstring="[hyper(63,a,13815,a,b,17672,a),flip(a)].">
      <j1 rule="hyper" parents="63 13815 17672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17790">
    <literal><![CDATA[
      (x \ y) * a(z,u,K(w,x)) = T(x,a(z,u,w)) \ y
    ]]></literal>
    <justification jstring="[para(14461(a,1),17672(a,2,1))].">
      <j1 rule="para" parents="14461 17672"/>
    </justification>
  </clause>

  <clause id="17792">
    <literal><![CDATA[
      K(L(x,y,z) * u,x * u) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(333,a,13802,a(flip),b,17707,a),flip(a)].">
      <j1 rule="hyper" parents="333 13802 17707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17793">
    <literal><![CDATA[
      (x / y) * a(x,z,K(u,w)) = L(x,z,K(u,w)) / y
    ]]></literal>
    <justification jstring="[para(14461(a,2),17716(a,2,1))].">
      <j1 rule="para" parents="14461 17716"/>
    </justification>
  </clause>

  <clause id="17794">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * w) = u * (K(x,K(y,z)) * w)
    ]]></literal>
    <justification jstring="[para(15475(a,2),17751(a,2,2))].">
      <j1 rule="para" parents="15475 17751"/>
    </justification>
  </clause>

  <clause id="17795">
    <literal><![CDATA[
      (x * (y * K(z,K(u,w)))) / v5 = K(z,K(u,w)) * ((x * y) / v5)
    ]]></literal>
    <justification jstring="[para(17751(a,1),17591(a,1,1))].">
      <j1 rule="para" parents="17751 17591"/>
    </justification>
  </clause>

  <clause id="17796">
    <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(18(a,2),17755(a,2,2))].">
      <j1 rule="para" parents="18 17755"/>
    </justification>
  </clause>

  <clause id="17797">
    <literal><![CDATA[
      K(x,K(y,z)) * (u \ K(y,z)) = u \ K(y,T(z,x))
    ]]></literal>
    <justification jstring="[para(6842(a,1),17755(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6842 17755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17798">
    <literal><![CDATA[
      K(x,K(y,z)) * (u \ (w \ 1)) = u \ (w \ K(x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(13126(a,1),17755(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13126 17755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17799">
    <literal><![CDATA[
      x \ T(K(y,K(z,u)) * w,v5) = K(y,K(z,u)) * (x \ T(w,v5))
    ]]></literal>
    <justification jstring="[para(15559(a,2),17755(a,1,2))].">
      <j1 rule="para" parents="15559 17755"/>
    </justification>
  </clause>

  <clause id="17800">
    <literal><![CDATA[
      x \ T(y * K(z,K(u,w)),v5) = K(z,K(u,w)) * (x \ T(y,v5))
    ]]></literal>
    <justification jstring="[para(15831(a,2),17755(a,1,2))].">
      <j1 rule="para" parents="15831 17755"/>
    </justification>
  </clause>

  <clause id="17801">
    <literal><![CDATA[
      K(x,(K(y,z) * ((K(u,w) \ v5) / K(y,z))) \ v6) = K(x,v5 \ (K(w,u) \ v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,16335,a,b,17760,a)].">
      <j1 rule="hyper" parents="63 16335 17760"/>
    </justification>
  </clause>

  <clause id="17802">
    <literal><![CDATA[
      K(x,(T(y,z) \ u) \ (K(y,z) \ w)) = K(x,(y \ u) \ w)
    ]]></literal>
    <justification jstring="[para(4548(a,1),17760(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4548 17760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17803">
    <literal><![CDATA[
      K(x,(y / z) \ (K(((z \ 1) / (y / z)) \ 1,u) \ w)) = K(x,(T(y,u) / z) \ w)
    ]]></literal>
    <justification jstring="[para(5218(a,1),17760(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5218 17760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17804">
    <literal><![CDATA[
      K(x,y \ (K(y / x,z) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(x \ y,z) \ (x \ u)) = w
    ]]></literal>
    <justification jstring="[para(17760(a,1),9704(a,1))].">
      <j1 rule="para" parents="17760 9704"/>
    </justification>
  </clause>

  <clause id="17805">
    <literal><![CDATA[
      K(x,(L(K(y,z),u,w) \ v5) \ v6) = K(x,v5 \ (K(L(z,u,w),y) \ v6))
    ]]></literal>
    <justification jstring="[para(10851(a,2),17760(a,1,2,1,1))].">
      <j1 rule="para" parents="10851 17760"/>
    </justification>
  </clause>

  <clause id="17806">
    <literal><![CDATA[
      K((x * y) / (K(z,u) * y),w) = K(y \ (K(u,z) * (y * x)),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,16018,a,b,17762,a)].">
      <j1 rule="hyper" parents="63 16018 17762"/>
    </justification>
  </clause>

  <clause id="17807">
    <literal><![CDATA[
      K(x \ (K(y,z) * u),w) = K((x \ K(y,z)) * u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,16478,a(flip),b,17762,a),flip(a)].">
      <j1 rule="hyper" parents="63 16478 17762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17808">
    <literal><![CDATA[
      K(x \ ((K(y,z) * L(K(y,u) \ 1,w,v5)) * v6),v7) = K((x * K(z,y)) \ (L(K(u,y),w,v5) * v6),v7)
    ]]></literal>
    <justification jstring="[para(8458(a,2),17762(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="8458 17762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17809">
    <literal><![CDATA[
      K(x,(y * K(z,u)) \ w) = K(x,y \ (w * K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,16334,a(flip),b,17769,a)].">
      <j1 rule="hyper" parents="63 16334 17769"/>
    </justification>
  </clause>

  <clause id="17810">
    <literal><![CDATA[
      K(x,(K(y,z) * u) / w) = K(x,u * (w \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(333,a,16463,a(flip),b,17771,a),flip(a)].">
      <j1 rule="hyper" parents="333 16463 17771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17811">
    <literal><![CDATA[
      K(x,y / (z * K(u,L(w,v5 / w,v6)))) = K(x,(L(K(w,u),v5,v6) * y) / z)
    ]]></literal>
    <justification jstring="[para(6297(a,1),17771(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="6297 17771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17812">
    <literal><![CDATA[
      K(x,(K(y,z) * u) / w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,u * (w \ K(y,z))) = v5
    ]]></literal>
    <justification jstring="[para(17771(a,2),16465(a,1))].">
      <j1 rule="para" parents="17771 16465"/>
    </justification>
  </clause>

  <clause id="17813">
    <literal><![CDATA[
      T(x,(y * K(z,u)) / w) = T(x,y * (w \ K(z,u)))
    ]]></literal>
    <justification jstring="[hyper(124,a,17773,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 17773 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17814">
    <literal><![CDATA[
      K(x,T(y,z) * (u \ K(w,y))) = K(x,T(T(y,w),z) / u)
    ]]></literal>
    <justification jstring="[hyper(63,a,16507,a(flip),b,17773,a),flip(a)].">
      <j1 rule="hyper" parents="63 16507 17773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17815">
    <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(63,a,10974,a(flip),b,17773,a),flip(a)].">
      <j1 rule="hyper" parents="63 10974 17773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17816">
    <literal><![CDATA[
      K(x,T(y / (z \ u),x) * (w \ K(z \ u,z))) = K(x,(y / (u / z)) / w)
    ]]></literal>
    <justification jstring="[hyper(63,a,9684,a(flip),b,17773,a),flip(a)].">
      <j1 rule="hyper" parents="63 9684 17773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17817">
    <literal><![CDATA[
      K(x,(y / z) * (u \ K(w,z))) = K(x,(y / T(z,w)) / u)
    ]]></literal>
    <justification jstring="[para(5450(a,1),17773(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5450 17773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17818">
    <literal><![CDATA[
      K(x,(y / z) * (u \ K(w,T(z,v5)))) = K(x,(y / T(z,T(w,v5))) / u)
    ]]></literal>
    <justification jstring="[para(6426(a,1),17773(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6426 17773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17819">
    <literal><![CDATA[
      (T(x,y) / z) \ K(x,K(y,u)) = (T(x,T(y,u)) / z) \ 1
    ]]></literal>
    <justification jstring="[para(17778(a,1),13270(a,1,1)),flip(a)].">
      <j1 rule="para" parents="17778 13270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17820">
    <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(17779(a,2),6833(a,1))].">
      <j1 rule="para" parents="17779 6833"/>
    </justification>
  </clause>

  <clause id="17821">
    <literal><![CDATA[
      K(x,T(y,(z * u) \ w)) = K(x,T(y,z \ (w / u)))
    ]]></literal>
    <justification jstring="[hyper(15606,a,17785,a)].">
      <j1 rule="hyper" parents="15606 17785"/>
    </justification>
  </clause>

  <clause id="17822">
    <literal><![CDATA[
      K(K(x,y) * L(y,z,u),w) = K(y,L(T(w,x),z,u))
    ]]></literal>
    <justification jstring="[hyper(15532,a,17788,a)].">
      <j1 rule="hyper" parents="15532 17788"/>
    </justification>
  </clause>

  <clause id="17823">
    <literal><![CDATA[
      K(L(x,y,z) * K(u \ 1,x),w / (v5 / (u * v5))) = K(x,L((v5 / (u * v5)) \ w,y,z))
    ]]></literal>
    <justification jstring="[para(3763(a,1),17788(a,2,2,1))].">
      <j1 rule="para" parents="3763 17788"/>
    </justification>
  </clause>

  <clause id="17824">
    <literal><![CDATA[
      T(x \ 1,a(y,z,u)) = T(x,a(y,z,u)) \ 1
    ]]></literal>
    <justification jstring="[hyper(13579,a,17790,a)].">
      <j1 rule="hyper" parents="13579 17790"/>
    </justification>
  </clause>

  <clause id="17825">
    <literal><![CDATA[
      K(x,y) / T(z \ 1,a(u,w,v5)) = K(x,y) * T(z,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(197,a,17824,a,b,13266,a)].">
      <j1 rule="hyper" parents="197 17824 13266"/>
    </justification>
  </clause>

  <clause id="17826">
    <literal><![CDATA[
      K(x,K(y,z)) \ (u * w) = u * (K(x,K(y,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(6833,a,17794,a)].">
      <j1 rule="hyper" parents="6833 17794"/>
    </justification>
  </clause>

  <clause id="17828">
    <literal><![CDATA[
      K(x,K(y,z)) \ (u * w) = u * (K(x,K(y,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(121,a,154,a(flip),b,17794,a)].">
      <j1 rule="hyper" parents="121 154 17794"/>
    </justification>
  </clause>

  <clause id="17830">
    <literal><![CDATA[
      K(x * (K(y,K(z,u)) * w),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x * w,v5) = v6
    ]]></literal>
    <justification jstring="[para(17794(a,1),16357(a,1,1))].">
      <j1 rule="para" parents="17794 16357"/>
    </justification>
  </clause>

  <clause id="17831">
    <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(17794(a,1),16489(a,1,2,2))].">
      <j1 rule="para" parents="17794 16489"/>
    </justification>
  </clause>

  <clause id="17832">
    <literal><![CDATA[
      (x \ T(K(y,z),u)) \ K(y,z) = (x \ K(y,z)) \ K(y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,16005,a(flip),b,17797,a)].">
      <j1 rule="hyper" parents="63 16005 17797"/>
    </justification>
  </clause>

  <clause id="17833">
    <literal><![CDATA[
      K(((x \ 1) \ K(y,z)) * u,w) = K(x * (K(y,z) * u),w)
    ]]></literal>
    <justification jstring="[hyper(13425,a,17807,a),flip(a)].">
      <j1 rule="hyper" parents="13425 17807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17834">
    <literal><![CDATA[
      T(x,(K(y,z) * u) / w) = T(x,u * (w \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(124,a,17810,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 17810 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17835">
    <literal><![CDATA[
      K(x,(y / (z \ u)) * (w \ K(z,u))) = K(x,(y / (T(z,u) \ u)) / w)
    ]]></literal>
    <justification jstring="[hyper(63,a,16806,a(flip),b,17810,a),flip(a)].">
      <j1 rule="hyper" parents="63 16806 17810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17836">
    <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(63,a,17175,a(flip),b,17813,a),flip(a)].">
      <j1 rule="hyper" parents="63 17175 17813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17837">
    <literal><![CDATA[
      K(x * K(y,z),T(u,K(y,z) \ (w / x))) = K(K(y,z) * x,T(u,w))
    ]]></literal>
    <justification jstring="[hyper(15657,a,17821,a),flip(a)].">
      <j1 rule="hyper" parents="15657 17821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17838">
    <literal><![CDATA[
      K(x,K(y,z)) \ (u * (w / x)) = u * (w / T(x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(15628(a,1),17826(a,2,2))].">
      <j1 rule="para" parents="15628 17826"/>
    </justification>
  </clause>

  <clause id="17839">
    <literal><![CDATA[
      K(x,K(y,z)) \ (u * (w \ x)) = u * (w \ T(x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(15691(a,1),17828(a,2,2))].">
      <j1 rule="para" parents="15691 17828"/>
    </justification>
  </clause>

  <clause id="17840">
    <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(63,a,16902,a(flip),b,17834,a)].">
      <j1 rule="hyper" parents="63 16902 17834"/>
    </justification>
  </clause>

  <clause id="17841">
    <literal><![CDATA[
      K(x,K(y,(z * u) \ w)) = K(x,K(y,z \ (w / u)))
    ]]></literal>
    <justification jstring="[hyper(16057,a,17664,a)].">
      <j1 rule="hyper" parents="16057 17664"/>
    </justification>
  </clause>

  <clause id="17842">
    <literal><![CDATA[
      K(x,K(y,(z * u) \ w)) = K(x,K(y,z \ (u \ w)))
    ]]></literal>
    <justification jstring="[hyper(333,a,16610,a(flip),b,17841,a),flip(a)].">
      <j1 rule="hyper" parents="333 16610 17841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17843">
    <literal><![CDATA[
      T(x,K(((y \ z) * y) / (u * y),w)) = x * K(x,K(w,y \ (z / u)))
    ]]></literal>
    <justification jstring="[para(17841(a,1),16114(a,2,2))].">
      <j1 rule="para" parents="17841 16114"/>
    </justification>
  </clause>

  <clause id="17845">
    <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(17842(a,1),7620(a,1,1))].">
      <j1 rule="para" parents="17842 7620"/>
    </justification>
  </clause>

  <clause id="17846">
    <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(17842(a,1),12701(a,1,1))].">
      <j1 rule="para" parents="17842 12701"/>
    </justification>
  </clause>

  <clause id="17847">
    <literal><![CDATA[
      L(x,y,L(K(y,x) * z,x,y)) = L(x,y,L(z,x,y))
    ]]></literal>
    <justification jstring="[para(10119(a,1),17686(a,1,3))].">
      <j1 rule="para" parents="10119 17686"/>
    </justification>
  </clause>

  <clause id="17848">
    <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(13821(a,1),17742(a,1))].">
      <j1 rule="para" parents="13821 17742"/>
    </justification>
  </clause>

  <clause id="17849">
    <literal><![CDATA[
      L(a(x,K(y,z),u),x * (K(y,z) * u),K(z,(x * (y \ u)) \ (x * u))) = (x * u) \ (K(z,(x * u) / (x * (y \ u))) * ((x * K(y,z)) * u))
    ]]></literal>
    <justification jstring="[hyper(17748,a,5361,a)].">
      <j1 rule="hyper" parents="17748 5361"/>
    </justification>
  </clause>

  <clause id="17850">
    <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(4963(a,1),17830(a,1,1,2))].">
      <j1 rule="para" parents="4963 17830"/>
    </justification>
  </clause>

  <clause id="17851">
    <literal><![CDATA[
      K(x,y) * (K(z,u) * w) = K(z,u) * (K(x,y) * w)
    ]]></literal>
    <justification jstring="[hyper(16540,a,17546,a)].">
      <j1 rule="hyper" parents="16540 17546"/>
    </justification>
  </clause>

  <clause id="17855">
    <literal><![CDATA[
      K(x,y) * (K(z,u) * (w * K(x,K(y,v5)))) = K(z,u) * (K(x,T(y,v5)) * w)
    ]]></literal>
    <justification jstring="[para(15634(a,1),17851(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15634 17851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17856">
    <literal><![CDATA[
      K(x,T(y,z \ ((u * z) / w))) = K(x,T(y,w \ T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,17821,a(flip),b,17629,a)].">
      <j1 rule="hyper" parents="63 17821 17629"/>
    </justification>
  </clause>

  <clause id="17857">
    <literal><![CDATA[
      T(x,(y \ L(y,z,u)) * w) = T(x,w * (y \ L(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(124,a,17637,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 17637 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17858">
    <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(17637(a,2),15355(a,1))].">
      <j1 rule="para" parents="17637 15355"/>
    </justification>
  </clause>

  <clause id="17859">
    <literal><![CDATA[
      L(x,y,K(z,u \ 1) / u) = L(x,y,u \ K(u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,12765,a(flip),b,17684,a),flip(a)].">
      <j1 rule="hyper" parents="63 12765 17684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17860">
    <literal><![CDATA[
      L(x,y,z \ K(u,z \ 1)) = L(x,y,z \ K(z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,17607,a(flip),b,17859,a)].">
      <j1 rule="hyper" parents="63 17607 17859"/>
    </justification>
  </clause>

  <clause id="17861">
    <literal><![CDATA[
      L(x,y,z \ K(z,y)) = L(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,10092,a(flip),b,17860,a),flip(a)].">
      <j1 rule="hyper" parents="63 10092 17860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17862">
    <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(13724(a,1),17861(a,1,3))].">
      <j1 rule="para" parents="13724 17861"/>
    </justification>
  </clause>

  <clause id="17863">
    <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(17689(a,1),13770(a,1))].">
      <j1 rule="para" parents="17689 13770"/>
    </justification>
  </clause>

  <clause id="17864">
    <literal><![CDATA[
      T(x,a(y \ 1,z,u)) = T(x,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(41,a,14198,a,b,17711,a(flip))].">
      <j1 rule="hyper" parents="41 14198 17711"/>
    </justification>
  </clause>

  <clause id="17865">
    <literal><![CDATA[
      L(K(x,(y / (z * K(u,w))) \ a(u,v5,K(v6,w))),a(u,v5,K(v6,w)),z * K(u,w)) = K(x,T((z * L(K(u,w),v5,v6)) / y,a(u,v5,K(v6,w))))
    ]]></literal>
    <justification jstring="[para(17712(a,1),14306(a,2,2,1,1))].">
      <j1 rule="para" parents="17712 14306"/>
    </justification>
  </clause>

  <clause id="17866">
    <literal><![CDATA[
      a(x,y,K(z * (u / w),u)) = a(x,y,K(w \ z,u))
    ]]></literal>
    <justification jstring="[hyper(13957,a,17720,a)].">
      <j1 rule="hyper" parents="13957 17720"/>
    </justification>
  </clause>

  <clause id="17867">
    <literal><![CDATA[
      a(x,y,K(z * (u \ w),w)) = a(x,y,K(u \ z,w))
    ]]></literal>
    <justification jstring="[para(12901(a,1),17866(a,1,3))].">
      <j1 rule="para" parents="12901 17866"/>
    </justification>
  </clause>

  <clause id="17868">
    <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(17867(a,1),13863(a,2,2))].">
      <j1 rule="para" parents="17867 13863"/>
    </justification>
  </clause>

  <clause id="17869">
    <literal><![CDATA[
      T((x \ (y * z)) / ((K(u,w) * z) / K(u,w)),z) = z \ (x \ (y * T(z,K(u,w))))
    ]]></literal>
    <justification jstring="[hyper(7674,a,17756,a)].">
      <j1 rule="hyper" parents="7674 17756"/>
    </justification>
  </clause>

  <clause id="17870">
    <literal><![CDATA[
      K(x,y \ (z * T(u,K(w,v5)))) = K(x,y \ (z * u))
    ]]></literal>
    <justification jstring="[para(17756(a,1),16328(a,1,2))].">
      <j1 rule="para" parents="17756 16328"/>
    </justification>
  </clause>

  <clause id="17871">
    <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(17756(a,1),16380(a,1,2))].">
      <j1 rule="para" parents="17756 16380"/>
    </justification>
  </clause>

  <clause id="17872">
    <literal><![CDATA[
      K(x,y \ (z * L(T(u,K(w,v5)),v6,v7))) = K(x,y \ (z * L(u,v6,v7)))
    ]]></literal>
    <justification jstring="[para(25(a,2),17870(a,1,2,2,2))].">
      <j1 rule="para" parents="25 17870"/>
    </justification>
  </clause>

  <clause id="17873">
    <literal><![CDATA[
      K(x,y \ (T(z,K(u,w)) * v5)) = K(x,y \ (z * v5))
    ]]></literal>
    <justification jstring="[para(17757(a,1),16328(a,1,2))].">
      <j1 rule="para" parents="17757 16328"/>
    </justification>
  </clause>

  <clause id="17874">
    <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(17757(a,1),16396(a,1,2,2))].">
      <j1 rule="para" parents="17757 16396"/>
    </justification>
  </clause>

  <clause id="17875">
    <literal><![CDATA[
      K(x,y \ (L(T(z,K(u,w)),v5,v6) * v7)) = K(x,y \ (L(z,v5,v6) * v7))
    ]]></literal>
    <justification jstring="[para(25(a,2),17873(a,1,2,2,1))].">
      <j1 rule="para" parents="25 17873"/>
    </justification>
  </clause>

  <clause id="17876">
    <literal><![CDATA[
      K(x,y \ (T(z,T(u,w)) * v5)) = K(x,y \ (T(z,u) * v5))
    ]]></literal>
    <justification jstring="[para(6191(a,1),17873(a,1,2,2,1))].">
      <j1 rule="para" parents="6191 17873"/>
    </justification>
  </clause>

  <clause id="17877">
    <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(63,a,14776,a(flip),b,17786,a)].">
      <j1 rule="hyper" parents="63 14776 17786"/>
    </justification>
  </clause>

  <clause id="17878">
    <literal><![CDATA[
      (T(x,T(y,z)) / z) \ 1 = K(y,x) * ((x / z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(16746,a,17819,a),flip(a)].">
      <j1 rule="hyper" parents="16746 17819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17879">
    <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(17878(a,2),17687(a,1,2,3,1))].">
      <j1 rule="para" parents="17878 17687"/>
    </justification>
  </clause>

  <clause id="17880">
    <literal><![CDATA[
      K((x * K(y,z)) * u,w) = K(x * (K(y,z) * u),w)
    ]]></literal>
    <justification jstring="[hyper(16745,a,17833,a)].">
      <j1 rule="hyper" parents="16745 17833"/>
    </justification>
  </clause>

  <clause id="17881">
    <literal><![CDATA[
      K((K(x,y) * z) * u,w) = K(z * (K(x,y) * u),w)
    ]]></literal>
    <justification jstring="[hyper(16393,a,17880,a)].">
      <j1 rule="hyper" parents="16393 17880"/>
    </justification>
  </clause>

  <clause id="17882">
    <literal><![CDATA[
      K((T(T(x,y),y) \ z) * (K(x,y) * u),w) = K(T(T(x,y) \ z,K(y,x)) * u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,15282,a(flip),b,17880,a),flip(a)].">
      <j1 rule="hyper" parents="63 15282 17880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17883">
    <literal><![CDATA[
      K((x / y) * (K(x,z) * u),w) = K((T(x,z) / y) * u,w)
    ]]></literal>
    <justification jstring="[para(13229(a,1),17881(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="13229 17881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17884">
    <literal><![CDATA[
      T(T(x,K(y,z)) * (u / x),w) = x * (T(u,w) / T(x,K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,15981,a(flip),b,17838,a)].">
      <j1 rule="hyper" parents="63 15981 17838"/>
    </justification>
  </clause>

  <clause id="17885">
    <literal><![CDATA[
      K(x,T(y,z \ ((u * z) / w))) = K(x,T(y,w \ u))
    ]]></literal>
    <justification jstring="[hyper(333,a,16538,a(flip),b,17856,a),flip(a)].">
      <j1 rule="hyper" parents="333 16538 17856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17886">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ (w * z)))) = K(x,T(y,u \ w))
    ]]></literal>
    <justification jstring="[hyper(16578,a,17885,a)].">
      <j1 rule="hyper" parents="16578 17885"/>
    </justification>
  </clause>

  <clause id="17888">
    <literal><![CDATA[
      T(x,y * (z \ L(z,u,u))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,a(u,u,z) \ y) = w
    ]]></literal>
    <justification jstring="[para(17857(a,1),14343(a,1))].">
      <j1 rule="para" parents="17857 14343"/>
    </justification>
  </clause>

  <clause id="17889">
    <literal><![CDATA[
      K(x,(y * T(z,u)) \ (T(y,z) * w)) = K(x,(T(z,u) * y) \ (y * w))
    ]]></literal>
    <justification jstring="[para(10115(a,1),17876(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10115 17876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17890">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (w * x) = w * L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(17574,a,14497,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="17574 14497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17891">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (w * z) = w * L(z,y,K(x,u))
    ]]></literal>
    <justification jstring="[para(16010(a,1),17890(a,1,1))].">
      <j1 rule="para" parents="16010 17890"/>
    </justification>
  </clause>

  <clause id="17892">
    <literal><![CDATA[
      (x \ y) * a(x,z,K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,z,K(w,u)) \ y = v5
    ]]></literal>
    <justification jstring="[para(13731(a,1),17680(a,1,2))].">
      <j1 rule="para" parents="13731 17680"/>
    </justification>
  </clause>

  <clause id="17893">
    <literal><![CDATA[
      T(x * y,a(y,z,u)) = T(x,a(y,z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(17747,a,13834,a)].">
      <j1 rule="hyper" parents="17747 13834"/>
    </justification>
  </clause>

  <clause id="17894">
    <literal><![CDATA[
      T(x * y,a(y,z,u)) = y * T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(333,a,13827,a(flip),b,17893,a),flip(a)].">
      <j1 rule="hyper" parents="333 13827 17893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17895">
    <literal><![CDATA[
      T(K(x,y) * z,a(z,u,w)) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(17538(a,1),17893(a,2,1))].">
      <j1 rule="para" parents="17538 17893"/>
    </justification>
  </clause>

  <clause id="17896">
    <literal><![CDATA[
      L(K(x,y) * z,u,K(w,z)) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(14530,a,17895,a)].">
      <j1 rule="hyper" parents="14530 17895"/>
    </justification>
  </clause>

  <clause id="17897">
    <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(17894(a,2),14987(a,1,2))].">
      <j1 rule="para" parents="17894 14987"/>
    </justification>
  </clause>

  <clause id="17898">
    <literal><![CDATA[
      K(x,T(y * K(z,u),u) / w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u) * (w \ K(z,u))) = v5
    ]]></literal>
    <justification jstring="[para(6647(a,2),17774(a,1,2,1))].">
      <j1 rule="para" parents="6647 17774"/>
    </justification>
  </clause>

  <clause id="17899">
    <literal><![CDATA[
      L(x,y,K(z,u)) \ (K(u,z) \ (y * x)) != w * v5
    ]]></literal>
    <literal><![CDATA[
      w \ T(K(u,z) \ y,x) = v5
    ]]></literal>
    <justification jstring="[para(17775(a,2),827(a,1))].">
      <j1 rule="para" parents="17775 827"/>
    </justification>
  </clause>

  <clause id="17900">
    <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(17850,a,16372,a),flip(a)].">
      <j1 rule="hyper" parents="17850 16372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17901">
    <literal><![CDATA[
      K(x,y \ (z * (K(u,w) * (v5 \ u)))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (z * (v5 \ T(u,w)))) = v6
    ]]></literal>
    <justification jstring="[para(13350(a,1),17871(a,1,2,2,2))].">
      <j1 rule="para" parents="13350 17871"/>
    </justification>
  </clause>

  <clause id="17902">
    <literal><![CDATA[
      T(x,a(y,y,z) \ u) = T(x,u * a(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(17888,a,16846,a)].">
      <j1 rule="hyper" parents="17888 16846"/>
    </justification>
  </clause>

  <clause id="17903">
    <literal><![CDATA[
      T(x,T((K(y,z) \ u) \ w,v5)) = T(x,T(u \ (K(z,y) \ w),v5))
    ]]></literal>
    <justification jstring="[para(4567(a,2),17575(a,1,2,1,1))].">
      <j1 rule="para" parents="4567 17575"/>
    </justification>
  </clause>

  <clause id="17904">
    <literal><![CDATA[
      T(x,K(y,a(z,u,w)) * v5) = v5 \ (x * v5)
    ]]></literal>
    <justification jstring="[para(17583(a,1),17602(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17583 17602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17905">
    <literal><![CDATA[
      T(x,K(y,a(z,u,w)) * v5) = T(x,v5)
    ]]></literal>
    <justification jstring="[hyper(333,a,22,a,b,17904,a),flip(a)].">
      <j1 rule="hyper" parents="333 22 17904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17906">
    <literal><![CDATA[
      T(x,K(y,a(z,u,w)) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,v5) = v6
    ]]></literal>
    <justification jstring="[para(17904(a,2),347(a,1))].">
      <j1 rule="para" parents="17904 347"/>
    </justification>
  </clause>

  <clause id="17908">
    <literal><![CDATA[
      T(x,a(y,z,K(u,w)) * v5) = T(x,v5)
    ]]></literal>
    <justification jstring="[para(13107(a,2),17905(a,1,2,1))].">
      <j1 rule="para" parents="13107 17905"/>
    </justification>
  </clause>

  <clause id="17909">
    <literal><![CDATA[
      T(x,y * a(z,u,K(w,v5))) = T(x,y)
    ]]></literal>
    <justification jstring="[para(17678(a,1),17905(a,1,2))].">
      <j1 rule="para" parents="17678 17905"/>
    </justification>
  </clause>

  <clause id="17910">
    <literal><![CDATA[
      K(a(x,y,K(z,u)) * w,v5) = v5 / T(v5,w)
    ]]></literal>
    <justification jstring="[hyper(197,a,17908,a(flip),b,4233,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="197 17908 4233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17911">
    <literal><![CDATA[
      T(x,L(K(y,z),u,w) * v5) = T(x,K(y,z) * v5)
    ]]></literal>
    <justification jstring="[para(9780(a,1),17908(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9780 17908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17912">
    <literal><![CDATA[
      T(x,(y * z) * K(u,w)) = T(x,y * (z * K(u,w)))
    ]]></literal>
    <justification jstring="[para(13589(a,1),17908(a,1,2))].">
      <j1 rule="para" parents="13589 17908"/>
    </justification>
  </clause>

  <clause id="17913">
    <literal><![CDATA[
      T(x,y * L(z,u,K(w,v5))) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(17890(a,1),17908(a,1,2))].">
      <j1 rule="para" parents="17890 17908"/>
    </justification>
  </clause>

  <clause id="17914">
    <literal><![CDATA[
      K((T(x,y) \ (y * a(z,u,K(w,v5)))) \ 1,v6) = K(((y * a(z,u,K(w,v5))) / x) \ 1,v6)
    ]]></literal>
    <justification jstring="[para(17909(a,1),12972(a,1,1,1,1))].">
      <j1 rule="para" parents="17909 12972"/>
    </justification>
  </clause>

  <clause id="17915">
    <literal><![CDATA[
      K(a(x,y,K(z,u)) * w,v5) = K(w,v5)
    ]]></literal>
    <justification jstring="[hyper(333,a,4212,a,b,17910,a),flip(a)].">
      <j1 rule="hyper" parents="333 4212 17910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17916">
    <literal><![CDATA[
      K(a(x,y,K(z,u)) * w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(w,v5) = v6
    ]]></literal>
    <justification jstring="[para(17910(a,2),4313(a,1))].">
      <j1 rule="para" parents="17910 4313"/>
    </justification>
  </clause>

  <clause id="17917">
    <literal><![CDATA[
      K(L(x,y,K(z,u)) \ w,v5) = K(x \ w,v5)
    ]]></literal>
    <justification jstring="[para(14539(a,1),17915(a,1,1))].">
      <j1 rule="para" parents="14539 17915"/>
    </justification>
  </clause>

  <clause id="17918">
    <literal><![CDATA[
      K(x * a(y,z,K(u,w)),v5) = K(x,v5)
    ]]></literal>
    <justification jstring="[para(17584(a,1),17915(a,1,1))].">
      <j1 rule="para" parents="17584 17915"/>
    </justification>
  </clause>

  <clause id="17919">
    <literal><![CDATA[
      T(x * a(y,z,K(u,w)),v5) / (x * a(y,z,K(u,w))) = K(x,v5)
    ]]></literal>
    <justification jstring="[hyper(4294,a,17918,a)].">
      <j1 rule="hyper" parents="4294 17918"/>
    </justification>
  </clause>

  <clause id="17920">
    <literal><![CDATA[
      K(x * T(y,a(z,u,w)),v5) = K(x * y,v5)
    ]]></literal>
    <justification jstring="[para(13179(a,1),17918(a,1,1))].">
      <j1 rule="para" parents="13179 17918"/>
    </justification>
  </clause>

  <clause id="17921">
    <literal><![CDATA[
      T(x,y * T(z,L(u,w,v5))) = T(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(14486(a,1),17913(a,1,2,2))].">
      <j1 rule="para" parents="14486 17913"/>
    </justification>
  </clause>

  <clause id="17922">
    <literal><![CDATA[
      T(x,y * (z / a(u,w,v5))) = T(x,y * (a(u,w,v5) \ z))
    ]]></literal>
    <justification jstring="[para(14489(a,1),17913(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14489 17913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17923">
    <literal><![CDATA[
      K(x \ (y * K(z,u)),w) = K((x \ y) * K(z,u),w)
    ]]></literal>
    <justification jstring="[para(14472(a,1),17917(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14472 17917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17924">
    <literal><![CDATA[
      K(T(x,y) * L(y,z,u),w) = K(L(y,z,u) * x,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,13836,a(flip),b,17920,a)].">
      <j1 rule="hyper" parents="63 13836 17920"/>
    </justification>
  </clause>

  <clause id="17925">
    <literal><![CDATA[
      T(x,T(y,a(z,u,w)) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,y * v5) = v6
    ]]></literal>
    <justification jstring="[para(4273(a,1),17906(a,1,2))].">
      <j1 rule="para" parents="4273 17906"/>
    </justification>
  </clause>

  <clause id="17926">
    <literal><![CDATA[
      T(x,(a(y,z,u) * w) \ v5) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,(w * a(y,z,u)) \ v5) = v6
    ]]></literal>
    <justification jstring="[para(10014(a,1),17906(a,1,2))].">
      <j1 rule="para" parents="10014 17906"/>
    </justification>
  </clause>

  <clause id="17927">
    <literal><![CDATA[
      T(x,T(y,a(z,u,w)) \ v5) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ v5) = v6
    ]]></literal>
    <justification jstring="[para(14925(a,1),17906(a,1))].">
      <j1 rule="para" parents="14925 17906"/>
    </justification>
  </clause>

  <clause id="17928">
    <literal><![CDATA[
      T(x,y * a(z,u,K(w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = v6
    ]]></literal>
    <justification jstring="[para(17678(a,1),17906(a,1,2))].">
      <j1 rule="para" parents="17678 17906"/>
    </justification>
  </clause>

  <clause id="17929">
    <literal><![CDATA[
      K(L(x,y,K(z,u)) \ w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x \ w,v5) = v6
    ]]></literal>
    <justification jstring="[para(14539(a,1),17916(a,1,1))].">
      <j1 rule="para" parents="14539 17916"/>
    </justification>
  </clause>

  <clause id="17930">
    <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(84(a,1),17928(a,1,2))].">
      <j1 rule="para" parents="84 17928"/>
    </justification>
  </clause>

  <clause id="17931">
    <literal><![CDATA[
      T(x,K(y,L(z,u,w)) * v5) = T(x,K(y,z) * v5)
    ]]></literal>
    <justification jstring="[para(9457(a,1),17911(a,1,2,1))].">
      <j1 rule="para" parents="9457 17911"/>
    </justification>
  </clause>

  <clause id="17932">
    <literal><![CDATA[
      T(x,L(K(y,z),u,w) \ v5) = T(x,K(z,y) * v5)
    ]]></literal>
    <justification jstring="[para(9408(a,2),17911(a,1,2))].">
      <j1 rule="para" parents="9408 17911"/>
    </justification>
  </clause>

  <clause id="17933">
    <literal><![CDATA[
      T(x,(y \ L(K(z,u) * w,v5,v6)) * T(y,K(z,u) * w)) != v7
    ]]></literal>
    <literal><![CDATA[
      T(x,L(w * K(z,u),v5,v6)) = v7
    ]]></literal>
    <justification jstring="[para(17921(a,1),16291(a,1))].">
      <j1 rule="para" parents="17921 16291"/>
    </justification>
  </clause>

  <clause id="17934">
    <literal><![CDATA[
      T(x,K(y,L(z,u,w)) * v5) = T(x,K(z,y) * v5)
    ]]></literal>
    <justification jstring="[hyper(333,a,14920,a,b,17931,a),flip(a)].">
      <j1 rule="hyper" parents="333 14920 17931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17936">
    <literal><![CDATA[
      K(K(x,L(y,z,u)) * w,v5) = v5 / T(v5,K(x,y) * w)
    ]]></literal>
    <justification jstring="[hyper(197,a,17931,a(flip),b,4233,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="197 17931 4233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17937">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w)) * v5) = x \ T(x,K(y,z) * v5)
    ]]></literal>
    <justification jstring="[hyper(121,a,17931,a(flip),b,4222,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="121 17931 4222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17938">
    <literal><![CDATA[
      T(x,L(K(y,z),u,w) \ v5) = T(x,K(y,z) \ v5)
    ]]></literal>
    <justification jstring="[para(4567(a,2),17932(a,2,2))].">
      <j1 rule="para" parents="4567 17932"/>
    </justification>
  </clause>

  <clause id="17939">
    <literal><![CDATA[
      T(x,(K(y,z) * u) * w) = T(x,K(z,y) * (u * w))
    ]]></literal>
    <justification jstring="[para(13872(a,1),17934(a,1,2))].">
      <j1 rule="para" parents="13872 17934"/>
    </justification>
  </clause>

  <clause id="17940">
    <literal><![CDATA[
      (T(x,K(y,z) * u) * K(z,L(T(y,x),w,v5))) / (K(z,L(y,w,v5)) * x) = K(x,u * K(z,L(y,w,v5)))
    ]]></literal>
    <justification jstring="[para(17934(a,1),16023(a,1,1,1))].">
      <j1 rule="para" parents="17934 16023"/>
    </justification>
  </clause>

  <clause id="17941">
    <literal><![CDATA[
      T(x,K(y,z) \ (u * w)) = T(x,u * (w * K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(15594,a,17912,a)].">
      <j1 rule="hyper" parents="15594 17912"/>
    </justification>
  </clause>

  <clause id="17942">
    <literal><![CDATA[
      T(x,(y \ z) * (y * K(u,w))) = T(x,T(K(u,w) * z,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,17163,a(flip),b,17912,a),flip(a)].">
      <j1 rule="hyper" parents="63 17163 17912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17943">
    <literal><![CDATA[
      x \ T(x,y * (z * K(u,w))) = K(x,(y * z) * K(u,w))
    ]]></literal>
    <justification jstring="[hyper(121,a,17912,a(flip),b,4222,a(flip))].">
      <j1 rule="hyper" parents="121 17912 4222"/>
    </justification>
  </clause>

  <clause id="17945">
    <literal><![CDATA[
      K(x \ (K(y,z) * u),w) = K((x \ u) * K(y,z),w)
    ]]></literal>
    <justification jstring="[hyper(16390,a,17923,a)].">
      <j1 rule="hyper" parents="16390 17923"/>
    </justification>
  </clause>

  <clause id="17947">
    <literal><![CDATA[
      K(L(x,y,z) * u,x * u) = K(u * L(x,y,z),x * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,8326,a(flip),b,17924,a),flip(a)].">
      <j1 rule="hyper" parents="63 8326 17924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17948">
    <literal><![CDATA[
      T(x,(a(y,z,u) / w) * v5) = T(x,(w \ a(y,z,u)) * v5)
    ]]></literal>
    <justification jstring="[hyper(17925,a,15026,a),flip(a)].">
      <j1 rule="hyper" parents="17925 15026"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17949">
    <literal><![CDATA[
      T(x,(K(a(y,z,u),w) * v5) * v6) != v7
    ]]></literal>
    <literal><![CDATA[
      T(x,v5 * v6) = v7
    ]]></literal>
    <justification jstring="[para(17939(a,2),17906(a,1))].">
      <j1 rule="para" parents="17939 17906"/>
    </justification>
  </clause>

  <clause id="17950">
    <literal><![CDATA[
      T(x,K(y,z) \ (u * w)) = T(x,u * (K(y,z) \ w))
    ]]></literal>
    <justification jstring="[hyper(16454,a,17941,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="16454 17941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17951">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,w) = K((x \ u) * K(z,y),w)
    ]]></literal>
    <justification jstring="[hyper(17764,a,17945,a)].">
      <j1 rule="hyper" parents="17764 17945"/>
    </justification>
  </clause>

  <clause id="17952">
    <literal><![CDATA[
      T(x,K(y,z) \ (u * (K(z,y) \ w))) = T(x,u * w)
    ]]></literal>
    <justification jstring="[para(4568(a,1),17950(a,2,2,2))].">
      <j1 rule="para" parents="4568 17950"/>
    </justification>
  </clause>

  <clause id="17953">
    <literal><![CDATA[
      T(x,K(y,L(z,u,w)) \ (v5 * v6)) = T(x,v5 * (L(K(y,z),u,w) \ v6))
    ]]></literal>
    <justification jstring="[para(10851(a,2),17950(a,2,2,2,1))].">
      <j1 rule="para" parents="10851 17950"/>
    </justification>
  </clause>

  <clause id="17954">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,w) = K(K(z,y) * (x \ u),w)
    ]]></literal>
    <justification jstring="[hyper(333,a,15518,a,b,17951,a),flip(a)].">
      <j1 rule="hyper" parents="333 15518 17951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17956">
    <literal><![CDATA[
      K(((x \ y) \ z) * K(u,y),w) = K((x \ T(y,u)) \ z,w)
    ]]></literal>
    <justification jstring="[para(13255(a,1),17951(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="13255 17951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17957">
    <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(17951(a,1),13744(a,2,3))].">
      <j1 rule="para" parents="17951 13744"/>
    </justification>
  </clause>

  <clause id="17958">
    <literal><![CDATA[
      K((x / ((y * z) / y)) \ u,w) = K(K(y,z) * ((x / z) \ u),w)
    ]]></literal>
    <justification jstring="[para(7664(a,2),17954(a,1,1,1))].">
      <j1 rule="para" parents="7664 17954"/>
    </justification>
  </clause>

  <clause id="17959">
    <literal><![CDATA[
      K(K(x,L(y,z,u)) * w,v5) = K(K(x,y) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(333,a,4212,a,b,17936,a),flip(a)].">
      <j1 rule="hyper" parents="333 4212 17936"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17960">
    <literal><![CDATA[
      K(K(L(x,y,z),u) * w,v5) = K(K(x,u) * w,v5)
    ]]></literal>
    <justification jstring="[para(10856(a,1),17959(a,1,1,1))].">
      <j1 rule="para" parents="10856 17959"/>
    </justification>
  </clause>

  <clause id="17961">
    <literal><![CDATA[
      K(K(x,y) * (z * (u * x)),w) = K(z * (u * T(x,y)),w)
    ]]></literal>
    <justification jstring="[hyper(16294,a,17960,a),flip(a)].">
      <j1 rule="hyper" parents="16294 17960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17962">
    <literal><![CDATA[
      K(x * K(L(y,z,u),w),v5) = K(K(y,w) * x,v5)
    ]]></literal>
    <justification jstring="[hyper(15531,a,17960,a)].">
      <j1 rule="hyper" parents="15531 17960"/>
    </justification>
  </clause>

  <clause id="17963">
    <literal><![CDATA[
      K(x * L(K(y,z),u,w),v5) = K(K(y,z) * x,v5)
    ]]></literal>
    <justification jstring="[para(6297(a,1),17962(a,1,1,2))].">
      <j1 rule="para" parents="6297 17962"/>
    </justification>
  </clause>

  <clause id="17964">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w)) * v5) = K(x,K(y,z) * v5)
    ]]></literal>
    <justification jstring="[hyper(333,a,4215,a,b,17937,a),flip(a)].">
      <j1 rule="hyper" parents="333 4215 17937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17965">
    <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(17937(a,2),4306(a,1))].">
      <j1 rule="para" parents="17937 4306"/>
    </justification>
  </clause>

  <clause id="17966">
    <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(63,a,17067,a(flip),b,17964,a),flip(a)].">
      <j1 rule="hyper" parents="63 17067 17964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17967">
    <literal><![CDATA[
      K(x,K(L(y,z,u),w) * v5) = K(x,K(y,w) * v5)
    ]]></literal>
    <justification jstring="[para(10856(a,1),17964(a,1,2,1))].">
      <j1 rule="para" parents="10856 17964"/>
    </justification>
  </clause>

  <clause id="17968">
    <literal><![CDATA[
      K(x,K((y \ z) \ u,w) * v5) = K(x,K(z \ (y * u),w) * v5)
    ]]></literal>
    <justification jstring="[para(10909(a,1),17964(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10909 17964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17969">
    <literal><![CDATA[
      K(x,(K(y,z) * u) * w) = K(x,K(y,z) * (u * w))
    ]]></literal>
    <justification jstring="[para(13872(a,1),17964(a,1,2))].">
      <j1 rule="para" parents="13872 17964"/>
    </justification>
  </clause>

  <clause id="17970">
    <literal><![CDATA[
      K(x,K(y,z) * ((y \ u) * w)) = K(x,(T(y,z) \ u) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,15283,a(flip),b,17967,a),flip(a)].">
      <j1 rule="hyper" parents="63 15283 17967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17971">
    <literal><![CDATA[
      K(x,(y * K(z,u)) * w) = K(x,K(z,u) * (y * w))
    ]]></literal>
    <justification jstring="[hyper(16394,a,17969,a)].">
      <j1 rule="hyper" parents="16394 17969"/>
    </justification>
  </clause>

  <clause id="17972">
    <literal><![CDATA[
      K(x,(y \ K(z,u)) \ w) = K(x,K(u,z) * (y * w))
    ]]></literal>
    <justification jstring="[hyper(13536,a,17969,a)].">
      <j1 rule="hyper" parents="13536 17969"/>
    </justification>
  </clause>

  <clause id="17973">
    <literal><![CDATA[
      K(x,(K(y,z) * u) * w) = K(x,K(z,y) * (u * w))
    ]]></literal>
    <justification jstring="[hyper(333,a,14926,a,b,17969,a),flip(a)].">
      <j1 rule="hyper" parents="333 14926 17969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17974">
    <literal><![CDATA[
      K(x,K(y,z) * ((z \ u) * w)) = K(x,(T(z,y) \ u) * w)
    ]]></literal>
    <justification jstring="[para(4555(a,1),17969(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4555 17969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17975">
    <literal><![CDATA[
      K(x,K(y,z) * ((y \ u) * w)) = K(x,(((z * y) / z) \ u) * w)
    ]]></literal>
    <justification jstring="[para(4519(a,2),17969(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4519 17969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17976">
    <literal><![CDATA[
      K(x,K(y,z) * ((y / u) * w)) = K(x,(T(y,z) / u) * w)
    ]]></literal>
    <justification jstring="[para(13229(a,1),17969(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13229 17969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17977">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(u,w) * (y * z)) = K(x,z * (K(u,w) * y))
    ]]></literal>
    <justification jstring="[para(17969(a,1),16636(a,1,2))].">
      <j1 rule="para" parents="17969 16636"/>
    </justification>
  </clause>

  <clause id="17978">
    <literal><![CDATA[
      K(x,(y * K(z,u)) * w) = K(x,K(u,z) * (y * w))
    ]]></literal>
    <justification jstring="[hyper(333,a,14926,a,b,17971,a),flip(a)].">
      <j1 rule="hyper" parents="333 14926 17971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17979">
    <literal><![CDATA[
      T(x,(y * K(z,u)) * w) = T(x,K(z,u) * (y * w))
    ]]></literal>
    <justification jstring="[hyper(124,a,17971,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 17971 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17980">
    <literal><![CDATA[
      K(x,K(y,z \ 1) * (u * z)) = K(x,u / T(z \ 1,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,13336,a(flip),b,17971,a),flip(a)].">
      <j1 rule="hyper" parents="63 13336 17971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17981">
    <literal><![CDATA[
      K(x,K(y,z) * ((u \ y) * w)) = K(x,(u \ T(y,z)) * w)
    ]]></literal>
    <justification jstring="[para(13255(a,1),17971(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13255 17971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17982">
    <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(17971(a,2),14927(a,1))].">
      <j1 rule="para" parents="17971 14927"/>
    </justification>
  </clause>

  <clause id="17983">
    <literal><![CDATA[
      K(x,(y * K(z,K(u,w))) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * v5) = v6
    ]]></literal>
    <justification jstring="[para(17971(a,2),16324(a,1))].">
      <j1 rule="para" parents="17971 16324"/>
    </justification>
  </clause>

  <clause id="17984">
    <literal><![CDATA[
      K(x,T(y,K(z,u)) * (w * K(z,u))) = K(x,K(w,y)) * K(x,K(z,T(u,y)) * (w * y))
    ]]></literal>
    <justification jstring="[para(17971(a,1),17235(a,2,2))].">
      <j1 rule="para" parents="17971 17235"/>
    </justification>
  </clause>

  <clause id="17985">
    <literal><![CDATA[
      K(x,(y \ K(z,u)) \ w) = K(x,K(z,u) * (y * w))
    ]]></literal>
    <justification jstring="[hyper(333,a,14926,a,b,17972,a),flip(a)].">
      <j1 rule="hyper" parents="333 14926 17972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17986">
    <literal><![CDATA[
      K(x,K(y,z) * (((z * y) / u) * w)) = K(x,(((y * z) / u) \ 1) \ w)
    ]]></literal>
    <justification jstring="[para(13482(a,1),17972(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13482 17972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17987">
    <literal><![CDATA[
      K(x,K(y,z) * ((z / u) * w)) = K(x,(T(z,y) / u) * w)
    ]]></literal>
    <justification jstring="[para(13229(a,1),17973(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13229 17973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17988">
    <literal><![CDATA[
      K(x,K(y,z) * (((z * y) / u) * w)) = K(x,((T(z,y) * y) / u) * w)
    ]]></literal>
    <justification jstring="[para(14585(a,1),17973(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14585 17973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17989">
    <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(17973(a,1),16779(a,1,2))].">
      <j1 rule="para" parents="17973 16779"/>
    </justification>
  </clause>

  <clause id="17990">
    <literal><![CDATA[
      K(x,(K(y,z) / u) \ w) = K(x,K(y,z) * (u * w))
    ]]></literal>
    <justification jstring="[hyper(13538,a,17978,a)].">
      <j1 rule="hyper" parents="13538 17978"/>
    </justification>
  </clause>

  <clause id="17991">
    <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(63,a,10972,a(flip),b,17978,a),flip(a)].">
      <j1 rule="hyper" parents="63 10972 17978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17992">
    <literal><![CDATA[
      K(x,K(y,z) * ((u \ z) * w)) = K(x,(u \ T(z,y)) * w)
    ]]></literal>
    <justification jstring="[para(13255(a,1),17978(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13255 17978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17993">
    <literal><![CDATA[
      K(x,K(y \ z,y) * ((u \ z) * w)) = K(x,(u \ (y * (z / y))) * w)
    ]]></literal>
    <justification jstring="[para(14611(a,1),17978(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14611 17978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17994">
    <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(17978(a,1),13453(a,1,1))].">
      <j1 rule="para" parents="17978 13453"/>
    </justification>
  </clause>

  <clause id="17995">
    <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(17978(a,1),13454(a,1,1))].">
      <j1 rule="para" parents="17978 13454"/>
    </justification>
  </clause>

  <clause id="17997">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w) * (v5 * v6))) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(z,v6 * (v5 * K(w,u)))) = v7
    ]]></literal>
    <justification jstring="[para(17978(a,1),17729(a,1,3))].">
      <j1 rule="para" parents="17978 17729"/>
    </justification>
  </clause>

  <clause id="17998">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(u,w) * (y * z)) = T(x,z * (y * K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,16729,a(flip),b,17979,a),flip(a)].">
      <j1 rule="hyper" parents="63 16729 17979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17999">
    <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(17979(a,2),15769(a,1))].">
      <j1 rule="para" parents="17979 15769"/>
    </justification>
  </clause>

  <clause id="18000">
    <literal><![CDATA[
      T(x,(y \ K(z,u)) \ w) = T(x,K(z,u) * (y * w))
    ]]></literal>
    <justification jstring="[hyper(124,a,17985,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 17985 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18001">
    <literal><![CDATA[
      K(x,K(y \ 1,z) * (y * u)) = K(x,T(y \ 1,z) \ u)
    ]]></literal>
    <justification jstring="[para(4227(a,1),17985(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4227 17985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18002">
    <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(17985(a,1),15121(a,1,1,2))].">
      <j1 rule="para" parents="17985 15121"/>
    </justification>
  </clause>

  <clause id="18003">
    <literal><![CDATA[
      T(x,(K(y,z) / u) \ w) = T(x,K(y,z) * (u * w))
    ]]></literal>
    <justification jstring="[hyper(124,a,17990,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 17990 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18004">
    <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(63,a,17456,a(flip),b,17990,a)].">
      <j1 rule="hyper" parents="63 17456 17990"/>
    </justification>
  </clause>

  <clause id="18005">
    <literal><![CDATA[
      T(x,K(y,z \ u) * ((u \ z) * w)) = T(x,T((u \ z) \ 1,y) \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,15123,a(flip),b,18000,a),flip(a)].">
      <j1 rule="hyper" parents="63 15123 18000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18006">
    <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(18000(a,2),15769(a,1))].">
      <j1 rule="para" parents="18000 15769"/>
    </justification>
  </clause>

  <clause id="18007">
    <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(18003(a,1),13559(a,1,2,1,1))].">
      <j1 rule="para" parents="18003 13559"/>
    </justification>
  </clause>

  <clause id="18008">
    <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(7565(a,1),17983(a,1,2,1))].">
      <j1 rule="para" parents="7565 17983"/>
    </justification>
  </clause>

  <clause id="18009">
    <literal><![CDATA[
      K(x,(y * z) * K(u,w)) = K(x,y * (z * K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(4306,a,17943,a),flip(a)].">
      <j1 rule="hyper" parents="4306 17943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18010">
    <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(17943(a,1),4306(a,1))].">
      <j1 rule="para" parents="17943 4306"/>
    </justification>
  </clause>

  <clause id="18011">
    <literal><![CDATA[
      K(x,K(y,z) * (u * w)) = K(x,u * (w * K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(15641,a,18009,a)].">
      <j1 rule="hyper" parents="15641 18009"/>
    </justification>
  </clause>

  <clause id="18012">
    <literal><![CDATA[
      K(x,K(y,z) \ (u * w)) = K(x,u * (w * K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(15601,a,18009,a)].">
      <j1 rule="hyper" parents="15601 18009"/>
    </justification>
  </clause>

  <clause id="18013">
    <literal><![CDATA[
      K(x,K(y,z) * (u * w)) = K(x,u * (w * K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(15533,a,18009,a)].">
      <j1 rule="hyper" parents="15533 18009"/>
    </justification>
  </clause>

  <clause id="18014">
    <literal><![CDATA[
      K(x,y * ((1 / z) * K(u,y / z))) = K(x,T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(13709,a,18009,a),flip(a)].">
      <j1 rule="hyper" parents="13709 18009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18015">
    <literal><![CDATA[
      K(x,y * (z * K(u,y * z))) = K(x,T(y * z,u))
    ]]></literal>
    <justification jstring="[hyper(7013,a,18009,a),flip(a)].">
      <j1 rule="hyper" parents="7013 18009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18016">
    <literal><![CDATA[
      K(x,y * (z * K(u,z * y))) = K(x,T(y * z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,16474,a(flip),b,18009,a),flip(a)].">
      <j1 rule="hyper" parents="63 16474 18009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18018">
    <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(17305(a,1),18009(a,1,2,2))].">
      <j1 rule="para" parents="17305 18009"/>
    </justification>
  </clause>

  <clause id="18019">
    <literal><![CDATA[
      K(x,K(y,z * u) * (w * v5)) = K(x,w * (v5 * K(y,u * z)))
    ]]></literal>
    <justification jstring="[hyper(16506,a,18011,a)].">
      <j1 rule="hyper" parents="16506 18011"/>
    </justification>
  </clause>

  <clause id="18020">
    <literal><![CDATA[
      K(x,K(y,z) * (u * (w * z))) = K(x,u * (w * T(z,y)))
    ]]></literal>
    <justification jstring="[para(5984(a,1),18011(a,2,2,2))].">
      <j1 rule="para" parents="5984 18011"/>
    </justification>
  </clause>

  <clause id="18021">
    <literal><![CDATA[
      K(x,K(y,z) * (u * (w \ 1))) = K(x,u * (w \ K(z,y)))
    ]]></literal>
    <justification jstring="[para(13126(a,1),18011(a,2,2,2))].">
      <j1 rule="para" parents="13126 18011"/>
    </justification>
  </clause>

  <clause id="18022">
    <literal><![CDATA[
      K(x,K(y,z) * (u * (z / w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,u * (T(z,y) / w)) = v5
    ]]></literal>
    <justification jstring="[para(18011(a,2),16438(a,1))].">
      <j1 rule="para" parents="18011 16438"/>
    </justification>
  </clause>

  <clause id="18023">
    <literal><![CDATA[
      K(x,K(y,z) \ (u * (w / y))) = K(x,u * (w / T(y,z)))
    ]]></literal>
    <justification jstring="[para(5450(a,1),18012(a,2,2,2))].">
      <j1 rule="para" parents="5450 18012"/>
    </justification>
  </clause>

  <clause id="18024">
    <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(10851(a,2),18012(a,2,2,2,2))].">
      <j1 rule="para" parents="10851 18012"/>
    </justification>
  </clause>

  <clause id="18025">
    <literal><![CDATA[
      K(x,y * (z * K(u,w))) = K(x,y * (z * K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,18011,a(flip),b,18013,a)].">
      <j1 rule="hyper" parents="63 18011 18013"/>
    </justification>
  </clause>

  <clause id="18026">
    <literal><![CDATA[
      K(x,y * (z * K(u,w * u))) = K(x,K(u,w) * (y * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,14962,a(flip),b,18013,a),flip(a)].">
      <j1 rule="hyper" parents="63 14962 18013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18027">
    <literal><![CDATA[
      K(x,y * (((z * y) \ u) * K(z,z \ u))) = K(x,T(y * ((z * y) \ u),z))
    ]]></literal>
    <justification jstring="[para(10661(a,1),18015(a,1,2,2,2))].">
      <j1 rule="para" parents="10661 18015"/>
    </justification>
  </clause>

  <clause id="18028">
    <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(14579(a,1),18016(a,1,2,2))].">
      <j1 rule="para" parents="14579 18016"/>
    </justification>
  </clause>

  <clause id="18029">
    <literal><![CDATA[
      K(x,y * ((z \ u) * K(w,u))) = K(x,y * (z \ T(u,w)))
    ]]></literal>
    <justification jstring="[para(13255(a,1),18025(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13255 18025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18030">
    <literal><![CDATA[
      K(x,y * ((z \ (u \ w)) * K(u,w))) = K(x,y * (z \ (u \ T(w,u))))
    ]]></literal>
    <justification jstring="[para(14621(a,1),18025(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14621 18025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18031">
    <literal><![CDATA[
      K(x * L(y,z,u),y * x) = a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,17792,a(flip),b,17947,a),flip(a)].">
      <j1 rule="hyper" parents="63 17792 17947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18032">
    <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(2905(a,1),18031(a,1,1,2))].">
      <j1 rule="para" parents="2905 18031"/>
    </justification>
  </clause>

  <clause id="18033">
    <literal><![CDATA[
      K(((x \ y) \ z) * K(y,u),w) = K((x \ T(y,u)) \ z,w)
    ]]></literal>
    <justification jstring="[hyper(15109,a,17956,a)].">
      <j1 rule="hyper" parents="15109 17956"/>
    </justification>
  </clause>

  <clause id="18035">
    <literal><![CDATA[
      K(x * ((y * z) * T(z,y)),u) = K(x * (z * (y * z)),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,16125,a(flip),b,17961,a),flip(a)].">
      <j1 rule="hyper" parents="63 16125 17961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18036">
    <literal><![CDATA[
      K(x,K(L(y,z,u),w) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,w) * v5) = v6
    ]]></literal>
    <justification jstring="[para(10856(a,1),17965(a,1,2,1))].">
      <j1 rule="para" parents="10856 17965"/>
    </justification>
  </clause>

  <clause id="18037">
    <literal><![CDATA[
      K(x,K(y,z) \ ((y \ u) * w)) = K(x,(T(y,z) \ u) * w)
    ]]></literal>
    <justification jstring="[hyper(15779,a,17970,a)].">
      <j1 rule="hyper" parents="15779 17970"/>
    </justification>
  </clause>

  <clause id="18039">
    <literal><![CDATA[
      K(x,(y \ z) * (u * K(w,y))) = K(x,(T(y,w) \ z) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,18011,a(flip),b,17970,a)].">
      <j1 rule="hyper" parents="63 18011 17970"/>
    </justification>
  </clause>

  <clause id="18040">
    <literal><![CDATA[
      K(x,(T(y,z) \ z) * u) = K(x,(z / y) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,14963,a(flip),b,17970,a),flip(a)].">
      <j1 rule="hyper" parents="63 14963 17970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18041">
    <literal><![CDATA[
      K(x,(y \ T(z,y)) * u) = K(x,(z / y) * u)
    ]]></literal>
    <justification jstring="[para(3628(a,1),18040(a,1,2,1))].">
      <j1 rule="para" parents="3628 18040"/>
    </justification>
  </clause>

  <clause id="18042">
    <literal><![CDATA[
      K(x,(T(y,T(z,u)) \ (u * (z / u))) * w) = K(x,((u * (z / u)) / y) * w)
    ]]></literal>
    <justification jstring="[para(12256(a,1),18040(a,1,2,1,1))].">
      <j1 rule="para" parents="12256 18040"/>
    </justification>
  </clause>

  <clause id="18043">
    <literal><![CDATA[
      T(x,(y \ T(z,y)) * u) = T(x,(z / y) * u)
    ]]></literal>
    <justification jstring="[hyper(124,a,18041,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 18041 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18044">
    <literal><![CDATA[
      K(x,(y / z) * T(u,z \ T(y,z))) = K(x,u * (z \ T(y,z)))
    ]]></literal>
    <justification jstring="[para(111(a,1),18041(a,1,2)),flip(a)].">
      <j1 rule="para" parents="111 18041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18045">
    <literal><![CDATA[
      K((x \ T(y,x)) * z,u) = (w * K(u,(y / x) * z)) \ w
    ]]></literal>
    <justification jstring="[para(18041(a,1),5990(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="18041 5990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18046">
    <literal><![CDATA[
      a(x * (y \ T(z,y)),u,K(w,v5)) = a(w,u,K(v5,(z / y) * x))
    ]]></literal>
    <justification jstring="[para(18041(a,1),17699(a,2,3))].">
      <j1 rule="para" parents="18041 17699"/>
    </justification>
  </clause>

  <clause id="18047">
    <literal><![CDATA[
      K(x,(K(y,z) * (z / u)) * w) = K(x,(T(z,y) / u) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,17973,a,b,17976,a)].">
      <j1 rule="hyper" parents="63 17973 17976"/>
    </justification>
  </clause>

  <clause id="18048">
    <literal><![CDATA[
      K(x,y / T(z \ 1,u)) = K(x,K(u,z) * (y * z))
    ]]></literal>
    <justification jstring="[hyper(15207,a,17980,a),flip(a)].">
      <j1 rule="hyper" parents="15207 17980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18049">
    <literal><![CDATA[
      K(x,y / T(z \ 1,u)) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(333,a,15698,a(flip),b,18048,a),flip(a)].">
      <j1 rule="hyper" parents="333 15698 18048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18050">
    <literal><![CDATA[
      K(x,y / T(z \ 1,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(18048(a,2),15879(a,1))].">
      <j1 rule="para" parents="18048 15879"/>
    </justification>
  </clause>

  <clause id="18051">
    <literal><![CDATA[
      K(x,y * T(z,z * (x * y))) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(13506,a,18049,a),flip(a)].">
      <j1 rule="hyper" parents="13506 18049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18052">
    <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(10963,a,18049,a)].">
      <j1 rule="hyper" parents="10963 18049"/>
    </justification>
  </clause>

  <clause id="18053">
    <literal><![CDATA[
      K(x,y * T(1 / z,u)) = K(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(79(a,1),18049(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="79 18049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18054">
    <literal><![CDATA[
      K(x,y * T(z \ 1,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(18049(a,1),13673(a,1))].">
      <j1 rule="para" parents="18049 13673"/>
    </justification>
  </clause>

  <clause id="18055">
    <literal><![CDATA[
      K(x,y * T(z,x * y)) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(12758,a,18051,a)].">
      <j1 rule="hyper" parents="12758 18051"/>
    </justification>
  </clause>

  <clause id="18056">
    <literal><![CDATA[
      T(x,y * T(z,x * y)) = T(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(124,a,18055,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 18055 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18057">
    <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(63,a,14916,a,b,18056,a)].">
      <j1 rule="hyper" parents="63 14916 18056"/>
    </justification>
  </clause>

  <clause id="18058">
    <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(63,a,15384,a(flip),b,18053,a),flip(a)].">
      <j1 rule="hyper" parents="63 15384 18053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18059">
    <literal><![CDATA[
      K(x,y / T((z * u) \ u,u)) = K(x,y * (((u * z) \ u) \ 1))
    ]]></literal>
    <justification jstring="[hyper(18054,a,14991,a)].">
      <j1 rule="hyper" parents="18054 14991"/>
    </justification>
  </clause>

  <clause id="18060">
    <literal><![CDATA[
      K(x,((y \ z) * K(u,z)) * w) = K(x,(y \ T(z,u)) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,17978,a,b,17981,a)].">
      <j1 rule="hyper" parents="63 17978 17981"/>
    </justification>
  </clause>

  <clause id="18061">
    <literal><![CDATA[
      K(x,K(y,z) * ((y / u) * w)) = K(x,(T(y,K(v5,v6) * z) / u) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,17154,a(flip),b,17987,a)].">
      <j1 rule="hyper" parents="63 17154 17987"/>
    </justification>
  </clause>

  <clause id="18062">
    <literal><![CDATA[
      K(x,(T(y,x) / z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y / z) * u) = w
    ]]></literal>
    <justification jstring="[para(17987(a,1),7407(a,1))].">
      <j1 rule="para" parents="17987 7407"/>
    </justification>
  </clause>

  <clause id="18063">
    <literal><![CDATA[
      K(x,L(y,z,z \ u) * u) = K(x,(T(u,y) / z) * (z * y))
    ]]></literal>
    <justification jstring="[para(14590(a,1),17987(a,1,2))].">
      <j1 rule="para" parents="14590 17987"/>
    </justification>
  </clause>

  <clause id="18064">
    <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(23(a,1),18062(a,1,2,1,1))].">
      <j1 rule="para" parents="23 18062"/>
    </justification>
  </clause>

  <clause id="18065">
    <literal><![CDATA[
      K(x,((y \ z) \ T(z,u)) * w) = K(x,K(u,z) * (T(y,z) * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,12748,a(flip),b,17992,a),flip(a)].">
      <j1 rule="hyper" parents="63 12748 17992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18066">
    <literal><![CDATA[
      K(x,(y \ T(z,x)) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y \ z) * u) = w
    ]]></literal>
    <justification jstring="[para(17992(a,1),7407(a,1))].">
      <j1 rule="para" parents="17992 7407"/>
    </justification>
  </clause>

  <clause id="18067">
    <literal><![CDATA[
      K(x,K(y * 1,z) * (y * u)) = K(x,T(y \ 1,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(16149,a,18001,a)].">
      <j1 rule="hyper" parents="16149 18001"/>
    </justification>
  </clause>

  <clause id="18068">
    <literal><![CDATA[
      K(x,y * (K(z,u \ y) / u)) = K(x,T(y / u,z))
    ]]></literal>
    <justification jstring="[para(13555(a,1),18014(a,1,2,2))].">
      <j1 rule="para" parents="13555 18014"/>
    </justification>
  </clause>

  <clause id="18069">
    <literal><![CDATA[
      K(x,y * (z \ K(u,z \ y))) = K(x,T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(16440,a,18068,a)].">
      <j1 rule="hyper" parents="16440 18068"/>
    </justification>
  </clause>

  <clause id="18070">
    <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(11410(a,1),18069(a,1,2,2,2))].">
      <j1 rule="para" parents="11410 18069"/>
    </justification>
  </clause>

  <clause id="18071">
    <literal><![CDATA[
      K(x * (y * z),K(u,K(w,z))) * K(u,(x * (y * z)) * K(w,z)) = K(u,x * (y * T(z,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,15860,a,b,18020,a)].">
      <j1 rule="hyper" parents="63 15860 18020"/>
    </justification>
  </clause>

  <clause id="18072">
    <literal><![CDATA[
      K(x,K(y,z) \ (u * (w * y))) = K(x,u * (w * T(y,z)))
    ]]></literal>
    <justification jstring="[para(4567(a,2),18020(a,1,2))].">
      <j1 rule="para" parents="4567 18020"/>
    </justification>
  </clause>

  <clause id="18073">
    <literal><![CDATA[
      K(x,K(y,z) * (u * (1 / w))) = K(x,u * (w \ K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(63,a,4803,a,b,18021,a)].">
      <j1 rule="hyper" parents="63 4803 18021"/>
    </justification>
  </clause>

  <clause id="18074">
    <literal><![CDATA[
      K(x,y * ((z / u) \ K(w,z \ u))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * T((z / u) \ 1,w)) = v5
    ]]></literal>
    <justification jstring="[para(18021(a,1),17170(a,1))].">
      <j1 rule="para" parents="18021 17170"/>
    </justification>
  </clause>

  <clause id="18075">
    <literal><![CDATA[
      K(x,K(y,z) * (u * (T(w,T(y,z)) / y))) = K(x,u * ((z / (z / y)) \ w))
    ]]></literal>
    <justification jstring="[hyper(63,a,16978,a(flip),b,18026,a),flip(a)].">
      <j1 rule="hyper" parents="63 16978 18026"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18076">
    <literal><![CDATA[
      K(x,y * ((z \ u) * K(w * v5,u))) = K(x,y * (z \ T(u,w \ v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,16263,a(flip),b,18029,a)].">
      <j1 rule="hyper" parents="63 16263 18029"/>
    </justification>
  </clause>

  <clause id="18077">
    <literal><![CDATA[
      K(x,y * (z \ ((u * w) / u))) = K(x,y * (z \ T(w,u)))
    ]]></literal>
    <justification jstring="[para(13413(a,2),18029(a,1,2,2))].">
      <j1 rule="para" parents="13413 18029"/>
    </justification>
  </clause>

  <clause id="18079">
    <literal><![CDATA[
      K((x \ T(y,x)) \ z,u) = K((y / x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,17066,a(flip),b,18033,a),flip(a)].">
      <j1 rule="hyper" parents="63 17066 18033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18080">
    <literal><![CDATA[
      K((T(x,y) \ y) \ z,u) = K((y / x) \ z,u)
    ]]></literal>
    <justification jstring="[para(3628(a,2),18079(a,1,1,1))].">
      <j1 rule="para" parents="3628 18079"/>
    </justification>
  </clause>

  <clause id="18082">
    <literal><![CDATA[
      K(x * ((y * z) * y),u) = K(x * (y * (z * y)),u)
    ]]></literal>
    <justification jstring="[para(968(a,1),18035(a,1,1,2))].">
      <j1 rule="para" parents="968 18035"/>
    </justification>
  </clause>

  <clause id="18083">
    <literal><![CDATA[
      (x * K(y * (z * (u * z)),w)) \ (x * w) = T(w,y * ((z * u) * z))
    ]]></literal>
    <justification jstring="[para(18082(a,1),5447(a,1,1,2))].">
      <j1 rule="para" parents="18082 5447"/>
    </justification>
  </clause>

  <clause id="18084">
    <literal><![CDATA[
      K(x,(T(y,z) \ (y * u)) * w) = K(x,K(y,z) \ (u * w))
    ]]></literal>
    <justification jstring="[para(9(a,1),18037(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="9 18037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18085">
    <literal><![CDATA[
      K(x,(T(y,z) \ u) * (w \ (y * z))) = K(x,(y \ u) * (w \ (z * y)))
    ]]></literal>
    <justification jstring="[para(14573(a,1),18039(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14573 18039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18086">
    <literal><![CDATA[
      K((x \ T(y,x)) * z,u) = K((y / x) * z,u)
    ]]></literal>
    <justification jstring="[hyper(333,a,5990,a(flip),b,18045,a),flip(a)].">
      <j1 rule="hyper" parents="333 5990 18045"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18087">
    <literal><![CDATA[
      K((x \ T(y,x)) / z,u) = K((y / x) * (z \ 1),u)
    ]]></literal>
    <justification jstring="[hyper(13493,a,18086,a)].">
      <j1 rule="hyper" parents="13493 18086"/>
    </justification>
  </clause>

  <clause id="18088">
    <literal><![CDATA[
      K((T(x,x \ y) \ T(y,T(x,x \ y))) * z,u) = K((x \ y) * z,u)
    ]]></literal>
    <justification jstring="[para(281(a,1),18086(a,2,1,1))].">
      <j1 rule="para" parents="281 18086"/>
    </justification>
  </clause>

  <clause id="18089">
    <literal><![CDATA[
      K((x \ T(y,x)) / z,u) = K((y / x) / z,u)
    ]]></literal>
    <justification jstring="[hyper(333,a,13173,a(flip),b,18087,a),flip(a)].">
      <j1 rule="hyper" parents="333 13173 18087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18090">
    <literal><![CDATA[
      K(x \ (y \ T(z,y)),u) = K((z / y) / x,T(u,x))
    ]]></literal>
    <justification jstring="[hyper(7067,a,18089,a)].">
      <j1 rule="hyper" parents="7067 18089"/>
    </justification>
  </clause>

  <clause id="18091">
    <literal><![CDATA[
      K(x \ (y \ T(z,y)),u) = K(x \ (z / y),u)
    ]]></literal>
    <justification jstring="[hyper(333,a,6431,a(flip),b,18090,a),flip(a)].">
      <j1 rule="hyper" parents="333 6431 18090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18092">
    <literal><![CDATA[
      T(x,y \ (z \ T(u,z))) = (w * K(y \ (u / z),x)) \ (w * x)
    ]]></literal>
    <justification jstring="[para(18091(a,1),5447(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="18091 5447"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18093">
    <literal><![CDATA[
      K(x,(T(y,z) / (u \ 1)) * w) = K(x,(y / (u \ K(y,z))) * w)
    ]]></literal>
    <justification jstring="[para(13451(a,1),18047(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13451 18047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18094">
    <literal><![CDATA[
      K(x,(T(y \ z,y) / u) * w) = K(x,((z / y) / u) * w)
    ]]></literal>
    <justification jstring="[para(13463(a,1),18047(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13463 18047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18095">
    <literal><![CDATA[
      K(x,(y \ ((z * u) / z)) * w) = K(x,(y \ T(u,z)) * w)
    ]]></literal>
    <justification jstring="[para(13413(a,2),18060(a,1,2,1))].">
      <j1 rule="para" parents="13413 18060"/>
    </justification>
  </clause>

  <clause id="18096">
    <literal><![CDATA[
      K(x,T(y \ 1,L(z,u,w)) \ v5) = K(x,K(y * 1,z) * (y * v5))
    ]]></literal>
    <justification jstring="[hyper(17965,a,18067,a),flip(a)].">
      <j1 rule="hyper" parents="17965 18067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18097">
    <literal><![CDATA[
      K(x,x * (y * T(z,u))) \ T(x,y * T(z,u)) = R(x,K(z,u) \ (y * z),x)
    ]]></literal>
    <justification jstring="[para(18072(a,1),16960(a,1,1))].">
      <j1 rule="para" parents="18072 16960"/>
    </justification>
  </clause>

  <clause id="18098">
    <literal><![CDATA[
      K(x,y * (z \ K(u,L(w,v5,v6)))) = K(x,K(w,u) * (y * (1 / z)))
    ]]></literal>
    <justification jstring="[hyper(18036,a,18073,a),flip(a)].">
      <j1 rule="hyper" parents="18036 18073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18099">
    <literal><![CDATA[
      K(x,K(y,z) * (u * (1 / w))) = K(x,u * (w \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(14927,a,18073,a)].">
      <j1 rule="hyper" parents="14927 18073"/>
    </justification>
  </clause>

  <clause id="18100">
    <literal><![CDATA[
      K(x,y * (z \ (L(u,w,u) * w))) = K(x,y * (z \ T(w * u,u)))
    ]]></literal>
    <justification jstring="[para(3722(a,1),18077(a,1,2,2,2))].">
      <j1 rule="para" parents="3722 18077"/>
    </justification>
  </clause>

  <clause id="18101">
    <literal><![CDATA[
      K(x,K(y,z) \ (u * w)) \ K(x,K(K(y,z) \ u,w)) = K(w * (T(y,z) \ (y * u)),x)
    ]]></literal>
    <justification jstring="[para(18084(a,1),15868(a,1,1))].">
      <j1 rule="para" parents="18084 15868"/>
    </justification>
  </clause>

  <clause id="18102">
    <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(14920(a,1),18094(a,1,2,1,1))].">
      <j1 rule="para" parents="14920 18094"/>
    </justification>
  </clause>

  <clause id="18103">
    <literal><![CDATA[
      T(x,(y \ ((z * u) / z)) * w) = T(x,(y \ T(u,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(124,a,18095,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 18095 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18104">
    <literal><![CDATA[
      K(x,y * (z \ K(u,w))) = K(x,y * (z \ K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,18073,a(flip),b,18099,a)].">
      <j1 rule="hyper" parents="63 18073 18099"/>
    </justification>
  </clause>

  <clause id="18105">
    <literal><![CDATA[
      K(x,y * (z \ K(z,u))) = K(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[hyper(13532,a,18104,a),flip(a)].">
      <j1 rule="hyper" parents="13532 18104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18106">
    <literal><![CDATA[
      K(x,y * ((z * u) \ K(u,w))) = K(x,y / (z * T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(333,a,16481,a(flip),b,18104,a),flip(a)].">
      <j1 rule="hyper" parents="333 16481 18104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18107">
    <literal><![CDATA[
      K(x,y * (z \ K(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(18104(a,1),13532(a,1))].">
      <j1 rule="para" parents="18104 13532"/>
    </justification>
  </clause>

  <clause id="18108">
    <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(13639(a,2),18105(a,2,2,2))].">
      <j1 rule="para" parents="13639 18105"/>
    </justification>
  </clause>

  <clause id="18109">
    <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(17999,a,17173,a)].">
      <j1 rule="hyper" parents="17999 17173"/>
    </justification>
  </clause>

  <clause id="18110">
    <literal><![CDATA[
      K(x,K(y,z \ u) * (w * (v5 * (u / z)))) = K(x,w * (v5 * T(u / z,y)))
    ]]></literal>
    <justification jstring="[hyper(18008,a,18020,a)].">
      <j1 rule="hyper" parents="18008 18020"/>
    </justification>
  </clause>

  <clause id="18111">
    <literal><![CDATA[
      K(x,K(y * (z \ u),y \ z) * w) = K(x,K(y * (u / z),u) * w)
    ]]></literal>
    <justification jstring="[hyper(18008,a,15276,a)].">
      <j1 rule="hyper" parents="18008 15276"/>
    </justification>
  </clause>

  <clause id="18112">
    <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(15637(a,2),18010(a,1))].">
      <j1 rule="para" parents="15637 18010"/>
    </justification>
  </clause>

  <clause id="18113">
    <literal><![CDATA[
      K(x,(T(y,z) / u) * (u * z)) = K(x,(z * u) * (u \ y))
    ]]></literal>
    <justification jstring="[hyper(63,a,17095,a(flip),b,18063,a),flip(a)].">
      <j1 rule="hyper" parents="63 17095 18063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18114">
    <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(8520(a,2),18113(a,1,2,2))].">
      <j1 rule="para" parents="8520 18113"/>
    </justification>
  </clause>

  <clause id="18115">
    <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(17151(a,1),18112(a,1))].">
      <j1 rule="para" parents="17151 18112"/>
    </justification>
  </clause>

  <clause id="18116">
    <literal><![CDATA[
      K(x,(y * z) / L(y,u,w)) = K(x,(L(y,u,w) \ z) * y)
    ]]></literal>
    <justification jstring="[hyper(12278,a,17625,a),flip(a)].">
      <j1 rule="hyper" parents="12278 17625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18117">
    <literal><![CDATA[
      K(x,L(y,z,u / (y * w))) = K(x,L(y,z,w \ u))
    ]]></literal>
    <justification jstring="[hyper(13770,a,17722,a),flip(a)].">
      <j1 rule="hyper" parents="13770 17722"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18118">
    <literal><![CDATA[
      K(x,L(y,z,(y * u) \ w)) = K(x,L(y,z,u \ w))
    ]]></literal>
    <justification jstring="[hyper(17863,a,18117,a)].">
      <j1 rule="hyper" parents="17863 18117"/>
    </justification>
  </clause>

  <clause id="18119">
    <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(17758(a,2),15484(a,1))].">
      <j1 rule="para" parents="17758 15484"/>
    </justification>
  </clause>

  <clause id="18120">
    <literal><![CDATA[
      x \ (y * (K(z,K(u,w)) * v5)) = (x \ (y * v5)) * K(z,K(u,w))
    ]]></literal>
    <justification jstring="[para(15475(a,2),17759(a,1,2,2))].">
      <j1 rule="para" parents="15475 17759"/>
    </justification>
  </clause>

  <clause id="18121">
    <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(14461(a,2),17825(a,1,2))].">
      <j1 rule="para" parents="14461 17825"/>
    </justification>
  </clause>

  <clause id="18122">
    <literal><![CDATA[
      ((x \ K(y,z)) \ K(y,T(z,u))) * K(y,K(z,w)) = (x \ T(K(y,z),u)) \ K(y,T(z,w))
    ]]></literal>
    <justification jstring="[para(17832(a,1),12319(a,1,1))].">
      <j1 rule="para" parents="17832 12319"/>
    </justification>
  </clause>

  <clause id="18123">
    <literal><![CDATA[
      T(x,T(y \ (K(z,u) \ w),y)) = T(x,w / (K(u,z) \ y))
    ]]></literal>
    <justification jstring="[hyper(16567,a,17903,a),flip(a)].">
      <j1 rule="hyper" parents="16567 17903"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18124">
    <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(18123(a,1),13513(a,1))].">
      <j1 rule="para" parents="18123 13513"/>
    </justification>
  </clause>

  <clause id="18125">
    <literal><![CDATA[
      T(x * a(y,z,K(u,w)),v5) = T(x,v5) * a(y,z,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(37,a,4259,a,b,17919,a),flip(a)].">
      <j1 rule="hyper" parents="37 4259 17919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18126">
    <literal><![CDATA[
      T(x,y * a(z,u,K(w,v5))) * a(v6,v7,K(v8,v9)) = T(x * a(v6,v7,K(v8,v9)),y)
    ]]></literal>
    <justification jstring="[hyper(17928,a,18125,a),flip(a)].">
      <j1 rule="hyper" parents="17928 18125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18127">
    <literal><![CDATA[
      T(x * a(y,z,K(u,w)),v5) = a(y,z,K(u,w)) * T(x,v5)
    ]]></literal>
    <justification jstring="[hyper(333,a,17584,a,b,18125,a),flip(a)].">
      <j1 rule="hyper" parents="333 17584 18125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18128">
    <literal><![CDATA[
      T(a(x,y,K(z,u)) * w,v5) = T(w,v5) * a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(17584(a,2),18125(a,1,1))].">
      <j1 rule="para" parents="17584 18125"/>
    </justification>
  </clause>

  <clause id="18129">
    <literal><![CDATA[
      x / T((a(y,z,K(u,w)) * x) * a(w,z,K(u,y)),v5) = K(v5,x / a(w,z,K(u,y)))
    ]]></literal>
    <justification jstring="[para(18127(a,2),13853(a,1,2))].">
      <j1 rule="para" parents="18127 13853"/>
    </justification>
  </clause>

  <clause id="18130">
    <literal><![CDATA[
      x \ (y * T((a(z,u,K(w,v5)) * (y \ x)) * a(v5,u,K(w,z)),v6)) = K((x \ (y * a(v5,u,K(w,z)))) \ 1,v6)
    ]]></literal>
    <justification jstring="[para(18127(a,2),13854(a,1,2,2))].">
      <j1 rule="para" parents="18127 13854"/>
    </justification>
  </clause>

  <clause id="18131">
    <literal><![CDATA[
      K(x,K(y \ (z * (u \ 1)),w) * v5) = K(x,K(w,u * (z \ y)) * v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,15213,a(flip),b,17968,a),flip(a)].">
      <j1 rule="hyper" parents="63 15213 17968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18132">
    <literal><![CDATA[
      K(x,(((y * z) / y) \ u) * w) = K(x,(T(z,y) \ u) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,17970,a(flip),b,17975,a),flip(a)].">
      <j1 rule="hyper" parents="63 17970 17975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18134">
    <literal><![CDATA[
      K(x,(T(T(y,z),z) \ u) * w) = K(x,(y \ u) * w)
    ]]></literal>
    <justification jstring="[para(239(a,1),18132(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="239 18132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18135">
    <literal><![CDATA[
      K(x,(T(y,y \ z) \ u) * w) = K(x,((z / (z / y)) \ u) * w)
    ]]></literal>
    <justification jstring="[para(3697(a,1),18132(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="3697 18132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18136">
    <literal><![CDATA[
      K(x,(y / T(z,y)) * u) = K(x,(z \ y) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,18040,a(flip),b,18134,a)].">
      <j1 rule="hyper" parents="63 18040 18134"/>
    </justification>
  </clause>

  <clause id="18137">
    <literal><![CDATA[
      K((T(T(x,y),y) \ z) * u,w) = (v5 * K(w,(x \ z) * u)) \ v5
    ]]></literal>
    <justification jstring="[para(18134(a,1),5990(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="18134 5990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18138">
    <literal><![CDATA[
      K(x / y,(y / x) * z) = K(x / y,(x \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,15848,a(flip),b,18136,a)].">
      <j1 rule="hyper" parents="63 15848 18136"/>
    </justification>
  </clause>

  <clause id="18139">
    <literal><![CDATA[
      K(x,(T(y,z) / z) * u) = K(x,(z \ y) * u)
    ]]></literal>
    <justification jstring="[para(3625(a,2),18136(a,1,2,1))].">
      <j1 rule="para" parents="3625 18136"/>
    </justification>
  </clause>

  <clause id="18140">
    <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(13328(a,1),18136(a,1,2,1,2))].">
      <j1 rule="para" parents="13328 18136"/>
    </justification>
  </clause>

  <clause id="18141">
    <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(17834(a,1),18136(a,1,2,1,2))].">
      <j1 rule="para" parents="17834 18136"/>
    </justification>
  </clause>

  <clause id="18142">
    <literal><![CDATA[
      a(x * (T(y,z) / z),u,K(w,v5)) = a(w,u,K(v5,(z \ y) * x))
    ]]></literal>
    <justification jstring="[para(18139(a,1),17699(a,2,3))].">
      <j1 rule="para" parents="18139 17699"/>
    </justification>
  </clause>

  <clause id="18143">
    <literal><![CDATA[
      K(x \ (x / (x / y)),z * (y \ (y * (x / y)))) = K(y / x,(y \ x) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,9055,a,b,18138,a)].">
      <j1 rule="hyper" parents="63 9055 18138"/>
    </justification>
  </clause>

  <clause id="18144">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(u,w) * (y * z)) = T(x,z * (y * K(w * u,w)))
    ]]></literal>
    <justification jstring="[hyper(16135,a,17998,a)].">
      <j1 rule="hyper" parents="16135 17998"/>
    </justification>
  </clause>

  <clause id="18145">
    <literal><![CDATA[
      K(x,y * (z * K((u * w) \ y,u * w))) = K(x,(((w * u) \ y) * (w * u)) * z)
    ]]></literal>
    <justification jstring="[para(12834(a,1),18019(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12834 18019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18146">
    <literal><![CDATA[
      K(x,(y / z) * T(u,y / z)) = K(x,u * (z \ T(y,z)))
    ]]></literal>
    <justification jstring="[para(12733(a,1),18044(a,1,2,2))].">
      <j1 rule="para" parents="12733 18044"/>
    </justification>
  </clause>

  <clause id="18147">
    <literal><![CDATA[
      K(x,y * (z \ T(u,z))) = K(x,y * (u / z))
    ]]></literal>
    <justification jstring="[para(111(a,1),18146(a,1,2)),flip(a)].">
      <j1 rule="para" parents="111 18146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18148">
    <literal><![CDATA[
      K(x,x * (((y * x) * z) \ T(u,(y * x) * z))) = K(x,u / (y * z))
    ]]></literal>
    <justification jstring="[hyper(333,a,11885,a(flip),b,18147,a),flip(a)].">
      <j1 rule="hyper" parents="333 11885 18147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18149">
    <literal><![CDATA[
      T(x,y * (z \ T(u,z))) = T(x,y * (u / z))
    ]]></literal>
    <justification jstring="[hyper(124,a,18147,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 18147 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18150">
    <literal><![CDATA[
      K(x,y * (T(z,u) \ u)) = K(x,y * (u / z))
    ]]></literal>
    <justification jstring="[para(3628(a,2),18147(a,1,2,2))].">
      <j1 rule="para" parents="3628 18147"/>
    </justification>
  </clause>

  <clause id="18151">
    <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(333,a,10898,a(flip),b,18052,a),flip(a)].">
      <j1 rule="hyper" parents="333 10898 18052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18152">
    <literal><![CDATA[
      K(x,y * (((z * u) \ z) \ 1)) = K(x,y / (z / (u * z)))
    ]]></literal>
    <justification jstring="[hyper(15138,a,18059,a),flip(a)].">
      <j1 rule="hyper" parents="15138 18059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18153">
    <literal><![CDATA[
      K(x,y / (z / (u * z))) = K(x,y / ((z * u) \ z))
    ]]></literal>
    <justification jstring="[hyper(13528,a,18152,a),flip(a)].">
      <j1 rule="hyper" parents="13528 18152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18154">
    <literal><![CDATA[
      K(x,y / (z / (u * z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / ((z * u) \ z)) = w
    ]]></literal>
    <justification jstring="[para(18152(a,1),13528(a,1))].">
      <j1 rule="para" parents="18152 13528"/>
    </justification>
  </clause>

  <clause id="18155">
    <literal><![CDATA[
      K(x,y / (z / (u * z))) = K(x,y / (z \ (z / u)))
    ]]></literal>
    <justification jstring="[hyper(333,a,13674,a(flip),b,18153,a),flip(a)].">
      <j1 rule="hyper" parents="333 13674 18153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18156">
    <literal><![CDATA[
      K(x,y / (z \ (z / u))) \ 1 = K(y / (z / (u * z)),x)
    ]]></literal>
    <justification jstring="[para(18155(a,1),4367(a,1,1))].">
      <j1 rule="para" parents="18155 4367"/>
    </justification>
  </clause>

  <clause id="18157">
    <literal><![CDATA[
      K(x / (y / (z * y)),u) = K(x / (y \ (y / z)),u)
    ]]></literal>
    <justification jstring="[hyper(4382,a,18156,a),flip(a)].">
      <j1 rule="hyper" parents="4382 18156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18158">
    <literal><![CDATA[
      K(x / (y \ (y / z)),T(u,x)) = K((y / (z * y)) \ x,u)
    ]]></literal>
    <justification jstring="[hyper(6700,a,18157,a),flip(a)].">
      <j1 rule="hyper" parents="6700 18157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18159">
    <literal><![CDATA[
      K((x / (y * x)) \ z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K((x \ (x / y)) \ z,u) = w
    ]]></literal>
    <justification jstring="[para(18158(a,1),6700(a,1))].">
      <j1 rule="para" parents="18158 6700"/>
    </justification>
  </clause>

  <clause id="18160">
    <literal><![CDATA[
      K((x / ((y * (y * x)) / y)) \ z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K((x \ (x / T(y,y * x))) \ z,u) = w
    ]]></literal>
    <justification jstring="[para(3353(a,2),18159(a,1,1,1,2))].">
      <j1 rule="para" parents="3353 18159"/>
    </justification>
  </clause>

  <clause id="18161">
    <literal><![CDATA[
      K(x,T(T(y,z) * u,T(y,z)) * w) = K(x,K(z,y) * (T(y * u,y) * w))
    ]]></literal>
    <justification jstring="[hyper(13436,a,18065,a)].">
      <j1 rule="hyper" parents="13436 18065"/>
    </justification>
  </clause>

  <clause id="18162">
    <literal><![CDATA[
      T(x,y \ (z \ T(u,z))) = T(x,y \ (u / z))
    ]]></literal>
    <justification jstring="[hyper(333,a,5447,a(flip),b,18092,a),flip(a)].">
      <j1 rule="hyper" parents="333 5447 18092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18163">
    <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(14461(a,2),18121(a,2,2))].">
      <j1 rule="para" parents="14461 18121"/>
    </justification>
  </clause>

  <clause id="18164">
    <literal><![CDATA[
      K((T(T(x,y),y) \ z) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K((x \ z) * u,w) = v5
    ]]></literal>
    <justification jstring="[para(18137(a,2),6024(a,1))].">
      <j1 rule="para" parents="18137 6024"/>
    </justification>
  </clause>

  <clause id="18165">
    <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(13693,a,18151,a)].">
      <j1 rule="hyper" parents="13693 18151"/>
    </justification>
  </clause>

  <clause id="18166">
    <literal><![CDATA[
      T(x * (T(y,x) * K(z,u)),K(z,u)) = (K(z,u) * y) * x
    ]]></literal>
    <justification jstring="[hyper(333,a,13872,a(flip),b,17614,a),flip(a)].">
      <j1 rule="hyper" parents="333 13872 17614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18167">
    <literal><![CDATA[
      T((K(x,y) * z) * u,K(x,y)) = u * (T(z,u) * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(6857,a,18166,a)].">
      <j1 rule="hyper" parents="6857 18166"/>
    </justification>
  </clause>

  <clause id="18168">
    <literal><![CDATA[
      K(x,(y * (T(z,y) * K(u,w))) / v5) = K(x,((K(u,w) * z) * y) / v5)
    ]]></literal>
    <justification jstring="[para(18166(a,1),16332(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="18166 16332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18169">
    <literal><![CDATA[
      K(x,(y * (T(z,y) * K(u,w))) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,((K(u,w) * z) * y) * v5) = v6
    ]]></literal>
    <justification jstring="[para(18167(a,1),16375(a,1,2,1))].">
      <j1 rule="para" parents="18167 16375"/>
    </justification>
  </clause>

  <clause id="18170">
    <literal><![CDATA[
      K(x,y \ (z * (T(u,z) * K(w,v5)))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ ((K(w,v5) * u) * z)) = v6
    ]]></literal>
    <justification jstring="[para(18167(a,1),16377(a,1,2,2))].">
      <j1 rule="para" parents="18167 16377"/>
    </justification>
  </clause>

  <clause id="18171">
    <literal><![CDATA[
      K(x,y / (z * (T(u,z) * K(w,v5)))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y / ((K(w,v5) * u) * z)) = v6
    ]]></literal>
    <justification jstring="[para(18167(a,1),16382(a,1,2,2))].">
      <j1 rule="para" parents="18167 16382"/>
    </justification>
  </clause>

  <clause id="18172">
    <literal><![CDATA[
      (x * (y / z)) * K(u,L(z,y,x)) = x * (y / T(z,u))
    ]]></literal>
    <justification jstring="[hyper(17618,a,14216,a)].">
      <j1 rule="hyper" parents="17618 14216"/>
    </justification>
  </clause>

  <clause id="18173">
    <literal><![CDATA[
      (x * (y / z)) * K(y,z) = x * (y / T(z,y))
    ]]></literal>
    <justification jstring="[para(10356(a,1),18172(a,1,2))].">
      <j1 rule="para" parents="10356 18172"/>
    </justification>
  </clause>

  <clause id="18174">
    <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(18172(a,1),17165(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18172 17165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18175">
    <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(18172(a,1),18025(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="18172 18025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18177">
    <literal><![CDATA[
      K(x,K(y,z) * (u * (w * (z / y)))) = K(x,u * (w * (z / T(y,z))))
    ]]></literal>
    <justification jstring="[para(18173(a,1),18011(a,2,2,2))].">
      <j1 rule="para" parents="18173 18011"/>
    </justification>
  </clause>

  <clause id="18178">
    <literal><![CDATA[
      K(x,L(y,z,(u * w) * (u \ 1))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,L(w,u,u \ 1))) = v5
    ]]></literal>
    <justification jstring="[para(17645(a,2),14123(a,1))].">
      <j1 rule="para" parents="17645 14123"/>
    </justification>
  </clause>

  <clause id="18180">
    <literal><![CDATA[
      a(x \ y,x,K(z,u)) * K(z,(x * u) / y) = K(z,x / (y / u))
    ]]></literal>
    <justification jstring="[hyper(63,a,13763,a(flip),b,17718,a)].">
      <j1 rule="hyper" parents="63 13763 17718"/>
    </justification>
  </clause>

  <clause id="18181">
    <literal><![CDATA[
      K(x,L(T(y,z) / u,y,z)) = K(x,(z * y) / (u * z))
    ]]></literal>
    <justification jstring="[hyper(17745,a,16226,a)].">
      <j1 rule="hyper" parents="17745 16226"/>
    </justification>
  </clause>

  <clause id="18182">
    <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(6728(a,1),17831(a,1,2,2,2))].">
      <j1 rule="para" parents="6728 17831"/>
    </justification>
  </clause>

  <clause id="18183">
    <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(7622(a,1),17831(a,1,2,2,2))].">
      <j1 rule="para" parents="7622 17831"/>
    </justification>
  </clause>

  <clause id="18185">
    <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(7508(a,1),18064(a,1))].">
      <j1 rule="para" parents="7508 18064"/>
    </justification>
  </clause>

  <clause id="18186">
    <literal><![CDATA[
      K(x,T(y \ 1,L(z,u,w)) \ v5) = K(x,K(y,z) * (y * v5))
    ]]></literal>
    <justification jstring="[para(8(a,1),18096(a,2,2,1,1))].">
      <j1 rule="para" parents="8 18096"/>
    </justification>
  </clause>

  <clause id="18187">
    <literal><![CDATA[
      K(x,T(y \ 1,L(z,u,w)) \ v5) = K(x,T(y,z) * v5)
    ]]></literal>
    <justification jstring="[para(4273(a,1),18186(a,2,2))].">
      <j1 rule="para" parents="4273 18186"/>
    </justification>
  </clause>

  <clause id="18188">
    <literal><![CDATA[
      K(x,T(y \ 1,z) \ u) = K(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[para(371(a,1),18187(a,1,2,1,2))].">
      <j1 rule="para" parents="371 18187"/>
    </justification>
  </clause>

  <clause id="18189">
    <literal><![CDATA[
      K(x,T(1 / y,z) \ u) = K(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(13586,a,18188,a)].">
      <j1 rule="hyper" parents="13586 18188"/>
    </justification>
  </clause>

  <clause id="18190">
    <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(10963,a,18188,a)].">
      <j1 rule="hyper" parents="10963 18188"/>
    </justification>
  </clause>

  <clause id="18191">
    <literal><![CDATA[
      T(x,T(y \ 1,z) \ u) = T(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(124,a,18188,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 18188 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18192">
    <literal><![CDATA[
      K(x,(((y * z) \ y) \ 1) \ u) = K(x,T((z * y) \ y,y) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,14971,a(flip),b,18188,a)].">
      <j1 rule="hyper" parents="63 14971 18188"/>
    </justification>
  </clause>

  <clause id="18193">
    <literal><![CDATA[
      K(x,T(y \ 1,z) * u) = K(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(76(a,1),18189(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="76 18189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18194">
    <literal><![CDATA[
      T(x,T(y \ 1,z) * u) = T(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(13612,a,18191,a),flip(a)].">
      <j1 rule="hyper" parents="13612 18191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18195">
    <literal><![CDATA[
      T(x,T(y \ 1,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z) \ u) = w
    ]]></literal>
    <justification jstring="[para(18191(a,1),13612(a,1))].">
      <j1 rule="para" parents="18191 13612"/>
    </justification>
  </clause>

  <clause id="18196">
    <literal><![CDATA[
      T(x,T(y \ 1,z \ T(u,w)) \ v5) = T(x,T(y,(u \ z) \ K(w,u)) * v5)
    ]]></literal>
    <justification jstring="[para(15059(a,1),18191(a,1,2,1))].">
      <j1 rule="para" parents="15059 18191"/>
    </justification>
  </clause>

  <clause id="18197">
    <literal><![CDATA[
      T(x,T(K(y,z) * u,w) \ v5) = T(x,T(u \ K(z,y),w) * v5)
    ]]></literal>
    <justification jstring="[para(13162(a,1),18194(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="13162 18194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18198">
    <literal><![CDATA[
      T(x,T(K(y,z) / u,w) \ v5) = T(x,T(u * K(z,y),w) * v5)
    ]]></literal>
    <justification jstring="[para(13252(a,1),18194(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="13252 18194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18199">
    <literal><![CDATA[
      T(x,T((y \ z) \ K(y,u),w) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,T(T(y,u) \ z,w) \ v5) = v6
    ]]></literal>
    <justification jstring="[para(13267(a,1),18195(a,1,2,1,1))].">
      <j1 rule="para" parents="13267 18195"/>
    </justification>
  </clause>

  <clause id="18200">
    <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(333,a,10898,a(flip),b,18190,a),flip(a)].">
      <j1 rule="hyper" parents="333 10898 18190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18201">
    <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(18190(a,2),10963(a,1))].">
      <j1 rule="para" parents="18190 10963"/>
    </justification>
  </clause>

  <clause id="18202">
    <literal><![CDATA[
      K(x,(((y * z) \ y) \ 1) \ u) = K(x,(y / (z * y)) * u)
    ]]></literal>
    <justification jstring="[hyper(333,a,16244,a(flip),b,18192,a),flip(a)].">
      <j1 rule="hyper" parents="333 16244 18192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18203">
    <literal><![CDATA[
      K(x,(y / (z * y)) * u) = K(x,((y * z) \ y) * u)
    ]]></literal>
    <justification jstring="[hyper(13421,a,18202,a),flip(a)].">
      <j1 rule="hyper" parents="13421 18202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18204">
    <literal><![CDATA[
      K(x,(y / (z * y)) * u) = K(x,(y \ (y / z)) * u)
    ]]></literal>
    <justification jstring="[hyper(333,a,4873,a(flip),b,18203,a),flip(a)].">
      <j1 rule="hyper" parents="333 4873 18203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18206">
    <literal><![CDATA[
      (x / T((y / (z * y)) * u,w)) \ (x * K(w,(y \ (y / z)) * u)) = (y / (z * y)) * u
    ]]></literal>
    <justification jstring="[para(18204(a,1),5461(a,1,2,2))].">
      <j1 rule="para" parents="18204 5461"/>
    </justification>
  </clause>

  <clause id="18207">
    <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(63,a,16914,a,b,18197,a)].">
      <j1 rule="hyper" parents="63 16914 18197"/>
    </justification>
  </clause>

  <clause id="18208">
    <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(79(a,1),18200(a,1,2,1,1,1)),flip(a)].">
      <j1 rule="para" parents="79 18200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18209">
    <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(18208(a,1),14236(a,1))].">
      <j1 rule="para" parents="18208 14236"/>
    </justification>
  </clause>

  <clause id="18210">
    <literal><![CDATA[
      K(x,y * (z \ K(u,L(w,v5,v6)))) = K(x,y * (z \ K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(333,a,18073,a(flip),b,18098,a),flip(a)].">
      <j1 rule="hyper" parents="333 18073 18098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18211">
    <literal><![CDATA[
      K(x,y * (z \ T(u * w,w))) = K(x,y * (z \ (w * u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,12836,a(flip),b,18100,a),flip(a)].">
      <j1 rule="hyper" parents="63 12836 18100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18213">
    <literal><![CDATA[
      K(x,y * (z \ (u * (w / u)))) = K(x,y * (z \ T(w,u)))
    ]]></literal>
    <justification jstring="[para(12(a,1),18211(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="12 18211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18214">
    <literal><![CDATA[
      a(x,y,K(z \ y,u)) * K(x,(y * u) / z) = K(x,y / (z / u))
    ]]></literal>
    <justification jstring="[para(13744(a,1),18180(a,1,1))].">
      <j1 rule="para" parents="13744 18180"/>
    </justification>
  </clause>

  <clause id="18215">
    <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(17692(a,1),18180(a,1,1))].">
      <j1 rule="para" parents="17692 18180"/>
    </justification>
  </clause>

  <clause id="18216">
    <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(113(a,1),18182(a,1,2,2,2,2))].">
      <j1 rule="para" parents="113 18182"/>
    </justification>
  </clause>

  <clause id="18217">
    <literal><![CDATA[
      K(x,(y * z) / u) * a(x,y,K(u \ y,z)) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[hyper(17586,a,18214,a)].">
      <j1 rule="hyper" parents="17586 18214"/>
    </justification>
  </clause>

  <clause id="18218">
    <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(11912(a,1),18214(a,1,1,3,1))].">
      <j1 rule="para" parents="11912 18214"/>
    </justification>
  </clause>

  <clause id="18219">
    <literal><![CDATA[
      K(x,(y * z) / u) * a(z,y,K(x,u \ y)) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[hyper(63,a,13742,a(flip),b,18217,a)].">
      <j1 rule="hyper" parents="63 13742 18217"/>
    </justification>
  </clause>

  <clause id="18220">
    <literal><![CDATA[
      K((x * K(y,z)) \ ((x * u) * K(y,z)),w) = K(u,T(T(w,x),x))
    ]]></literal>
    <justification jstring="[hyper(333,a,6935,a(flip),b,17565,a),flip(a)].">
      <j1 rule="hyper" parents="333 6935 17565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18221">
    <literal><![CDATA[
      K((x * K(y,z)) \ ((x * u) * K(y,z)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(u,w) = v5
    ]]></literal>
    <justification jstring="[para(18220(a,2),7064(a,1))].">
      <j1 rule="para" parents="18220 7064"/>
    </justification>
  </clause>

  <clause id="18224">
    <literal><![CDATA[
      T(x,(y / (z \ T(u,K(w,v5)))) * K(u,K(w,v5))) = T(x,y / (z \ u))
    ]]></literal>
    <justification jstring="[para(17782(a,1),17571(a,1,2))].">
      <j1 rule="para" parents="17782 17571"/>
    </justification>
  </clause>

  <clause id="18226">
    <literal><![CDATA[
      (x \ L(T(y,y * K(z,u)),w,v5)) * K(y,K(z,u)) = x \ L(y,w,v5)
    ]]></literal>
    <justification jstring="[para(25(a,2),17665(a,1,1,2))].">
      <j1 rule="para" parents="25 17665"/>
    </justification>
  </clause>

  <clause id="18227">
    <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(11155(a,1),17721(a,1,2))].">
      <j1 rule="para" parents="11155 17721"/>
    </justification>
  </clause>

  <clause id="18228">
    <literal><![CDATA[
      K(x,(L(K(y,z),u,w) * v5) \ v6) = K(x,v5 \ (L(K(z,y),u,w) * v6))
    ]]></literal>
    <justification jstring="[para(9408(a,1),17746(a,1,2,1))].">
      <j1 rule="para" parents="9408 17746"/>
    </justification>
  </clause>

  <clause id="18229">
    <literal><![CDATA[
      T(T(x,y \ (z * z)),K(u,y \ (z * z))) = T(x,T((z \ y) \ z,u))
    ]]></literal>
    <justification jstring="[para(13408(a,1),17783(a,1,1))].">
      <j1 rule="para" parents="13408 17783"/>
    </justification>
  </clause>

  <clause id="18230">
    <literal><![CDATA[
      K(x,(y / T(z,T(u,w))) / v5) = K(x,(y / z) * (v5 \ K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(16491,a,17818,a),flip(a)].">
      <j1 rule="hyper" parents="16491 17818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18231">
    <literal><![CDATA[
      K(x,(y / T(z,T(u,w))) / v5) = K(x,(y / T(z,u)) / v5)
    ]]></literal>
    <justification jstring="[hyper(333,a,17817,a(flip),b,18230,a),flip(a)].">
      <j1 rule="hyper" parents="333 17817 18230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18232">
    <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(16700,a,18231,a)].">
      <j1 rule="hyper" parents="16700 18231"/>
    </justification>
  </clause>

  <clause id="18233">
    <literal><![CDATA[
      K(x * K(y,z),T(u,w / x)) = K(K(y,z) * x,T(u,w))
    ]]></literal>
    <justification jstring="[hyper(16555,a,17837,a)].">
      <j1 rule="hyper" parents="16555 17837"/>
    </justification>
  </clause>

  <clause id="18234">
    <literal><![CDATA[
      K(x * K(y,z),T(u,x \ w)) = K(K(y,z) * x,T(u,w))
    ]]></literal>
    <justification jstring="[hyper(15606,a,18233,a)].">
      <j1 rule="hyper" parents="15606 18233"/>
    </justification>
  </clause>

  <clause id="18236">
    <literal><![CDATA[
      T(x,K(((y \ z) * y) / (u * y),w)) = T(x,K(w,y \ (z / u)))
    ]]></literal>
    <justification jstring="[hyper(4307,a,17843,a),flip(a)].">
      <j1 rule="hyper" parents="4307 17843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18237">
    <literal><![CDATA[
      T(x,K(y,((z \ u) * z) / (w * z))) = T(x,K(y,z \ (u / w)))
    ]]></literal>
    <justification jstring="[hyper(6868,a,18236,a)].">
      <j1 rule="hyper" parents="6868 18236"/>
    </justification>
  </clause>

  <clause id="18238">
    <literal><![CDATA[
      T(x,K(y,z \ (((u \ w) * u) / u))) = T(x,K(y,u \ (w / z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,17743,a(flip),b,18237,a)].">
      <j1 rule="hyper" parents="63 17743 18237"/>
    </justification>
  </clause>

  <clause id="18239">
    <literal><![CDATA[
      T(x,K(y,z \ (u \ w))) = T(x,K(y,u \ (w / z)))
    ]]></literal>
    <justification jstring="[para(11(a,1),18238(a,1,2,2,2))].">
      <j1 rule="para" parents="11 18238"/>
    </justification>
  </clause>

  <clause id="18240">
    <literal><![CDATA[
      T(x,K(y,z \ (u \ (w * z)))) = T(x,K(y,u \ w))
    ]]></literal>
    <justification jstring="[para(11(a,1),18239(a,2,2,2,2))].">
      <j1 rule="para" parents="11 18239"/>
    </justification>
  </clause>

  <clause id="18242">
    <literal><![CDATA[
      K(x,K(y,z \ (u \ (w * z)))) = x \ T(x,K(y,u \ w))
    ]]></literal>
    <justification jstring="[hyper(121,a,18240,a(flip),b,4222,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="121 18240 4222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18243">
    <literal><![CDATA[
      K(x,K(y,z \ (u \ (w * z)))) = K(x,K(y,u \ w))
    ]]></literal>
    <justification jstring="[hyper(333,a,4215,a,b,18242,a),flip(a)].">
      <j1 rule="hyper" parents="333 4215 18242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18244">
    <literal><![CDATA[
      K(x,K(y,z \ (u \ w))) = K(x,K(y,u \ (w / z)))
    ]]></literal>
    <justification jstring="[para(12(a,1),18243(a,1,2,2,2,2))].">
      <j1 rule="para" parents="12 18243"/>
    </justification>
  </clause>

  <clause id="18245">
    <literal><![CDATA[
      K(x,K(y,z \ (u \ w))) = K(x,K(y,u \ (z \ w)))
    ]]></literal>
    <justification jstring="[hyper(333,a,16610,a(flip),b,18244,a)].">
      <j1 rule="hyper" parents="333 16610 18244"/>
    </justification>
  </clause>

  <clause id="18246">
    <literal><![CDATA[
      K(x,K(y,z \ (T(u,w) \ v5))) = K(x,K(y,u \ (z \ v5)))
    ]]></literal>
    <justification jstring="[hyper(333,a,16605,a(flip),b,18245,a),flip(a)].">
      <j1 rule="hyper" parents="333 16605 18245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18247">
    <literal><![CDATA[
      L(x,T(y,z),(y / z) \ 1) = L(x,T(y,z),(z \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,11860,a(flip),b,17862,a)].">
      <j1 rule="hyper" parents="63 11860 17862"/>
    </justification>
  </clause>

  <clause id="18248">
    <literal><![CDATA[
      L(x,T(y,z),(z \ y) \ 1) = L(x,y,(y / z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(14727,a,18247,a),flip(a)].">
      <j1 rule="hyper" parents="14727 18247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18249">
    <literal><![CDATA[
      L(x,y,(y / z) \ 1) = L(x,y,(z \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,14723,a(flip),b,18248,a),flip(a)].">
      <j1 rule="hyper" parents="63 14723 18248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18250">
    <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(864(a,1),18249(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="864 18249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18251">
    <literal><![CDATA[
      K(x,L(y,z,u * (w \ T(y,v5)))) = K(x,L(y,z,w \ u))
    ]]></literal>
    <justification jstring="[hyper(333,a,13764,a(flip),b,17868,a),flip(a)].">
      <j1 rule="hyper" parents="333 13764 17868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18252">
    <literal><![CDATA[
      K(x,L(y \ (L(T(z,K(u,w)),v5,v6) * v7),y,K(v7,L(T(z,K(u,w)),v5,v6)))) = K(x,(K(L(T(z,K(u,w)),v5,v6),v7) \ y) \ (v7 * L(z,v5,v6)))
    ]]></literal>
    <justification jstring="[para(5184(a,2),17872(a,1,2))].">
      <j1 rule="para" parents="5184 17872"/>
    </justification>
  </clause>

  <clause id="18253">
    <literal><![CDATA[
      T(x,L(K(y,z),u,w) \ (v5 * v6)) = T(x,v5 * (L(K(y,z),u,w) \ v6))
    ]]></literal>
    <justification jstring="[para(10851(a,2),17953(a,1,2,1))].">
      <j1 rule="para" parents="10851 17953"/>
    </justification>
  </clause>

  <clause id="18254">
    <literal><![CDATA[
      K(x,(((y * z) / u) \ 1) \ w) = K(x,((T(z,y) * y) / u) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,17986,a(flip),b,17988,a)].">
      <j1 rule="hyper" parents="63 17986 17988"/>
    </justification>
  </clause>

  <clause id="18255">
    <literal><![CDATA[
      K(x,((T(y,z) * z) / u) * w) = K(x,((z * y) / u) * w)
    ]]></literal>
    <justification jstring="[hyper(13421,a,18254,a),flip(a)].">
      <j1 rule="hyper" parents="13421 18254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18256">
    <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(15767,a,17989,a)].">
      <j1 rule="hyper" parents="15767 17989"/>
    </justification>
  </clause>

  <clause id="18257">
    <literal><![CDATA[
      K(x,K(y,z) * ((u \ y) * w)) = K(x,(u \ (z * (y / z))) * w)
    ]]></literal>
    <justification jstring="[hyper(12838,a,17993,a)].">
      <j1 rule="hyper" parents="12838 17993"/>
    </justification>
  </clause>

  <clause id="18258">
    <literal><![CDATA[
      K(x,(y \ (z * (u / z))) * w) = K(x,(y \ T(u,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,17981,a(flip),b,18257,a),flip(a)].">
      <j1 rule="hyper" parents="63 17981 18257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18259">
    <literal><![CDATA[
      K(x \ K(y \ K(z,u),w),v5) = K(x \ K(w,y * K(z,u)),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,16701,a(flip),b,18002,a),flip(a)].">
      <j1 rule="hyper" parents="63 16701 18002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18260">
    <literal><![CDATA[
      T(x,(y \ z) * (K(u,z \ y) * w)) = T(x,T((y \ z) \ 1,u) \ w)
    ]]></literal>
    <justification jstring="[para(8474(a,1),18005(a,1,2))].">
      <j1 rule="para" parents="8474 18005"/>
    </justification>
  </clause>

  <clause id="18261">
    <literal><![CDATA[
      K(x,y * (z \ (u \ T(w,u)))) = K(x,y * (z \ (w / u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,16752,a(flip),b,18030,a),flip(a)].">
      <j1 rule="hyper" parents="63 16752 18030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18262">
    <literal><![CDATA[
      K(x,y * (z \ ((u / (T(w,v5) \ 1)) \ T(v5,u / (T(w,v5) \ 1))))) = K(x,y * (z \ (T(v5,w) / (u / (w \ 1)))))
    ]]></literal>
    <justification jstring="[para(13349(a,2),18261(a,2,2,2,2))].">
      <j1 rule="para" parents="13349 18261"/>
    </justification>
  </clause>

  <clause id="18263">
    <literal><![CDATA[
      K(x,(T(y,K(z,u) * w) / v5) * v6) = K(x,(T(y,w) / v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,17976,a(flip),b,18061,a),flip(a)].">
      <j1 rule="hyper" parents="63 17976 18061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18264">
    <literal><![CDATA[
      K(x,y * (z \ T(u,w \ v5))) = K(x,y * (z \ T(u,w * v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,18029,a(flip),b,18076,a),flip(a)].">
      <j1 rule="hyper" parents="63 18029 18076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18265">
    <literal><![CDATA[
      T(x,y * ((z * u) * z)) = T(x,y * (z * (u * z)))
    ]]></literal>
    <justification jstring="[hyper(5458,a,18083,a),flip(a)].">
      <j1 rule="hyper" parents="5458 18083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18266">
    <literal><![CDATA[
      T(x,y * ((z * u) * z)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y * (z * (u * z))) = w
    ]]></literal>
    <justification jstring="[para(18083(a,1),5458(a,1))].">
      <j1 rule="para" parents="18083 5458"/>
    </justification>
  </clause>

  <clause id="18267">
    <literal><![CDATA[
      T(T(x,K(y,z * ((z \ 1) * u))),y * ((z \ 1) * (u * (z \ 1)))) = T(x,(((z \ 1) * u) * (z \ 1)) * y)
    ]]></literal>
    <justification jstring="[hyper(15823,a,18265,a),flip(a)].">
      <j1 rule="hyper" parents="15823 18265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18268">
    <literal><![CDATA[
      T(x,y * (z * ((((z \ 1) \ u) * (z \ 1)) * z))) = T(x,y * (T(z * u,z \ 1) * z))
    ]]></literal>
    <justification jstring="[para(962(a,1),18265(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="962 18265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18269">
    <literal><![CDATA[
      K((T(x,x \ y) \ T(y,x)) * z,u) = K((x \ y) * z,u)
    ]]></literal>
    <justification jstring="[para(3369(a,1),18088(a,1,1,1,2))].">
      <j1 rule="para" parents="3369 18088"/>
    </justification>
  </clause>

  <clause id="18270">
    <literal><![CDATA[
      K((T(x \ y,x) * K(y,x)) * z,u) = K((x \ y) * z,u)
    ]]></literal>
    <justification jstring="[para(13367(a,1),18269(a,1,1,1))].">
      <j1 rule="para" parents="13367 18269"/>
    </justification>
  </clause>

  <clause id="18271">
    <literal><![CDATA[
      K(T((x \ y) * K(y,x),x) * z,u) = K((x \ y) * z,u)
    ]]></literal>
    <justification jstring="[para(6647(a,2),18270(a,1,1,1))].">
      <j1 rule="para" parents="6647 18270"/>
    </justification>
  </clause>

  <clause id="18272">
    <literal><![CDATA[
      K(T(x \ T(y,x),x) * z,u) = K((x \ y) * z,u)
    ]]></literal>
    <justification jstring="[para(5454(a,1),18271(a,1,1,1,1))].">
      <j1 rule="para" parents="5454 18271"/>
    </justification>
  </clause>

  <clause id="18273">
    <literal><![CDATA[
      K((T(x,y) / y) * z,u) = K((y \ x) * z,u)
    ]]></literal>
    <justification jstring="[hyper(15125,a,18272,a)].">
      <j1 rule="hyper" parents="15125 18272"/>
    </justification>
  </clause>

  <clause id="18274">
    <literal><![CDATA[
      K((T(T(x,y),z) / y) * u,w) = K((y \ T(x,z)) * u,w)
    ]]></literal>
    <justification jstring="[para(23(a,1),18273(a,1,1,1,1))].">
      <j1 rule="para" parents="23 18273"/>
    </justification>
  </clause>

  <clause id="18275">
    <literal><![CDATA[
      K(x,K(y * (z \ u),y \ z) * w) = K(x,K(y * (z \ u),u) * w)
    ]]></literal>
    <justification jstring="[para(12901(a,1),18111(a,2,2,1))].">
      <j1 rule="para" parents="12901 18111"/>
    </justification>
  </clause>

  <clause id="18276">
    <literal><![CDATA[
      T(x,K(y \ (z * (u \ 1)),w) * v5) = T(x,K(w,u * (z \ y)) * v5)
    ]]></literal>
    <justification jstring="[hyper(124,a,18131,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 18131 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18277">
    <literal><![CDATA[
      T(x,y * (z * K(u * w,u))) = T(x,y * (z * K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,17998,a(flip),b,18144,a),flip(a)].">
      <j1 rule="hyper" parents="63 17998 18144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18278">
    <literal><![CDATA[
      T(x,y * ((z * u) * K(u,w))) = T(x,y * (z * ((w \ u) * w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,16265,a(flip),b,18277,a),flip(a)].">
      <j1 rule="hyper" parents="63 16265 18277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18279">
    <literal><![CDATA[
      T(x,y * (z * ((u \ w) * u))) = T(x,y * (z * T(w,u)))
    ]]></literal>
    <justification jstring="[para(5984(a,1),18278(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5984 18278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18280">
    <literal><![CDATA[
      T(x,y * T(z * ((u \ w) * u),z)) = T(x,y * (z * T((z * w) / z,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,15906,a(flip),b,18279,a)].">
      <j1 rule="hyper" parents="63 15906 18279"/>
    </justification>
  </clause>

  <clause id="18281">
    <literal><![CDATA[
      K(x,(y * z) \ T(u,(y * x) * z)) = K(x,u / (y * z))
    ]]></literal>
    <justification jstring="[hyper(14288,a,18148,a)].">
      <j1 rule="hyper" parents="14288 18148"/>
    </justification>
  </clause>

  <clause id="18282">
    <literal><![CDATA[
      K(x,(y * z) \ T(u,z * (y * x))) = K(x,u / (y * z))
    ]]></literal>
    <justification jstring="[hyper(16443,a,18281,a)].">
      <j1 rule="hyper" parents="16443 18281"/>
    </justification>
  </clause>

  <clause id="18283">
    <literal><![CDATA[
      T(x,y / (z \ T(u,K(w,v5)))) = T(x,y / (z \ u))
    ]]></literal>
    <justification jstring="[hyper(16385,a,18224,a)].">
      <j1 rule="hyper" parents="16385 18224"/>
    </justification>
  </clause>

  <clause id="18285">
    <literal><![CDATA[
      (x \ L(T(y,K(z,u)),w,v5)) * K(y,K(z,u)) = x \ L(y,w,v5)
    ]]></literal>
    <justification jstring="[para(12960(a,1),18226(a,1,1,2,1))].">
      <j1 rule="para" parents="12960 18226"/>
    </justification>
  </clause>

  <clause id="18286">
    <literal><![CDATA[
      T(x,K(y,z)) \ L(x,u,w) = x \ L(T(x,K(y,z)),u,w)
    ]]></literal>
    <justification jstring="[hyper(15633,a,18285,a),flip(a)].">
      <j1 rule="hyper" parents="15633 18285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18287">
    <literal><![CDATA[
      K(x,(y * L(K(z,u),w,v5)) \ v6) = K(x,y \ (L(K(u,z),w,v5) * v6))
    ]]></literal>
    <justification jstring="[hyper(16447,a,18228,a)].">
      <j1 rule="hyper" parents="16447 18228"/>
    </justification>
  </clause>

  <clause id="18288">
    <literal><![CDATA[
      K(x,((K(y,z) \ u) * L((K(y,z) \ u) \ u,w,v5)) \ v6) = K(x,(K(y,z) \ u) \ (L(K(z,y),w,v5) * v6))
    ]]></literal>
    <justification jstring="[para(670(a,2),18228(a,1,2,1))].">
      <j1 rule="para" parents="670 18228"/>
    </justification>
  </clause>

  <clause id="18289">
    <literal><![CDATA[
      T(x,T((y \ z) \ y,u)) = T(x,T(z \ (y * y),u))
    ]]></literal>
    <justification jstring="[hyper(6883,a,18229,a),flip(a)].">
      <j1 rule="hyper" parents="6883 18229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18290">
    <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(13221(a,1),18289(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="13221 18289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18291">
    <literal><![CDATA[
      T(x,y * (L(K(z,u),w,v5) \ v6)) = T(x,K(z,u) \ (y * v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,17938,a(flip),b,18253,a),flip(a)].">
      <j1 rule="hyper" parents="63 17938 18253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18293">
    <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(17178(a,1),18256(a,1,1))].">
      <j1 rule="para" parents="17178 18256"/>
    </justification>
  </clause>

  <clause id="18294">
    <literal><![CDATA[
      T(x,(y \ z) * (u * K(w,z \ y))) = T(x,T((y \ z) \ 1,w) \ u)
    ]]></literal>
    <justification jstring="[hyper(16319,a,18260,a)].">
      <j1 rule="hyper" parents="16319 18260"/>
    </justification>
  </clause>

  <clause id="18295">
    <literal><![CDATA[
      K(x,K(y * (z \ u),y \ z) * w) = K(x,K(z \ y,u) * w)
    ]]></literal>
    <justification jstring="[hyper(333,a,17169,a(flip),b,18275,a),flip(a)].">
      <j1 rule="hyper" parents="333 17169 18275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18296">
    <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(63,a,17069,a(flip),b,18295,a),flip(a)].">
      <j1 rule="hyper" parents="63 17069 18295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18297">
    <literal><![CDATA[
      T(x,y * K(z,u \ (w * (v5 \ 1)))) = T(x,K(z,v5 * (w \ u)) * y)
    ]]></literal>
    <justification jstring="[hyper(15771,a,18276,a)].">
      <j1 rule="hyper" parents="15771 18276"/>
    </justification>
  </clause>

  <clause id="18298">
    <literal><![CDATA[
      (x * K(y,z \ (L(K(u,w),v5,v6) * v7))) \ x = K((z * L(K(w,u),v5,v6)) \ v7,y)
    ]]></literal>
    <justification jstring="[para(18287(a,1),5990(a,1,1,2))].">
      <j1 rule="para" parents="18287 5990"/>
    </justification>
  </clause>

  <clause id="18299">
    <literal><![CDATA[
      T(x,T(K(y,z \ u) * z,u)) = T(x,T((u \ z) \ 1,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,17942,a(flip),b,18294,a)].">
      <j1 rule="hyper" parents="63 17942 18294"/>
    </justification>
  </clause>

  <clause id="18300">
    <literal><![CDATA[
      T(x,T(y * K(z,y \ u),u)) = T(x,T((u \ y) \ 1,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(15598,a,18299,a)].">
      <j1 rule="hyper" parents="15598 18299"/>
    </justification>
  </clause>

  <clause id="18301">
    <literal><![CDATA[
      T(x,T((y \ z) \ 1,u) \ y) = T(x,T(z \ y,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(9505,a,18300,a),flip(a)].">
      <j1 rule="hyper" parents="9505 18300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18302">
    <literal><![CDATA[
      T(x,T(y \ z,u) \ z) = T(x,T(z \ y,u) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,18191,a(flip),b,18301,a),flip(a)].">
      <j1 rule="hyper" parents="63 18191 18301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18303">
    <literal><![CDATA[
      T(x,T(y \ z,u) \ z) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,z * T(y / z,u)) = w
    ]]></literal>
    <justification jstring="[para(18302(a,2),12279(a,1))].">
      <j1 rule="para" parents="18302 12279"/>
    </justification>
  </clause>

  <clause id="18304">
    <literal><![CDATA[
      T(T(x,K(y,z)),z * T(y / z,u)) = T(x,T(z / y,u) \ z)
    ]]></literal>
    <justification jstring="[hyper(18303,a,16086,a)].">
      <j1 rule="hyper" parents="18303 16086"/>
    </justification>
  </clause>

  <clause id="18305">
    <literal><![CDATA[
      T(x,T(y / z,u) \ y) = T(x,y * T(y \ z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,16092,a(flip),b,18304,a),flip(a)].">
      <j1 rule="hyper" parents="63 16092 18304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18306">
    <literal><![CDATA[
      K(x,K(y,z)) \ (K(y,x) \ (z * u)) = (z * K(x,y)) * L(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(4567(a,2),17530(a,1,2))].">
      <j1 rule="para" parents="4567 17530"/>
    </justification>
  </clause>

  <clause id="18308">
    <literal><![CDATA[
      T(x,T(a(y,z,u),w) * v5) = T(x,v5 * a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(17949,a,17682,a),flip(a)].">
      <j1 rule="hyper" parents="17949 17682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18309">
    <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(18308(a,1),15592(a,1,2,1))].">
      <j1 rule="para" parents="18308 15592"/>
    </justification>
  </clause>

  <clause id="18310">
    <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(17519(a,1),17796(a,1,2))].">
      <j1 rule="para" parents="17519 17796"/>
    </justification>
  </clause>

  <clause id="18311">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1) * (y \ u)) = K(x,u * a(y,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(17858,a,14744,a),flip(a)].">
      <j1 rule="hyper" parents="17858 14744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18312">
    <literal><![CDATA[
      K(x,a(y \ 1,y,z) \ u) = K(x,u * a(z,y,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,14746,a(flip),b,18311,a)].">
      <j1 rule="hyper" parents="63 14746 18311"/>
    </justification>
  </clause>

  <clause id="18313">
    <literal><![CDATA[
      K(x,(L(y,z,u) \ w) * y) = K(x,y * (w / L(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(17557,a,17897,a)].">
      <j1 rule="hyper" parents="17557 17897"/>
    </justification>
  </clause>

  <clause id="18314">
    <literal><![CDATA[
      K(x,(y * z) / L(y,u,w)) = K(x,y * (z / L(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,18116,a,b,18313,a)].">
      <j1 rule="hyper" parents="63 18116 18313"/>
    </justification>
  </clause>

  <clause id="18316">
    <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(18115,a,16793,a)].">
      <j1 rule="hyper" parents="18115 16793"/>
    </justification>
  </clause>

  <clause id="18317">
    <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(17519(a,1),18310(a,1,2,2))].">
      <j1 rule="para" parents="17519 18310"/>
    </justification>
  </clause>

  <clause id="18318">
    <literal><![CDATA[
      L(x * K(y,K(z,u)),w,v5) = K(y,K(z,u)) * L(x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(504,a,18317,a)].">
      <j1 rule="hyper" parents="504 18317"/>
    </justification>
  </clause>

  <clause id="18319">
    <literal><![CDATA[
      L(x * K(y,K(z,u)),w,v5) = L(x,w,v5) * K(y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(333,a,15475,a(flip),b,18318,a),flip(a)].">
      <j1 rule="hyper" parents="333 15475 18318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18320">
    <literal><![CDATA[
      K(x,L(y * K(z,K(u,w)),v5,v6)) = K(x,L(y,v5,v6))
    ]]></literal>
    <justification jstring="[para(18318(a,2),16323(a,1,2))].">
      <j1 rule="para" parents="18318 16323"/>
    </justification>
  </clause>

  <clause id="18321">
    <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(18318(a,2),16489(a,1,2,2))].">
      <j1 rule="para" parents="18318 16489"/>
    </justification>
  </clause>

  <clause id="18322">
    <literal><![CDATA[
      K(x,L(y \ K(z,T(u,w)),v5,v6)) = K(x,L(y \ K(z,u),v5,v6))
    ]]></literal>
    <justification jstring="[para(12319(a,1),18320(a,1,2,1))].">
      <j1 rule="para" parents="12319 18320"/>
    </justification>
  </clause>

  <clause id="18323">
    <literal><![CDATA[
      K(x,L(T(y,K(z,u)) \ w,v5,v6)) = K(x,L(y \ w,v5,v6))
    ]]></literal>
    <justification jstring="[para(15625(a,1),18320(a,1,2,1))].">
      <j1 rule="para" parents="15625 18320"/>
    </justification>
  </clause>

  <clause id="18324">
    <literal><![CDATA[
      L(K(x,K(y,z)) * u,w,v5) = L(u,w,v5) * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(15475(a,2),18319(a,1,1))].">
      <j1 rule="para" parents="15475 18319"/>
    </justification>
  </clause>

  <clause id="18325">
    <literal><![CDATA[
      T(L((x * K(y,x)) * K(y,K(z,u)),w,v5),y * K(u,z)) = y \ T(y * L(x,w,v5),K(z,u))
    ]]></literal>
    <justification jstring="[para(18319(a,2),16049(a,1,1))].">
      <j1 rule="para" parents="18319 16049"/>
    </justification>
  </clause>

  <clause id="18326">
    <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(6191(a,1),18323(a,1,2,1,1))].">
      <j1 rule="para" parents="6191 18323"/>
    </justification>
  </clause>

  <clause id="18327">
    <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(18324(a,2),16340(a,1,2,2))].">
      <j1 rule="para" parents="18324 16340"/>
    </justification>
  </clause>

  <clause id="18328">
    <literal><![CDATA[
      K(x,T((y * K(z,T(u,w))) / v5,y \ v5)) = K(x,L((v5 / y) \ K(z,T(u,y)),v5 / y,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,16055,a(flip),b,18322,a)].">
      <j1 rule="hyper" parents="63 16055 18322"/>
    </justification>
  </clause>

  <clause id="18329">
    <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(4830(a,1),18327(a,1,2,2,1))].">
      <j1 rule="para" parents="4830 18327"/>
    </justification>
  </clause>

  <clause id="18330">
    <literal><![CDATA[
      K(x,L(y,z,u / (T(w,x) * v5))) = K(x,L(y,z,(w * v5) \ u))
    ]]></literal>
    <justification jstring="[hyper(13771,a,17719,a),flip(a)].">
      <j1 rule="hyper" parents="13771 17719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18331">
    <literal><![CDATA[
      K(x,L(y,z,(T(u,x) * w) \ v5)) = K(x,L(y,z,(u * w) \ v5))
    ]]></literal>
    <justification jstring="[hyper(17863,a,18330,a)].">
      <j1 rule="hyper" parents="17863 18330"/>
    </justification>
  </clause>

  <clause id="18332">
    <literal><![CDATA[
      K(x,L(y,z,(y * z) \ u)) * u = (y * z) * ((T(y,x) * z) \ u)
    ]]></literal>
    <justification jstring="[para(18331(a,1),14077(a,1,1))].">
      <j1 rule="para" parents="18331 14077"/>
    </justification>
  </clause>

  <clause id="18333">
    <literal><![CDATA[
      K(x,L(y,z,z \ u)) * u = (y * z) * ((T(y,x) * z) \ u)
    ]]></literal>
    <justification jstring="[para(18118(a,1),18332(a,1,1))].">
      <j1 rule="para" parents="18118 18332"/>
    </justification>
  </clause>

  <clause id="18334">
    <literal><![CDATA[
      (x * y) * ((T(x,z) * y) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      (K(z,x) * y) * (y \ u) = w
    ]]></literal>
    <justification jstring="[para(18333(a,1),13874(a,1))].">
      <j1 rule="para" parents="18333 13874"/>
    </justification>
  </clause>

  <clause id="18335">
    <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(18334,a,16684,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="18334 16684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18336">
    <literal><![CDATA[
      a(x,y,K((z / (u / w)) * K(w,z),v5)) = a(x,y,K((u / T(w,z)) \ z,v5))
    ]]></literal>
    <justification jstring="[hyper(333,a,17694,a(flip),b,17723,a),flip(a)].">
      <j1 rule="hyper" parents="333 17694 17723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18337">
    <literal><![CDATA[
      T(T(x,x * y),a(x * y,z,u)) = T(T(x,x * y),a(y,z,u))
    ]]></literal>
    <justification jstring="[para(9(a,1),17737(a,1,2,1))].">
      <j1 rule="para" parents="9 17737"/>
    </justification>
  </clause>

  <clause id="18339">
    <literal><![CDATA[
      T(T(x,x * y),a(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,L(x * y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(18337(a,1),14537(a,1))].">
      <j1 rule="para" parents="18337 14537"/>
    </justification>
  </clause>

  <clause id="18340">
    <literal><![CDATA[
      L(T(x,L(y,z,u)),y,x) = T(x,L(x * y,z,u))
    ]]></literal>
    <justification jstring="[hyper(18339,a,13835,a),flip(a)].">
      <j1 rule="hyper" parents="18339 13835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18341">
    <literal><![CDATA[
      R(T(x,L(x * y,z,u)),y,x) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(41,a,3753,a,b,18340,a)].">
      <j1 rule="hyper" parents="41 3753 18340"/>
    </justification>
  </clause>

  <clause id="18342">
    <literal><![CDATA[
      L(K(x,x * y),z,u) \ T(x,L(y,z,u)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(18341(a,1),10927(a,1,2))].">
      <j1 rule="para" parents="18341 10927"/>
    </justification>
  </clause>

  <clause id="18343">
    <literal><![CDATA[
      L(K(x,x * (y / (z / ((u \ 1) \ 1)))),u \ z,u) \ T(x,(y * u) / z) = R(x,y / (z / ((u \ 1) \ 1)),x)
    ]]></literal>
    <justification jstring="[para(14668(a,1),18342(a,1,2))].">
      <j1 rule="para" parents="14668 18342"/>
    </justification>
  </clause>

  <clause id="18344">
    <literal><![CDATA[
      K(x,(K(y,z) * ((K(u,T(w,v5)) \ v6) / K(y,z))) \ v7) = K(x,v6 \ (K(w,T(u,v5)) \ v7))
    ]]></literal>
    <justification jstring="[para(6370(a,1),17801(a,1,2,1,2,1,1))].">
      <j1 rule="para" parents="6370 17801"/>
    </justification>
  </clause>

  <clause id="18345">
    <literal><![CDATA[
      K(x,(L(K(y,z),u,w) * v5) / v6) = K(x,v5 / (v6 * L(K(z,y),u,w)))
    ]]></literal>
    <justification jstring="[para(9453(a,1),17811(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="9453 17811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18346">
    <literal><![CDATA[
      K(x,(y * L(K(z,u),w,v5)) / v6) = K(x,y / (v6 * L(K(u,z),w,v5)))
    ]]></literal>
    <justification jstring="[hyper(16446,a,18345,a)].">
      <j1 rule="hyper" parents="16446 18345"/>
    </justification>
  </clause>

  <clause id="18347">
    <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(333,a,17836,a(flip),b,17840,a),flip(a)].">
      <j1 rule="hyper" parents="333 17836 17840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18348">
    <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(17900(a,2),13492(a,1))].">
      <j1 rule="para" parents="17900 13492"/>
    </justification>
  </clause>

  <clause id="18349">
    <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(18348,a,17266,a)].">
      <j1 rule="hyper" parents="18348 17266"/>
    </justification>
  </clause>

  <clause id="18350">
    <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(15002,a,17966,a)].">
      <j1 rule="hyper" parents="15002 17966"/>
    </justification>
  </clause>

  <clause id="18352">
    <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(63,a,17974,a(flip),b,18350,a)].">
      <j1 rule="hyper" parents="63 17974 18350"/>
    </justification>
  </clause>

  <clause id="18353">
    <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(7670(a,1),18350(a,1,2,2,2,1))].">
      <j1 rule="para" parents="7670 18350"/>
    </justification>
  </clause>

  <clause id="18354">
    <literal><![CDATA[
      K(x,y * ((z * y) \ (z * (u / z)))) = K(x,T(y * ((z * y) \ u),z))
    ]]></literal>
    <justification jstring="[para(14611(a,1),18027(a,1,2,2))].">
      <j1 rule="para" parents="14611 18027"/>
    </justification>
  </clause>

  <clause id="18355">
    <literal><![CDATA[
      K(x,T(y * ((z * y) \ u),z)) = K(x,y * ((z * y) \ T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,18213,a(flip),b,18354,a),flip(a)].">
      <j1 rule="hyper" parents="63 18213 18354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18356">
    <literal><![CDATA[
      K(x,(T(y,T(z,u)) \ T(z,u)) * w) = K(x,((u * (z / u)) / y) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,18258,a(flip),b,18042,a)].">
      <j1 rule="hyper" parents="63 18258 18042"/>
    </justification>
  </clause>

  <clause id="18357">
    <literal><![CDATA[
      K(x,((y * (z / y)) / u) * w) = K(x,(T(z,y) / u) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,18040,a(flip),b,18356,a),flip(a)].">
      <j1 rule="hyper" parents="63 18040 18356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18358">
    <literal><![CDATA[
      K(x,(T(y * z,y) / u) * w) = K(x,((T(y,z) * z) / u) * w)
    ]]></literal>
    <justification jstring="[para(3311(a,2),18357(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="3311 18357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18359">
    <literal><![CDATA[
      K(x,(T(y * z,y) / u) * w) = K(x,((z * y) / u) * w)
    ]]></literal>
    <justification jstring="[hyper(333,a,18255,a(flip),b,18358,a),flip(a)].">
      <j1 rule="hyper" parents="333 18255 18358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18360">
    <literal><![CDATA[
      K(x,K(y,z) * (u * (w * (z / y)))) = K(x,u * (w * T(z / y,y)))
    ]]></literal>
    <justification jstring="[hyper(15002,a,18110,a)].">
      <j1 rule="hyper" parents="15002 18110"/>
    </justification>
  </clause>

  <clause id="18361">
    <literal><![CDATA[
      K(x,K(y,z) * (u * (w * (z / y)))) = K(x,u * (w * (y \ z)))
    ]]></literal>
    <justification jstring="[para(113(a,1),18360(a,2,2,2,2))].">
      <j1 rule="para" parents="113 18360"/>
    </justification>
  </clause>

  <clause id="18362">
    <literal><![CDATA[
      K(x,y * (z * (u / T(w,u)))) = K(x,y * (z * (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,18177,a(flip),b,18361,a)].">
      <j1 rule="hyper" parents="63 18177 18361"/>
    </justification>
  </clause>

  <clause id="18363">
    <literal><![CDATA[
      T(x,y * (z * (u / T(w,u)))) = T(x,y * (z * (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(124,a,18362,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 18362 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18364">
    <literal><![CDATA[
      T(x,y * (T(z,u \ w) * (u \ w))) = T(x,y * (K(w,u) * ((w / u) * z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,16995,a(flip),b,18363,a),flip(a)].">
      <j1 rule="hyper" parents="63 16995 18363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18366">
    <literal><![CDATA[
      K(x \ (x / (x / y)),z * (y \ (y * (x / y)))) = K(x \ y,(y \ z) * x)
    ]]></literal>
    <justification jstring="[hyper(333,a,17320,a(flip),b,18143,a),flip(a)].">
      <j1 rule="hyper" parents="333 17320 18143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18367">
    <literal><![CDATA[
      K(x,K(y,z) * (T(z * u,z) * w)) = K(x,(u * T(z,y)) * w)
    ]]></literal>
    <justification jstring="[hyper(12790,a,18161,a),flip(a)].">
      <j1 rule="hyper" parents="12790 18161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18368">
    <literal><![CDATA[
      K(x,((y \ z) * T(y,u)) * w) = K(x,K(u,y) * (T(z,y) * w))
    ]]></literal>
    <justification jstring="[para(10(a,1),18367(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="10 18367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18369">
    <literal><![CDATA[
      K(x,(T(y,z) * (u / y)) * w) = K(x,K(z,y) * (T(u,y) * w))
    ]]></literal>
    <justification jstring="[hyper(16460,a,18368,a)].">
      <j1 rule="hyper" parents="16460 18368"/>
    </justification>
  </clause>

  <clause id="18370">
    <literal><![CDATA[
      K(x,((T(y,z) \ u) * y) * w) = K(x,K(z,y) * (T(u,y) * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,15237,a,b,18369,a)].">
      <j1 rule="hyper" parents="63 15237 18369"/>
    </justification>
  </clause>

  <clause id="18371">
    <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(18165(a,2),16245(a,1))].">
      <j1 rule="para" parents="18165 16245"/>
    </justification>
  </clause>

  <clause id="18372">
    <literal><![CDATA[
      T(x,T(y \ 1,z * T(u,w)) \ v5) = T(x,T(y,(u \ z) \ K(w,u)) * v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,16153,a(flip),b,18196,a)].">
      <j1 rule="hyper" parents="63 16153 18196"/>
    </justification>
  </clause>

  <clause id="18373">
    <literal><![CDATA[
      K(x,y \ (z / T(u,T(w,v5)))) = K(x,y \ (z / T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(333,a,16466,a(flip),b,18232,a),flip(a)].">
      <j1 rule="hyper" parents="333 16466 18232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18374">
    <literal><![CDATA[
      T(x,y * T(z * ((u \ w) * u),z)) = T(x,y * (z * T(T(w,u),z)))
    ]]></literal>
    <justification jstring="[hyper(333,a,16108,a(flip),b,18280,a),flip(a)].">
      <j1 rule="hyper" parents="333 16108 18280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18375">
    <literal><![CDATA[
      T(x,y * T(z * ((u \ w) * u),z)) = T(x,y * (T(w,u) * z))
    ]]></literal>
    <justification jstring="[para(111(a,1),18374(a,2,2,2))].">
      <j1 rule="para" parents="111 18374"/>
    </justification>
  </clause>

  <clause id="18376">
    <literal><![CDATA[
      T(x,y * (((z \ u) * z) * w)) = T(x,y * (T(u,z) * w))
    ]]></literal>
    <justification jstring="[hyper(12908,a,18375,a)].">
      <j1 rule="hyper" parents="12908 18375"/>
    </justification>
  </clause>

  <clause id="18377">
    <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(13316(a,1),18290(a,2,2,1))].">
      <j1 rule="para" parents="13316 18290"/>
    </justification>
  </clause>

  <clause id="18378">
    <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(3678(a,1),18377(a,2,2,1,2))].">
      <j1 rule="para" parents="3678 18377"/>
    </justification>
  </clause>

  <clause id="18379">
    <literal><![CDATA[
      T(x,T(T(y * z,y) \ (y * y),u)) = T(x,T(z \ T(y,z),u))
    ]]></literal>
    <justification jstring="[hyper(14237,a,18378,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="14237 18378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18380">
    <literal><![CDATA[
      T(x,T(T(y * z,y) \ (y * y),u)) = T(x,T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(333,a,12905,a(flip),b,18379,a),flip(a)].">
      <j1 rule="hyper" parents="333 12905 18379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18381">
    <literal><![CDATA[
      T(x,T((y * z) \ (z * z),u)) = T(x,T(z / y,u))
    ]]></literal>
    <justification jstring="[hyper(12982,a,18380,a)].">
      <j1 rule="hyper" parents="12982 18380"/>
    </justification>
  </clause>

  <clause id="18382">
    <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(444,a,18381,a,b,13335,a)].">
      <j1 rule="hyper" parents="444 18381 13335"/>
    </justification>
  </clause>

  <clause id="18383">
    <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(333,a,18009,a(flip),b,18316,a),flip(a)].">
      <j1 rule="hyper" parents="333 18009 18316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18384">
    <literal><![CDATA[
      a(x,y,K((z / T(u,w)) \ w,v5)) = a(x,y,K(T(w,u) / (z / u),v5))
    ]]></literal>
    <justification jstring="[para(15704(a,1),18336(a,1,3)),flip(a)].">
      <j1 rule="para" parents="15704 18336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18385">
    <literal><![CDATA[
      a(x,y,K((z / T(u,w)) \ w,v5)) = a(x,y,K((z / u) \ T(w,u),v5))
    ]]></literal>
    <justification jstring="[hyper(333,a,17694,a(flip),b,18384,a),flip(a)].">
      <j1 rule="hyper" parents="333 17694 18384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18386">
    <literal><![CDATA[
      K(x,(y / z) * L(z / y,u,w)) = K(x,(z \ y) * L(y \ z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,18040,a(flip),b,18352,a)].">
      <j1 rule="hyper" parents="63 18040 18352"/>
    </justification>
  </clause>

  <clause id="18387">
    <literal><![CDATA[
      T(x,y * (K(z,u) * ((z / u) * w))) = T(x,y * ((u \ z) * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,16036,a(flip),b,18364,a),flip(a)].">
      <j1 rule="hyper" parents="63 16036 18364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18388">
    <literal><![CDATA[
      T(x,y * ((z / T(u,z)) * w)) = T(x,y * ((u \ z) * w))
    ]]></literal>
    <justification jstring="[para(11847(a,1),18387(a,1,2,2))].">
      <j1 rule="para" parents="11847 18387"/>
    </justification>
  </clause>

  <clause id="18389">
    <literal><![CDATA[
      T(x,y * ((T(z,u) / T(u,z)) * w)) = T(x,y * ((u \ T(z,u)) * w))
    ]]></literal>
    <justification jstring="[para(3613(a,1),18388(a,1,2,2,1,2))].">
      <j1 rule="para" parents="3613 18388"/>
    </justification>
  </clause>

  <clause id="18390">
    <literal><![CDATA[
      T(x,y * ((T(z,u) / u) * w)) = T(x,y * ((u \ z) * w))
    ]]></literal>
    <justification jstring="[para(3625(a,2),18388(a,1,2,2,1))].">
      <j1 rule="para" parents="3625 18388"/>
    </justification>
  </clause>

  <clause id="18391">
    <literal><![CDATA[
      T(x,y * ((T(z,u) \ u) * ((u / z) * w))) = T(x,y * ((z \ u) * ((z \ u) * w)))
    ]]></literal>
    <justification jstring="[para(11913(a,1),18388(a,1,2,2))].">
      <j1 rule="para" parents="11913 18388"/>
    </justification>
  </clause>

  <clause id="18392">
    <literal><![CDATA[
      T(x,y * ((T(z,R(u,u,u)) / R(u,u,u)) * w)) = T(x,y * ((((u \ 1) \ 1) \ z) * w))
    ]]></literal>
    <justification jstring="[para(816(a,1),18390(a,2,2,2,1))].">
      <j1 rule="para" parents="816 18390"/>
    </justification>
  </clause>

  <clause id="18393">
    <literal><![CDATA[
      K(x \ (x / (x / y)),z * (x / y)) = K(x \ y,(y \ z) * x)
    ]]></literal>
    <justification jstring="[para(9(a,1),18366(a,1,2,2))].">
      <j1 rule="para" parents="9 18366"/>
    </justification>
  </clause>

  <clause id="18394">
    <literal><![CDATA[
      K((x / y) \ 1,z * (x / y)) = K(x \ y,(y \ z) * x)
    ]]></literal>
    <justification jstring="[hyper(5933,a,18393,a)].">
      <j1 rule="hyper" parents="5933 18393"/>
    </justification>
  </clause>

  <clause id="18396">
    <literal><![CDATA[
      K(x / y,z * (x \ y)) = K(y \ x,(x \ z) * y)
    ]]></literal>
    <justification jstring="[hyper(8642,a,18394,a)].">
      <j1 rule="hyper" parents="8642 18394"/>
    </justification>
  </clause>

  <clause id="18398">
    <literal><![CDATA[
      K(x \ y,(y \ z) * x) * K(y,K(x,z * (y \ x))) = K(x \ y,(y \ x) * z)
    ]]></literal>
    <justification jstring="[para(18396(a,1),8630(a,1,1))].">
      <j1 rule="para" parents="18396 8630"/>
    </justification>
  </clause>

  <clause id="18399">
    <literal><![CDATA[
      T(x,T(y,(z \ u) \ K(w,z)) * v5) = T(x,T(y \ 1,z * u) \ v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,17281,a(flip),b,18372,a),flip(a)].">
      <j1 rule="hyper" parents="63 17281 18372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18401">
    <literal><![CDATA[
      T(x,T(y,(z \ u) \ K(w,z)) * v5) = T(x,T(y,z * u) * v5)
    ]]></literal>
    <justification jstring="[hyper(333,a,18191,a(flip),b,18399,a),flip(a)].">
      <j1 rule="hyper" parents="333 18191 18399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18402">
    <literal><![CDATA[
      T(x,T(y,z \ T(u,w)) * v5) = T(x,T(y,u * z) * v5)
    ]]></literal>
    <justification jstring="[para(15059(a,1),18401(a,1,2,1))].">
      <j1 rule="para" parents="15059 18401"/>
    </justification>
  </clause>

  <clause id="18403">
    <literal><![CDATA[
      T(x,T(y,z * T(u,w)) * v5) = T(x,T(y,u * z) * v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,16136,a(flip),b,18402,a)].">
      <j1 rule="hyper" parents="63 16136 18402"/>
    </justification>
  </clause>

  <clause id="18404">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(z,u * w) * y) = T(x,y * T(z,w * T(u,v5)))
    ]]></literal>
    <justification jstring="[hyper(15591,a,18403,a),flip(a)].">
      <j1 rule="hyper" parents="15591 18403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18405">
    <literal><![CDATA[
      T(x,y * T(z,u * T(w,v5))) = T(x,y * T(z,w * u))
    ]]></literal>
    <justification jstring="[hyper(15591,a,18404,a),flip(a)].">
      <j1 rule="hyper" parents="15591 18404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18406">
    <literal><![CDATA[
      T(x,y * T(z,(u \ w) * T(u,v5))) = T(x,y * T(z,w))
    ]]></literal>
    <justification jstring="[para(10(a,1),18405(a,2,2,2,2))].">
      <j1 rule="para" parents="10 18405"/>
    </justification>
  </clause>

  <clause id="18407">
    <literal><![CDATA[
      T(x,y * T(z,T(K(u,w) * v5,u))) = T(x,y * T(z,v5))
    ]]></literal>
    <justification jstring="[para(16888(a,2),18406(a,1,2,2))].">
      <j1 rule="para" parents="16888 18406"/>
    </justification>
  </clause>

  <clause id="18408">
    <literal><![CDATA[
      T(x,y * T(z,K(u,w) * v5)) = T(x,y * T(z,v5))
    ]]></literal>
    <justification jstring="[hyper(16455,a,18407,a)].">
      <j1 rule="hyper" parents="16455 18407"/>
    </justification>
  </clause>

  <clause id="18410">
    <literal><![CDATA[
      K(x,y * (z * K(u,w \ v5))) = K(x,y * (z * K(u,v5 * w)))
    ]]></literal>
    <justification jstring="[para(182(a,1),18383(a,1,2,2,2,1))].">
      <j1 rule="para" parents="182 18383"/>
    </justification>
  </clause>

  <clause id="18411">
    <literal><![CDATA[
      K(x,y * (z * K(u,w / v5))) = K(x,y * (z * K(u,w * v5)))
    ]]></literal>
    <justification jstring="[hyper(18183,a,18410,a)].">
      <j1 rule="hyper" parents="18183 18410"/>
    </justification>
  </clause>

  <clause id="18412">
    <literal><![CDATA[
      K(x,y * ((z / u) * K(z,w * v5))) = K(x,y * (T(z,w / v5) / u))
    ]]></literal>
    <justification jstring="[hyper(16438,a,18411,a),flip(a)].">
      <j1 rule="hyper" parents="16438 18411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18413">
    <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(18412(a,1),16438(a,1))].">
      <j1 rule="para" parents="18412 16438"/>
    </justification>
  </clause>

  <clause id="18414">
    <literal><![CDATA[
      K(x,y * (T(z,u \ w) / v5)) = K(x,y * (T(z,w * u) / v5))
    ]]></literal>
    <justification jstring="[hyper(18413,a,16476,a),flip(a)].">
      <j1 rule="hyper" parents="18413 16476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18415">
    <literal><![CDATA[
      L(K(x,T(y,z)),u,u \ z) * z = (K(y,x) \ u) * (u \ T(z,K(y,x)))
    ]]></literal>
    <justification jstring="[hyper(63,a,17839,a(flip),b,17529,a),flip(a)].">
      <j1 rule="hyper" parents="63 17839 17529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18417">
    <literal><![CDATA[
      (K(x,y) \ z) * (z \ T(u,K(x,y))) = (u / z) * (z * K(y,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,10129,a(flip),b,18415,a),flip(a)].">
      <j1 rule="hyper" parents="63 10129 18415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18418">
    <literal><![CDATA[
      a(x,(y \ T(z,K(u,w))) \ ((K(u,w) \ y) \ v5),x) = a(x,((z / y) * (y * K(w,u))) \ v5,x)
    ]]></literal>
    <justification jstring="[para(18417(a,1),12882(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="18417 12882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18419">
    <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(385(a,1),17787(a,2,2,1))].">
      <j1 rule="para" parents="385 17787"/>
    </justification>
  </clause>

  <clause id="18420">
    <literal><![CDATA[
      K(x,T(y * z,x) * (u \ K(w,v5))) = K(x,(y * (z * K(w,v5))) / u)
    ]]></literal>
    <justification jstring="[hyper(63,a,18210,a(flip),b,17815,a)].">
      <j1 rule="hyper" parents="63 18210 17815"/>
    </justification>
  </clause>

  <clause id="18422">
    <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(18420(a,1),7529(a,1))].">
      <j1 rule="para" parents="18420 7529"/>
    </justification>
  </clause>

  <clause id="18423">
    <literal><![CDATA[
      K(x,(y * T(z,y)) * (u \ K(w,v5))) = K(x,((K(w,v5) * z) * y) / u)
    ]]></literal>
    <justification jstring="[hyper(18422,a,18168,a)].">
      <j1 rule="hyper" parents="18422 18168"/>
    </justification>
  </clause>

  <clause id="18424">
    <literal><![CDATA[
      K(x,((K(y,z) * u) * w) / v5) = K(x,(u * w) * (v5 \ K(y,z)))
    ]]></literal>
    <justification jstring="[para(111(a,1),18423(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="111 18423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18425">
    <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(10898(a,1),17991(a,1,2,1))].">
      <j1 rule="para" parents="10898 17991"/>
    </justification>
  </clause>

  <clause id="18426">
    <literal><![CDATA[
      R(x,K(y,z) \ (u * y),x) = R(x,u * T(y,z),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,4737,a(flip),b,18097,a),flip(a)].">
      <j1 rule="hyper" parents="63 4737 18097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18427">
    <literal><![CDATA[
      R(x,y * (y \ (K(y,z) \ u)),x) = R(x,(y \ u) * T(y,z),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,13043,a(flip),b,18426,a)].">
      <j1 rule="hyper" parents="63 13043 18426"/>
    </justification>
  </clause>

  <clause id="18428">
    <literal><![CDATA[
      R(x,y * (y \ (K(y,z) \ u)),x) = R(x,y \ (T(y,z) * u),x)
    ]]></literal>
    <justification jstring="[hyper(333,a,13042,a,b,18427,a),flip(a)].">
      <j1 rule="hyper" parents="333 13042 18427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18429">
    <literal><![CDATA[
      R(x,y \ (T(y,z) * u),x) = R(x,K(y,z) \ u,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),18428(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 18428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18430">
    <literal><![CDATA[
      a(x,y \ (T(y,z) * u),x) = R(x,K(y,z) \ u,x) / x
    ]]></literal>
    <justification jstring="[hyper(123,a,18429,a(flip),b,8222,a),flip(a)].">
      <j1 rule="hyper" parents="123 18429 8222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18432">
    <literal><![CDATA[
      a(x,y \ (T(y,z) * u),x) = a(x,K(y,z) \ u,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,8213,a(flip),b,18430,a),flip(a)].">
      <j1 rule="hyper" parents="333 8213 18430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18433">
    <literal><![CDATA[
      a(x,K(y,z) \ u,x) = a(x,K(z,y) \ u,x)
    ]]></literal>
    <justification jstring="[para(4547(a,1),18432(a,1,2))].">
      <j1 rule="para" parents="4547 18432"/>
    </justification>
  </clause>

  <clause id="18434">
    <literal><![CDATA[
      a(x,K(y,z) \ (y * u),x) = a(x,T(y,z) * u,x)
    ]]></literal>
    <justification jstring="[para(4598(a,1),18433(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4598 18433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18435">
    <literal><![CDATA[
      a(x,K(y \ (y / z),u) \ ((y \ (y / z)) * w),x) = a(x,T(T(y \ (y / z),u),z \ 1) * w,x)
    ]]></literal>
    <justification jstring="[para(5836(a,2),18434(a,2,2,1))].">
      <j1 rule="para" parents="5836 18434"/>
    </justification>
  </clause>

  <clause id="18436">
    <literal><![CDATA[
      x \ ((y * a(z,u,K(w,v5))) * x) = T(y,x * a(v6,v7,K(v8,v9))) * a(z,u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(333,a,22,a(flip),b,18126,a)].">
      <j1 rule="hyper" parents="333 22 18126"/>
    </justification>
  </clause>

  <clause id="18437">
    <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(10898(a,1),18175(a,1,2,2,2))].">
      <j1 rule="para" parents="10898 18175"/>
    </justification>
  </clause>

  <clause id="18438">
    <literal><![CDATA[
      K(x,y * (z * ((u / w) * K(w,v5)))) = K(x,y * (z * (u / T(w,v5))))
    ]]></literal>
    <justification jstring="[para(10976(a,1),18437(a,1,2,2))].">
      <j1 rule="para" parents="10976 18437"/>
    </justification>
  </clause>

  <clause id="18439">
    <literal><![CDATA[
      K(x,y) * (T(K(y,L(x,z,u)) * K(x,K(y,w)),w) * v5) = a(y,z,K(u,x)) * v5
    ]]></literal>
    <justification jstring="[para(6788(a,1),17613(a,1,2,1,1,2))].">
      <j1 rule="para" parents="6788 17613"/>
    </justification>
  </clause>

  <clause id="18441">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * ((u \ 1) * (z * u))) = T(x,((u \ 1) * (z * u)) * y)
    ]]></literal>
    <justification jstring="[para(1715(a,1),17636(a,1,2,2))].">
      <j1 rule="para" parents="1715 17636"/>
    </justification>
  </clause>

  <clause id="18443">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * (u * (z * (u \ 1)))) = T(x,((u \ 1) * (z * u)) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,16843,a(flip),b,18441,a)].">
      <j1 rule="hyper" parents="63 16843 18441"/>
    </justification>
  </clause>

  <clause id="18444">
    <literal><![CDATA[
      T(x,((y \ 1) * (z * y)) * u) = T(x,(y * (z * (y \ 1))) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,15915,a(flip),b,18443,a),flip(a)].">
      <j1 rule="hyper" parents="63 15915 18443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18445">
    <literal><![CDATA[
      T(x,(((y \ 1) * z) * y) * u) = T(x,(y * (z * (y \ 1))) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,17034,a,b,18444,a)].">
      <j1 rule="hyper" parents="63 17034 18444"/>
    </justification>
  </clause>

  <clause id="18446">
    <literal><![CDATA[
      T(x,(y * ((z / y) * (y \ 1))) * u) = T(x,((y \ 1) * z) * u)
    ]]></literal>
    <justification jstring="[para(12(a,1),18444(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="12 18444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18447">
    <literal><![CDATA[
      T(x,(y * ((((y \ 1) * (y \ z)) / (y \ 1)) * (y \ 1))) * u) = T(x,(y * ((z / y) * (y \ 1))) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,17458,a,b,18445,a)].">
      <j1 rule="hyper" parents="63 17458 18445"/>
    </justification>
  </clause>

  <clause id="18448">
    <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(14008(a,1),17646(a,1,1,1))].">
      <j1 rule="para" parents="14008 17646"/>
    </justification>
  </clause>

  <clause id="18450">
    <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(13875(a,1),18448(a,1,1))].">
      <j1 rule="para" parents="13875 18448"/>
    </justification>
  </clause>

  <clause id="18451">
    <literal><![CDATA[
      R(K(x,y) * z,u,u \ 1) = K(x,y) * R(z,u,u \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,5741,a(flip),b,18450,a)].">
      <j1 rule="hyper" parents="63 5741 18450"/>
    </justification>
  </clause>

  <clause id="18453">
    <literal><![CDATA[
      R(K(x,y) * (z / u),u,u \ 1) = K(x,y) * (z * (u \ 1))
    ]]></literal>
    <justification jstring="[para(554(a,1),18451(a,2,2))].">
      <j1 rule="para" parents="554 18451"/>
    </justification>
  </clause>

  <clause id="18454">
    <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(18451(a,2),14639(a,1,2))].">
      <j1 rule="para" parents="18451 14639"/>
    </justification>
  </clause>

  <clause id="18455">
    <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(18453(a,1),612(a,1,1))].">
      <j1 rule="para" parents="18453 612"/>
    </justification>
  </clause>

  <clause id="18456">
    <literal><![CDATA[
      a(K(x,y) * z,u,u \ 1) = z \ R(z,u,u \ 1)
    ]]></literal>
    <justification jstring="[para(4558(a,1),18454(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4558 18454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18457">
    <literal><![CDATA[
      a(K(x,y) * z,u,u \ 1) = a(z,u,u \ 1)
    ]]></literal>
    <justification jstring="[hyper(333,a,767,a(flip),b,18456,a),flip(a)].">
      <j1 rule="hyper" parents="333 767 18456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18458">
    <literal><![CDATA[
      a(x / y,z,z \ 1) = a(y \ x,z,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,11960,a(flip),b,18457,a)].">
      <j1 rule="hyper" parents="63 11960 18457"/>
    </justification>
  </clause>

  <clause id="18459">
    <literal><![CDATA[
      a(T(x,y),z,z \ 1) = a(x,z,z \ 1)
    ]]></literal>
    <justification jstring="[para(2065(a,2),18457(a,1,1))].">
      <j1 rule="para" parents="2065 18457"/>
    </justification>
  </clause>

  <clause id="18460">
    <literal><![CDATA[
      a(x \ T(y,z),u,u \ 1) = a(x \ y,u,u \ 1)
    ]]></literal>
    <justification jstring="[para(4840(a,1),18457(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4840 18457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18461">
    <literal><![CDATA[
      T(x,y) * a(x,z,z \ 1) = R(T(x,y),z,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(126,a,18459,a(flip),b,767,a)].">
      <j1 rule="hyper" parents="126 18459 767"/>
    </justification>
  </clause>

  <clause id="18462">
    <literal><![CDATA[
      a(x \ (y / z),u,u \ 1) = a(x \ (z \ y),u,u \ 1)
    ]]></literal>
    <justification jstring="[para(113(a,1),18460(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="113 18460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18463">
    <literal><![CDATA[
      ((x * y) / x) * R(x,z,z \ 1) = y * R(T(x,y),z,z \ 1)
    ]]></literal>
    <justification jstring="[para(18461(a,1),5031(a,2,2))].">
      <j1 rule="para" parents="18461 5031"/>
    </justification>
  </clause>

  <clause id="18464">
    <literal><![CDATA[
      (R(x,y,y \ 1) * z) / R(x,y,y \ 1) = (x * z) / x
    ]]></literal>
    <justification jstring="[hyper(123,a,252,a(flip),b,18463,a)].">
      <j1 rule="hyper" parents="123 252 18463"/>
    </justification>
  </clause>

  <clause id="18465">
    <literal><![CDATA[
      (L(x,y,y \ 1) * z) / L(x,y,y \ 1) = (x * z) / x
    ]]></literal>
    <justification jstring="[hyper(63,a,14437,a(flip),b,18464,a)].">
      <j1 rule="hyper" parents="63 14437 18464"/>
    </justification>
  </clause>

  <clause id="18466">
    <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(13254(a,1),18465(a,2,1))].">
      <j1 rule="para" parents="13254 18465"/>
    </justification>
  </clause>

  <clause id="18467">
    <literal><![CDATA[
      (L(x,y,z) * (u / L(x,y,z))) / K(x,L(x,y,z) \ u) = T(u,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(333,a,13819,a(flip),b,17714,a),flip(a)].">
      <j1 rule="hyper" parents="333 13819 17714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18468">
    <literal><![CDATA[
      (L(x,y,z) * (u / L(x,y,z))) * K(L(x,y,z) \ u,x) = T(u,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(5999,a,18467,a)].">
      <j1 rule="hyper" parents="5999 18467"/>
    </justification>
  </clause>

  <clause id="18469">
    <literal><![CDATA[
      L(x,y,z) * T(u / L(x,y,z),T(x,u)) = T(u,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(6488,a,18468,a)].">
      <j1 rule="hyper" parents="6488 18468"/>
    </justification>
  </clause>

  <clause id="18470">
    <literal><![CDATA[
      L(x,y,z) * T(u / L(x,y,z),x) = T(u,a(z,y,x))
    ]]></literal>
    <justification jstring="[para(9873(a,1),18469(a,1,2))].">
      <j1 rule="para" parents="9873 18469"/>
    </justification>
  </clause>

  <clause id="18471">
    <literal><![CDATA[
      T(x * L(y,z,u),a(u,z,y)) = L(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(11(a,1),18470(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11 18470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18472">
    <literal><![CDATA[
      K(x,L(y,z,u) * T(w,y)) = K(x,w * L(y,z,u))
    ]]></literal>
    <justification jstring="[para(18471(a,1),17553(a,1,2))].">
      <j1 rule="para" parents="18471 17553"/>
    </justification>
  </clause>

  <clause id="18473">
    <literal><![CDATA[
      K(x,L(y \ z,u,w) * T(y,z)) = K(x,y * L(y \ z,u,w))
    ]]></literal>
    <justification jstring="[hyper(16202,a,18472,a)].">
      <j1 rule="hyper" parents="16202 18472"/>
    </justification>
  </clause>

  <clause id="18475">
    <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(8598(a,1),18473(a,1,2,1,1))].">
      <j1 rule="para" parents="8598 18473"/>
    </justification>
  </clause>

  <clause id="18476">
    <literal><![CDATA[
      T((x \ (y * z)) / T(z,K(u,w)),z) = z \ (x \ (y * T(z,K(u,w))))
    ]]></literal>
    <justification jstring="[para(6862(a,1),17869(a,1,1,2))].">
      <j1 rule="para" parents="6862 17869"/>
    </justification>
  </clause>

  <clause id="18477">
    <literal><![CDATA[
      T(x,K(y,z)) \ (u \ (w * x)) = x \ (u \ (w * T(x,K(y,z))))
    ]]></literal>
    <justification jstring="[hyper(15538,a,18476,a)].">
      <j1 rule="hyper" parents="15538 18476"/>
    </justification>
  </clause>

  <clause id="18478">
    <literal><![CDATA[
      K(T(T(x,y) \ z,K(y,x)) * u,w) = K((x \ z) * (K(x,y) * u),w)
    ]]></literal>
    <justification jstring="[hyper(18164,a,17882,a),flip(a)].">
      <j1 rule="hyper" parents="18164 17882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18479">
    <literal><![CDATA[
      K((x \ y) * (K(x,z) * u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K((T(x,z) \ y) * u,w) = v5
    ]]></literal>
    <justification jstring="[para(18478(a,1),16387(a,1))].">
      <j1 rule="para" parents="18478 16387"/>
    </justification>
  </clause>

  <clause id="18480">
    <literal><![CDATA[
      K((T(x,T(y,z)) \ u) * w,v5) = K((x \ u) * (K(x,y) * w),v5)
    ]]></literal>
    <justification jstring="[hyper(18479,a,16421,a)].">
      <j1 rule="hyper" parents="18479 16421"/>
    </justification>
  </clause>

  <clause id="18481">
    <literal><![CDATA[
      K((T(x,T(y,z)) \ u) * w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K((T(x,y) \ u) * w,v5) = v6
    ]]></literal>
    <justification jstring="[para(18480(a,2),18479(a,1))].">
      <j1 rule="para" parents="18480 18479"/>
    </justification>
  </clause>

  <clause id="18482">
    <literal><![CDATA[
      K(x,y * ((z \ (u * y)) \ K(u,u \ z))) = K(x,T(y / (z \ (u * y)),u))
    ]]></literal>
    <justification jstring="[hyper(16491,a,18070,a)].">
      <j1 rule="hyper" parents="16491 18070"/>
    </justification>
  </clause>

  <clause id="18483">
    <literal><![CDATA[
      K(x,y * (z * K((u * w) \ y,u * w))) = K(x,T(y,w * u) * z)
    ]]></literal>
    <justification jstring="[hyper(333,a,12792,a(flip),b,18145,a),flip(a)].">
      <j1 rule="hyper" parents="333 12792 18145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18484">
    <literal><![CDATA[
      K(x,y * (z * K(u \ (w \ y),w * u))) = K(x,T(y,u * w) * z)
    ]]></literal>
    <justification jstring="[para(13405(a,1),18483(a,1,2,2,2))].">
      <j1 rule="para" parents="13405 18483"/>
    </justification>
  </clause>

  <clause id="18485">
    <literal><![CDATA[
      K(x,y * (z * K(u * (w \ y),w * u))) = K(x,T(y,u * w) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,16263,a(flip),b,18484,a)].">
      <j1 rule="hyper" parents="63 16263 18484"/>
    </justification>
  </clause>

  <clause id="18486">
    <literal><![CDATA[
      K(x,L((y * z) / u,y,z \ 1)) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[hyper(63,a,18217,a(flip),b,18227,a),flip(a)].">
      <j1 rule="hyper" parents="63 18217 18227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18487">
    <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(13693,a,18486,a)].">
      <j1 rule="hyper" parents="13693 18486"/>
    </justification>
  </clause>

  <clause id="18488">
    <literal><![CDATA[
      K(x,L((y * z) * u,y,z \ 1)) = K(x,y / ((u \ 1) / z))
    ]]></literal>
    <justification jstring="[hyper(13631,a,18486,a)].">
      <j1 rule="hyper" parents="13631 18486"/>
    </justification>
  </clause>

  <clause id="18489">
    <literal><![CDATA[
      K(x,y * (K(z,u \ w) * v5)) = K(x,y * (K(z,w * u) * v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,18256,a(flip),b,18293,a),flip(a)].">
      <j1 rule="hyper" parents="63 18256 18293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18490">
    <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(63,a,17214,a(flip),b,18489,a),flip(a)].">
      <j1 rule="hyper" parents="63 17214 18489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18491">
    <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(18022,a,18296,a)].">
      <j1 rule="hyper" parents="18022 18296"/>
    </justification>
  </clause>

  <clause id="18492">
    <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(18491(a,2),16376(a,1))].">
      <j1 rule="para" parents="18491 16376"/>
    </justification>
  </clause>

  <clause id="18493">
    <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(18414(a,1),18492(a,1))].">
      <j1 rule="para" parents="18414 18492"/>
    </justification>
  </clause>

  <clause id="18494">
    <literal><![CDATA[
      K((x * L(K(y,z),u,w)) \ v5,v6) = K(x \ (L(K(z,y),u,w) * v5),v6)
    ]]></literal>
    <justification jstring="[hyper(6024,a,18298,a),flip(a)].">
      <j1 rule="hyper" parents="6024 18298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18495">
    <literal><![CDATA[
      K(((x \ y) * x) / T(L(K(z,u),w,v5) * x,K(v6,v7)),v8) = K(x \ (L(K(u,z),w,v5) * y),v8)
    ]]></literal>
    <justification jstring="[hyper(63,a,16765,a,b,18494,a)].">
      <j1 rule="hyper" parents="63 16765 18494"/>
    </justification>
  </clause>

  <clause id="18496">
    <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(5994(a,1),18329(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5994 18329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18497">
    <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(4515(a,1),18349(a,1,1,2,1))].">
      <j1 rule="para" parents="4515 18349"/>
    </justification>
  </clause>

  <clause id="18498">
    <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(17799(a,1),18497(a,1,1))].">
      <j1 rule="para" parents="17799 18497"/>
    </justification>
  </clause>

  <clause id="18499">
    <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(63,a,14416,a(flip),b,18498,a)].">
      <j1 rule="hyper" parents="63 14416 18498"/>
    </justification>
  </clause>

  <clause id="18500">
    <literal><![CDATA[
      K(x \ T(y,K(z,u) * w),v5) = K(x \ T(y,w),v5)
    ]]></literal>
    <justification jstring="[hyper(16357,a,18499,a),flip(a)].">
      <j1 rule="hyper" parents="16357 18499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18501">
    <literal><![CDATA[
      K((x * y) \ T(x,z),u) = K(y \ K(x,z * K(w,v5)),u)
    ]]></literal>
    <justification jstring="[hyper(16703,a,18500,a),flip(a)].">
      <j1 rule="hyper" parents="16703 18500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18503">
    <literal><![CDATA[
      K(x \ K(y,z * K(u,w)),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x \ K(y,z),v5) = v6
    ]]></literal>
    <justification jstring="[para(18501(a,1),8013(a,1))].">
      <j1 rule="para" parents="18501 8013"/>
    </justification>
  </clause>

  <clause id="18504">
    <literal><![CDATA[
      K(x \ K(y,K(z,u) * w),v5) = K(x \ K(y,w),v5)
    ]]></literal>
    <justification jstring="[hyper(18503,a,16702,a),flip(a)].">
      <j1 rule="hyper" parents="18503 16702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18505">
    <literal><![CDATA[
      K(x \ K(y \ K(z,u),w),v5) = K(x \ K(w,y),v5)
    ]]></literal>
    <justification jstring="[hyper(18503,a,18259,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="18503 18259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18506">
    <literal><![CDATA[
      K(x,y \ K(z,K(u,w) * v5)) = (v6 * K(y \ K(z,v5),x)) \ v6
    ]]></literal>
    <justification jstring="[para(18504(a,1),5990(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="18504 5990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18507">
    <literal><![CDATA[
      K((x / y) \ K(y,z),u) = K(T(y,z \ K(w,v5 \ w)) / x,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,15897,a(flip),b,18505,a),flip(a)].">
      <j1 rule="hyper" parents="63 15897 18505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18509">
    <literal><![CDATA[
      K(x,y \ K(z,K(u,w) * v5)) = K(x,y \ K(z,v5))
    ]]></literal>
    <justification jstring="[hyper(333,a,5990,a(flip),b,18506,a),flip(a)].">
      <j1 rule="hyper" parents="333 5990 18506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18510">
    <literal><![CDATA[
      K(x,y \ K(z * K(u,w),v5)) = K(x,y \ K(v5,z))
    ]]></literal>
    <justification jstring="[hyper(16709,a,18509,a)].">
      <j1 rule="hyper" parents="16709 18509"/>
    </justification>
  </clause>

  <clause id="18511">
    <literal><![CDATA[
      K(T(x,y \ K(z,u \ z)) / w,v5) = K(T(x,y) / w,v5)
    ]]></literal>
    <justification jstring="[hyper(15895,a,18507,a),flip(a)].">
      <j1 rule="hyper" parents="15895 18507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18513">
    <literal><![CDATA[
      K(T(x,y \ K(z,u)) / w,v5) = K(T(x,y) / w,v5)
    ]]></literal>
    <justification jstring="[para(79(a,1),18511(a,1,1,1,2,2,2))].">
      <j1 rule="para" parents="79 18511"/>
    </justification>
  </clause>

  <clause id="18514">
    <literal><![CDATA[
      K(T((x * y) * (1 / x),x) / z,u) = K(L(y,x,x \ 1) / z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,16964,a(flip),b,18513,a),flip(a)].">
      <j1 rule="hyper" parents="63 16964 18513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18515">
    <literal><![CDATA[
      K(T(x,y \ T(z,u)) / w,v5) = K(T(x,z \ y) / w,v5)
    ]]></literal>
    <justification jstring="[para(15059(a,1),18513(a,1,1,1))].">
      <j1 rule="para" parents="15059 18513"/>
    </justification>
  </clause>

  <clause id="18516">
    <literal><![CDATA[
      K(x,T(y,z \ T(u,w)) / v5) = (v6 * K(T(y,u \ z) / v5,x)) \ v6
    ]]></literal>
    <justification jstring="[para(18515(a,1),5990(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="18515 5990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18518">
    <literal><![CDATA[
      K(((x * y) * (1 / y)) / z,u) = K(L(x,y,y \ 1) / z,u)
    ]]></literal>
    <justification jstring="[para(2259(a,1),18514(a,1,1,1))].">
      <j1 rule="para" parents="2259 18514"/>
    </justification>
  </clause>

  <clause id="18519">
    <literal><![CDATA[
      K(x,T(y,z \ T(u,w)) / v5) = K(x,T(y,u \ z) / v5)
    ]]></literal>
    <justification jstring="[hyper(333,a,5990,a(flip),b,18516,a),flip(a)].">
      <j1 rule="hyper" parents="333 5990 18516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18520">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ z)) / w) = K(x,T(y,u) / w)
    ]]></literal>
    <justification jstring="[para(6344(a,1),18519(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6344 18519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18521">
    <literal><![CDATA[
      K(x,T(y,z \ y) / u) = K(x,T(y,z) / u)
    ]]></literal>
    <justification jstring="[hyper(63,a,12714,a(flip),b,18520,a)].">
      <j1 rule="hyper" parents="63 12714 18520"/>
    </justification>
  </clause>

  <clause id="18522">
    <literal><![CDATA[
      K(x,T(y,y / z) / u) = K(x,T(y,z) / u)
    ]]></literal>
    <justification jstring="[hyper(63,a,16367,a,b,18521,a)].">
      <j1 rule="hyper" parents="63 16367 18521"/>
    </justification>
  </clause>

  <clause id="18523">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ y)) / w) = K(x,T(y,u * z) / w)
    ]]></literal>
    <justification jstring="[para(13416(a,1),18521(a,1,2,1))].">
      <j1 rule="para" parents="13416 18521"/>
    </justification>
  </clause>

  <clause id="18524">
    <literal><![CDATA[
      K(x,T(((y / z) * u) \ y,u)) = K(x,T(y,z) / (u * (y / z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,14144,a,b,18522,a)].">
      <j1 rule="hyper" parents="63 14144 18522"/>
    </justification>
  </clause>

  <clause id="18525">
    <literal><![CDATA[
      K(x,T(y,z \ (y / u)) / w) = K(x,T(y,u * z) / w)
    ]]></literal>
    <justification jstring="[para(9786(a,2),18523(a,1,2,1))].">
      <j1 rule="para" parents="9786 18523"/>
    </justification>
  </clause>

  <clause id="18526">
    <literal><![CDATA[
      K(x,T(y,z * u) / ((y / z) / u)) = K(x,((y / z) / u) \ y)
    ]]></literal>
    <justification jstring="[hyper(16470,a,18525,a),flip(a)].">
      <j1 rule="hyper" parents="16470 18525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18527">
    <literal><![CDATA[
      K(x,T(((y / z) * u) \ y,u)) = K(x,y / (u * (z \ y)))
    ]]></literal>
    <justification jstring="[hyper(333,a,16224,a(flip),b,18524,a),flip(a)].">
      <j1 rule="hyper" parents="333 16224 18524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18528">
    <literal><![CDATA[
      K(x \ y,(y \ z) * x) * K(y,K(x,x * z)) = K(x \ y,(y \ x) * z)
    ]]></literal>
    <justification jstring="[para(16121(a,1),18398(a,1,2))].">
      <j1 rule="para" parents="16121 18398"/>
    </justification>
  </clause>

  <clause id="18529">
    <literal><![CDATA[
      K(x \ y,(y \ z) * x) * K(y,K(x,z)) = K(x \ y,(y \ x) * z)
    ]]></literal>
    <justification jstring="[para(6874(a,1),18528(a,1,2))].">
      <j1 rule="para" parents="6874 18528"/>
    </justification>
  </clause>

  <clause id="18530">
    <literal><![CDATA[
      K(x \ y,(y \ x) * z) = K(x \ y,x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(63,a,14763,a(flip),b,18529,a),flip(a)].">
      <j1 rule="hyper" parents="63 14763 18529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18531">
    <literal><![CDATA[
      (((x \ y) * z) \ z) * ((x \ y) * z) = z * K(y \ x,y * (x \ z))
    ]]></literal>
    <justification jstring="[para(18530(a,1),5870(a,2,2))].">
      <j1 rule="para" parents="18530 5870"/>
    </justification>
  </clause>

  <clause id="18532">
    <literal><![CDATA[
      (((x \ y) * z) \ z) * ((x \ y) * z) = (y \ x) * (z / (y \ x))
    ]]></literal>
    <justification jstring="[hyper(333,a,11404,a(flip),b,18531,a),flip(a)].">
      <j1 rule="hyper" parents="333 11404 18531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18533">
    <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(18532(a,1),14386(a,1,2,2,2,2))].">
      <j1 rule="para" parents="18532 14386"/>
    </justification>
  </clause>

  <clause id="18534">
    <literal><![CDATA[
      T(K(x,y) * (z / T(y,a(u,w,v5))),y) = T(T(y,a(u,w,v5)),x) \ z
    ]]></literal>
    <justification jstring="[para(17553(a,1),17604(a,1,1,1))].">
      <j1 rule="para" parents="17553 17604"/>
    </justification>
  </clause>

  <clause id="18535">
    <literal><![CDATA[
      (T(x,y) \ z) * K(a(u,w,v5),x) = T(T(x,a(u,w,v5)),y) \ z
    ]]></literal>
    <justification jstring="[hyper(63,a,7758,a(flip),b,18534,a)].">
      <j1 rule="hyper" parents="63 7758 18534"/>
    </justification>
  </clause>

  <clause id="18537">
    <literal><![CDATA[
      (T(x,y) \ z) * a(u,w,K(v5,x)) = T(T(x,a(u,w,v5)),y) \ z
    ]]></literal>
    <justification jstring="[para(13539(a,2),18535(a,1,2))].">
      <j1 rule="para" parents="13539 18535"/>
    </justification>
  </clause>

  <clause id="18538">
    <literal><![CDATA[
      T(T(T(x,a(y,z,u)),y) \ R(T(x,y),z,u),y) = T(x,y) \ R(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(18537(a,1),13816(a,1,1))].">
      <j1 rule="para" parents="18537 13816"/>
    </justification>
  </clause>

  <clause id="18539">
    <literal><![CDATA[
      T(T(x,L(y,z,u)) \ R(T(x,y),z,u),y) = T(x,y) \ R(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(13808(a,1),18538(a,1,1,1))].">
      <j1 rule="para" parents="13808 18538"/>
    </justification>
  </clause>

  <clause id="18540">
    <literal><![CDATA[
      T(x,y) \ R(T(x,y),z,u) = T(x \ R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(14221(a,1),18539(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14221 18539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18541">
    <literal><![CDATA[
      L(T(x \ R(x,y,z),u),T(x,u),y * z) = a(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(18540(a,1),14051(a,2,1)),flip(a)].">
      <j1 rule="para" parents="18540 14051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18543">
    <literal><![CDATA[
      L(T(x \ R(x,K(y,z),T(u * K(z,y),w)),v5),T(x,v5),T(u * K(u * K(z,y),w),K(z,y))) = a(T(x,v5),K(y,z),T(u * K(z,y),w))
    ]]></literal>
    <justification jstring="[para(16093(a,2),18541(a,1,3))].">
      <j1 rule="para" parents="16093 18541"/>
    </justification>
  </clause>

  <clause id="18544">
    <literal><![CDATA[
      (x * T(y,T(z,u))) \ (w * T(y,T(z,u))) = (x * T(y,z)) \ (w * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(952,a,17655,a),flip(a)].">
      <j1 rule="hyper" parents="952 17655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18545">
    <literal><![CDATA[
      (x * T(y,T(z,u))) \ (z * T(y,T(z,u))) = (x * T(y,z)) \ (y * z)
    ]]></literal>
    <justification jstring="[para(111(a,1),18544(a,2,2))].">
      <j1 rule="para" parents="111 18544"/>
    </justification>
  </clause>

  <clause id="18546">
    <literal><![CDATA[
      K(x * (1 / (1 / (y \ z))),(z \ y) \ x) = a(1 / (z \ y),z \ y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(13530,a,18032,a)].">
      <j1 rule="hyper" parents="13530 18032"/>
    </justification>
  </clause>

  <clause id="18547">
    <literal><![CDATA[
      K(x * (y \ z),(z \ y) \ x) = a(1 / (z \ y),z \ y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,4759,a(flip),b,18546,a)].">
      <j1 rule="hyper" parents="63 4759 18546"/>
    </justification>
  </clause>

  <clause id="18548">
    <literal><![CDATA[
      K(x * (y \ z),(z \ y) \ x) = 1
    ]]></literal>
    <justification jstring="[hyper(14336,a,18547,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="14336 18547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18549">
    <literal><![CDATA[
      K(x * (y \ z),x / (z \ y)) = 1
    ]]></literal>
    <justification jstring="[hyper(17217,a,18548,a)].">
      <j1 rule="hyper" parents="17217 18548"/>
    </justification>
  </clause>

  <clause id="18550">
    <literal><![CDATA[
      K(x,y / a(z,u,K(w,v5))) = y / T(y,x)
    ]]></literal>
    <justification jstring="[para(17675(a,1),18129(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="17675 18129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18551">
    <literal><![CDATA[
      K(x,y / a(z,u,K(w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v6
    ]]></literal>
    <justification jstring="[para(18550(a,2),4313(a,1))].">
      <j1 rule="para" parents="18550 4313"/>
    </justification>
  </clause>

  <clause id="18552">
    <literal><![CDATA[
      K(x,y \ a(z,u,K(w,v5))) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(18551,a,5061,a)].">
      <j1 rule="hyper" parents="18551 5061"/>
    </justification>
  </clause>

  <clause id="18553">
    <literal><![CDATA[
      K(x,a(y,z,K(u,w)) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,v5) = v6
    ]]></literal>
    <justification jstring="[para(17674(a,1),18551(a,1,2))].">
      <j1 rule="para" parents="17674 18551"/>
    </justification>
  </clause>

  <clause id="18554">
    <literal><![CDATA[
      K(x,y / T(z,a(u,w,v5))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(18553,a,15738,a),flip(a)].">
      <j1 rule="hyper" parents="18553 15738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18555">
    <literal><![CDATA[
      K(x,a(y,z,K(u,w)) * v5) = K(x,v5)
    ]]></literal>
    <justification jstring="[hyper(18553,a,xx),flip(a)].">
      <j1 rule="hyper" parents="18553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18557">
    <literal><![CDATA[
      K(x,L(y,z,K(u,w)) \ v5) = K(x,y \ v5)
    ]]></literal>
    <justification jstring="[para(14539(a,1),18555(a,1,2))].">
      <j1 rule="para" parents="14539 18555"/>
    </justification>
  </clause>

  <clause id="18558">
    <literal><![CDATA[
      K(x,y * a(z,u,K(w,v5))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(17584(a,1),18555(a,1,2))].">
      <j1 rule="para" parents="17584 18555"/>
    </justification>
  </clause>

  <clause id="18559">
    <literal><![CDATA[
      K(x,y * L(z,u,K(w,v5))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(17890(a,1),18555(a,1,2))].">
      <j1 rule="para" parents="17890 18555"/>
    </justification>
  </clause>

  <clause id="18560">
    <literal><![CDATA[
      T(x,K(y,z)) / ((z * a(u,w,K(v5,v6))) * T((z * a(u,w,K(v5,v6))) \ x,y)) = K(y,(x \ (z * a(u,w,K(v5,v6)))) \ 1)
    ]]></literal>
    <justification jstring="[para(18558(a,1),8882(a,1,1,2))].">
      <j1 rule="para" parents="18558 8882"/>
    </justification>
  </clause>

  <clause id="18561">
    <literal><![CDATA[
      K(x,y / (a(z,u,w) / v5)) = K(x,y / (v5 \ a(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(15138,a,18554,a)].">
      <j1 rule="hyper" parents="15138 18554"/>
    </justification>
  </clause>

  <clause id="18564">
    <literal><![CDATA[
      K(x,(y * (z * u)) / T(L(u,z,y),a(w,v5,v6))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(190(a,1),18554(a,2,2))].">
      <j1 rule="para" parents="190 18554"/>
    </justification>
  </clause>

  <clause id="18565">
    <literal><![CDATA[
      K(x,y / L(z,u,K(w,v5))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(14461(a,2),18554(a,1,2,2))].">
      <j1 rule="para" parents="14461 18554"/>
    </justification>
  </clause>

  <clause id="18566">
    <literal><![CDATA[
      K(x,T(y,L(z,u,w)) \ v5) = K(x,T(y,z) \ v5)
    ]]></literal>
    <justification jstring="[para(14486(a,1),18557(a,1,2,1))].">
      <j1 rule="para" parents="14486 18557"/>
    </justification>
  </clause>

  <clause id="18567">
    <literal><![CDATA[
      K(x,y \ (z * K(u,w))) = K(x,(y \ z) * K(u,w))
    ]]></literal>
    <justification jstring="[para(14472(a,1),18557(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14472 18557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18568">
    <literal><![CDATA[
      K(x,y * T((K(z,u) * w) \ v5,v6)) = K(x,y * T(w \ (K(z,u) \ v5),v6))
    ]]></literal>
    <justification jstring="[para(576(a,1),18559(a,1,2,2))].">
      <j1 rule="para" parents="576 18559"/>
    </justification>
  </clause>

  <clause id="18569">
    <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(577(a,1),18559(a,1,2,2))].">
      <j1 rule="para" parents="577 18559"/>
    </justification>
  </clause>

  <clause id="18570">
    <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(13427(a,1),18559(a,1,2,2))].">
      <j1 rule="para" parents="13427 18559"/>
    </justification>
  </clause>

  <clause id="18571">
    <literal><![CDATA[
      K(x,y / ((z * ((K(u,w) * z) \ v5)) / z)) = K(x,y / ((K(u,w) \ v5) / z))
    ]]></literal>
    <justification jstring="[para(898(a,1),18565(a,1,2,2))].">
      <j1 rule="para" parents="898 18565"/>
    </justification>
  </clause>

  <clause id="18572">
    <literal><![CDATA[
      K(x,y / ((K(z,u) * w) \ v5)) = K(x,y / (w \ (K(u,z) * v5)))
    ]]></literal>
    <justification jstring="[para(4581(a,1),18565(a,1,2,2))].">
      <j1 rule="para" parents="4581 18565"/>
    </justification>
  </clause>

  <clause id="18573">
    <literal><![CDATA[
      K(x,T(y,z) \ L(z,u,w)) = K(x,L(z,u,w) / y)
    ]]></literal>
    <justification jstring="[hyper(15099,a,18566,a),flip(a)].">
      <j1 rule="hyper" parents="15099 18566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18574">
    <literal><![CDATA[
      K(x,y \ (z * K(u,w))) = K(x,K(u,w) * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(333,a,15489,a,b,18567,a),flip(a)].">
      <j1 rule="hyper" parents="333 15489 18567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18575">
    <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(10874(a,1),18567(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10874 18567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18576">
    <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(18567(a,2),15533(a,1))].">
      <j1 rule="para" parents="18567 15533"/>
    </justification>
  </clause>

  <clause id="18577">
    <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(619(a,1),18573(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="619 18573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18578">
    <literal><![CDATA[
      K(x,y \ (K(z,u) * w)) = K(x,K(z,u) * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(16398,a,18574,a)].">
      <j1 rule="hyper" parents="16398 18574"/>
    </justification>
  </clause>

  <clause id="18579">
    <literal><![CDATA[
      K(x,K(y,z) * (T(u,w / T(y,z)) \ (w / y))) = K(x,((w / y) * K(y,z)) / u)
    ]]></literal>
    <justification jstring="[hyper(15103,a,18574,a),flip(a)].">
      <j1 rule="hyper" parents="15103 18574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18580">
    <literal><![CDATA[
      T(x,y \ (z * K(u,w))) = T(x,K(u,w) * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(124,a,18574,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 18574 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18581">
    <literal><![CDATA[
      K(x,(y * K(z,u)) \ w) = K(x,K(u,z) * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(63,a,17809,a,b,18574,a)].">
      <j1 rule="hyper" parents="63 17809 18574"/>
    </justification>
  </clause>

  <clause id="18582">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ w) = K(x,K(z,y) * (u \ w))
    ]]></literal>
    <justification jstring="[hyper(63,a,17769,a,b,18574,a)].">
      <j1 rule="hyper" parents="63 17769 18574"/>
    </justification>
  </clause>

  <clause id="18583">
    <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(63,a,12204,a(flip),b,18574,a)].">
      <j1 rule="hyper" parents="63 12204 18574"/>
    </justification>
  </clause>

  <clause id="18584">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ (w * y))) = K(x,u \ (w * T(y,z)))
    ]]></literal>
    <justification jstring="[para(5984(a,1),18574(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5984 18574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18585">
    <literal><![CDATA[
      K(x,K(y \ z,y) * (u \ (w / (y \ z)))) = K(x,u \ (w / (z / y)))
    ]]></literal>
    <justification jstring="[para(6012(a,1),18574(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6012 18574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18586">
    <literal><![CDATA[
      K(x,K(y \ z,y) * (u \ (w * z))) = K(x,u \ (w * ((y \ z) * y)))
    ]]></literal>
    <justification jstring="[para(10318(a,1),18574(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10318 18574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18587">
    <literal><![CDATA[
      K(x,K(y,y \ z) * (u \ (w * z))) = K(x,u \ (w * (y * (z / y))))
    ]]></literal>
    <justification jstring="[para(10324(a,1),18574(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10324 18574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18588">
    <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(15218,a,18578,a),flip(a)].">
      <j1 rule="hyper" parents="15218 18578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18589">
    <literal><![CDATA[
      K(x,K(y,z \ 1) * (T(u,K(y,z) * w) \ w)) = K(x,(K(y,z \ 1) * w) / u)
    ]]></literal>
    <justification jstring="[hyper(15210,a,18578,a),flip(a)].">
      <j1 rule="hyper" parents="15210 18578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18590">
    <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(15102,a,18578,a),flip(a)].">
      <j1 rule="hyper" parents="15102 18578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18591">
    <literal><![CDATA[
      K(x,K(y,y \ z) * (T(u,K(y,z) * w) \ w)) = K(x,(K(y,y \ z) * w) / u)
    ]]></literal>
    <justification jstring="[hyper(15101,a,18578,a),flip(a)].">
      <j1 rule="hyper" parents="15101 18578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18593">
    <literal><![CDATA[
      T(x,y \ (K(z,u) * w)) = T(x,K(z,u) * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(124,a,18578,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 18578 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18594">
    <literal><![CDATA[
      K(x,K(y,z) * ((z * u) \ w)) = K(x,(T(z,y) * u) \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,17761,a(flip),b,18578,a),flip(a)].">
      <j1 rule="hyper" parents="63 17761 18578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18596">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ (y * w))) = K(x,u \ (T(y,z) * w))
    ]]></literal>
    <justification jstring="[para(4273(a,1),18578(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4273 18578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18597">
    <literal><![CDATA[
      K(x,y \ (z * (K(u,z) * w))) = K(x,K(u,z) * (y \ (z * w)))
    ]]></literal>
    <justification jstring="[para(4712(a,1),18578(a,1,2,2))].">
      <j1 rule="para" parents="4712 18578"/>
    </justification>
  </clause>

  <clause id="18598">
    <literal><![CDATA[
      K(x,K(y \ z,y) * (u \ ((z / y) * w))) = K(x,u \ ((y \ z) * w))
    ]]></literal>
    <justification jstring="[para(5049(a,1),18578(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5049 18578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18599">
    <literal><![CDATA[
      K(x,K(y,T(z,u)) * (w \ (u / z))) = K(x,w \ (u / T(z,y)))
    ]]></literal>
    <justification jstring="[para(7888(a,1),18578(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7888 18578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18600">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ ((z * y) * w))) = K(x,u \ ((y * z) * w))
    ]]></literal>
    <justification jstring="[para(10080(a,1),18578(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10080 18578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18601">
    <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(18580(a,1),16364(a,1,2,2))].">
      <j1 rule="para" parents="18580 16364"/>
    </justification>
  </clause>

  <clause id="18602">
    <literal><![CDATA[
      T(x,(y * K(z,u)) \ w) = T(x,K(u,z) * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(124,a,18581,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 18581 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18603">
    <literal><![CDATA[
      K(x,(y \ K(z,u)) * w) = K(x,K(z,u) * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(63,a,16457,a(flip),b,18581,a)].">
      <j1 rule="hyper" parents="63 16457 18581"/>
    </justification>
  </clause>

  <clause id="18604">
    <literal><![CDATA[
      K(x,(y * K(z,u)) \ w) = K(x,K(z,u) \ (y \ w))
    ]]></literal>
    <justification jstring="[para(4567(a,2),18581(a,2,2))].">
      <j1 rule="para" parents="4567 18581"/>
    </justification>
  </clause>

  <clause id="18605">
    <literal><![CDATA[
      K(x,K(y,z) * ((u / y) \ w)) = K(x,(u / T(y,z)) \ w)
    ]]></literal>
    <justification jstring="[para(5450(a,1),18581(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5450 18581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18606">
    <literal><![CDATA[
      T(x,(K(y,z) * u) \ w) = T(x,K(z,y) * (u \ w))
    ]]></literal>
    <justification jstring="[hyper(124,a,18582,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 18582 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18607">
    <literal><![CDATA[
      K(x,R(y * z,K(u,L(w,y,z)),K(u,L(w,y,z))) \ v5) = K(x,K(L(u,y,z),w) * (((K(u,w) * y) * z) \ v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,17288,a,b,18582,a)].">
      <j1 rule="hyper" parents="63 17288 18582"/>
    </justification>
  </clause>

  <clause id="18608">
    <literal><![CDATA[
      K(x,K(y,z) * ((y \ u) \ w)) = K(x,(T(y,z) \ u) \ w)
    ]]></literal>
    <justification jstring="[para(4555(a,1),18582(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4555 18582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18609">
    <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(63,a,18347,a(flip),b,18593,a),flip(a)].">
      <j1 rule="hyper" parents="63 18347 18593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18610">
    <literal><![CDATA[
      T(x,K(y,T(z,u)) * (w \ (u / z))) = T(x,w \ (u / T(z,y)))
    ]]></literal>
    <justification jstring="[para(7888(a,1),18593(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7888 18593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18611">
    <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(18593(a,1),5157(a,1,1))].">
      <j1 rule="para" parents="18593 5157"/>
    </justification>
  </clause>

  <clause id="18612">
    <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(63,a,15284,a,b,18602,a)].">
      <j1 rule="hyper" parents="63 15284 18602"/>
    </justification>
  </clause>

  <clause id="18613">
    <literal><![CDATA[
      T(x,(y * K(z,u)) \ w) = T(x,K(z,u) \ (y \ w))
    ]]></literal>
    <justification jstring="[para(4567(a,2),18602(a,2,2))].">
      <j1 rule="para" parents="4567 18602"/>
    </justification>
  </clause>

  <clause id="18614">
    <literal><![CDATA[
      T(x,K(y,z) * ((u / y) \ w)) = T(x,(u / T(y,z)) \ w)
    ]]></literal>
    <justification jstring="[para(5450(a,1),18602(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5450 18602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18615">
    <literal><![CDATA[
      T(x,K(y \ z,y) * ((u \ (y \ z)) \ w)) = T(x,(u \ (z / y)) \ w)
    ]]></literal>
    <justification jstring="[para(13414(a,1),18602(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13414 18602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18616">
    <literal><![CDATA[
      T(x,(y \ K(z,u)) * w) = T(x,K(z,u) * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(124,a,18603,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 18603 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18618">
    <literal><![CDATA[
      K(x,K(y,z) \ ((u / z) \ w)) = K(x,(u / T(z,y)) \ w)
    ]]></literal>
    <justification jstring="[para(5450(a,1),18604(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5450 18604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18619">
    <literal><![CDATA[
      K(x,K(y,z) \ ((u * y) \ w)) = K(x,(u * T(y,z)) \ w)
    ]]></literal>
    <justification jstring="[para(5984(a,1),18604(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5984 18604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18620">
    <literal><![CDATA[
      T(x,K(y,z) * ((z / u) \ w)) = T(x,(T(z,y) / u) \ w)
    ]]></literal>
    <justification jstring="[para(13229(a,1),18606(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13229 18606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18621">
    <literal><![CDATA[
      T(x,K(y,z) \ ((K(y,z) \ u) \ w)) = T(x,T(u,K(y,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,12730,a(flip),b,18613,a),flip(a)].">
      <j1 rule="hyper" parents="63 12730 18613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18622">
    <literal><![CDATA[
      T(x,K(y,T(z,u)) * ((u * z) \ w)) = T(x,((u * T(z,y)) \ 1) * w)
    ]]></literal>
    <justification jstring="[para(13271(a,1),18616(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13271 18616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18623">
    <literal><![CDATA[
      T(x,K(y,T(z,u)) * ((u \ z) \ w)) = T(x,((u \ T(z,y)) \ 1) * w)
    ]]></literal>
    <justification jstring="[para(13724(a,1),18616(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13724 18616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18624">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ (w * z))) = K(x,u \ (w * T(z,y)))
    ]]></literal>
    <justification jstring="[hyper(14927,a,18584,a)].">
      <j1 rule="hyper" parents="14927 18584"/>
    </justification>
  </clause>

  <clause id="18625">
    <literal><![CDATA[
      K(x,K(y,z) * ((y * u) \ w)) = K(x,(T(y,z) * u) \ w)
    ]]></literal>
    <justification jstring="[hyper(14927,a,18594,a)].">
      <j1 rule="hyper" parents="14927 18594"/>
    </justification>
  </clause>

  <clause id="18627">
    <literal><![CDATA[
      K(x,K(y,z) \ (u \ (y * w))) = K(x,u \ (T(y,z) * w))
    ]]></literal>
    <justification jstring="[hyper(15779,a,18596,a)].">
      <j1 rule="hyper" parents="15779 18596"/>
    </justification>
  </clause>

  <clause id="18628">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ (z * w))) = K(x,u \ (T(z,y) * w))
    ]]></literal>
    <justification jstring="[hyper(14927,a,18596,a)].">
      <j1 rule="hyper" parents="14927 18596"/>
    </justification>
  </clause>

  <clause id="18629">
    <literal><![CDATA[
      K(x,K(y,z) \ (u \ (z * w))) = K(x,u \ (T(z,y) * w))
    ]]></literal>
    <justification jstring="[para(4567(a,2),18596(a,1,2))].">
      <j1 rule="para" parents="4567 18596"/>
    </justification>
  </clause>

  <clause id="18630">
    <literal><![CDATA[
      K(K(x,y) * ((z / x) \ u),w) = (v5 * K(w,(z / T(x,y)) \ u)) \ v5
    ]]></literal>
    <justification jstring="[para(18605(a,1),5990(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="18605 5990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18631">
    <literal><![CDATA[
      K(x,K(y,z) * ((z \ u) \ w)) = K(x,(T(z,y) \ u) \ w)
    ]]></literal>
    <justification jstring="[hyper(14927,a,18608,a)].">
      <j1 rule="hyper" parents="14927 18608"/>
    </justification>
  </clause>

  <clause id="18632">
    <literal><![CDATA[
      T(x,(K(y,z) / T(u,w)) \ v5) = T(x,T(K(y,z) / u,w) \ v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,16911,a(flip),b,18614,a),flip(a)].">
      <j1 rule="hyper" parents="63 16911 18614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18633">
    <literal><![CDATA[
      K(x,(y / T(z,z \ u)) \ w) = K(x,K(u,z) \ ((y / z) \ w))
    ]]></literal>
    <justification jstring="[hyper(63,a,12864,a(flip),b,18618,a),flip(a)].">
      <j1 rule="hyper" parents="63 12864 18618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18634">
    <literal><![CDATA[
      K(x,K(y,z) \ ((u * z) \ w)) = K(x,(u * T(z,y)) \ w)
    ]]></literal>
    <justification jstring="[hyper(15780,a,18619,a)].">
      <j1 rule="hyper" parents="15780 18619"/>
    </justification>
  </clause>

  <clause id="18635">
    <literal><![CDATA[
      K(x,(y * T(z,K(u,w))) \ v5) = K(x,(y * z) \ v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,16325,a(flip),b,18619,a),flip(a)].">
      <j1 rule="hyper" parents="63 16325 18619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18636">
    <literal><![CDATA[
      K(x,(y * (K(z,u) \ w)) \ v5) = K(x,(y * (w * K(u,z))) \ v5)
    ]]></literal>
    <justification jstring="[para(6020(a,1),18635(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="6020 18635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18637">
    <literal><![CDATA[
      K(x,(T(y,z) * z) \ u) = K(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[para(10014(a,1),18625(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10014 18625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18638">
    <literal><![CDATA[
      K(x,((y \ z) * (K(y,u) \ y)) \ w) = K(x,(y * (z / T(y,u))) \ w)
    ]]></literal>
    <justification jstring="[para(6267(a,1),18637(a,1,2,1))].">
      <j1 rule="para" parents="6267 18637"/>
    </justification>
  </clause>

  <clause id="18639">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ (z * x))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u \ (x * T(z,y))) = w
    ]]></literal>
    <justification jstring="[para(18628(a,2),12727(a,1))].">
      <j1 rule="para" parents="18628 12727"/>
    </justification>
  </clause>

  <clause id="18640">
    <literal><![CDATA[
      K(x,K(y,z) \ (u \ (T(y,w) * v5))) = K(x,u \ (T(T(y,w),z) * v5))
    ]]></literal>
    <justification jstring="[hyper(16434,a,18629,a)].">
      <j1 rule="hyper" parents="16434 18629"/>
    </justification>
  </clause>

  <clause id="18641">
    <literal><![CDATA[
      K(x,((y * z) / u) \ (T(y,w) * z)) = K(x,K(w,y) \ u)
    ]]></literal>
    <justification jstring="[para(79(a,1),18629(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="79 18629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18642">
    <literal><![CDATA[
      K(x,(T(y,z) \ z) \ u) = K(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,12824,a(flip),b,18631,a),flip(a)].">
      <j1 rule="hyper" parents="63 12824 18631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18643">
    <literal><![CDATA[
      K(x,(y / z) \ T(u,y / z)) = K(x,u / (T(z,y) \ y))
    ]]></literal>
    <justification jstring="[hyper(15105,a,18642,a),flip(a)].">
      <j1 rule="hyper" parents="15105 18642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18644">
    <literal><![CDATA[
      T(x,(T(y,z) \ z) \ u) = T(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[hyper(124,a,18642,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 18642 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18645">
    <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(6946(a,1),18644(a,1,2,1,1))].">
      <j1 rule="para" parents="6946 18644"/>
    </justification>
  </clause>

  <clause id="18646">
    <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(18644(a,1),16467(a,1,2,2))].">
      <j1 rule="para" parents="18644 16467"/>
    </justification>
  </clause>

  <clause id="18647">
    <literal><![CDATA[
      K(x,y / (T(z,u) \ u)) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[hyper(15100,a,18643,a),flip(a)].">
      <j1 rule="hyper" parents="15100 18643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18648">
    <literal><![CDATA[
      K(x,y / (T(z,u) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (u / z)) = w
    ]]></literal>
    <justification jstring="[para(18643(a,1),15100(a,1))].">
      <j1 rule="para" parents="18643 15100"/>
    </justification>
  </clause>

  <clause id="18649">
    <literal><![CDATA[
      K(T(x,y),T(z,y) / (y / x)) = K(T(x,y),y \ (z * T(x,y)))
    ]]></literal>
    <justification jstring="[hyper(63,a,15143,a(flip),b,18647,a),flip(a)].">
      <j1 rule="hyper" parents="63 15143 18647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18650">
    <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(12733(a,1),18648(a,1,2,2,1))].">
      <j1 rule="para" parents="12733 18648"/>
    </justification>
  </clause>

  <clause id="18651">
    <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(17769(a,2),18576(a,1))].">
      <j1 rule="para" parents="17769 18576"/>
    </justification>
  </clause>

  <clause id="18652">
    <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(17809(a,2),18576(a,1))].">
      <j1 rule="para" parents="17809 18576"/>
    </justification>
  </clause>

  <clause id="18653">
    <literal><![CDATA[
      K(x,y \ (z * (K(u,z) * x))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,z) * ((z \ y) \ x)) = w
    ]]></literal>
    <justification jstring="[para(9830(a,1),18651(a,1))].">
      <j1 rule="para" parents="9830 18651"/>
    </justification>
  </clause>

  <clause id="18654">
    <literal><![CDATA[
      K(x,(y * (z * u)) / L(T(u,a(w,v5,v6)),z,y)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(25(a,2),18564(a,1,2,2))].">
      <j1 rule="para" parents="25 18564"/>
    </justification>
  </clause>

  <clause id="18655">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ (w / y))) = K(x,u \ (w / T(y,z)))
    ]]></literal>
    <justification jstring="[hyper(16428,a,18599,a)].">
      <j1 rule="hyper" parents="16428 18599"/>
    </justification>
  </clause>

  <clause id="18657">
    <literal><![CDATA[
      K(x,K(y,z * K(u,w)) * (v5 \ ((y * z) * v6))) = K(x,v5 \ ((z * y) * v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,17153,a,b,18600,a)].">
      <j1 rule="hyper" parents="63 17153 18600"/>
    </justification>
  </clause>

  <clause id="18658">
    <literal><![CDATA[
      K(x,T(y,z \ (u / T(w,v5)))) = K(x,T(y,z \ (w \ u)))
    ]]></literal>
    <justification jstring="[para(18610(a,1),16713(a,1,2))].">
      <j1 rule="para" parents="18610 16713"/>
    </justification>
  </clause>

  <clause id="18659">
    <literal><![CDATA[
      K(x,T(y,z \ (T(u,w) \ v5))) = K(x,T(y,z \ (u \ v5)))
    ]]></literal>
    <justification jstring="[hyper(16578,a,18658,a)].">
      <j1 rule="hyper" parents="16578 18658"/>
    </justification>
  </clause>

  <clause id="18660">
    <literal><![CDATA[
      T(x,K(y,z) \ ((K(y,z) \ u) \ w)) = T(x,u \ w)
    ]]></literal>
    <justification jstring="[hyper(333,a,16306,a(flip),b,18621,a),flip(a)].">
      <j1 rule="hyper" parents="333 16306 18621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18662">
    <literal><![CDATA[
      T(x,K(y,z) \ K(K(y,z) \ u,w)) = T(x,u \ T(K(y,z) \ u,w))
    ]]></literal>
    <justification jstring="[para(4215(a,2),18660(a,1,2,2))].">
      <j1 rule="para" parents="4215 18660"/>
    </justification>
  </clause>

  <clause id="18663">
    <literal><![CDATA[
      T(x,T(K(y,z) / u,w) \ v5) = T(x,K(y,z) * (T(u,w) * v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,18003,a(flip),b,18632,a),flip(a)].">
      <j1 rule="hyper" parents="63 18003 18632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18664">
    <literal><![CDATA[
      K(x,(y / T(z,z \ u)) \ w) = K(x,(y / T(z,u)) \ w)
    ]]></literal>
    <justification jstring="[hyper(333,a,18618,a(flip),b,18633,a),flip(a)].">
      <j1 rule="hyper" parents="333 18618 18633"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18665">
    <literal><![CDATA[
      K(x,(y / ((z \ u) \ u)) \ w) = K(x,(y / T(z,u)) \ w)
    ]]></literal>
    <justification jstring="[para(112(a,1),18664(a,1,2,1,2))].">
      <j1 rule="para" parents="112 18664"/>
    </justification>
  </clause>

  <clause id="18666">
    <literal><![CDATA[
      K(x,(y / T(z,y)) \ u) = K(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[para(281(a,1),18664(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="281 18664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18667">
    <literal><![CDATA[
      K(x,(T(y,z) / z) \ u) = K(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[para(3625(a,2),18666(a,1,2,1))].">
      <j1 rule="para" parents="3625 18666"/>
    </justification>
  </clause>

  <clause id="18668">
    <literal><![CDATA[
      T(x,(T(y,z) / z) \ u) = T(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[hyper(124,a,18667,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 18667 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18669">
    <literal><![CDATA[
      K(T(x,y),y \ (z * T(x,y))) = K(x,T(T(z,y) / (y / x),y))
    ]]></literal>
    <justification jstring="[hyper(6695,a,18649,a),flip(a)].">
      <j1 rule="hyper" parents="6695 18649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18670">
    <literal><![CDATA[
      K(x,y * (z * K(a(u,w,v5),v6))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(10977(a,1),18654(a,1,2))].">
      <j1 rule="para" parents="10977 18654"/>
    </justification>
  </clause>

  <clause id="18671">
    <literal><![CDATA[
      K(x,y * (z * a(u,w,K(v5,v6)))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(13539(a,2),18670(a,1,2,2,2))].">
      <j1 rule="para" parents="13539 18670"/>
    </justification>
  </clause>

  <clause id="18673">
    <literal><![CDATA[
      K(x,y * (T(z,y) * a(u,w,K(v5,v6)))) = K(x,z * y)
    ]]></literal>
    <justification jstring="[para(111(a,1),18671(a,2,2))].">
      <j1 rule="para" parents="111 18671"/>
    </justification>
  </clause>

  <clause id="18674">
    <literal><![CDATA[
      K(x,y * ((z * u) * K(w,v5))) = K(x,y * (z * (u * K(w,v5))))
    ]]></literal>
    <justification jstring="[para(84(a,1),18671(a,1,2,2))].">
      <j1 rule="para" parents="84 18671"/>
    </justification>
  </clause>

  <clause id="18675">
    <literal><![CDATA[
      K(x,y * (R(z,z \ (u / a(w,v5,K(v6,v7))),a(w,v5,K(v6,v7))) \ u)) = K(x,y * (z \ (u / a(w,v5,K(v6,v7)))))
    ]]></literal>
    <justification jstring="[para(797(a,2),18671(a,1,2,2))].">
      <j1 rule="para" parents="797 18671"/>
    </justification>
  </clause>

  <clause id="18677">
    <literal><![CDATA[
      K(x,y * (L(z,u,K(w,v5)) \ v6)) = K(x,y * (z \ v6))
    ]]></literal>
    <justification jstring="[para(17672(a,1),18671(a,1,2,2))].">
      <j1 rule="para" parents="17672 18671"/>
    </justification>
  </clause>

  <clause id="18678">
    <literal><![CDATA[
      K(x,y * T(a(z,u,K(w,v5)) * v6,y)) = K(x,v6 * y)
    ]]></literal>
    <justification jstring="[para(18128(a,2),18673(a,1,2,2))].">
      <j1 rule="para" parents="18128 18673"/>
    </justification>
  </clause>

  <clause id="18679">
    <literal><![CDATA[
      K(x,y * (L(z,u,a(w,v5,K(v6,v7))) \ v8)) = K(x,y * (z \ v8))
    ]]></literal>
    <justification jstring="[para(13061(a,1),18677(a,1,2,2,1,3))].">
      <j1 rule="para" parents="13061 18677"/>
    </justification>
  </clause>

  <clause id="18680">
    <literal><![CDATA[
      K(x,(a(y,z,K(u,w)) * v5) * v6) = K(x,v5 * v6)
    ]]></literal>
    <justification jstring="[para(111(a,1),18678(a,1,2))].">
      <j1 rule="para" parents="111 18678"/>
    </justification>
  </clause>

  <clause id="18681">
    <literal><![CDATA[
      K(x,(y * a(z,u,K(w,v5))) * v6) = K(x,y * v6)
    ]]></literal>
    <justification jstring="[para(17584(a,1),18680(a,1,2,1))].">
      <j1 rule="para" parents="17584 18680"/>
    </justification>
  </clause>

  <clause id="18682">
    <literal><![CDATA[
      K(x,(L(y,z,K(u,w)) / v5) * v6) = K(x,(y / v5) * v6)
    ]]></literal>
    <justification jstring="[para(17793(a,1),18681(a,1,2,1))].">
      <j1 rule="para" parents="17793 18681"/>
    </justification>
  </clause>

  <clause id="18683">
    <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(576(a,1),18682(a,1,2,1,1))].">
      <j1 rule="para" parents="576 18682"/>
    </justification>
  </clause>

  <clause id="18684">
    <literal><![CDATA[
      T(x,T(y * K(z,u),w) * v5) = T(x,K(u,z) * (T(y,w) * v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,18198,a(flip),b,18663,a)].">
      <j1 rule="hyper" parents="63 18198 18663"/>
    </justification>
  </clause>

  <clause id="18685">
    <literal><![CDATA[
      K(T(x,y),y \ (z * T(x,y))) = K(x,T(T(z,y) / (x \ y),y))
    ]]></literal>
    <justification jstring="[hyper(333,a,9655,a(flip),b,18669,a),flip(a)].">
      <j1 rule="hyper" parents="333 9655 18669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18686">
    <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(18674(a,1),15603(a,1))].">
      <j1 rule="para" parents="18674 15603"/>
    </justification>
  </clause>

  <clause id="18687">
    <literal><![CDATA[
      T(x,T(K(y,z) * u,w) * v5) = T(x,K(z,y) * (T(u,w) * v5))
    ]]></literal>
    <justification jstring="[hyper(16451,a,18684,a)].">
      <j1 rule="hyper" parents="16451 18684"/>
    </justification>
  </clause>

  <clause id="18688">
    <literal><![CDATA[
      K(T(x,y),y \ (z * T(x,y))) = K(x,y \ (x * T(z,y)))
    ]]></literal>
    <justification jstring="[hyper(333,a,9947,a(flip),b,18685,a),flip(a)].">
      <j1 rule="hyper" parents="333 9947 18685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18689">
    <literal><![CDATA[
      K(x,(y * T(x,z)) / z) = K(x,z \ (x * T(y,z)))
    ]]></literal>
    <justification jstring="[hyper(7073,a,18688,a)].">
      <j1 rule="hyper" parents="7073 18688"/>
    </justification>
  </clause>

  <clause id="18690">
    <literal><![CDATA[
      K(x,y \ (x * T(z,y))) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / (x \ y)) = u
    ]]></literal>
    <justification jstring="[para(18689(a,1),9685(a,1))].">
      <j1 rule="para" parents="18689 9685"/>
    </justification>
  </clause>

  <clause id="18691">
    <literal><![CDATA[
      K(x,(y / T(z,u)) \ (x * T(w,y / ((z \ u) \ u)))) = K(x,w / (x \ (y / ((z \ u) \ u))))
    ]]></literal>
    <justification jstring="[hyper(18690,a,18665,a),flip(a)].">
      <j1 rule="hyper" parents="18690 18665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18692">
    <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(13474,a,18687,a),flip(a)].">
      <j1 rule="hyper" parents="13474 18687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18693">
    <literal><![CDATA[
      K(x,T(y,z) * (u * (w / y))) = K(x,y * (u * (w / T(y,z))))
    ]]></literal>
    <justification jstring="[hyper(18686,a,18438,a)].">
      <j1 rule="hyper" parents="18686 18438"/>
    </justification>
  </clause>

  <clause id="18694">
    <literal><![CDATA[
      K(x,y * (z * (u / T(y,u * z)))) = K(x,(z * (u / y)) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,16801,a(flip),b,18693,a),flip(a)].">
      <j1 rule="hyper" parents="63 16801 18693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18695">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ (u / (y / z))) = K(x,z \ (u / (z \ y)))
    ]]></literal>
    <justification jstring="[para(4929(a,1),18585(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4929 18585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18696">
    <literal><![CDATA[
      K(x,y \ (z * ((u \ w) * u))) = K(x,K(w,u) * (y \ (z * w)))
    ]]></literal>
    <justification jstring="[hyper(12838,a,18586,a),flip(a)].">
      <j1 rule="hyper" parents="12838 18586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18697">
    <literal><![CDATA[
      K(x,y \ (z * ((u \ w) * u))) = K(x,y \ (z * T(w,u)))
    ]]></literal>
    <justification jstring="[hyper(333,a,18584,a(flip),b,18696,a),flip(a)].">
      <j1 rule="hyper" parents="333 18584 18696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18698">
    <literal><![CDATA[
      K(x,y \ (z * T(u * w,u))) = K(x,y \ (z * (w * u)))
    ]]></literal>
    <justification jstring="[para(9(a,1),18697(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="9 18697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18699">
    <literal><![CDATA[
      K(x,y \ (z * (u * (w / u)))) = K(x,K(u,w) * (y \ (z * w)))
    ]]></literal>
    <justification jstring="[hyper(15002,a,18587,a),flip(a)].">
      <j1 rule="hyper" parents="15002 18587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18700">
    <literal><![CDATA[
      K(x,y \ (z * (u * (w / u)))) = K(x,y \ (z * T(w,u)))
    ]]></literal>
    <justification jstring="[hyper(333,a,18624,a(flip),b,18699,a),flip(a)].">
      <j1 rule="hyper" parents="333 18624 18699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18701">
    <literal><![CDATA[
      K(x,y \ (z * T(u * w,w))) = K(x,y \ (z * (w * u)))
    ]]></literal>
    <justification jstring="[para(11(a,1),18700(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="11 18700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18702">
    <literal><![CDATA[
      K(x,y \ (T(z,u * w) * (u * w))) = K(x,y \ (T(w * u,u) * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,15185,a(flip),b,18701,a),flip(a)].">
      <j1 rule="hyper" parents="63 15185 18701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18703">
    <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(333,a,17810,a(flip),b,18590,a),flip(a)].">
      <j1 rule="hyper" parents="333 17810 18590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18704">
    <literal><![CDATA[
      K(x,K(y \ z,y) * (T(u,K(z,y) * w) \ w)) = K(x,(K(y \ z,y) * w) / u)
    ]]></literal>
    <justification jstring="[para(14921(a,1),18590(a,1,2,2,1))].">
      <j1 rule="para" parents="14921 18590"/>
    </justification>
  </clause>

  <clause id="18705">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ ((y / z) * w))) = K(x,u \ ((z \ y) * w))
    ]]></literal>
    <justification jstring="[hyper(12838,a,18598,a)].">
      <j1 rule="hyper" parents="12838 18598"/>
    </justification>
  </clause>

  <clause id="18706">
    <literal><![CDATA[
      T(x,K(y,z) * ((u * y) \ w)) = T(x,((u * T(y,z)) \ 1) * w)
    ]]></literal>
    <justification jstring="[hyper(16401,a,18622,a)].">
      <j1 rule="hyper" parents="16401 18622"/>
    </justification>
  </clause>

  <clause id="18707">
    <literal><![CDATA[
      T(x,K(y,z) * ((u * y) \ w)) = T(x,(u * T(y,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(333,a,13284,a(flip),b,18706,a),flip(a)].">
      <j1 rule="hyper" parents="333 13284 18706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18709">
    <literal><![CDATA[
      T(x,(K(y,z) * T(u,w)) \ v5) = T(x,T(u \ K(z,y),w) * v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,18207,a(flip),b,18707,a),flip(a)].">
      <j1 rule="hyper" parents="63 18207 18707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18710">
    <literal><![CDATA[
      T(x,(y * T(z,u)) \ T(z,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,(y * z) \ T(T(z,w),u)) = v5
    ]]></literal>
    <justification jstring="[para(18707(a,1),16502(a,1))].">
      <j1 rule="para" parents="18707 16502"/>
    </justification>
  </clause>

  <clause id="18711">
    <literal><![CDATA[
      T(x,T(y \ K(z,u),w) * v5) = T(x,K(z,u) * (T(y,w) \ v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,18606,a(flip),b,18709,a),flip(a)].">
      <j1 rule="hyper" parents="63 18606 18709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18712">
    <literal><![CDATA[
      T(x,K(y,z) * (T(y \ u,w) \ v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,T(T(y,z) \ u,w) \ v5) = v6
    ]]></literal>
    <justification jstring="[para(18711(a,1),18199(a,1))].">
      <j1 rule="para" parents="18711 18199"/>
    </justification>
  </clause>

  <clause id="18713">
    <literal><![CDATA[
      T(x,K(y,z) * ((u \ y) \ w)) = T(x,((u \ T(y,z)) \ 1) * w)
    ]]></literal>
    <justification jstring="[hyper(16401,a,18623,a)].">
      <j1 rule="hyper" parents="16401 18623"/>
    </justification>
  </clause>

  <clause id="18714">
    <literal><![CDATA[
      T(x,K(y,z) * ((u \ y) \ w)) = T(x,(u \ T(y,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(333,a,13284,a(flip),b,18713,a),flip(a)].">
      <j1 rule="hyper" parents="333 13284 18713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18715">
    <literal><![CDATA[
      T(x,(y \ T(z \ u,z)) \ w) = T(x,(y \ (u / z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,18615,a(flip),b,18714,a),flip(a)].">
      <j1 rule="hyper" parents="63 18615 18714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18716">
    <literal><![CDATA[
      K(K(x,y) * ((z / x) \ u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K((z / T(x,y)) \ u,w) = v5
    ]]></literal>
    <justification jstring="[para(18630(a,2),6024(a,1))].">
      <j1 rule="para" parents="18630 6024"/>
    </justification>
  </clause>

  <clause id="18717">
    <literal><![CDATA[
      K(K(x,y) * ((z / y) \ u),w) = K((z / T(y,x)) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(18716,a,15701,a),flip(a)].">
      <j1 rule="hyper" parents="18716 15701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18718">
    <literal><![CDATA[
      K((x / ((y * z) / y)) \ u,w) = K((x / T(z,y)) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,17958,a,b,18717,a)].">
      <j1 rule="hyper" parents="63 17958 18717"/>
    </justification>
  </clause>

  <clause id="18719">
    <literal><![CDATA[
      K(x,y \ (T(z * u,u) * w)) = K(x,y \ ((u * z) * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,15184,a(flip),b,18702,a),flip(a)].">
      <j1 rule="hyper" parents="63 15184 18702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18720">
    <literal><![CDATA[
      K(x,y \ ((z * (u / z)) * w)) = K(x,y \ (T(u,z) * w))
    ]]></literal>
    <justification jstring="[para(12(a,1),18719(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="12 18719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18721">
    <literal><![CDATA[
      R(T(K(x,y \ z),y * u),y,u) = K(x,(y * u) \ (T(z,y) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,14309,a(flip),b,18720,a)].">
      <j1 rule="hyper" parents="63 14309 18720"/>
    </justification>
  </clause>

  <clause id="18722">
    <literal><![CDATA[
      R(K(x,T(y \ z,y * u)),y,u) = K(x,(y * u) \ (T(z,y) * u))
    ]]></literal>
    <justification jstring="[para(6365(a,2),18721(a,1,1))].">
      <j1 rule="para" parents="6365 18721"/>
    </justification>
  </clause>

  <clause id="18723">
    <literal><![CDATA[
      K(x,L(T(y \ z,y * u),y,u)) = K(x,(y * u) \ (T(z,y) * u))
    ]]></literal>
    <justification jstring="[hyper(13899,a,18722,a)].">
      <j1 rule="hyper" parents="13899 18722"/>
    </justification>
  </clause>

  <clause id="18724">
    <literal><![CDATA[
      K(x,(y * (z \ u)) \ (T(z,y) * (z \ u))) = K(x,u / ((u / z) * y))
    ]]></literal>
    <justification jstring="[hyper(63,a,16848,a(flip),b,18723,a),flip(a)].">
      <j1 rule="hyper" parents="63 16848 18723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18725">
    <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(14927,a,18703,a)].">
      <j1 rule="hyper" parents="14927 18703"/>
    </justification>
  </clause>

  <clause id="18726">
    <literal><![CDATA[
      K(x,(y * (z \ u)) \ (K(z,y) * u)) = K(x,u / ((u / z) * y))
    ]]></literal>
    <justification jstring="[para(4242(a,1),18724(a,1,2,2))].">
      <j1 rule="para" parents="4242 18724"/>
    </justification>
  </clause>

  <clause id="18727">
    <literal><![CDATA[
      K(x,(T(y,z) * (z \ u)) \ u) = K(x,u / ((u / z) * y))
    ]]></literal>
    <justification jstring="[hyper(63,a,17761,a(flip),b,18726,a)].">
      <j1 rule="hyper" parents="63 17761 18726"/>
    </justification>
  </clause>

  <clause id="18728">
    <literal><![CDATA[
      K(x,K(y,z) * ((z \ u) \ x)) = K(x,K(y,z) * (u \ (z * x)))
    ]]></literal>
    <justification jstring="[hyper(18653,a,18597,a)].">
      <j1 rule="hyper" parents="18653 18597"/>
    </justification>
  </clause>

  <clause id="18729">
    <literal><![CDATA[
      K(x,K(y,z) * ((z \ u) \ x)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u \ (x * T(z,y))) = w
    ]]></literal>
    <justification jstring="[para(18728(a,2),18639(a,1))].">
      <j1 rule="para" parents="18728 18639"/>
    </justification>
  </clause>

  <clause id="18730">
    <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(18710,a,15086,a)].">
      <j1 rule="hyper" parents="18710 15086"/>
    </justification>
  </clause>

  <clause id="18731">
    <literal><![CDATA[
      K(x,y * T((K(z,u) * w) \ v5,v6)) = K(x,y * T(w \ (K(u,z) * v5),v6))
    ]]></literal>
    <justification jstring="[para(4567(a,1),18568(a,2,2,2,1,2))].">
      <j1 rule="para" parents="4567 18568"/>
    </justification>
  </clause>

  <clause id="18732">
    <literal><![CDATA[
      K(x,y / T((K(z,u) * w) \ v5,w)) = K(x,y / ((K(z,u) \ v5) / w))
    ]]></literal>
    <justification jstring="[hyper(63,a,15166,a(flip),b,18571,a)].">
      <j1 rule="hyper" parents="63 15166 18571"/>
    </justification>
  </clause>

  <clause id="18733">
    <literal><![CDATA[
      T(x,(T(y,z / u) \ (z / u)) \ w) = T(x,(T(u \ z,u) / y) \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,18715,a(flip),b,18645,a)].">
      <j1 rule="hyper" parents="63 18715 18645"/>
    </justification>
  </clause>

  <clause id="18734">
    <literal><![CDATA[
      T(x,(T(y \ z,y) / u) \ w) = T(x,((z / y) / u) \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,18644,a(flip),b,18733,a),flip(a)].">
      <j1 rule="hyper" parents="63 18644 18733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18735">
    <literal><![CDATA[
      T(x,((((y \ z) \ z) \ z) / u) \ w) = T(x,((z / y) / u) \ w)
    ]]></literal>
    <justification jstring="[para(3674(a,1),18734(a,1,2,1,1))].">
      <j1 rule="para" parents="3674 18734"/>
    </justification>
  </clause>

  <clause id="18736">
    <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(63,a,16039,a(flip),b,18692,a)].">
      <j1 rule="hyper" parents="63 16039 18692"/>
    </justification>
  </clause>

  <clause id="18737">
    <literal><![CDATA[
      K(x,y * T(z \ (K(u,w) * v5),z)) = K(x,y * (v5 / (K(w,u) * z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,16785,a(flip),b,18731,a),flip(a)].">
      <j1 rule="hyper" parents="63 16785 18731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18738">
    <literal><![CDATA[
      K(x,y * ((K(z,u) * w) / v5)) = K(x,y * (w / (K(u,z) * v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,14987,a(flip),b,18737,a)].">
      <j1 rule="hyper" parents="63 14987 18737"/>
    </justification>
  </clause>

  <clause id="18739">
    <literal><![CDATA[
      K(x,y * T(z \ (u * K(w,v5)),u)) = K(x,y * (u / (K(v5,w) * z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,17184,a,b,18738,a)].">
      <j1 rule="hyper" parents="63 17184 18738"/>
    </justification>
  </clause>

  <clause id="18740">
    <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(63,a,18109,a(flip),b,18736,a),flip(a)].">
      <j1 rule="hyper" parents="63 18109 18736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18741">
    <literal><![CDATA[
      K(x,(x * y) \ (x * T(z,y * x))) = K(x,R(z,z \ (x * y),z) / y)
    ]]></literal>
    <justification jstring="[hyper(18729,a,18583,a(flip))].">
      <j1 rule="hyper" parents="18729 18583"/>
    </justification>
  </clause>

  <clause id="18742">
    <literal><![CDATA[
      K(x,y \ (x \ (x * T(z,y * x)))) = K(x,R(z,z \ (x * y),z) / y)
    ]]></literal>
    <justification jstring="[hyper(9700,a,18741,a)].">
      <j1 rule="hyper" parents="9700 18741"/>
    </justification>
  </clause>

  <clause id="18743">
    <literal><![CDATA[
      K(x,R(y,y \ (x * z),y) / z) = K(x,z \ T(y,z * x))
    ]]></literal>
    <justification jstring="[para(9(a,1),18742(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 18742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18744">
    <literal><![CDATA[
      K(x,y \ T(z,y * x)) = K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(12668,a,18743,a),flip(a)].">
      <j1 rule="hyper" parents="12668 18743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18746">
    <literal><![CDATA[
      K(x,(1 / y) \ T(T(z,y),(1 / y) * x)) = K(x,z / (K(y,z) / y))
    ]]></literal>
    <justification jstring="[para(12474(a,1),18744(a,2,2))].">
      <j1 rule="para" parents="12474 18744"/>
    </justification>
  </clause>

  <clause id="18747">
    <literal><![CDATA[
      K(x,(1 / y) \ T(T(z,y),y \ x)) = K(x,z / (K(y,z) / y))
    ]]></literal>
    <justification jstring="[para(13260(a,1),18746(a,1,2,2))].">
      <j1 rule="para" parents="13260 18746"/>
    </justification>
  </clause>

  <clause id="18748">
    <literal><![CDATA[
      K(x,y / (K(z,y) / z)) = K(x,z * T(T(y,z),z \ x))
    ]]></literal>
    <justification jstring="[hyper(13505,a,18747,a),flip(a)].">
      <j1 rule="hyper" parents="13505 18747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18749">
    <literal><![CDATA[
      K(x,y / (K(z,y) / z)) = K(x,T(y,z \ x) * z)
    ]]></literal>
    <justification jstring="[para(250(a,1),18748(a,2,2))].">
      <j1 rule="para" parents="250 18748"/>
    </justification>
  </clause>

  <clause id="18750">
    <literal><![CDATA[
      K(x,T(y,z \ x) * z) = K(x,y * (z * K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(13518,a,18749,a),flip(a)].">
      <j1 rule="hyper" parents="13518 18749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18751">
    <literal><![CDATA[
      K(x,T(y,z \ x) * z) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(333,a,12270,a(flip),b,18750,a),flip(a)].">
      <j1 rule="hyper" parents="333 12270 18750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18752">
    <literal><![CDATA[
      K(x,T(y,(x * z) \ x) * (x * z)) = K(x,(z * x) * y)
    ]]></literal>
    <justification jstring="[hyper(333,a,7486,a,b,18751,a),flip(a)].">
      <j1 rule="hyper" parents="333 7486 18751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18753">
    <literal><![CDATA[
      K(x,T(y,z * x) * z) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,16929,a(flip),b,18751,a)].">
      <j1 rule="hyper" parents="63 16929 18751"/>
    </justification>
  </clause>

  <clause id="18754">
    <literal><![CDATA[
      K(x,y * T(z,y * x)) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,14975,a(flip),b,18753,a),flip(a)].">
      <j1 rule="hyper" parents="63 14975 18753"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18755">
    <literal><![CDATA[
      K(T(x,y),z * T(u,z * x)) = K(T(x,y),u * z)
    ]]></literal>
    <justification jstring="[hyper(16786,a,18754,a)].">
      <j1 rule="hyper" parents="16786 18754"/>
    </justification>
  </clause>

  <clause id="18756">
    <literal><![CDATA[
      K(x,T(y,z \ 1) * (x * z)) = K(x,(z * x) * y)
    ]]></literal>
    <justification jstring="[para(5801(a,1),18752(a,1,2,1))].">
      <j1 rule="para" parents="5801 18752"/>
    </justification>
  </clause>

  <clause id="18757">
    <literal><![CDATA[
      K(x,T(y,z) * (x * z)) = K(x,(z * x) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,16930,a(flip),b,18756,a)].">
      <j1 rule="hyper" parents="63 16930 18756"/>
    </justification>
  </clause>

  <clause id="18759">
    <literal><![CDATA[
      K(x,y * (T(z,y) * x)) = K(x,(z * x) * y)
    ]]></literal>
    <justification jstring="[hyper(15850,a,18757,a)].">
      <j1 rule="hyper" parents="15850 18757"/>
    </justification>
  </clause>

  <clause id="18760">
    <literal><![CDATA[
      K(x,(y * (T(z,y) * u)) * K(u,(z * u) * y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y * (T(z,y) * u),u)) = w
    ]]></literal>
    <justification jstring="[para(18759(a,1),7013(a,1,2,2))].">
      <j1 rule="para" parents="18759 7013"/>
    </justification>
  </clause>

  <clause id="18761">
    <literal><![CDATA[
      T(x,T(T(y \ z,u) \ z,w)) = T(x,T(T(y,w) \ z,u) \ z)
    ]]></literal>
    <justification jstring="[hyper(18712,a,18609,a),flip(a)].">
      <j1 rule="hyper" parents="18712 18609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18762">
    <literal><![CDATA[
      T(x,T(T(y \ z,u) \ z,w)) = T(x,z * T(T(y,w) / z,u))
    ]]></literal>
    <justification jstring="[hyper(18303,a,18761,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="18303 18761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18764">
    <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(333,a,18740,a(flip),b,18762,a),flip(a)].">
      <j1 rule="hyper" parents="333 18740 18762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18765">
    <literal><![CDATA[
      T(x,T(T(y \ z,u) \ z,w)) = T(x,T(z * T(y / z,u),w))
    ]]></literal>
    <justification jstring="[hyper(15595,a,18764,a)].">
      <j1 rule="hyper" parents="15595 18764"/>
    </justification>
  </clause>

  <clause id="18767">
    <literal><![CDATA[
      T(x,T(y * T(z / y,u),w)) = T(x,y * T(T(z,w) / y,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,18762,a(flip),b,18765,a),flip(a)].">
      <j1 rule="hyper" parents="63 18762 18765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18769">
    <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(18767(a,1),15595(a,1))].">
      <j1 rule="para" parents="18767 15595"/>
    </justification>
  </clause>

  <clause id="18770">
    <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(110(a,1),18769(a,1,2,2,1,1,2))].">
      <j1 rule="para" parents="110 18769"/>
    </justification>
  </clause>

  <clause id="18771">
    <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(4567(a,1),18569(a,2,2,2,1,2))].">
      <j1 rule="para" parents="4567 18569"/>
    </justification>
  </clause>

  <clause id="18772">
    <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(333,a,13210,a(flip),b,18577,a),flip(a)].">
      <j1 rule="hyper" parents="333 13210 18577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18773">
    <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(18772(a,1),13514(a,1))].">
      <j1 rule="para" parents="18772 13514"/>
    </justification>
  </clause>

  <clause id="18774">
    <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(18386(a,1),18773(a,1))].">
      <j1 rule="para" parents="18386 18773"/>
    </justification>
  </clause>

  <clause id="18775">
    <literal><![CDATA[
      K(x,T(y,z / T(u,w)) \ (z / T(u,w))) = K(x,((z / u) * K(u,w)) / y)
    ]]></literal>
    <justification jstring="[hyper(63,a,18655,a(flip),b,18579,a)].">
      <j1 rule="hyper" parents="63 18655 18579"/>
    </justification>
  </clause>

  <clause id="18776">
    <literal><![CDATA[
      K(x,((y / z) * K(z,u)) / w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(y / T(z,u)) / w) = v5
    ]]></literal>
    <justification jstring="[para(18775(a,1),15099(a,1))].">
      <j1 rule="para" parents="18775 15099"/>
    </justification>
  </clause>

  <clause id="18777">
    <literal><![CDATA[
      K(x,((y * z) / T(y,u)) / w) = K(x,T(z * K(y,u),y) / w)
    ]]></literal>
    <justification jstring="[hyper(18776,a,15047,a)].">
      <j1 rule="hyper" parents="18776 15047"/>
    </justification>
  </clause>

  <clause id="18778">
    <literal><![CDATA[
      K(x,T(y * K(z,u),u) / w) = K(x,T(y * K(u,z),u) / w)
    ]]></literal>
    <justification jstring="[hyper(63,a,15046,a(flip),b,18777,a)].">
      <j1 rule="hyper" parents="63 15046 18777"/>
    </justification>
  </clause>

  <clause id="18779">
    <literal><![CDATA[
      K(x,T(y * K(z,u),z) / w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z) * (w \ K(u,z))) = v5
    ]]></literal>
    <justification jstring="[para(18778(a,1),17898(a,1))].">
      <j1 rule="para" parents="18778 17898"/>
    </justification>
  </clause>

  <clause id="18780">
    <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(15214,a,18588,a)].">
      <j1 rule="hyper" parents="15214 18588"/>
    </justification>
  </clause>

  <clause id="18781">
    <literal><![CDATA[
      K(x,(K(y \ z,z) * u) / w) = K(x,u * (w \ K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(63,a,18725,a(flip),b,18780,a),flip(a)].">
      <j1 rule="hyper" parents="63 18725 18780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18782">
    <literal><![CDATA[
      K(x,y * (z \ K(u \ w,w))) = K(x,y * (z \ K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(17812,a,18781,a)].">
      <j1 rule="hyper" parents="17812 18781"/>
    </justification>
  </clause>

  <clause id="18783">
    <literal><![CDATA[
      K(x,K(y,z) * (T(u,K(y,z) * w) \ w)) = K(x,(K(y,z \ 1) * w) / u)
    ]]></literal>
    <justification jstring="[hyper(15207,a,18589,a)].">
      <j1 rule="hyper" parents="15207 18589"/>
    </justification>
  </clause>

  <clause id="18784">
    <literal><![CDATA[
      K(x,(K(y,z \ 1) * u) / w) = K(x,u * (w \ K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(63,a,18725,a(flip),b,18783,a),flip(a)].">
      <j1 rule="hyper" parents="63 18725 18783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18785">
    <literal><![CDATA[
      K(x,y * (z \ K(u,w \ 1))) = K(x,y * (z \ K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(17812,a,18784,a)].">
      <j1 rule="hyper" parents="17812 18784"/>
    </justification>
  </clause>

  <clause id="18786">
    <literal><![CDATA[
      K(x,y * (z \ K(u,w \ 1))) = K(x,y * (z \ K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(333,a,18104,a,b,18785,a),flip(a)].">
      <j1 rule="hyper" parents="333 18104 18785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18787">
    <literal><![CDATA[
      K(x,K(y,z) * (T(u,K(y,z) * w) \ w)) = K(x,(K(y,y \ z) * w) / u)
    ]]></literal>
    <justification jstring="[hyper(15002,a,18591,a)].">
      <j1 rule="hyper" parents="15002 18591"/>
    </justification>
  </clause>

  <clause id="18788">
    <literal><![CDATA[
      K(x,(K(y,y \ z) * u) / w) = K(x,u * (w \ K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(63,a,18725,a(flip),b,18787,a),flip(a)].">
      <j1 rule="hyper" parents="63 18725 18787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18789">
    <literal><![CDATA[
      K(x,y * (z \ K(u,u \ w))) = K(x,y * (z \ K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(17812,a,18788,a)].">
      <j1 rule="hyper" parents="17812 18788"/>
    </justification>
  </clause>

  <clause id="18790">
    <literal><![CDATA[
      K(x,y * T((z / u) \ 1,z)) = K(x,y * ((z / u) \ K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(18074,a,18789,a)].">
      <j1 rule="hyper" parents="18074 18789"/>
    </justification>
  </clause>

  <clause id="18791">
    <literal><![CDATA[
      K(x,y * ((z \ (u * y)) \ K(z,u))) = K(x,T(y / (z \ (u * y)),u))
    ]]></literal>
    <justification jstring="[hyper(63,a,18482,a(flip),b,18789,a),flip(a)].">
      <j1 rule="hyper" parents="63 18482 18789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18792">
    <literal><![CDATA[
      K(x,y * (z \ K(u * w,w))) = K(x,y * (z \ K(w,u)))
    ]]></literal>
    <justification jstring="[para(4394(a,1),18789(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4394 18789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18793">
    <literal><![CDATA[
      K(x,y * T((z / u) \ 1,z)) = K(x,y / (z / T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(333,a,16480,a(flip),b,18790,a),flip(a)].">
      <j1 rule="hyper" parents="333 16480 18790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18794">
    <literal><![CDATA[
      K(x,y / (z / T(u,z))) = K(x,y / T(z / u,z))
    ]]></literal>
    <justification jstring="[hyper(18054,a,18793,a),flip(a)].">
      <j1 rule="hyper" parents="18054 18793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18795">
    <literal><![CDATA[
      K(x,y / (z / T(u,z))) = K(x,y / (u \ z))
    ]]></literal>
    <justification jstring="[hyper(333,a,15171,a(flip),b,18794,a),flip(a)].">
      <j1 rule="hyper" parents="333 15171 18794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18796">
    <literal><![CDATA[
      K(x,y / (T(z,u) / u)) = K(x,y / (u \ z))
    ]]></literal>
    <justification jstring="[para(3625(a,2),18795(a,1,2,2))].">
      <j1 rule="para" parents="3625 18795"/>
    </justification>
  </clause>

  <clause id="18797">
    <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(18791(a,1),13534(a,1))].">
      <j1 rule="para" parents="18791 13534"/>
    </justification>
  </clause>

  <clause id="18798">
    <literal><![CDATA[
      K(x,K(y,z) * (T(u,K(y,z) * w) \ w)) = K(x,(K(z \ y,z) * w) / u)
    ]]></literal>
    <justification jstring="[hyper(12838,a,18704,a)].">
      <j1 rule="hyper" parents="12838 18704"/>
    </justification>
  </clause>

  <clause id="18799">
    <literal><![CDATA[
      K(x,(K(y \ z,y) * u) / w) = K(x,u * (w \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,18725,a(flip),b,18798,a),flip(a)].">
      <j1 rule="hyper" parents="63 18725 18798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18800">
    <literal><![CDATA[
      K(x,y * (z \ K(u \ w,u))) = K(x,y * (z \ K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(17812,a,18799,a)].">
      <j1 rule="hyper" parents="17812 18799"/>
    </justification>
  </clause>

  <clause id="18801">
    <literal><![CDATA[
      K(x,(y * (1 / z)) * (u \ K(z,y))) = K(x,T(y * (1 / z),z) / u)
    ]]></literal>
    <justification jstring="[para(8575(a,1),18799(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8575 18799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18802">
    <literal><![CDATA[
      K(x,T(y / (z \ u),x) * (w \ K(z,u))) = K(x,(y / (u / z)) / w)
    ]]></literal>
    <justification jstring="[hyper(63,a,17816,a(flip),b,18800,a),flip(a)].">
      <j1 rule="hyper" parents="63 17816 18800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18803">
    <literal><![CDATA[
      K(x,y * (T(z \ (u \ w),x) \ K(u,w))) = K(x,y / (z \ (w / u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,16479,a(flip),b,18800,a),flip(a)].">
      <j1 rule="hyper" parents="63 16479 18800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18804">
    <literal><![CDATA[
      K(x,(y * (1 / z)) * (u \ K(z,y))) = K(x,((1 / z) * y) / u)
    ]]></literal>
    <justification jstring="[hyper(333,a,12904,a(flip),b,18801,a),flip(a)].">
      <j1 rule="hyper" parents="333 12904 18801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18805">
    <literal><![CDATA[
      K(x,(y * (1 / z)) * (u \ K(z,y))) = K(x,((z \ 1) * y) / u)
    ]]></literal>
    <justification jstring="[hyper(333,a,5024,a(flip),b,18804,a),flip(a)].">
      <j1 rule="hyper" parents="333 5024 18804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18806">
    <literal><![CDATA[
      K(x,(y / (z \ u)) * (w \ K(z,u))) = K(x,(y / (u / z)) / w)
    ]]></literal>
    <justification jstring="[hyper(7529,a,18802,a)].">
      <j1 rule="hyper" parents="7529 18802"/>
    </justification>
  </clause>

  <clause id="18807">
    <literal><![CDATA[
      K(x,(y / (T(z,u) \ u)) / w) = K(x,(y / (u / z)) / w)
    ]]></literal>
    <justification jstring="[hyper(63,a,17835,a(flip),b,18806,a)].">
      <j1 rule="hyper" parents="63 17835 18806"/>
    </justification>
  </clause>

  <clause id="18808">
    <literal><![CDATA[
      K(x,(y / (y / z)) / u) = K(x,T(z,y) / u)
    ]]></literal>
    <justification jstring="[para(76(a,1),18807(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="76 18807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18809">
    <literal><![CDATA[
      K(x,T(y * T(z,u),T(z,u)) / w) = K(x,(T(z,u) / (z / (y * z))) / w)
    ]]></literal>
    <justification jstring="[para(13318(a,1),18808(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="13318 18808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18810">
    <literal><![CDATA[
      K(x,y * ((z \ (u \ w)) \ K(u,w))) = K(x,y / (z \ (w / u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,9432,a(flip),b,18803,a)].">
      <j1 rule="hyper" parents="63 9432 18803"/>
    </justification>
  </clause>

  <clause id="18811">
    <literal><![CDATA[
      K(x,y / (z \ (u \ T(w,u)))) = K(x,y / (z \ (w / u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,16483,a(flip),b,18810,a)].">
      <j1 rule="hyper" parents="63 16483 18810"/>
    </justification>
  </clause>

  <clause id="18812">
    <literal><![CDATA[
      K((x \ (x / T(y,y * x))) \ z,u) = K((x / T(y * x,y)) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(18160,a,18718,a)].">
      <j1 rule="hyper" parents="18160 18718"/>
    </justification>
  </clause>

  <clause id="18813">
    <literal><![CDATA[
      K((x \ (x / T(y,x * y))) \ z,u) = K((x / T(y * x,y)) \ z,u)
    ]]></literal>
    <justification jstring="[para(3678(a,2),18812(a,1,1,1,2,2))].">
      <j1 rule="para" parents="3678 18812"/>
    </justification>
  </clause>

  <clause id="18814">
    <literal><![CDATA[
      K(x,y / (T(z,u / w) \ (u / w))) = K(x,y / ((w \ T(u,w)) / z))
    ]]></literal>
    <justification jstring="[hyper(18650,a,18811,a),flip(a)].">
      <j1 rule="hyper" parents="18650 18811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18815">
    <literal><![CDATA[
      K(x,y / ((z \ T(u,z)) / w)) = K(x,y / ((u / z) / w))
    ]]></literal>
    <justification jstring="[hyper(18648,a,18814,a),flip(a)].">
      <j1 rule="hyper" parents="18648 18814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18816">
    <literal><![CDATA[
      K(x,y / ((T(z,u) \ u) / w)) = K(x,y / ((u / z) / w))
    ]]></literal>
    <justification jstring="[hyper(63,a,8451,a,b,18815,a)].">
      <j1 rule="hyper" parents="63 8451 18815"/>
    </justification>
  </clause>

  <clause id="18817">
    <literal><![CDATA[
      K(L(x,y,z) * K(u \ 1,x),w / ((v5 * u) \ v5)) = K(x,L((v5 / (u * v5)) \ w,y,z))
    ]]></literal>
    <justification jstring="[hyper(18154,a,17823,a)].">
      <j1 rule="hyper" parents="18154 17823"/>
    </justification>
  </clause>

  <clause id="18818">
    <literal><![CDATA[
      K(x,T(y,K(z,u)) * (w * K(z,u))) = K(x,K(w,y)) * K(x,K(u,z) * (w * y))
    ]]></literal>
    <justification jstring="[para(16427(a,1),17984(a,2,2))].">
      <j1 rule="para" parents="16427 17984"/>
    </justification>
  </clause>

  <clause id="18819">
    <literal><![CDATA[
      K(x,T(y,K(z,u)) * (w * K(z,u))) = K(x,y * (K(u,z) * w))
    ]]></literal>
    <justification jstring="[hyper(333,a,17977,a(flip),b,18818,a),flip(a)].">
      <j1 rule="hyper" parents="333 17977 18818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18821">
    <literal><![CDATA[
      K(x,y * (K(z,u) * w)) = K(x,y * (w * K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(16375,a,18819,a),flip(a)].">
      <j1 rule="hyper" parents="16375 18819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18823">
    <literal><![CDATA[
      K(x,K(y,z) * (u * w)) = K(x,u * (K(z,y) * w))
    ]]></literal>
    <justification jstring="[hyper(333,a,18013,a,b,18821,a)].">
      <j1 rule="hyper" parents="333 18013 18821"/>
    </justification>
  </clause>

  <clause id="18824">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (w * v5))) = K(x,y * (w * (v5 * K(u,z))))
    ]]></literal>
    <justification jstring="[hyper(333,a,18674,a(flip),b,18821,a),flip(a)].">
      <j1 rule="hyper" parents="333 18674 18821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18825">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (w / z))) = K(x,y * (w / T(z,u)))
    ]]></literal>
    <justification jstring="[para(5450(a,1),18821(a,2,2,2))].">
      <j1 rule="para" parents="5450 18821"/>
    </justification>
  </clause>

  <clause id="18826">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (w / T(u,z)))) = K(x,y * (w / u))
    ]]></literal>
    <justification jstring="[para(5975(a,1),18821(a,2,2,2))].">
      <j1 rule="para" parents="5975 18821"/>
    </justification>
  </clause>

  <clause id="18827">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (w * u))) = K(x,y * (w * T(u,z)))
    ]]></literal>
    <justification jstring="[para(5984(a,1),18821(a,2,2,2))].">
      <j1 rule="para" parents="5984 18821"/>
    </justification>
  </clause>

  <clause id="18828">
    <literal><![CDATA[
      K(x,y * (K(z,y) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(18821(a,2),15603(a,1))].">
      <j1 rule="para" parents="18821 15603"/>
    </justification>
  </clause>

  <clause id="18829">
    <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(18821(a,1),16439(a,1))].">
      <j1 rule="para" parents="18821 16439"/>
    </justification>
  </clause>

  <clause id="18830">
    <literal><![CDATA[
      K(x,y * (K(z,x) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * u) = w
    ]]></literal>
    <justification jstring="[para(18823(a,1),7407(a,1))].">
      <j1 rule="para" parents="18823 7407"/>
    </justification>
  </clause>

  <clause id="18831">
    <literal><![CDATA[
      K(x,K(y,z) * (u * (w / y))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,u * (w / T(y,z))) = v5
    ]]></literal>
    <justification jstring="[para(18823(a,2),16436(a,1))].">
      <j1 rule="para" parents="18823 16436"/>
    </justification>
  </clause>

  <clause id="18832">
    <literal><![CDATA[
      K(x,y * (T(z,x) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z * u)) = w
    ]]></literal>
    <justification jstring="[para(4273(a,1),18830(a,1,2,2))].">
      <j1 rule="para" parents="4273 18830"/>
    </justification>
  </clause>

  <clause id="18835">
    <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(18832,a,18425,a)].">
      <j1 rule="hyper" parents="18832 18425"/>
    </justification>
  </clause>

  <clause id="18836">
    <literal><![CDATA[
      K(x,y * (z / (u / (u / w)))) = K(x,y * (z / T(w,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,16697,a,b,18825,a)].">
      <j1 rule="hyper" parents="63 16697 18825"/>
    </justification>
  </clause>

  <clause id="18837">
    <literal><![CDATA[
      K(x,y * (z / T(T(u,w),w))) = K(x,y * (z / u))
    ]]></literal>
    <justification jstring="[hyper(16759,a,18826,a)].">
      <j1 rule="hyper" parents="16759 18826"/>
    </justification>
  </clause>

  <clause id="18838">
    <literal><![CDATA[
      K(x,y * (z / T(u,u \ w))) = K(x,y * (z / (w / (w / u))))
    ]]></literal>
    <justification jstring="[para(3701(a,1),18837(a,1,2,2,2,1))].">
      <j1 rule="para" parents="3701 18837"/>
    </justification>
  </clause>

  <clause id="18839">
    <literal><![CDATA[
      K(x,y * (z * (u * (w / u)))) = K(x,y * (z * T(w,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,16698,a(flip),b,18827,a)].">
      <j1 rule="hyper" parents="63 16698 18827"/>
    </justification>
  </clause>

  <clause id="18840">
    <literal><![CDATA[
      K(x,y * (z * (K(u,z) * w))) = K(x,y * (z * (w * K(z,u))))
    ]]></literal>
    <justification jstring="[para(4712(a,1),18824(a,1,2,2))].">
      <j1 rule="para" parents="4712 18824"/>
    </justification>
  </clause>

  <clause id="18841">
    <literal><![CDATA[
      K(x,y * (z / T(u,u \ w))) = K(x,y * (z / T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(333,a,18836,a(flip),b,18838,a),flip(a)].">
      <j1 rule="hyper" parents="333 18836 18838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18842">
    <literal><![CDATA[
      K(x,y * (z / ((u \ w) \ w))) = K(x,y * (z / T(u,w)))
    ]]></literal>
    <justification jstring="[para(112(a,1),18841(a,1,2,2,2))].">
      <j1 rule="para" parents="112 18841"/>
    </justification>
  </clause>

  <clause id="18843">
    <literal><![CDATA[
      K(x,y * (z * (K(u,z) * w))) = K(x,y * (T(z,u) * w))
    ]]></literal>
    <justification jstring="[hyper(333,a,16361,a(flip),b,18840,a),flip(a)].">
      <j1 rule="hyper" parents="333 16361 18840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18844">
    <literal><![CDATA[
      T(x,y * (z * (K(u,z) * w))) = T(x,y * (T(z,u) * w))
    ]]></literal>
    <justification jstring="[hyper(124,a,18843,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 18843 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18845">
    <literal><![CDATA[
      K(x,y * (((z * u) / z) * w)) = K(x,y * (T(u,z) * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,9910,a,b,18843,a)].">
      <j1 rule="hyper" parents="63 9910 18843"/>
    </justification>
  </clause>

  <clause id="18846">
    <literal><![CDATA[
      K(x,y * (T(z \ u,z) * w)) = K(x,y * ((u / z) * w))
    ]]></literal>
    <justification jstring="[para(4624(a,1),18843(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4624 18843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18847">
    <literal><![CDATA[
      T(x,y * (T(z \ u,z) * w)) = T(x,y * ((u / z) * w))
    ]]></literal>
    <justification jstring="[para(4624(a,1),18844(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4624 18844"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18849">
    <literal><![CDATA[
      K(x,y * (T(z / u,u) * (w \ 1))) = K(x,y * ((z / u) * (w \ K(u,z))))
    ]]></literal>
    <justification jstring="[hyper(63,a,17028,a(flip),b,18845,a),flip(a)].">
      <j1 rule="hyper" parents="63 17028 18845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18850">
    <literal><![CDATA[
      K(x,y * (T(T(z,u),u) * w)) = K(x,y * (z * w))
    ]]></literal>
    <justification jstring="[para(239(a,1),18845(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="239 18845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18851">
    <literal><![CDATA[
      K(x,y * (z * (T(T(z,u),u) \ w))) = K(x,y * w)
    ]]></literal>
    <justification jstring="[para(10(a,1),18850(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 18850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18852">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (K(z,u) * w))) = K(x,y * w)
    ]]></literal>
    <justification jstring="[para(5205(a,2),18851(a,1,2,2))].">
      <j1 rule="para" parents="5205 18851"/>
    </justification>
  </clause>

  <clause id="18853">
    <literal><![CDATA[
      K(x,y * (z \ T(u,w \ v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z \ T(u,w * v5))) = v6
    ]]></literal>
    <justification jstring="[para(18076(a,1),18829(a,1))].">
      <j1 rule="para" parents="18076 18829"/>
    </justification>
  </clause>

  <clause id="18854">
    <literal><![CDATA[
      K(x,y * (T(z,T(u,w)) / T(u,w))) = K(x,y * ((w / (w / u)) \ z))
    ]]></literal>
    <justification jstring="[hyper(18831,a,18075,a)].">
      <j1 rule="hyper" parents="18831 18075"/>
    </justification>
  </clause>

  <clause id="18856">
    <literal><![CDATA[
      K(x,y * ((z / (z / u)) \ w)) = K(x,y * (T(u,z) \ w))
    ]]></literal>
    <justification jstring="[hyper(12755,a,18854,a),flip(a)].">
      <j1 rule="hyper" parents="12755 18854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18857">
    <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(15033,a,18856,a),flip(a)].">
      <j1 rule="hyper" parents="15033 18856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18858">
    <literal><![CDATA[
      K(x,(y * (z * K(u,w))) * v5) = K(x,K(w,u) * ((y * z) * v5))
    ]]></literal>
    <justification jstring="[hyper(17965,a,18835,a),flip(a)].">
      <j1 rule="hyper" parents="17965 18835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18859">
    <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(18835(a,1),17965(a,1))].">
      <j1 rule="para" parents="18835 17965"/>
    </justification>
  </clause>

  <clause id="18860">
    <literal><![CDATA[
      K(x,K(y,z) * ((u * T(w,u)) * v5)) = K(x,((K(z,y) * w) * u) * v5)
    ]]></literal>
    <justification jstring="[hyper(18169,a,18858,a),flip(a)].">
      <j1 rule="hyper" parents="18169 18858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18862">
    <literal><![CDATA[
      K(x,((K(y,z) * u) * w) * v5) = K(x,K(z,y) * ((u * w) * v5))
    ]]></literal>
    <justification jstring="[para(111(a,1),18860(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="111 18860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18863">
    <literal><![CDATA[
      K(x,((y / K(z,u)) * w) * v5) = K(x,K(z,u) * ((y * w) * v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,16459,a,b,18862,a)].">
      <j1 rule="hyper" parents="63 16459 18862"/>
    </justification>
  </clause>

  <clause id="18864">
    <literal><![CDATA[
      K(x,((y * K(z,u)) * w) * v5) = K(x,K(u,z) * ((y * w) * v5))
    ]]></literal>
    <justification jstring="[para(5994(a,1),18863(a,1,2,1,1))].">
      <j1 rule="para" parents="5994 18863"/>
    </justification>
  </clause>

  <clause id="18865">
    <literal><![CDATA[
      K(x,y * ((z / u) * (w \ K(u,z)))) = K(x,y * ((u \ z) * (w \ 1)))
    ]]></literal>
    <justification jstring="[para(113(a,1),18849(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="113 18849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18866">
    <literal><![CDATA[
      K(x,((y / (y / z)) \ u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(T(z,y) \ u) * w) = v5
    ]]></literal>
    <justification jstring="[para(18857(a,1),12284(a,1))].">
      <j1 rule="para" parents="18857 12284"/>
    </justification>
  </clause>

  <clause id="18867">
    <literal><![CDATA[
      K(x,(T(y,y \ z) \ u) * w) = K(x,(T(y,z) \ u) * w)
    ]]></literal>
    <justification jstring="[hyper(18866,a,18135,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="18866 18135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18868">
    <literal><![CDATA[
      K(x,(((y \ z) \ z) \ u) * w) = K(x,(T(y,z) \ u) * w)
    ]]></literal>
    <justification jstring="[para(112(a,1),18867(a,1,2,1,1))].">
      <j1 rule="para" parents="112 18867"/>
    </justification>
  </clause>

  <clause id="18869">
    <literal><![CDATA[
      K(x,y * (z * K((u \ w) \ v5,u \ w))) = K(x,(y * z) * K(w \ u,v5))
    ]]></literal>
    <justification jstring="[hyper(14374,a,18018,a),flip(a)].">
      <j1 rule="hyper" parents="14374 18018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18870">
    <literal><![CDATA[
      K(x,y * (z * K((u \ w) \ y,u \ w))) = K(x,T(y,w \ u) * z)
    ]]></literal>
    <justification jstring="[hyper(333,a,15662,a(flip),b,18869,a),flip(a)].">
      <j1 rule="hyper" parents="333 15662 18869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18871">
    <literal><![CDATA[
      K(x,y * (z * K(u * (w \ y),u \ w))) = K(x,T(y,w \ u) * z)
    ]]></literal>
    <justification jstring="[para(13667(a,1),18870(a,1,2,2,2))].">
      <j1 rule="para" parents="13667 18870"/>
    </justification>
  </clause>

  <clause id="18872">
    <literal><![CDATA[
      K(x,y * (z * K(u * (w \ y),w * u))) = K(x,T(y,w \ u) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,18410,a(flip),b,18871,a)].">
      <j1 rule="hyper" parents="63 18410 18871"/>
    </justification>
  </clause>

  <clause id="18873">
    <literal><![CDATA[
      K(x,T(y,z \ u) * w) = K(x,T(y,u * z) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,18485,a(flip),b,18872,a),flip(a)].">
      <j1 rule="hyper" parents="63 18485 18872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18874">
    <literal><![CDATA[
      K(x,T(y,z / u) * w) = K(x,T(y,z * u) * w)
    ]]></literal>
    <justification jstring="[hyper(16435,a,18873,a)].">
      <j1 rule="hyper" parents="16435 18873"/>
    </justification>
  </clause>

  <clause id="18875">
    <literal><![CDATA[
      K(x * (T(y,z) \ (y * u)),w) = K(w,K(y,z) \ (u * x)) \ K(u,K(w,x))
    ]]></literal>
    <justification jstring="[para(16638(a,1),18101(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16638 18101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18876">
    <literal><![CDATA[
      K(x * (T(y,z) \ (y * u)),w) = K(w,K(y,z) \ (u * x)) \ K(w,K(u,x))
    ]]></literal>
    <justification jstring="[para(6785(a,1),18875(a,2,2))].">
      <j1 rule="para" parents="6785 18875"/>
    </justification>
  </clause>

  <clause id="18878">
    <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(5941(a,1),18108(a,1,2,2,2))].">
      <j1 rule="para" parents="5941 18108"/>
    </justification>
  </clause>

  <clause id="18879">
    <literal><![CDATA[
      K(x,y / ((z \ K(z \ u,u)) * u)) = K(x,y * (((z \ 1) * u) \ K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,18782,a(flip),b,18878,a),flip(a)].">
      <j1 rule="hyper" parents="63 18782 18878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18880">
    <literal><![CDATA[
      K(x,y * (((z \ 1) * u) \ K(u,z))) = K(x,y / T((z \ 1) * u,u))
    ]]></literal>
    <justification jstring="[para(13639(a,1),18879(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13639 18879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18881">
    <literal><![CDATA[
      (x \ T(K(y,z),u)) \ K(y,T(z,w)) = (x \ K(y,z)) \ K(y,T(T(z,u),w))
    ]]></literal>
    <justification jstring="[hyper(63,a,15574,a(flip),b,18122,a),flip(a)].">
      <j1 rule="hyper" parents="63 15574 18122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18882">
    <literal><![CDATA[
      (x \ K(y,T(z,u))) \ K(y,T(z,w)) = (x \ K(y,z)) \ K(y,T(T(z,u),w))
    ]]></literal>
    <justification jstring="[para(6365(a,2),18881(a,1,1,2))].">
      <j1 rule="para" parents="6365 18881"/>
    </justification>
  </clause>

  <clause id="18883">
    <literal><![CDATA[
      (x / T((y / (z * y)) * z,u)) \ (x * 1) = (y / (z * y)) * z
    ]]></literal>
    <justification jstring="[para(8396(a,1),18206(a,1,2,2))].">
      <j1 rule="para" parents="8396 18206"/>
    </justification>
  </clause>

  <clause id="18884">
    <literal><![CDATA[
      (x / T((y / (z * y)) * z,u)) \ x = (y / (z * y)) * z
    ]]></literal>
    <justification jstring="[hyper(348,a,18883,a)].">
      <j1 rule="hyper" parents="348 18883"/>
    </justification>
  </clause>

  <clause id="18885">
    <literal><![CDATA[
      T(x,(y / (z * y)) * z) = x
    ]]></literal>
    <justification jstring="[hyper(3660,a,18884,a)].">
      <j1 rule="hyper" parents="3660 18884"/>
    </justification>
  </clause>

  <clause id="18887">
    <literal><![CDATA[
      T(x,y * R(y \ 1,y,z)) = x
    ]]></literal>
    <justification jstring="[para(692(a,1),18885(a,1,2))].">
      <j1 rule="para" parents="692 18885"/>
    </justification>
  </clause>

  <clause id="18888">
    <literal><![CDATA[
      T(x * R(x \ 1,x,y),z) = x * R(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(54,a,18887,a)].">
      <j1 rule="hyper" parents="54 18887"/>
    </justification>
  </clause>

  <clause id="18889">
    <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(333,a,14709,a(flip),b,18250,a),flip(a)].">
      <j1 rule="hyper" parents="333 14709 18250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18890">
    <literal><![CDATA[
      T(x,y * (z * ((((z \ 1) \ u) * (z \ 1)) * z))) = T(x,y * (T(z * u,z * 1) * z))
    ]]></literal>
    <justification jstring="[hyper(333,a,16938,a(flip),b,18268,a),flip(a)].">
      <j1 rule="hyper" parents="333 16938 18268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18891">
    <literal><![CDATA[
      K(x,(K(y,T(z,u)) * ((K(w,T(v5,v6)) \ v7) * K(z,T(y,u)))) \ v8) = K(x,v7 \ (K(v5,T(w,v6)) \ v8))
    ]]></literal>
    <justification jstring="[para(6424(a,1),18344(a,1,2,1,2))].">
      <j1 rule="para" parents="6424 18344"/>
    </justification>
  </clause>

  <clause id="18892">
    <literal><![CDATA[
      T(x,y * ((T(z,u) / R(u,u,u)) * w)) = T(x,y * ((((u \ 1) \ 1) \ z) * w))
    ]]></literal>
    <justification jstring="[para(6338(a,1),18392(a,1,2,2,1,1))].">
      <j1 rule="para" parents="6338 18392"/>
    </justification>
  </clause>

  <clause id="18894">
    <literal><![CDATA[
      T(x,y * ((((z \ 1) \ 1) \ u) * w)) = T(x,y * (((z \ (u / z)) * z) * w))
    ]]></literal>
    <justification jstring="[para(15978(a,1),18892(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="15978 18892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18895">
    <literal><![CDATA[
      T(x,y * (T(z / u,u) * w)) = T(x,y * ((((u \ 1) \ 1) \ z) * w))
    ]]></literal>
    <justification jstring="[hyper(333,a,18376,a(flip),b,18894,a)].">
      <j1 rule="hyper" parents="333 18376 18894"/>
    </justification>
  </clause>

  <clause id="18896">
    <literal><![CDATA[
      T(x,y * ((((z \ 1) \ 1) \ u) * w)) = T(x,y * ((z \ u) * w))
    ]]></literal>
    <justification jstring="[para(113(a,1),18895(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="113 18895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18897">
    <literal><![CDATA[
      K(x,y * (z * T(u / w,v5 \ v6))) = K(x,y * (z * T(u / w,v6 * v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,17214,a(flip),b,18490,a),flip(a)].">
      <j1 rule="hyper" parents="63 17214 18490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18898">
    <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(333,a,12823,a(flip),b,18612,a),flip(a)].">
      <j1 rule="hyper" parents="333 12823 18612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18899">
    <literal><![CDATA[
      T(x,(((y \ z) \ z) / u) \ w) = T(x,K(z,y) * ((y / u) \ w))
    ]]></literal>
    <justification jstring="[hyper(16383,a,18898,a)].">
      <j1 rule="hyper" parents="16383 18898"/>
    </justification>
  </clause>

  <clause id="18900">
    <literal><![CDATA[
      T(x,(((y \ z) \ z) / u) \ w) = T(x,(T(y,z) / u) \ w)
    ]]></literal>
    <justification jstring="[hyper(333,a,18620,a(flip),b,18899,a),flip(a)].">
      <j1 rule="hyper" parents="333 18620 18899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18902">
    <literal><![CDATA[
      T(x,(T(y \ z,z) / u) \ w) = T(x,((z / y) / u) \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,18735,a(flip),b,18900,a),flip(a)].">
      <j1 rule="hyper" parents="63 18735 18900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18903">
    <literal><![CDATA[
      T(x,((y / z) / y) \ u) = T(x,(y \ (z \ y)) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,18668,a(flip),b,18902,a),flip(a)].">
      <j1 rule="hyper" parents="63 18668 18902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18904">
    <literal><![CDATA[
      T(x,(y \ ((z \ K(z,y)) \ y)) \ u) = T(x,(y \ (y / (z \ 1))) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,15248,a(flip),b,18903,a),flip(a)].">
      <j1 rule="hyper" parents="63 15248 18903"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18905">
    <literal><![CDATA[
      T(x,(((y \ 1) \ z) / z) \ u) = T(x,(z \ (z / (y \ 1))) \ u)
    ]]></literal>
    <justification jstring="[para(8521(a,1),18904(a,1,2,1))].">
      <j1 rule="para" parents="8521 18904"/>
    </justification>
  </clause>

  <clause id="18906">
    <literal><![CDATA[
      T(x,(y \ (y / ((z \ 1) \ 1))) \ u) = T(x,((z \ y) / y) \ u)
    ]]></literal>
    <justification jstring="[hyper(13613,a,18905,a),flip(a)].">
      <j1 rule="hyper" parents="13613 18905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18907">
    <literal><![CDATA[
      T(x,((y \ z) / z) \ u) = T(x,(z \ (z / y)) \ u)
    ]]></literal>
    <justification jstring="[hyper(13614,a,18906,a),flip(a)].">
      <j1 rule="hyper" parents="13614 18906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18908">
    <literal><![CDATA[
      T(x,((y \ z) / z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(z \ (z / y)) \ u) = w
    ]]></literal>
    <justification jstring="[para(18906(a,1),13614(a,1))].">
      <j1 rule="para" parents="18906 13614"/>
    </justification>
  </clause>

  <clause id="18909">
    <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(4567(a,1),18683(a,2,2,1,1,1,2))].">
      <j1 rule="para" parents="4567 18683"/>
    </justification>
  </clause>

  <clause id="18910">
    <literal><![CDATA[
      K(K(x,y) * L(y,z,u),w / ((v5 * x) \ v5)) = K(y,L((v5 / (x * v5)) \ w,z,u))
    ]]></literal>
    <justification jstring="[hyper(15773,a,18817,a)].">
      <j1 rule="hyper" parents="15773 18817"/>
    </justification>
  </clause>

  <clause id="18911">
    <literal><![CDATA[
      K(x,L(T(y / ((z * u) \ z),u),w,v5)) = K(x,L((z / (u * z)) \ y,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,17822,a(flip),b,18910,a)].">
      <j1 rule="hyper" parents="63 17822 18910"/>
    </justification>
  </clause>

  <clause id="18912">
    <literal><![CDATA[
      K(x,L((y / (z * y)) \ u,w,v5)) = K(x,L(((y * z) \ y) \ u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,15984,a(flip),b,18911,a),flip(a)].">
      <j1 rule="hyper" parents="63 15984 18911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18913">
    <literal><![CDATA[
      K(x,L(((y * z) \ y) \ T(u,z),w,v5)) = K(x,L(u / (y / (z * y)),w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,17080,a(flip),b,18912,a),flip(a)].">
      <j1 rule="hyper" parents="63 17080 18912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18914">
    <literal><![CDATA[
      K(x,L(y / (z / (u * z)),w,v5)) = K(x,L(y / ((z * u) \ z),w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,17079,a(flip),b,18913,a),flip(a)].">
      <j1 rule="hyper" parents="63 17079 18913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18915">
    <literal><![CDATA[
      L(x,(y * z) / y,(y \ z) \ 1) = L(x,y * (z / y),(z / y) \ 1)
    ]]></literal>
    <justification jstring="[para(3384(a,1),18889(a,1,3,1))].">
      <j1 rule="para" parents="3384 18889"/>
    </justification>
  </clause>

  <clause id="18916">
    <literal><![CDATA[
      L(x,y * (z / y),(z / y) \ 1) = L(x,y * (z / y),(y \ z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,14709,a(flip),b,18915,a),flip(a)].">
      <j1 rule="hyper" parents="63 14709 18915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18917">
    <literal><![CDATA[
      L(x,y * (z / y),(z / y) \ 1) = L(x,z,(y \ z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(333,a,14724,a(flip),b,18916,a),flip(a)].">
      <j1 rule="hyper" parents="333 14724 18916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18918">
    <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(18917(a,1),9562(a,1,2))].">
      <j1 rule="para" parents="18917 9562"/>
    </justification>
  </clause>

  <clause id="18919">
    <literal><![CDATA[
      T(x,y * (z * ((((z \ 1) \ u) * (z \ 1)) * z))) = T(x,y * (T(z * u,z) * z))
    ]]></literal>
    <justification jstring="[para(8(a,1),18890(a,2,2,2,1,2))].">
      <j1 rule="para" parents="8 18890"/>
    </justification>
  </clause>

  <clause id="18920">
    <literal><![CDATA[
      T(x,y * (z * ((((z \ 1) \ u) * (z \ 1)) * z))) = T(x,y * (z * (z * u)))
    ]]></literal>
    <justification jstring="[hyper(333,a,16036,a(flip),b,18919,a),flip(a)].">
      <j1 rule="hyper" parents="333 16036 18919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18921">
    <literal><![CDATA[
      T(x,y * (z * T(u * z,z \ 1))) = T(x,y * (z * (z * u)))
    ]]></literal>
    <justification jstring="[para(4109(a,1),18920(a,1,2,2,2))].">
      <j1 rule="para" parents="4109 18920"/>
    </justification>
  </clause>

  <clause id="18922">
    <literal><![CDATA[
      T(x,y * (z * T(u * z,z * 1))) = T(x,y * (z * (z * u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,16853,a(flip),b,18921,a)].">
      <j1 rule="hyper" parents="63 16853 18921"/>
    </justification>
  </clause>

  <clause id="18923">
    <literal><![CDATA[
      T(x,y * (z * T(u * z,z))) = T(x,y * (z * (z * u)))
    ]]></literal>
    <justification jstring="[para(8(a,1),18922(a,1,2,2,2,2))].">
      <j1 rule="para" parents="8 18922"/>
    </justification>
  </clause>

  <clause id="18924">
    <literal><![CDATA[
      T(x,y * ((z * u) * u)) = T(x,y * (u * (u * z)))
    ]]></literal>
    <justification jstring="[para(111(a,1),18923(a,1,2,2))].">
      <j1 rule="para" parents="111 18923"/>
    </justification>
  </clause>

  <clause id="18925">
    <literal><![CDATA[
      T(x,y * L(z * (u * u),u,u)) = T(x,y * (u * (u * z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,16981,a,b,18924,a)].">
      <j1 rule="hyper" parents="63 16981 18924"/>
    </justification>
  </clause>

  <clause id="18926">
    <literal><![CDATA[
      T(x,y * ((((z \ u) * z) * (z \ 1)) * (z \ 1))) = T(x,y * ((z \ 1) * T((z \ 1) * u,z)))
    ]]></literal>
    <justification jstring="[para(1714(a,1),18924(a,2,2,2,2))].">
      <j1 rule="para" parents="1714 18924"/>
    </justification>
  </clause>

  <clause id="18927">
    <literal><![CDATA[
      T(x,y * (K(z,u) * (K(z,u) * w))) = T(x,y * (w * (K(z,u) * K(z,u))))
    ]]></literal>
    <justification jstring="[para(8165(a,1),18924(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8165 18924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18928">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * (u * (u * z))) = T(x,(u * (u * T(z,u * u))) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,17105,a(flip),b,18925,a),flip(a)].">
      <j1 rule="hyper" parents="63 17105 18925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18929">
    <literal><![CDATA[
      T(x,y * (K(z,u) * (K(z,u) * (w * v5)))) = T(x,y * (w * (v5 * (K(z,u) * K(z,u)))))
    ]]></literal>
    <justification jstring="[para(33(a,1),18927(a,2,2,2))].">
      <j1 rule="para" parents="33 18927"/>
    </justification>
  </clause>

  <clause id="18930">
    <literal><![CDATA[
      T(x,y * (z * (T(T(z,u),u) \ w))) = T(x,y * (w * (K(u,z) * K(u,z))))
    ]]></literal>
    <justification jstring="[para(5205(a,1),18927(a,1,2,2))].">
      <j1 rule="para" parents="5205 18927"/>
    </justification>
  </clause>

  <clause id="18931">
    <literal><![CDATA[
      T(x,(y * (y * T(z,y * y))) * u) = T(x,(y * (y * z)) * u)
    ]]></literal>
    <justification jstring="[hyper(15822,a,18928,a),flip(a)].">
      <j1 rule="hyper" parents="15822 18928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18932">
    <literal><![CDATA[
      T(x,(L(y,z,z) * (z * z)) * u) = T(x,(z * (z * y)) * u)
    ]]></literal>
    <justification jstring="[para(664(a,1),18931(a,1,2,1))].">
      <j1 rule="para" parents="664 18931"/>
    </justification>
  </clause>

  <clause id="18933">
    <literal><![CDATA[
      T(x,L(y,z,z) * ((z * z) * u)) = T(x,(z * (z * y)) * u)
    ]]></literal>
    <justification jstring="[para(32(a,1),18932(a,1,2))].">
      <j1 rule="para" parents="32 18932"/>
    </justification>
  </clause>

  <clause id="18934">
    <literal><![CDATA[
      T(x,y * (z * (T(T(z,u),u) \ w))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y * w) = v5
    ]]></literal>
    <justification jstring="[para(18930(a,2),15788(a,1))].">
      <j1 rule="para" parents="18930 15788"/>
    </justification>
  </clause>

  <clause id="18935">
    <literal><![CDATA[
      T(x,y * ((z / u) * (w * (K(z,u) * K(z,u))))) = T(x,y * (K(z,u) * ((z / T(u,z)) * w)))
    ]]></literal>
    <justification jstring="[para(11847(a,1),18929(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="11847 18929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18936">
    <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(13669(a,1),17717(a,1,1))].">
      <j1 rule="para" parents="13669 17717"/>
    </justification>
  </clause>

  <clause id="18937">
    <literal><![CDATA[
      L(K(x,K(y,z)) * ((u * w) \ v5),K(x,K(y,z)),u * w) = (u * (w * K(x,K(y,z)))) \ v5
    ]]></literal>
    <justification jstring="[para(6799(a,1),17752(a,1,1,1))].">
      <j1 rule="para" parents="6799 17752"/>
    </justification>
  </clause>

  <clause id="18939">
    <literal><![CDATA[
      K(x,((y * z) / z) / (u * (y / (z * y)))) = K(x,L((y * z) / u,y,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,16770,a(flip),b,17877,a)].">
      <j1 rule="hyper" parents="63 16770 17877"/>
    </justification>
  </clause>

  <clause id="18940">
    <literal><![CDATA[
      K(x,L((y * z) / u,y,z \ 1)) = K(x,y / (u * (y / (z * y))))
    ]]></literal>
    <justification jstring="[para(11(a,1),18939(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11 18939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18941">
    <literal><![CDATA[
      K(x,y / (z * (y / (u * y)))) = K(x,y / (z / u))
    ]]></literal>
    <justification jstring="[hyper(63,a,18486,a(flip),b,18940,a),flip(a)].">
      <j1 rule="hyper" parents="63 18486 18940"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18942">
    <literal><![CDATA[
      K(x,(y \ z) / (u * ((y \ z) / z))) = K(x,(y \ z) / (u / y))
    ]]></literal>
    <justification jstring="[para(10(a,1),18941(a,1,2,2,2,2))].">
      <j1 rule="para" parents="10 18941"/>
    </justification>
  </clause>

  <clause id="18944">
    <literal><![CDATA[
      K(x,T((y * K(z,T(u,w))) / v5,y \ v5)) = K(x,(y * (v5 / y)) \ (K(z,u) * y))
    ]]></literal>
    <justification jstring="[para(6400(a,1),18328(a,2,2))].">
      <j1 rule="para" parents="6400 18328"/>
    </justification>
  </clause>

  <clause id="18945">
    <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(18371,a,18487,a)].">
      <j1 rule="hyper" parents="18371 18487"/>
    </justification>
  </clause>

  <clause id="18946">
    <literal><![CDATA[
      K(x,y / (T((z \ u) \ 1,u) / w)) = K(x,y / (((u / z) \ 1) / w))
    ]]></literal>
    <justification jstring="[hyper(63,a,18488,a(flip),b,18945,a),flip(a)].">
      <j1 rule="hyper" parents="63 18488 18945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18947">
    <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(451,a,18219,a,b,18946,a)].">
      <j1 rule="hyper" parents="451 18219 18946"/>
    </justification>
  </clause>

  <clause id="18948">
    <literal><![CDATA[
      K(x,(y / (z / u)) / T(w,(z / u) \ y)) = K(x,w \ (y / (T(u,z) \ z)))
    ]]></literal>
    <justification jstring="[hyper(18646,a,18807,a),flip(a)].">
      <j1 rule="hyper" parents="18646 18807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18949">
    <literal><![CDATA[
      K(x,y \ (z / (T(u,w) \ w))) = K(x,y \ (z / (w / u)))
    ]]></literal>
    <justification jstring="[hyper(16467,a,18948,a),flip(a)].">
      <j1 rule="hyper" parents="16467 18948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18950">
    <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(18948(a,1),16467(a,1))].">
      <j1 rule="para" parents="18948 16467"/>
    </justification>
  </clause>

  <clause id="18951">
    <literal><![CDATA[
      K(x,y \ (z / (z / u))) = K(x,y \ T(u,z))
    ]]></literal>
    <justification jstring="[para(76(a,1),18949(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="76 18949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18952">
    <literal><![CDATA[
      K(x,y \ T(z \ u,u)) = K(x,y \ (u / z))
    ]]></literal>
    <justification jstring="[para(76(a,1),18951(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="76 18951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18953">
    <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(7540(a,1),18951(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="7540 18951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18954">
    <literal><![CDATA[
      K(x,y \ (z \ T(u,z \ 1))) = K(x,y \ (u / z))
    ]]></literal>
    <justification jstring="[hyper(63,a,15181,a(flip),b,18952,a)].">
      <j1 rule="hyper" parents="63 15181 18952"/>
    </justification>
  </clause>

  <clause id="18955">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ (u / (y / z))) = K(x,z \ ((z \ y) \ T(u,(y / z) \ 1)))
    ]]></literal>
    <justification jstring="[para(5074(a,1),18954(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5074 18954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18956">
    <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(333,a,16872,a(flip),b,18953,a),flip(a)].">
      <j1 rule="hyper" parents="333 16872 18953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18957">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ (u / (y / z))) = K(x,z \ ((z \ y) \ T(u,z / y)))
    ]]></literal>
    <justification jstring="[para(3760(a,1),18955(a,2,2,2,2))].">
      <j1 rule="para" parents="3760 18955"/>
    </justification>
  </clause>

  <clause id="18958">
    <literal><![CDATA[
      K(x,y \ (T((z * u) \ z,w) \ z)) = K(x,y \ ((u * K(w,u \ 1)) * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,12682,a(flip),b,18956,a),flip(a)].">
      <j1 rule="hyper" parents="63 12682 18956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18959">
    <literal><![CDATA[
      K(x,y \ (T((z * u) \ z,w) \ z)) = K(x,y \ (u * (K(w,u \ 1) * z)))
    ]]></literal>
    <justification jstring="[para(5229(a,1),18958(a,2,2,2))].">
      <j1 rule="para" parents="5229 18958"/>
    </justification>
  </clause>

  <clause id="18960">
    <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(18760,a,15254,a),flip(a)].">
      <j1 rule="hyper" parents="18760 15254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18961">
    <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(18010,a,18960,a)].">
      <j1 rule="hyper" parents="18010 18960"/>
    </justification>
  </clause>

  <clause id="18962">
    <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(63,a,18674,a(flip),b,18961,a)].">
      <j1 rule="hyper" parents="63 18674 18961"/>
    </justification>
  </clause>

  <clause id="18963">
    <literal><![CDATA[
      K(x,y * ((y \ T(z * y,u)) * u)) = K(x,T(y * (T(z,y) * u),u))
    ]]></literal>
    <justification jstring="[para(13557(a,1),18962(a,1,2,2))].">
      <j1 rule="para" parents="13557 18962"/>
    </justification>
  </clause>

  <clause id="18964">
    <literal><![CDATA[
      K(x,T(y * (T(z,y) * u),u)) = K(x,(u * ((z * y) / y)) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,17091,a(flip),b,18963,a),flip(a)].">
      <j1 rule="hyper" parents="63 17091 18963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18965">
    <literal><![CDATA[
      K(x,T(y * (T(z,y) * u),u)) = K(x,(u * z) * y)
    ]]></literal>
    <justification jstring="[para(11(a,1),18964(a,2,2,1,2))].">
      <j1 rule="para" parents="11 18964"/>
    </justification>
  </clause>

  <clause id="18966">
    <literal><![CDATA[
      K(x,L(y,z,u) * (z * u)) = K(x,(y * z) * u)
    ]]></literal>
    <justification jstring="[hyper(17631,a,18965,a)].">
      <j1 rule="hyper" parents="17631 18965"/>
    </justification>
  </clause>

  <clause id="18967">
    <literal><![CDATA[
      T(x,L(y,z,u) * (z * u)) = T(x,(y * z) * u)
    ]]></literal>
    <justification jstring="[hyper(124,a,18966,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 18966 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18968">
    <literal><![CDATA[
      K(x,((y * z) \ (z * u)) * (y * z)) = K(x,((T(y,z) \ u) * y) * z)
    ]]></literal>
    <justification jstring="[para(10084(a,1),18966(a,1,2,1))].">
      <j1 rule="para" parents="10084 18966"/>
    </justification>
  </clause>

  <clause id="18970">
    <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(4774(a,1),18967(a,1,2,2))].">
      <j1 rule="para" parents="4774 18967"/>
    </justification>
  </clause>

  <clause id="18971">
    <literal><![CDATA[
      K(x,((T(y,z) \ u) * y) * z) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z * u,y * z)) = w
    ]]></literal>
    <justification jstring="[para(18968(a,1),12272(a,1))].">
      <j1 rule="para" parents="18968 12272"/>
    </justification>
  </clause>

  <clause id="18972">
    <literal><![CDATA[
      K(x,K(y,z) * (T(u,z) * y)) = K(x,T(y * u,z * y))
    ]]></literal>
    <justification jstring="[hyper(18971,a,18370,a),flip(a)].">
      <j1 rule="hyper" parents="18971 18370"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18973">
    <literal><![CDATA[
      K(x,T(y * z,u * y)) = K(x,T(z,u) * T(y,u))
    ]]></literal>
    <justification jstring="[hyper(15605,a,18972,a),flip(a)].">
      <j1 rule="hyper" parents="15605 18972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18974">
    <literal><![CDATA[
      K(x,T(y * (z \ u),z * y)) = K(x,(u / z) * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(333,a,14976,a(flip),b,18973,a),flip(a)].">
      <j1 rule="hyper" parents="333 14976 18973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18975">
    <literal><![CDATA[
      (K(x,y) * z) * (K(y,x) * L(K(x,y),u,w)) = z * ((z * L(K(x,y),u,w)) / z)
    ]]></literal>
    <justification jstring="[para(6858(a,1),17633(a,1,1))].">
      <j1 rule="para" parents="6858 17633"/>
    </justification>
  </clause>

  <clause id="18977">
    <literal><![CDATA[
      (K(x,y) * z) * (K(y,x) * L(K(x,y),u,w)) = z * L(K(x,T(y,z)),u,w)
    ]]></literal>
    <justification jstring="[para(6963(a,1),18975(a,2,2))].">
      <j1 rule="para" parents="6963 18975"/>
    </justification>
  </clause>

  <clause id="18978">
    <literal><![CDATA[
      (K(x,y) * z) * (K(y,x) * L(K(x,y),u,w)) = L(K(x,y),u,w) * z
    ]]></literal>
    <justification jstring="[hyper(333,a,6399,a(flip),b,18977,a),flip(a)].">
      <j1 rule="hyper" parents="333 6399 18977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18979">
    <literal><![CDATA[
      (K(x,y) * (z * (K(y,x) * L(K(x,y),u,w)))) * a(x,z,K(K(y,x) * L(K(x,y),u,w),y)) = L(K(x,y),u,w) * z
    ]]></literal>
    <justification jstring="[hyper(63,a,13733,a,b,18978,a)].">
      <j1 rule="hyper" parents="63 13733 18978"/>
    </justification>
  </clause>

  <clause id="18980">
    <literal><![CDATA[
      (K(x,y) * z) * a(x,u,K(w,y)) = L(K(x,y),u,w) * z
    ]]></literal>
    <justification jstring="[para(13752(a,1),18978(a,1,2))].">
      <j1 rule="para" parents="13752 18978"/>
    </justification>
  </clause>

  <clause id="18981">
    <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(12863(a,1),17846(a,1,2))].">
      <j1 rule="para" parents="12863 17846"/>
    </justification>
  </clause>

  <clause id="18982">
    <literal><![CDATA[
      K(x,y / (T(z * u,z) \ w)) = K(x,y / ((u * z) \ w))
    ]]></literal>
    <justification jstring="[hyper(63,a,17845,a(flip),b,18981,a),flip(a)].">
      <j1 rule="hyper" parents="63 17845 18981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18983">
    <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(23(a,1),18057(a,1,2,1,2))].">
      <j1 rule="para" parents="23 18057"/>
    </justification>
  </clause>

  <clause id="18984">
    <literal><![CDATA[
      1 * K(x,(y * (z * u)) * K(w,u)) = K(x,y * (z * T(u,w)))
    ]]></literal>
    <justification jstring="[para(15466(a,1),18071(a,1,1))].">
      <j1 rule="para" parents="15466 18071"/>
    </justification>
  </clause>

  <clause id="18986">
    <literal><![CDATA[
      1 * K(x,y * ((z * u) * K(w,u))) = K(x,y * (z * T(u,w)))
    ]]></literal>
    <justification jstring="[para(18009(a,1),18984(a,1,2))].">
      <j1 rule="para" parents="18009 18984"/>
    </justification>
  </clause>

  <clause id="18987">
    <literal><![CDATA[
      1 * K(x,y * (z * (u * K(w,u)))) = K(x,y * (z * T(u,w)))
    ]]></literal>
    <justification jstring="[para(5750(a,1),18986(a,1,2,2,2))].">
      <j1 rule="para" parents="5750 18986"/>
    </justification>
  </clause>

  <clause id="18988">
    <literal><![CDATA[
      K(x,y * (z * (u * K(w,u)))) = K(x,y * (z * T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(127,a,18987,a)].">
      <j1 rule="hyper" parents="127 18987"/>
    </justification>
  </clause>

  <clause id="18989">
    <literal><![CDATA[
      K(x,y * (z * ((u * w) / u))) = K(x,y * (z * T(w,u)))
    ]]></literal>
    <justification jstring="[para(4238(a,2),18988(a,1,2,2,2))].">
      <j1 rule="para" parents="4238 18988"/>
    </justification>
  </clause>

  <clause id="18990">
    <literal><![CDATA[
      K(x,y * (z * T(T(u,w),w))) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(4271(a,1),18988(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4271 18988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18991">
    <literal><![CDATA[
      K(x,y * (z * T(u \ w,u))) = K(x,y * (z * (w / u)))
    ]]></literal>
    <justification jstring="[para(4292(a,1),18988(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4292 18988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18992">
    <literal><![CDATA[
      K(x,T(y,z * u) * (z * u)) = K(x,(z * T(T(u,w),w)) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,14994,a(flip),b,18990,a),flip(a)].">
      <j1 rule="hyper" parents="63 14994 18990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18993">
    <literal><![CDATA[
      K(x,y * (T(z,u \ w) * (w / u))) = K(x,y * (T(u \ w,u) * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,16760,a(flip),b,18991,a),flip(a)].">
      <j1 rule="hyper" parents="63 16760 18991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18994">
    <literal><![CDATA[
      K(x,(y * T(T(z,u),u)) * w) = K(x,(y * z) * w)
    ]]></literal>
    <justification jstring="[hyper(12284,a,18992,a),flip(a)].">
      <j1 rule="hyper" parents="12284 18992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18996">
    <literal><![CDATA[
      K(x,(y * (z * K(u,z))) * w) = K(x,(y * T(z,u)) * w)
    ]]></literal>
    <justification jstring="[para(4239(a,1),18994(a,1,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4239 18994"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18997">
    <literal><![CDATA[
      T(x,(y * (z * K(u,z))) * w) = T(x,(y * T(z,u)) * w)
    ]]></literal>
    <justification jstring="[hyper(124,a,18996,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 18996 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18998">
    <literal><![CDATA[
      K(x,((y \ z) * T(y,u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * (z / T(y,u))) * w) = v5
    ]]></literal>
    <justification jstring="[para(18996(a,1),15155(a,1))].">
      <j1 rule="para" parents="18996 15155"/>
    </justification>
  </clause>

  <clause id="18999">
    <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(63,a,16486,a(flip),b,18997,a),flip(a)].">
      <j1 rule="hyper" parents="63 16486 18997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19000">
    <literal><![CDATA[
      K(x,(y * (z / T(y,u))) * w) = K(x,K(u,y) * (T(z,y) * w))
    ]]></literal>
    <justification jstring="[hyper(18998,a,18368,a)].">
      <j1 rule="hyper" parents="18998 18368"/>
    </justification>
  </clause>

  <clause id="19001">
    <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(18185,a,19000,a),flip(a)].">
      <j1 rule="hyper" parents="18185 19000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19002">
    <literal><![CDATA[
      K(x,T(T(y,x) / (z \ 1),y) * u) = K(x,(T(y,z) / (z \ 1)) * u)
    ]]></literal>
    <justification jstring="[hyper(7407,a,19001,a)].">
      <j1 rule="hyper" parents="7407 19001"/>
    </justification>
  </clause>

  <clause id="19004">
    <literal><![CDATA[
      K(x,((y \ 1) \ T(z,x)) * u) = K(x,(T(z,y) / (y \ 1)) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,16407,a(flip),b,19002,a)].">
      <j1 rule="hyper" parents="63 16407 19002"/>
    </justification>
  </clause>

  <clause id="19005">
    <literal><![CDATA[
      K(x,(T(y,z) / (z \ 1)) * u) = K(x,((z \ 1) \ y) * u)
    ]]></literal>
    <justification jstring="[hyper(18066,a,19004,a),flip(a)].">
      <j1 rule="hyper" parents="18066 19004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19006">
    <literal><![CDATA[
      K(x,(y / (z \ K(y,z))) * u) = K(x,((z \ 1) \ y) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,18093,a(flip),b,19005,a)].">
      <j1 rule="hyper" parents="63 18093 19005"/>
    </justification>
  </clause>

  <clause id="19007">
    <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(63,a,16484,a(flip),b,18999,a),flip(a)].">
      <j1 rule="hyper" parents="63 16484 18999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19008">
    <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(63,a,18909,a(flip),b,18102,a)].">
      <j1 rule="hyper" parents="63 18909 18102"/>
    </justification>
  </clause>

  <clause id="19009">
    <literal><![CDATA[
      T(L(x * (K(y,x) * K(y,K(z,u))),w,v5),y * K(u,z)) = y \ T(y * L(x,w,v5),K(z,u))
    ]]></literal>
    <justification jstring="[para(3542(a,1),18325(a,1,1,1))].">
      <j1 rule="para" parents="3542 18325"/>
    </justification>
  </clause>

  <clause id="19010">
    <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(4370(a,1),18335(a,2,1,1))].">
      <j1 rule="para" parents="4370 18335"/>
    </justification>
  </clause>

  <clause id="19011">
    <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(4273(a,1),19010(a,1,2,1))].">
      <j1 rule="para" parents="4273 19010"/>
    </justification>
  </clause>

  <clause id="19012">
    <literal><![CDATA[
      (K(x,y) * (z * K(y,x))) * ((z * K(y,x)) \ u) = (K(x,y) * z) * (z \ u)
    ]]></literal>
    <justification jstring="[hyper(18334,a,19011,a)].">
      <j1 rule="hyper" parents="18334 19011"/>
    </justification>
  </clause>

  <clause id="19013">
    <literal><![CDATA[
      T(x,K(y,z)) * ((x * K(y,z)) \ u) = (K(z,y) * x) * (x \ u)
    ]]></literal>
    <justification jstring="[para(4565(a,1),19012(a,1,1))].">
      <j1 rule="para" parents="4565 19012"/>
    </justification>
  </clause>

  <clause id="19014">
    <literal><![CDATA[
      (K(x,y) * z) \ (z * ((K(y,x) * z) \ u)) = z \ u
    ]]></literal>
    <justification jstring="[hyper(10040,a,19013,a)].">
      <j1 rule="hyper" parents="10040 19013"/>
    </justification>
  </clause>

  <clause id="19015">
    <literal><![CDATA[
      (K(x,y) * z) * (z \ u) != w
    ]]></literal>
    <literal><![CDATA[
      z * ((K(y,x) * z) \ u) = w
    ]]></literal>
    <justification jstring="[para(19013(a,1),10032(a,1))].">
      <j1 rule="para" parents="19013 10032"/>
    </justification>
  </clause>

  <clause id="19016">
    <literal><![CDATA[
      (K(x,y) * z) \ (z * u) = z \ ((K(y,x) * z) * u)
    ]]></literal>
    <justification jstring="[para(9(a,1),19014(a,1,2,2))].">
      <j1 rule="para" parents="9 19014"/>
    </justification>
  </clause>

  <clause id="19017">
    <literal><![CDATA[
      x \ ((K(y,z) * x) * (K(z,T(y,x)) * u)) = L(u,K(z,y),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,10120,a(flip),b,19016,a),flip(a)].">
      <j1 rule="hyper" parents="63 10120 19016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19018">
    <literal><![CDATA[
      x \ ((x * K(y,z)) * (K(z,y) * u)) = L(u,K(z,y),x)
    ]]></literal>
    <justification jstring="[para(10018(a,1),19017(a,1,2))].">
      <j1 rule="para" parents="10018 19017"/>
    </justification>
  </clause>

  <clause id="19019">
    <literal><![CDATA[
      L(x,K(y,z),u * K(z,y)) = L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(6037,a,19018,a)].">
      <j1 rule="hyper" parents="6037 19018"/>
    </justification>
  </clause>

  <clause id="19020">
    <literal><![CDATA[
      (x * K(y,z)) * (K(z,y) * u) = x * L(u,K(z,y),x)
    ]]></literal>
    <justification jstring="[hyper(142,a,19018,a),flip(a)].">
      <j1 rule="hyper" parents="142 19018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19021">
    <literal><![CDATA[
      L(x,K(y,z),K(z,y) * u) = L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(17667,a,19019,a)].">
      <j1 rule="hyper" parents="17667 19019"/>
    </justification>
  </clause>

  <clause id="19022">
    <literal><![CDATA[
      L(x,K(y,z),u \ T(z,y)) = L(x,K(y,z),u \ z)
    ]]></literal>
    <justification jstring="[para(13255(a,1),19019(a,1,3))].">
      <j1 rule="para" parents="13255 19019"/>
    </justification>
  </clause>

  <clause id="19023">
    <literal><![CDATA[
      x * L(K(y,z) * u,K(z,y),x) = (x * K(y,z)) * u
    ]]></literal>
    <justification jstring="[para(4558(a,1),19020(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4558 19020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19024">
    <literal><![CDATA[
      (x * K(y,z)) * (x \ u) = x * ((x * K(z,y)) \ u)
    ]]></literal>
    <justification jstring="[para(4591(a,1),19023(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4591 19023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19025">
    <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(19023(a,1),18211(a,1,2,2,2,1))].">
      <j1 rule="para" parents="19023 18211"/>
    </justification>
  </clause>

  <clause id="19026">
    <literal><![CDATA[
      (x * K(y,z)) \ (x * L(u \ 1,u,u \ (x * K(z,y)))) = x \ ((x * K(z,y)) / u)
    ]]></literal>
    <justification jstring="[hyper(121,a,10047,a,b,19024,a)].">
      <j1 rule="hyper" parents="121 10047 19024"/>
    </justification>
  </clause>

  <clause id="19027">
    <literal><![CDATA[
      a(x,(y \ T(z,K(u,w))) \ ((K(u,w) \ y) \ v5),x) = a(x,(y * K(w,u)) \ ((z / y) \ v5),x)
    ]]></literal>
    <justification jstring="[hyper(333,a,12882,a(flip),b,18418,a),flip(a)].">
      <j1 rule="hyper" parents="333 12882 18418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19028">
    <literal><![CDATA[
      K(((x \ y) * x) / (L(K(z,u),w,v5) * x),v6) = K(x \ (L(K(u,z),w,v5) * y),v6)
    ]]></literal>
    <justification jstring="[hyper(16388,a,18495,a)].">
      <j1 rule="hyper" parents="16388 18495"/>
    </justification>
  </clause>

  <clause id="19029">
    <literal><![CDATA[
      K(x,(y / T(z,u)) \ (x * T(w,y / T(z,u)))) = K(x,w / (x \ (y / ((z \ u) \ u))))
    ]]></literal>
    <justification jstring="[para(12655(a,1),18691(a,1,2,2,2))].">
      <j1 rule="para" parents="12655 18691"/>
    </justification>
  </clause>

  <clause id="19030">
    <literal><![CDATA[
      K(x,y / (x \ (z / ((u \ w) \ w)))) = K(x,y / (x \ (z / T(u,w))))
    ]]></literal>
    <justification jstring="[hyper(18690,a,19029,a),flip(a)].">
      <j1 rule="hyper" parents="18690 19029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19031">
    <literal><![CDATA[
      K(x,((y / ((z \ u) \ u)) / w) \ x) = K(x,w / (x \ (y / T(z,u))))
    ]]></literal>
    <justification jstring="[hyper(9631,a,19030,a)].">
      <j1 rule="hyper" parents="9631 19030"/>
    </justification>
  </clause>

  <clause id="19032">
    <literal><![CDATA[
      K(x,((y / ((z \ u) \ u)) / w) \ x) = K(x,((y / T(z,u)) / w) \ x)
    ]]></literal>
    <justification jstring="[hyper(333,a,9622,a(flip),b,19031,a),flip(a)].">
      <j1 rule="hyper" parents="333 9622 19031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19033">
    <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(15122,a,18730,a)].">
      <j1 rule="hyper" parents="15122 18730"/>
    </justification>
  </clause>

  <clause id="19034">
    <literal><![CDATA[
      T(x,y * (R(z \ u,z,z) * (z \ 1))) = T(x,y * ((z \ 1) * T((z \ 1) * u,z)))
    ]]></literal>
    <justification jstring="[para(810(a,1),18926(a,1,2,2,1))].">
      <j1 rule="para" parents="810 18926"/>
    </justification>
  </clause>

  <clause id="19035">
    <literal><![CDATA[
      T(x,y * R((z \ u) * (1 / z),z,z)) = T(x,y * ((z \ 1) * T((z \ 1) * u,z)))
    ]]></literal>
    <justification jstring="[para(1192(a,2),19034(a,1,2,2))].">
      <j1 rule="para" parents="1192 19034"/>
    </justification>
  </clause>

  <clause id="19036">
    <literal><![CDATA[
      T(x,y * L((z \ u) * (1 / z),z,z)) = T(x,y * ((z \ 1) * T((z \ 1) * u,z)))
    ]]></literal>
    <justification jstring="[hyper(16838,a,19035,a)].">
      <j1 rule="hyper" parents="16838 19035"/>
    </justification>
  </clause>

  <clause id="19037">
    <literal><![CDATA[
      T(x,y * L((z \ u) * (1 / z),z,z)) = T(x,y * (((z \ 1) * u) * (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(333,a,16857,a(flip),b,19036,a),flip(a)].">
      <j1 rule="hyper" parents="333 16857 19036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19038">
    <literal><![CDATA[
      T(x,y * L((z \ u) * (1 / z),z,z)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y * ((z \ 1) * (u * (z \ 1)))) = w
    ]]></literal>
    <justification jstring="[para(19037(a,2),18266(a,1))].">
      <j1 rule="para" parents="19037 18266"/>
    </justification>
  </clause>

  <clause id="19039">
    <literal><![CDATA[
      T(x,y * ((z / u) * (w * (K(z,u) * K(z,u))))) = T(x,y * ((T(z,u) / T(u,z)) * w))
    ]]></literal>
    <justification jstring="[para(11920(a,1),18935(a,2,2,2))].">
      <j1 rule="para" parents="11920 18935"/>
    </justification>
  </clause>

  <clause id="19040">
    <literal><![CDATA[
      T(x,y * ((T(z,u) / T(u,z)) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y * ((z / u) * w)) = v5
    ]]></literal>
    <justification jstring="[para(19039(a,1),15999(a,1))].">
      <j1 rule="para" parents="19039 15999"/>
    </justification>
  </clause>

  <clause id="19041">
    <literal><![CDATA[
      T(x,y * ((z \ T(u,z)) * w)) = T(x,y * ((u / z) * w))
    ]]></literal>
    <justification jstring="[hyper(19040,a,18389,a),flip(a)].">
      <j1 rule="hyper" parents="19040 18389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19043">
    <literal><![CDATA[
      T(x,y * ((T(z,u) \ u) * w)) = T(x,y * ((u / z) * w))
    ]]></literal>
    <justification jstring="[para(3628(a,2),19041(a,1,2,2,1))].">
      <j1 rule="para" parents="3628 19041"/>
    </justification>
  </clause>

  <clause id="19044">
    <literal><![CDATA[
      T(x,y * ((z / u) * ((z / u) * w))) = T(x,y * ((u \ z) * ((u \ z) * w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,18391,a(flip),b,19043,a),flip(a)].">
      <j1 rule="hyper" parents="63 18391 19043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19045">
    <literal><![CDATA[
      T(x,y * ((R(T(z,u),z,z) \ u) * w)) = T(x,y * ((u / ((z \ 1) \ 1)) * w))
    ]]></literal>
    <justification jstring="[para(817(a,1),19043(a,1,2,2,1,1))].">
      <j1 rule="para" parents="817 19043"/>
    </justification>
  </clause>

  <clause id="19046">
    <literal><![CDATA[
      T(x,y * ((z / ((u \ 1) \ 1)) * w)) = T(x,y * (((u \ (u \ z)) * u) * w))
    ]]></literal>
    <justification jstring="[para(15968(a,1),19045(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="15968 19045"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19047">
    <literal><![CDATA[
      T(x,y * (T(z \ u,z) * w)) = T(x,y * ((u / ((z \ 1) \ 1)) * w))
    ]]></literal>
    <justification jstring="[hyper(333,a,18376,a(flip),b,19046,a)].">
      <j1 rule="hyper" parents="333 18376 19046"/>
    </justification>
  </clause>

  <clause id="19048">
    <literal><![CDATA[
      T(x,y * ((z / ((u \ 1) \ 1)) * w)) = T(x,y * ((z / u) * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,18847,a(flip),b,19047,a),flip(a)].">
      <j1 rule="hyper" parents="63 18847 19047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19049">
    <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(6840(a,1),18983(a,1,2))].">
      <j1 rule="para" parents="6840 18983"/>
    </justification>
  </clause>

  <clause id="19050">
    <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(63,a,18263,a(flip),b,19008,a)].">
      <j1 rule="hyper" parents="63 18263 19008"/>
    </justification>
  </clause>

  <clause id="19052">
    <literal><![CDATA[
      K(x,(((K(y,z) * u) / w) / v5) * v6) = K(x,((u / (K(z,y) * w)) / v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,18094,a(flip),b,19050,a)].">
      <j1 rule="hyper" parents="63 18094 19050"/>
    </justification>
  </clause>

  <clause id="19053">
    <literal><![CDATA[
      T(L((x * y) / T(x,K(z,u)),w,v5),x * K(u,z)) = x \ T(x * L(y,w,v5),K(z,u))
    ]]></literal>
    <justification jstring="[para(6835(a,1),19009(a,1,1,1))].">
      <j1 rule="para" parents="6835 19009"/>
    </justification>
  </clause>

  <clause id="19054">
    <literal><![CDATA[
      L(T((x * y) / T(x,K(z,u)),x * K(u,z)),w,v5) = x \ T(x * L(y,w,v5),K(z,u))
    ]]></literal>
    <justification jstring="[hyper(10114,a,19053,a)].">
      <j1 rule="hyper" parents="10114 19053"/>
    </justification>
  </clause>

  <clause id="19055">
    <literal><![CDATA[
      L(x \ T(x * y,K(z,u)),w,v5) = x \ T(x * L(y,w,v5),K(z,u))
    ]]></literal>
    <justification jstring="[para(15899(a,1),19054(a,1,1))].">
      <j1 rule="para" parents="15899 19054"/>
    </justification>
  </clause>

  <clause id="19056">
    <literal><![CDATA[
      L(K(x,K(y,z * L(u \ 1,u,w))),(w * u) \ w,w * u) = w \ ((w * u) * L(z \ T(z * (u \ 1),K(x,y)),u,w))
    ]]></literal>
    <justification jstring="[para(19055(a,2),12316(a,2,2,2))].">
      <j1 rule="para" parents="19055 12316"/>
    </justification>
  </clause>

  <clause id="19057">
    <literal><![CDATA[
      a(x,(y \ T(z,K(u,w))) \ ((K(u,w) \ y) \ v5),x) = a(x,K(w,u) \ (y \ ((z / y) \ v5)),x)
    ]]></literal>
    <justification jstring="[hyper(333,a,12882,a(flip),b,19027,a),flip(a)].">
      <j1 rule="hyper" parents="333 12882 19027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19058">
    <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(15900(a,1),19049(a,1,2))].">
      <j1 rule="para" parents="15900 19049"/>
    </justification>
  </clause>

  <clause id="19059">
    <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(63,a,11611,a(flip),b,19058,a)].">
      <j1 rule="hyper" parents="63 11611 19058"/>
    </justification>
  </clause>

  <clause id="19060">
    <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(16651(a,2),19059(a,1,2))].">
      <j1 rule="para" parents="16651 19059"/>
    </justification>
  </clause>

  <clause id="19061">
    <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(12199(a,1),19060(a,1,2,1))].">
      <j1 rule="para" parents="12199 19060"/>
    </justification>
  </clause>

  <clause id="19062">
    <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(13226(a,1),19061(a,1,2))].">
      <j1 rule="para" parents="13226 19061"/>
    </justification>
  </clause>

  <clause id="19063">
    <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(4567(a,1),19062(a,1,2))].">
      <j1 rule="para" parents="4567 19062"/>
    </justification>
  </clause>

  <clause id="19064">
    <literal><![CDATA[
      K(x,T(y,z)) * T(u * K(y,x),z) = T(u,z * K(y,x))
    ]]></literal>
    <justification jstring="[hyper(7330,a,19063,a)].">
      <j1 rule="hyper" parents="7330 19063"/>
    </justification>
  </clause>

  <clause id="19065">
    <literal><![CDATA[
      K(x,y) * T(z * K(y,T(x,u)),u) = T(z,u * K(y,x))
    ]]></literal>
    <justification jstring="[hyper(17058,a,19064,a)].">
      <j1 rule="hyper" parents="17058 19064"/>
    </justification>
  </clause>

  <clause id="19066">
    <literal><![CDATA[
      T(x * K(y,T(z,u)),u) = K(y,z) * T(x,u * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(4577,a,19065,a),flip(a)].">
      <j1 rule="hyper" parents="4577 19065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19067">
    <literal><![CDATA[
      (x * (y * K(z,u))) / T(x * K(z,T(u,y)),y) = R(y,K(z,u),x)
    ]]></literal>
    <justification jstring="[hyper(197,a,19066,a,b,14586,a)].">
      <j1 rule="hyper" parents="197 19066 14586"/>
    </justification>
  </clause>

  <clause id="19069">
    <literal><![CDATA[
      L(x,K(y,T(z,x)),u) = R(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(13642,a,19067,a)].">
      <j1 rule="hyper" parents="13642 19067"/>
    </justification>
  </clause>

  <clause id="19070">
    <literal><![CDATA[
      a(x,(y \ T(z,K(u,w))) \ ((K(w,u) \ y) \ v5),x) = a(x,K(u,w) \ (y \ ((z / y) \ v5)),x)
    ]]></literal>
    <justification jstring="[para(6840(a,1),19057(a,1,2,1,2))].">
      <j1 rule="para" parents="6840 19057"/>
    </justification>
  </clause>

  <clause id="19071">
    <literal><![CDATA[
      a(x,T(y,K(z,u)) \ (w * ((K(u,z) \ w) \ v5)),x) = a(x,K(z,u) \ (w \ ((y / w) \ v5)),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,12883,a(flip),b,19070,a)].">
      <j1 rule="hyper" parents="63 12883 19070"/>
    </justification>
  </clause>

  <clause id="19072">
    <literal><![CDATA[
      K((x * K(y,z)) * L(u,x,K(y,z)),w) = K(w,K(z,y) \ (u * x)) \ K(w,K(u,x))
    ]]></literal>
    <justification jstring="[para(16598(a,1),17566(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16598 17566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19075">
    <literal><![CDATA[
      T(x,(y \ L(K(z,u) * w,v5,v6)) * T(y,w)) = T(x,L(w * K(z,u),v5,v6))
    ]]></literal>
    <justification jstring="[hyper(17933,a,18408,a),flip(a)].">
      <j1 rule="hyper" parents="17933 18408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19077">
    <literal><![CDATA[
      T(x,T(K(y,z) * L(K(u,w) * z,v5,v6),y)) = T(x,L(z * K(u,w),v5,v6))
    ]]></literal>
    <justification jstring="[hyper(16889,a,19075,a)].">
      <j1 rule="hyper" parents="16889 19075"/>
    </justification>
  </clause>

  <clause id="19078">
    <literal><![CDATA[
      T(x,T(a(y,z,K(u,w)) * L(K(v5,v6) * w,v7,v8),L(u,z,y) \ u)) = T(x,L(w * K(v5,v6),v7,v8))
    ]]></literal>
    <justification jstring="[para(13542(a,1),19077(a,1,2,1,1))].">
      <j1 rule="para" parents="13542 19077"/>
    </justification>
  </clause>

  <clause id="19079">
    <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(14134,a,18918,a)].">
      <j1 rule="hyper" parents="14134 18918"/>
    </justification>
  </clause>

  <clause id="19080">
    <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(15192,a,19079,a),flip(a)].">
      <j1 rule="hyper" parents="15192 19079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19081">
    <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(14582(a,1),18936(a,1,2,2))].">
      <j1 rule="para" parents="14582 18936"/>
    </justification>
  </clause>

  <clause id="19082">
    <literal><![CDATA[
      T(x,y * (T(z,u * (w * K(v5,K(v6,v7)))) * v8)) = T(x,y * (T(z,(u * w) \ 1) * v8))
    ]]></literal>
    <justification jstring="[para(16311(a,1),17753(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="16311 17753"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19083">
    <literal><![CDATA[
      T(x,y * (T(z,u * (w * K(v5,K(v6,v7)))) * v8)) = T(x,y * (T(z,w \ (u \ 1)) * v8))
    ]]></literal>
    <justification jstring="[para(13409(a,1),19082(a,2,2,2,1))].">
      <j1 rule="para" parents="13409 19082"/>
    </justification>
  </clause>

  <clause id="19085">
    <literal><![CDATA[
      T(x,y * (T(z,u * (w * K(v5,K(v6,v7)))) * v8)) = T(x,y * (T(z,w * (u \ 1)) * v8))
    ]]></literal>
    <justification jstring="[hyper(333,a,16938,a(flip),b,19083,a),flip(a)].">
      <j1 rule="hyper" parents="333 16938 19083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19086">
    <literal><![CDATA[
      T(x,y * (T(z,u * (w * K(v5,K(v6,v7)))) * v8)) = T(x,y * (T(z,w / u) * v8))
    ]]></literal>
    <justification jstring="[para(13244(a,1),19085(a,2,2,2,1))].">
      <j1 rule="para" parents="13244 19085"/>
    </justification>
  </clause>

  <clause id="19087">
    <literal><![CDATA[
      T(x,y * (T(z,u / w) * v5)) = T(x,y * (T(z,w * u) * v5))
    ]]></literal>
    <justification jstring="[para(182(a,1),19086(a,1,2,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="182 19086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19088">
    <literal><![CDATA[
      K(x,T(T((y * K(z,u)) / w,K(y,v5)),y \ w)) = K(x,(y * K(z,u)) / T(w,K(y,v5)))
    ]]></literal>
    <justification jstring="[hyper(16555,a,17784,a)].">
      <j1 rule="hyper" parents="16555 17784"/>
    </justification>
  </clause>

  <clause id="19089">
    <literal><![CDATA[
      K(x,T((y * K(z,u)) / w,y \ w)) = K(x,(y * K(z,u)) / T(w,K(y,v5)))
    ]]></literal>
    <justification jstring="[hyper(15546,a,19088,a)].">
      <j1 rule="hyper" parents="15546 19088"/>
    </justification>
  </clause>

  <clause id="19091">
    <literal><![CDATA[
      K(x,T((y * K(z,u)) / w,y \ w)) = K(x,(y * K(z,u)) / w)
    ]]></literal>
    <justification jstring="[hyper(333,a,16329,a(flip),b,19089,a),flip(a)].">
      <j1 rule="hyper" parents="333 16329 19089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19093">
    <literal><![CDATA[
      K(x,(y * (z / y)) \ (K(u,w) * y)) = K(x,(y * K(u,T(w,v5))) / z)
    ]]></literal>
    <justification jstring="[hyper(63,a,18944,a(flip),b,19091,a)].">
      <j1 rule="hyper" parents="63 18944 19091"/>
    </justification>
  </clause>

  <clause id="19094">
    <literal><![CDATA[
      K(x,(y * (z / y)) \ (K(u,w) * y)) = K(x,(y * K(u,w)) / z)
    ]]></literal>
    <justification jstring="[para(110(a,1),19093(a,2,2,1,2,2))].">
      <j1 rule="para" parents="110 19093"/>
    </justification>
  </clause>

  <clause id="19095">
    <literal><![CDATA[
      K(x,(y * (z / y)) \ (K(u,w) * y)) = K(x,y / (z * K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(333,a,17564,a(flip),b,19094,a),flip(a)].">
      <j1 rule="hyper" parents="333 17564 19094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19096">
    <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(63,a,19052,a(flip),b,18141,a)].">
      <j1 rule="hyper" parents="63 19052 18141"/>
    </justification>
  </clause>

  <clause id="19097">
    <literal><![CDATA[
      a(x,K(y \ 1,z) \ ((u \ (u / y)) * w),x) = a(x,T(T(u \ (u / y),z),y \ 1) * w,x)
    ]]></literal>
    <justification jstring="[para(5863(a,1),18435(a,1,2,1))].">
      <j1 rule="para" parents="5863 18435"/>
    </justification>
  </clause>

  <clause id="19099">
    <literal><![CDATA[
      T(x,(y * ((((y \ 1) * (y \ z)) / (y \ 1)) * (y \ 1))) * u) = T(x,((y \ 1) * z) * u)
    ]]></literal>
    <justification jstring="[hyper(333,a,18446,a(flip),b,18447,a),flip(a)].">
      <j1 rule="hyper" parents="333 18446 18447"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19100">
    <literal><![CDATA[
      T(x,(y * ((y \ 1) * (y \ z))) * u) = T(x,((y \ 1) * z) * u)
    ]]></literal>
    <justification jstring="[para(12(a,1),19099(a,1,2,1,2))].">
      <j1 rule="para" parents="12 19099"/>
    </justification>
  </clause>

  <clause id="19102">
    <literal><![CDATA[
      T(x,L(y \ z,y,y) * u) = T(x,((y \ 1) * z) * u)
    ]]></literal>
    <justification jstring="[para(2599(a,1),19100(a,1,2,1))].">
      <j1 rule="para" parents="2599 19100"/>
    </justification>
  </clause>

  <clause id="19103">
    <literal><![CDATA[
      K(x,(K(y,T(z,u)) * (K(w,T(v5,v6)) \ (v7 * K(z,T(y,u))))) \ v8) = K(x,v7 \ (K(v5,T(w,v6)) \ v8))
    ]]></literal>
    <justification jstring="[para(17544(a,2),18891(a,1,2,1,2))].">
      <j1 rule="para" parents="17544 18891"/>
    </justification>
  </clause>

  <clause id="19104">
    <literal><![CDATA[
      K(x,(y \ ((K(z,u) * w) / v5)) * v6) = K(x,(y \ (w / (K(u,z) * v5))) * v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,18140,a(flip),b,19096,a),flip(a)].">
      <j1 rule="hyper" parents="63 18140 19096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19105">
    <literal><![CDATA[
      K(x,(y * K(z,T(u,w))) \ v5) = K(x,y \ (K(z,T(u,w)) \ v5))
    ]]></literal>
    <justification jstring="[para(10(a,1),19103(a,1,2,1))].">
      <j1 rule="para" parents="10 19103"/>
    </justification>
  </clause>

  <clause id="19106">
    <literal><![CDATA[
      K(x,K(y,T(z,u)) \ (w \ v5)) = K(x,w \ (K(y,T(z,u)) \ v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,18604,a(flip),b,19105,a)].">
      <j1 rule="hyper" parents="63 18604 19105"/>
    </justification>
  </clause>

  <clause id="19107">
    <literal><![CDATA[
      K(x,y \ (K(z,T(u,w)) \ v5)) = K(x,K(z,u) \ (y \ v5))
    ]]></literal>
    <justification jstring="[hyper(16432,a,19106,a),flip(a)].">
      <j1 rule="hyper" parents="16432 19106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19108">
    <literal><![CDATA[
      K(x,y \ (K(z,T(u,w)) \ v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,z) \ (y \ v5)) = v6
    ]]></literal>
    <justification jstring="[para(19106(a,1),16434(a,1))].">
      <j1 rule="para" parents="19106 16434"/>
    </justification>
  </clause>

  <clause id="19110">
    <literal><![CDATA[
      K(x,(y * z) \ (K(z,T(u,w)) \ v5)) = K(x,(y * T(z,u)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(333,a,18619,a(flip),b,19107,a),flip(a)].">
      <j1 rule="hyper" parents="333 18619 19107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19111">
    <literal><![CDATA[
      K(x,K(y,z) \ (u \ w)) = K(x,u \ (K(y,z) \ w))
    ]]></literal>
    <justification jstring="[para(110(a,1),19107(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="110 19107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19112">
    <literal><![CDATA[
      K(x,K(y,z) \ (u \ w)) = K(x,u \ (K(z,y) \ w))
    ]]></literal>
    <justification jstring="[hyper(15780,a,19111,a)].">
      <j1 rule="hyper" parents="15780 19111"/>
    </justification>
  </clause>

  <clause id="19113">
    <literal><![CDATA[
      K(x,y \ (K(z,T(u,w)) \ v5)) = K(x,y \ (K(z,u) \ v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,19107,a,b,19111,a)].">
      <j1 rule="hyper" parents="63 19107 19111"/>
    </justification>
  </clause>

  <clause id="19115">
    <literal><![CDATA[
      K(x,y \ (K(z,K(u,w)) \ v5)) = K(x,y \ v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,16325,a(flip),b,19111,a),flip(a)].">
      <j1 rule="hyper" parents="63 16325 19111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19116">
    <literal><![CDATA[
      K(x,y \ (K(z \ 1,u) \ w)) = K(x,K(u,z) \ (y \ w))
    ]]></literal>
    <justification jstring="[hyper(63,a,15035,a(flip),b,19111,a),flip(a)].">
      <j1 rule="hyper" parents="63 15035 19111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19117">
    <literal><![CDATA[
      K(x,K(y,z) \ (u \ (T(y,z) * w))) = K(x,u \ (y * w))
    ]]></literal>
    <justification jstring="[para(4295(a,1),19111(a,2,2,2))].">
      <j1 rule="para" parents="4295 19111"/>
    </justification>
  </clause>

  <clause id="19119">
    <literal><![CDATA[
      T(x,y \ (K(z,K(u,w)) \ v5)) = T(x,y \ v5)
    ]]></literal>
    <justification jstring="[hyper(124,a,19115,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 19115 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19120">
    <literal><![CDATA[
      K(x,y \ (z \ T(u,K(w,v5)))) = K(x,y \ (z \ u))
    ]]></literal>
    <justification jstring="[para(15691(a,1),19115(a,1,2,2))].">
      <j1 rule="para" parents="15691 19115"/>
    </justification>
  </clause>

  <clause id="19121">
    <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(15838(a,1),19115(a,1,2,2))].">
      <j1 rule="para" parents="15838 19115"/>
    </justification>
  </clause>

  <clause id="19122">
    <literal><![CDATA[
      K(x,(K(y,K(z,u)) \ w) \ v5) = K(x,w \ v5)
    ]]></literal>
    <justification jstring="[para(17776(a,1),19115(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17776 19115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19123">
    <literal><![CDATA[
      T(x,y \ (T(z,K(u,w)) \ v5)) = T(x,y \ (z \ v5))
    ]]></literal>
    <justification jstring="[para(4511(a,1),19119(a,1,2,2))].">
      <j1 rule="para" parents="4511 19119"/>
    </justification>
  </clause>

  <clause id="19124">
    <literal><![CDATA[
      K(x,T(T(y,K(z,u)) * w,v5) \ v6) = K(x,T(y * w,v5) \ v6)
    ]]></literal>
    <justification jstring="[para(15871(a,1),19122(a,1,2,1))].">
      <j1 rule="para" parents="15871 19122"/>
    </justification>
  </clause>

  <clause id="19125">
    <literal><![CDATA[
      K(x,K(y,z) \ ((T(z,y) \ u) \ w)) = K(x,(z \ u) \ w)
    ]]></literal>
    <justification jstring="[hyper(333,a,17802,a(flip),b,19112,a),flip(a)].">
      <j1 rule="hyper" parents="333 17802 19112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19126">
    <literal><![CDATA[
      K(x,y \ (K(z,u) \ (y * w))) = K(x,K(u,z) \ w)
    ]]></literal>
    <justification jstring="[para(9(a,1),19112(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 19112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19127">
    <literal><![CDATA[
      T((x / T(y,K(z,u))) * T(T(y,K(z,u)),K(w,v5) \ (y \ x)),K(w,v5)) = y * T(x / y,K(w,v5))
    ]]></literal>
    <justification jstring="[para(19123(a,1),17242(a,1,1,2))].">
      <j1 rule="para" parents="19123 17242"/>
    </justification>
  </clause>

  <clause id="19128">
    <literal><![CDATA[
      K(x,y \ (K(z / u,w) \ v5)) = K(x,y \ (K(u \ z,w) \ v5))
    ]]></literal>
    <justification jstring="[para(6382(a,1),19113(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="6382 19113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19129">
    <literal><![CDATA[
      K(x,K(y,(z \ 1) / (u / z)) \ ((u / z) \ w)) = K(x,(T(u,y) / z) \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,17803,a(flip),b,19116,a),flip(a)].">
      <j1 rule="hyper" parents="63 17803 19116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19130">
    <literal><![CDATA[
      K(x,y \ (T(T(z,u),u) * w)) = K(x,y \ (z * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,18640,a(flip),b,19117,a)].">
      <j1 rule="hyper" parents="63 18640 19117"/>
    </justification>
  </clause>

  <clause id="19131">
    <literal><![CDATA[
      K(x,y \ (T(T(z,u),u) * T(w,z))) = K(x,y \ (w * z))
    ]]></literal>
    <justification jstring="[para(111(a,1),19130(a,2,2,2))].">
      <j1 rule="para" parents="111 19130"/>
    </justification>
  </clause>

  <clause id="19132">
    <literal><![CDATA[
      K(x,K(y,z) * ((T(y,z) \ u) \ w)) = K(x,(y \ u) \ w)
    ]]></literal>
    <justification jstring="[para(4567(a,1),19125(a,1,2))].">
      <j1 rule="para" parents="4567 19125"/>
    </justification>
  </clause>

  <clause id="19133">
    <literal><![CDATA[
      K(x,y \ (z * T(T(u,w),w))) = K(x,y \ (z * u))
    ]]></literal>
    <justification jstring="[para(6945(a,1),19131(a,1,2,2))].">
      <j1 rule="para" parents="6945 19131"/>
    </justification>
  </clause>

  <clause id="19134">
    <literal><![CDATA[
      K(x,y \ (z * T(u \ w,u))) = K(x,y \ (z * (w / u)))
    ]]></literal>
    <justification jstring="[para(113(a,1),19133(a,1,2,2,2,1))].">
      <j1 rule="para" parents="113 19133"/>
    </justification>
  </clause>

  <clause id="19135">
    <literal><![CDATA[
      K(x,T(y,z) \ (K(z,T(u,w)) \ v5)) = K(x,((z \ y) * T(z,u)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,12700,a(flip),b,19110,a)].">
      <j1 rule="hyper" parents="63 12700 19110"/>
    </justification>
  </clause>

  <clause id="19136">
    <literal><![CDATA[
      K(x,T((T(y,z) \ 1) \ z,u) \ w) = K(x,T(T(y,K(v5,v6)) * (((y \ 1) \ z) / y),u) \ w)
    ]]></literal>
    <justification jstring="[para(10269(a,2),19124(a,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="10269 19124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19137">
    <literal><![CDATA[
      K(x,y \ (K(x \ y,z) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(x \ y,z) \ (x \ u)) = w
    ]]></literal>
    <justification jstring="[para(19128(a,1),17804(a,1))].">
      <j1 rule="para" parents="19128 17804"/>
    </justification>
  </clause>

  <clause id="19138">
    <literal><![CDATA[
      K(x,((y \ z) * T(y,u)) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,y) \ (T(z,y) \ w)) = v5
    ]]></literal>
    <justification jstring="[para(19135(a,1),19108(a,1))].">
      <j1 rule="para" parents="19135 19108"/>
    </justification>
  </clause>

  <clause id="19139">
    <literal><![CDATA[
      K(x,T(x \ y,z) \ (x \ (y * u))) = K(x,K(z,x \ y) \ u)
    ]]></literal>
    <justification jstring="[hyper(19137,a,19126,a)].">
      <j1 rule="hyper" parents="19137 19126"/>
    </justification>
  </clause>

  <clause id="19140">
    <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(5994(a,1),19121(a,1,2,2,1))].">
      <j1 rule="para" parents="5994 19121"/>
    </justification>
  </clause>

  <clause id="19141">
    <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(17002(a,1),19140(a,1,2,2))].">
      <j1 rule="para" parents="17002 19140"/>
    </justification>
  </clause>

  <clause id="19142">
    <literal><![CDATA[
      K(x,y \ T(z,u / K(w,v5))) = K(x,y \ (u \ (z * u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,19120,a(flip),b,19141,a),flip(a)].">
      <j1 rule="hyper" parents="63 19120 19141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19144">
    <literal><![CDATA[
      K(x,y \ T(z,u / K(w,v5))) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(22(a,2),19142(a,2,2,2))].">
      <j1 rule="para" parents="22 19142"/>
    </justification>
  </clause>

  <clause id="19145">
    <literal><![CDATA[
      K(x,y \ T(z,u * (w / v5))) = K(x,y \ T(z,u * (v5 \ w)))
    ]]></literal>
    <justification jstring="[para(6009(a,1),19144(a,1,2,2,2))].">
      <j1 rule="para" parents="6009 19144"/>
    </justification>
  </clause>

  <clause id="19146">
    <literal><![CDATA[
      K(x,y \ T(z,K(u,w) * v5)) = K(x,y \ T(z,v5))
    ]]></literal>
    <justification jstring="[para(6388(a,1),19144(a,1,2,2,2))].">
      <j1 rule="para" parents="6388 19144"/>
    </justification>
  </clause>

  <clause id="19147">
    <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(63,a,18601,a(flip),b,19146,a),flip(a)].">
      <j1 rule="hyper" parents="63 18601 19146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19148">
    <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(527(a,1),19146(a,1,2)),flip(a)].">
      <j1 rule="para" parents="527 19146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19149">
    <literal><![CDATA[
      K(x,y \ T(z,T(u,w) * v5)) = K(x,y \ T(z,u * v5))
    ]]></literal>
    <justification jstring="[para(4273(a,1),19146(a,1,2,2,2))].">
      <j1 rule="para" parents="4273 19146"/>
    </justification>
  </clause>

  <clause id="19150">
    <literal><![CDATA[
      K(x,y \ T(z,u * T(w,v5))) = K(x,y \ T(z,w * u))
    ]]></literal>
    <justification jstring="[hyper(16443,a,19149,a)].">
      <j1 rule="hyper" parents="16443 19149"/>
    </justification>
  </clause>

  <clause id="19152">
    <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(19147(a,2),16382(a,1))].">
      <j1 rule="para" parents="19147 16382"/>
    </justification>
  </clause>

  <clause id="19153">
    <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(16195(a,1),19152(a,1))].">
      <j1 rule="para" parents="16195 19152"/>
    </justification>
  </clause>

  <clause id="19154">
    <literal><![CDATA[
      K(x,T((T(y,z) \ 1) \ z,u) \ w) = K(x,(y * (T((y \ 1) \ z,u) / T(y,K(v5,v6)))) \ w)
    ]]></literal>
    <justification jstring="[para(17884(a,1),19136(a,2,2,1))].">
      <j1 rule="para" parents="17884 19136"/>
    </justification>
  </clause>

  <clause id="19155">
    <literal><![CDATA[
      T(x * K(T(y,K(z,u)),K(w,v5) \ (y \ x)),K(w,v5)) = y * T(x / y,K(w,v5))
    ]]></literal>
    <justification jstring="[para(5974(a,1),19127(a,1,1))].">
      <j1 rule="para" parents="5974 19127"/>
    </justification>
  </clause>

  <clause id="19157">
    <literal><![CDATA[
      T(x * K(y,K(z,u) \ (y \ x)),K(z,u)) = y * T(x / y,K(z,u))
    ]]></literal>
    <justification jstring="[para(1242(a,1),19155(a,1,1,2,1))].">
      <j1 rule="para" parents="1242 19155"/>
    </justification>
  </clause>

  <clause id="19158">
    <literal><![CDATA[
      T(K(x \ (y / K(z,u)),x) \ y,K(z,u)) = x * T(y / x,K(z,u))
    ]]></literal>
    <justification jstring="[para(10542(a,2),19157(a,1,1))].">
      <j1 rule="para" parents="10542 19157"/>
    </justification>
  </clause>

  <clause id="19159">
    <literal><![CDATA[
      T(K(x \ (y * K(z,u)),x) \ y,K(u,z)) = x * T(y / x,K(u,z))
    ]]></literal>
    <justification jstring="[para(5994(a,1),19158(a,1,1,1,1,2))].">
      <j1 rule="para" parents="5994 19158"/>
    </justification>
  </clause>

  <clause id="19160">
    <literal><![CDATA[
      T(K(x \ (K(y,z) \ u),x) \ u,K(y,z)) = x * T(u / x,K(y,z))
    ]]></literal>
    <justification jstring="[para(16370(a,2),19159(a,1,1,1))].">
      <j1 rule="para" parents="16370 19159"/>
    </justification>
  </clause>

  <clause id="19161">
    <literal><![CDATA[
      K(x \ (K(y,z) \ u),x) \ T(u,K(y,z)) = x * T(u / x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,16652,a(flip),b,19160,a)].">
      <j1 rule="hyper" parents="63 16652 19160"/>
    </justification>
  </clause>

  <clause id="19162">
    <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(18201,a,17641,a)].">
      <j1 rule="hyper" parents="18201 17641"/>
    </justification>
  </clause>

  <clause id="19164">
    <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(3678(a,1),19162(a,1,2,1,1))].">
      <j1 rule="para" parents="3678 19162"/>
    </justification>
  </clause>

  <clause id="19165">
    <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(12910,a,19164,a)].">
      <j1 rule="hyper" parents="12910 19164"/>
    </justification>
  </clause>

  <clause id="19166">
    <literal><![CDATA[
      (K(x,L(y,z,u)) * T(w,K(y,x) * v5)) / (K(x,L(y,z,u)) * w) = K(w,v5 * K(x,L(y,z,u)))
    ]]></literal>
    <justification jstring="[para(15845(a,1),17940(a,1,1))].">
      <j1 rule="para" parents="15845 17940"/>
    </justification>
  </clause>

  <clause id="19168">
    <literal><![CDATA[
      K(x,T(K(y,z) * u,K(z,L(y,w,v5)))) = K(x,u * K(z,L(y,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(7719,a,19166,a)].">
      <j1 rule="hyper" parents="7719 19166"/>
    </justification>
  </clause>

  <clause id="19169">
    <literal><![CDATA[
      K(x,y * K(z,L(u,w,v5))) = K(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[para(17617(a,1),19168(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17617 19168"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19170">
    <literal><![CDATA[
      K(x,y \ (z * (u * K(w,v5)))) = K(x,(y \ (z * u)) * K(v5,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,18575,a(flip),b,19169,a)].">
      <j1 rule="hyper" parents="63 18575 19169"/>
    </justification>
  </clause>

  <clause id="19172">
    <literal><![CDATA[
      K(x,(y \ (z * T(u,z))) * K(w,v5)) = K(x,y \ ((K(v5,w) * u) * z))
    ]]></literal>
    <justification jstring="[hyper(18170,a,19170,a),flip(a)].">
      <j1 rule="hyper" parents="18170 19170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19174">
    <literal><![CDATA[
      K(x,y \ (z * (u * K(w,v5)))) = K(x,K(w,v5) * (y \ (z * u)))
    ]]></literal>
    <justification jstring="[hyper(333,a,15637,a,b,19170,a),flip(a)].">
      <j1 rule="hyper" parents="333 15637 19170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19175">
    <literal><![CDATA[
      K(x,K(y,T(z,u)) * (w \ (v5 * u))) = K(x,w \ (v5 * (K(y,z) * u)))
    ]]></literal>
    <justification jstring="[para(6390(a,1),19174(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="6390 19174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19176">
    <literal><![CDATA[
      K(x,y \ ((K(z,u) * w) * v5)) = K(x,(y \ (w * v5)) * K(u,z))
    ]]></literal>
    <justification jstring="[para(111(a,1),19172(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="111 19172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19177">
    <literal><![CDATA[
      K(x,y \ ((K(z,u) * w) * v5)) = K(x,K(z,u) * (y \ (w * v5)))
    ]]></literal>
    <justification jstring="[hyper(333,a,15637,a,b,19176,a),flip(a)].">
      <j1 rule="hyper" parents="333 15637 19176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19178">
    <literal><![CDATA[
      K(x,K(y,z) * (((K(y,z) * u) * w) \ (u * (w * v5)))) = K(x,L(v5,w,K(y,z) * u))
    ]]></literal>
    <justification jstring="[para(18(a,2),19177(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18 19177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19179">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ ((y * w) * v5))) = K(x,u \ ((T(y,z) * w) * v5))
    ]]></literal>
    <justification jstring="[para(4273(a,1),19177(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4273 19177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19180">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ ((y / z) * w))) = K(x,u \ ((T(y,z) / z) * w))
    ]]></literal>
    <justification jstring="[para(4820(a,1),19177(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4820 19177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19182">
    <literal><![CDATA[
      K(x,y \ (z * (K(u,w) * v5))) = K(x,K(w,u) * (y \ (z * v5)))
    ]]></literal>
    <justification jstring="[hyper(16428,a,19175,a),flip(a)].">
      <j1 rule="hyper" parents="16428 19175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19183">
    <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(19175(a,1),16428(a,1))].">
      <j1 rule="para" parents="19175 16428"/>
    </justification>
  </clause>

  <clause id="19184">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ (w * (v5 \ z)))) = K(x,u \ (w * (v5 \ T(z,y))))
    ]]></literal>
    <justification jstring="[hyper(17901,a,19182,a),flip(a)].">
      <j1 rule="hyper" parents="17901 19182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19187">
    <literal><![CDATA[
      K(x,y \ (T((z * u) \ z,w) \ z)) = K(x,K(u \ 1,w) * (y \ (u * z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,18959,a,b,19182,a)].">
      <j1 rule="hyper" parents="63 18959 19182"/>
    </justification>
  </clause>

  <clause id="19188">
    <literal><![CDATA[
      K(x,K(y,y \ z) * (u \ (z * w))) = K(x,u \ (((y \ z) * y) * w))
    ]]></literal>
    <justification jstring="[para(10011(a,1),19182(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10011 19182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19189">
    <literal><![CDATA[
      K(x,y \ ((T(z,u * K(w,v5)) * u) * v6)) = K(x,y \ ((u * z) * v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,18657,a(flip),b,19179,a),flip(a)].">
      <j1 rule="hyper" parents="63 18657 19179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19190">
    <literal><![CDATA[
      K(x,y \ ((T(z,u) / u) * w)) = K(x,y \ ((u \ z) * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,18705,a(flip),b,19180,a),flip(a)].">
      <j1 rule="hyper" parents="63 18705 19180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19191">
    <literal><![CDATA[
      K(x,L(T(y,z) \ u,y,y \ z)) = K(x,z \ ((y \ z) * u))
    ]]></literal>
    <justification jstring="[para(14713(a,2),19190(a,1,2))].">
      <j1 rule="para" parents="14713 19190"/>
    </justification>
  </clause>

  <clause id="19192">
    <literal><![CDATA[
      K(x,(((y \ z) \ 1) * z) \ (((z / y) \ 1) * u)) = K(x,y \ ((z \ y) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,19080,a,b,19191,a)].">
      <j1 rule="hyper" parents="63 19080 19191"/>
    </justification>
  </clause>

  <clause id="19193">
    <literal><![CDATA[
      K(x,T(y,z) \ (u * (w \ y))) = K(x,y \ (u * (w \ T(y,z))))
    ]]></literal>
    <justification jstring="[para(4555(a,1),19184(a,1,2))].">
      <j1 rule="para" parents="4555 19184"/>
    </justification>
  </clause>

  <clause id="19194">
    <literal><![CDATA[
      K(x,y \ (((z \ u) * z) * w)) = K(x,K(z,u) * (y \ (u * w)))
    ]]></literal>
    <justification jstring="[hyper(15002,a,19188,a),flip(a)].">
      <j1 rule="hyper" parents="15002 19188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19195">
    <literal><![CDATA[
      K(x,y \ (((z \ u) * z) * w)) = K(x,y \ (T(u,z) * w))
    ]]></literal>
    <justification jstring="[hyper(333,a,18628,a(flip),b,19194,a),flip(a)].">
      <j1 rule="hyper" parents="333 18628 19194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19196">
    <literal><![CDATA[
      K(x,y \ ((z / (T(u,z) \ 1)) * w)) = K(x,y \ (T(z / (u \ 1),z) * w))
    ]]></literal>
    <justification jstring="[para(6209(a,1),19195(a,1,2,2,1))].">
      <j1 rule="para" parents="6209 19195"/>
    </justification>
  </clause>

  <clause id="19197">
    <literal><![CDATA[
      K(x,y \ ((T(z,u) * u) * w)) = K(x,y \ ((u * z) * w))
    ]]></literal>
    <justification jstring="[para(182(a,1),19189(a,1,2,2,1,1,2))].">
      <j1 rule="para" parents="182 19189"/>
    </justification>
  </clause>

  <clause id="19198">
    <literal><![CDATA[
      K(x,y \ (T((z * u) \ z,w) \ z)) = K(x,K(u,w) * (y \ (u * z)))
    ]]></literal>
    <justification jstring="[hyper(333,a,15200,a(flip),b,19187,a),flip(a)].">
      <j1 rule="hyper" parents="333 15200 19187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19199">
    <literal><![CDATA[
      K(x,y \ (T((z * u) \ z,w) \ z)) = K(x,y \ (T(u,w) * z))
    ]]></literal>
    <justification jstring="[hyper(333,a,18596,a(flip),b,19198,a),flip(a)].">
      <j1 rule="hyper" parents="333 18596 19198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19200">
    <literal><![CDATA[
      K(x,y \ T(z * (1 / T(u,w)),z)) = K(x,y \ (T(1 / u,w) * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,15084,a(flip),b,19199,a)].">
      <j1 rule="hyper" parents="63 15084 19199"/>
    </justification>
  </clause>

  <clause id="19201">
    <literal><![CDATA[
      K(x,y \ T(z * (1 / T(u,w)),z)) = K(x,y \ (T(u \ 1,w) * z))
    ]]></literal>
    <justification jstring="[hyper(333,a,5143,a(flip),b,19200,a),flip(a)].">
      <j1 rule="hyper" parents="333 5143 19200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19202">
    <literal><![CDATA[
      K(x,y \ ((1 / T(z,u)) * w)) = K(x,y \ (T(z \ 1,u) * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,12682,a(flip),b,19201,a)].">
      <j1 rule="hyper" parents="63 12682 19201"/>
    </justification>
  </clause>

  <clause id="19203">
    <literal><![CDATA[
      K(x,y \ (T(z \ 1,u) * w)) = K(x,y \ ((T(z,u) \ 1) * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,5013,a(flip),b,19202,a),flip(a)].">
      <j1 rule="hyper" parents="63 5013 19202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19204">
    <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(333,a,10991,a(flip),b,19203,a),flip(a)].">
      <j1 rule="hyper" parents="333 10991 19203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19205">
    <literal><![CDATA[
      K(x,(y * ((y / z) \ 1)) \ (((y / z) \ 1) * u)) = K(x,z \ ((y \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(15141,a,19192,a)].">
      <j1 rule="hyper" parents="15141 19192"/>
    </justification>
  </clause>

  <clause id="19206">
    <literal><![CDATA[
      K(x,y \ ((z / (T(u,z) \ 1)) * w)) = K(x,y \ (((u \ 1) \ z) * w))
    ]]></literal>
    <justification jstring="[hyper(333,a,12797,a(flip),b,19196,a),flip(a)].">
      <j1 rule="hyper" parents="333 12797 19196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19207">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ ((y / z) \ u)) = K(x,z \ ((y \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,14758,a(flip),b,19205,a)].">
      <j1 rule="hyper" parents="63 14758 19205"/>
    </justification>
  </clause>

  <clause id="19208">
    <literal><![CDATA[
      K(x,y \ ((y \ z) \ u)) = K(x,y \ ((z \ y) * u))
    ]]></literal>
    <justification jstring="[para(5074(a,1),19207(a,1,2))].">
      <j1 rule="para" parents="5074 19207"/>
    </justification>
  </clause>

  <clause id="19209">
    <literal><![CDATA[
      T(x,y \ ((y \ z) \ u)) = T(x,y \ ((z \ y) * u))
    ]]></literal>
    <justification jstring="[hyper(124,a,19208,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 19208 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19210">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ (u / (y / z))) = K(x,z \ ((y \ z) * T(u,z / y)))
    ]]></literal>
    <justification jstring="[hyper(63,a,18957,a,b,19208,a)].">
      <j1 rule="hyper" parents="63 18957 19208"/>
    </justification>
  </clause>

  <clause id="19211">
    <literal><![CDATA[
      K(x,y \ (((K(z,y) * u) \ y) * w)) = K(x,y \ ((T(y,z) \ u) \ w))
    ]]></literal>
    <justification jstring="[para(4576(a,1),19208(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4576 19208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19212">
    <literal><![CDATA[
      K(x,K(y,z \ u)) * K(x,y \ ((z \ y) * u)) = K(x,((y \ z) \ u) / y)
    ]]></literal>
    <justification jstring="[para(19208(a,1),10390(a,1,2))].">
      <j1 rule="para" parents="19208 10390"/>
    </justification>
  </clause>

  <clause id="19213">
    <literal><![CDATA[
      T(T(x,K(y,(y \ z) \ u)),y \ ((z \ y) * u)) = T(x,((y \ z) \ u) / y)
    ]]></literal>
    <justification jstring="[hyper(7577,a,19209,a),flip(a)].">
      <j1 rule="hyper" parents="7577 19209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19214">
    <literal><![CDATA[
      K(x,y \ ((T(y,z) \ u) \ w)) = K(x,y \ ((u \ T(y,z)) * w))
    ]]></literal>
    <justification jstring="[para(13231(a,1),19211(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="13231 19211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19215">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ (u / (y / z))) = K(x,z \ T(u * (y \ z),K(y,z)))
    ]]></literal>
    <justification jstring="[para(7770(a,2),19210(a,2,2,2))].">
      <j1 rule="para" parents="7770 19210"/>
    </justification>
  </clause>

  <clause id="19216">
    <literal><![CDATA[
      K(x,((y \ z) \ u) / y) = K(x,((z \ y) * u) / y)
    ]]></literal>
    <justification jstring="[hyper(63,a,13570,a(flip),b,19212,a),flip(a)].">
      <j1 rule="hyper" parents="63 13570 19212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19217">
    <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(3790(a,1),19216(a,2,2,1))].">
      <j1 rule="para" parents="3790 19216"/>
    </justification>
  </clause>

  <clause id="19218">
    <literal><![CDATA[
      T(T(x,K(y,z \ (y * u))),y \ ((z \ y) * u)) = T(x,((y \ z) \ u) / y)
    ]]></literal>
    <justification jstring="[para(9480(a,1),19213(a,1,1,2))].">
      <j1 rule="para" parents="9480 19213"/>
    </justification>
  </clause>

  <clause id="19219">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ (u / (y / z))) = K(x,z \ (u * (y \ z)))
    ]]></literal>
    <justification jstring="[hyper(333,a,16326,a(flip),b,19215,a),flip(a)].">
      <j1 rule="hyper" parents="333 16326 19215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19221">
    <literal><![CDATA[
      K(x,y \ (z / (y \ u))) = K(x,y \ (z * (u \ y)))
    ]]></literal>
    <justification jstring="[hyper(63,a,18695,a(flip),b,19219,a)].">
      <j1 rule="hyper" parents="63 18695 19219"/>
    </justification>
  </clause>

  <clause id="19222">
    <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(6461(a,1),19221(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="6461 19221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19223">
    <literal><![CDATA[
      T(T(x,K(y,z * (y * u))),y \ ((z \ y) * u)) = T(x,((y \ z) \ u) / y)
    ]]></literal>
    <justification jstring="[para(15806(a,1),19218(a,1,1))].">
      <j1 rule="para" parents="15806 19218"/>
    </justification>
  </clause>

  <clause id="19224">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),y \ ((u \ y) * z)) = T(x,((y \ u) \ z) / y)
    ]]></literal>
    <justification jstring="[para(15950(a,1),19223(a,1,1))].">
      <j1 rule="para" parents="15950 19223"/>
    </justification>
  </clause>

  <clause id="19225">
    <literal><![CDATA[
      K(x,((((y \ z) * u) \ u) \ u) / z) = K(x,((z \ y) \ (((z \ y) \ u) * (z \ y))) / z)
    ]]></literal>
    <justification jstring="[para(17312(a,1),19217(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="17312 19217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19226">
    <literal><![CDATA[
      K(x,T((y \ z) \ u,y \ z) / y) = K(x,((((z \ y) * u) \ u) \ u) / y)
    ]]></literal>
    <justification jstring="[para(22(a,2),19225(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="22 19225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19227">
    <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(63,a,17889,a(flip),b,19204,a),flip(a)].">
      <j1 rule="hyper" parents="63 17889 19204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19228">
    <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(333,a,14758,a(flip),b,19227,a),flip(a)].">
      <j1 rule="hyper" parents="333 14758 19227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19229">
    <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(333,a,18667,a(flip),b,19228,a),flip(a)].">
      <j1 rule="hyper" parents="333 18667 19228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19230">
    <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(13261(a,1),18004(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13261 18004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19231">
    <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(3757(a,1),18114(a,1,2,1,1))].">
      <j1 rule="para" parents="3757 18114"/>
    </justification>
  </clause>

  <clause id="19232">
    <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(2983(a,1),19231(a,1,2,1,1))].">
      <j1 rule="para" parents="2983 19231"/>
    </justification>
  </clause>

  <clause id="19234">
    <literal><![CDATA[
      K(x,(T(y,z) / u) * (u / (z \ 1))) = K(x,((((z \ 1) \ u) / u) * u) * (u \ y))
    ]]></literal>
    <justification jstring="[hyper(63,a,16215,a(flip),b,19232,a)].">
      <j1 rule="hyper" parents="63 16215 19232"/>
    </justification>
  </clause>

  <clause id="19235">
    <literal><![CDATA[
      K(x,(T(y,z) / u) * (u / (z \ 1))) = K(x,((z \ 1) \ u) * (u \ y))
    ]]></literal>
    <justification jstring="[para(12(a,1),19234(a,2,2,1))].">
      <j1 rule="para" parents="12 19234"/>
    </justification>
  </clause>

  <clause id="19236">
    <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(63,a,8787,a(flip),b,19235,a)].">
      <j1 rule="hyper" parents="63 8787 19235"/>
    </justification>
  </clause>

  <clause id="19238">
    <literal><![CDATA[
      K(x,((((y * z) \ y) \ y) / u) * (u / T(z,1))) = K(x,(((z \ 1) \ 1) \ u) * (u \ (y * z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,18842,a(flip),b,19236,a)].">
      <j1 rule="hyper" parents="63 18842 19236"/>
    </justification>
  </clause>

  <clause id="19239">
    <literal><![CDATA[
      K(x,(((y \ 1) \ 1) \ z) * (z \ (u * y))) = K(x,((((u * y) \ u) \ u) / z) * (z / y))
    ]]></literal>
    <justification jstring="[para(199(a,1),19238(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="199 19238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19240">
    <literal><![CDATA[
      K(x,(((y \ 1) \ 1) \ z) * (z \ (u * y))) = K(x,(T(u * y,u) / z) * (z / y))
    ]]></literal>
    <justification jstring="[hyper(333,a,16925,a(flip),b,19239,a),flip(a)].">
      <j1 rule="hyper" parents="333 16925 19239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19241">
    <literal><![CDATA[
      K(x,(((y \ 1) \ 1) \ z) * (z \ (u * y))) = K(x,((y * u) / z) * (z / y))
    ]]></literal>
    <justification jstring="[hyper(333,a,18359,a(flip),b,19240,a),flip(a)].">
      <j1 rule="hyper" parents="333 18359 19240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19242">
    <literal><![CDATA[
      K(x,(T(y,1) \ z) * (z \ (u * y))) = K(x,((y * u) / z) * (z / y))
    ]]></literal>
    <justification jstring="[hyper(63,a,18868,a(flip),b,19241,a)].">
      <j1 rule="hyper" parents="63 18868 19241"/>
    </justification>
  </clause>

  <clause id="19243">
    <literal><![CDATA[
      K(x,((y * z) / u) * (u / y)) = K(x,(y \ u) * (u \ (z * y)))
    ]]></literal>
    <justification jstring="[para(199(a,1),19242(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="199 19242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19244">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * ((u \ 1) * (z * (u \ 1)))) = T(x,(((u \ 1) * z) * (u \ 1)) * y)
    ]]></literal>
    <justification jstring="[para(13140(a,1),18267(a,1,1,2))].">
      <j1 rule="para" parents="13140 18267"/>
    </justification>
  </clause>

  <clause id="19246">
    <literal><![CDATA[
      K(x,((K(y,z) * u) * L((K(z,y) \ u) \ u,w,v5)) \ v6) = K(x,(K(z,y) \ u) \ (L(K(y,z),w,v5) * v6))
    ]]></literal>
    <justification jstring="[para(4567(a,1),18288(a,1,2,1,1))].">
      <j1 rule="para" parents="4567 18288"/>
    </justification>
  </clause>

  <clause id="19247">
    <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(4376(a,1),18353(a,1,2,1))].">
      <j1 rule="para" parents="4376 18353"/>
    </justification>
  </clause>

  <clause id="19248">
    <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(63,a,15017,a(flip),b,19033,a)].">
      <j1 rule="hyper" parents="63 15017 19033"/>
    </justification>
  </clause>

  <clause id="19249">
    <literal><![CDATA[
      T((x * y) \ y,K(y,y \ z)) = (x * T(y,y \ z)) \ ((y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,16804,a(flip),b,19248,a)].">
      <j1 rule="hyper" parents="63 16804 19248"/>
    </justification>
  </clause>

  <clause id="19250">
    <literal><![CDATA[
      (x * T(y,y \ z)) \ ((y \ z) \ z) = T((x * y) \ y,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(7215,a,19249,a),flip(a)].">
      <j1 rule="hyper" parents="7215 19249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19251">
    <literal><![CDATA[
      K(x,((K(y,z) * u) * L(K(z,T(y,u)),w,v5)) \ v6) = K(x,(K(z,y) \ u) \ (L(K(y,z),w,v5) * v6))
    ]]></literal>
    <justification jstring="[para(6372(a,1),19246(a,1,2,1,2,1))].">
      <j1 rule="para" parents="6372 19246"/>
    </justification>
  </clause>

  <clause id="19252">
    <literal><![CDATA[
      K(x,(K(y,z) * (u * L(K(z,T(y,u)),w,v5))) \ v6) = K(x,(K(z,y) \ u) \ (L(K(y,z),w,v5) * v6))
    ]]></literal>
    <justification jstring="[para(17548(a,1),19251(a,1,2,1))].">
      <j1 rule="para" parents="17548 19251"/>
    </justification>
  </clause>

  <clause id="19253">
    <literal><![CDATA[
      K(x,(K(y,z) * (L(K(z,y),u,w) * v5)) \ v6) = K(x,(K(z,y) \ v5) \ (L(K(y,z),u,w) * v6))
    ]]></literal>
    <justification jstring="[para(6399(a,1),19252(a,1,2,1,2))].">
      <j1 rule="para" parents="6399 19252"/>
    </justification>
  </clause>

  <clause id="19254">
    <literal><![CDATA[
      K(x,(K(y,z) \ u) \ (L(K(z,y),w,v5) * v6)) = K(x,(a(y,w,K(v5,z)) * u) \ v6)
    ]]></literal>
    <justification jstring="[para(13762(a,1),19253(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13762 19253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19255">
    <literal><![CDATA[
      L(x,a(y,z,K(u,w)),v5) * (v5 * a(y,z,K(u,w))) = (x * a(y,z,K(u,w))) * v5
    ]]></literal>
    <justification jstring="[hyper(38,a,18436,a,b,17677,a),flip(a)].">
      <j1 rule="hyper" parents="38 18436 17677"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19256">
    <literal><![CDATA[
      (x * a(y,z,K(u,w))) * v5 != v6 * (v5 * a(y,z,K(u,w)))
    ]]></literal>
    <literal><![CDATA[
      L(x,a(y,z,K(u,w)),v5) = v6
    ]]></literal>
    <justification jstring="[para(19255(a,1),44(a,1))].">
      <j1 rule="para" parents="19255 44"/>
    </justification>
  </clause>

  <clause id="19258">
    <literal><![CDATA[
      K((x \ (y * a(z,u,K(w,v5)))) \ 1,v6) = x \ (y * T(y \ x,v6))
    ]]></literal>
    <justification jstring="[para(17675(a,1),18130(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="17675 18130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19259">
    <literal><![CDATA[
      K((x \ (y * a(z,u,K(w,v5)))) \ 1,v6) != v7
    ]]></literal>
    <literal><![CDATA[
      K((x \ y) \ 1,v6) = v7
    ]]></literal>
    <justification jstring="[para(19258(a,2),4909(a,1))].">
      <j1 rule="para" parents="19258 4909"/>
    </justification>
  </clause>

  <clause id="19261">
    <literal><![CDATA[
      K((T(x,y) \ y) \ 1,z) = K(((y * a(u,w,K(v5,v6))) / x) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(19259,a,17914,a)].">
      <j1 rule="hyper" parents="19259 17914"/>
    </justification>
  </clause>

  <clause id="19262">
    <literal><![CDATA[
      K(((x * a(y,z,K(u,w))) / v5) \ 1,v6) = K((x / v5) \ 1,v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,18080,a(flip),b,19261,a),flip(a)].">
      <j1 rule="hyper" parents="63 18080 19261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19263">
    <literal><![CDATA[
      K(x / (y * a(z,u,K(w,v5))),v6) = K((y / x) \ 1,v6)
    ]]></literal>
    <justification jstring="[hyper(5090,a,19262,a)].">
      <j1 rule="hyper" parents="5090 19262"/>
    </justification>
  </clause>

  <clause id="19264">
    <literal><![CDATA[
      K(x / (y * a(z,u,K(w,v5))),v6) = K(x / y,v6)
    ]]></literal>
    <justification jstring="[hyper(333,a,4965,a(flip),b,19263,a),flip(a)].">
      <j1 rule="hyper" parents="333 4965 19263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19265">
    <literal><![CDATA[
      K(x / (L(K(y,z),u,w) * v5),v6) = K(x / (K(y,z) * v5),v6)
    ]]></literal>
    <justification jstring="[para(18980(a,1),19264(a,1,1,2))].">
      <j1 rule="para" parents="18980 19264"/>
    </justification>
  </clause>

  <clause id="19266">
    <literal><![CDATA[
      K(x \ (L(K(y,z),u,w) * v5),v6) = K(((x \ v5) * x) / (K(z,y) * x),v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,19028,a(flip),b,19265,a)].">
      <j1 rule="hyper" parents="63 19028 19265"/>
    </justification>
  </clause>

  <clause id="19268">
    <literal><![CDATA[
      K(x \ (L(K(y,z),u,w) * v5),v6) = K(x \ (K(y,z) * (x * (x \ v5))),v6)
    ]]></literal>
    <justification jstring="[hyper(333,a,17806,a(flip),b,19266,a),flip(a)].">
      <j1 rule="hyper" parents="333 17806 19266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19269">
    <literal><![CDATA[
      K(x \ (L(K(y,z),u,w) * v5),v6) = K(x \ (K(y,z) * v5),v6)
    ]]></literal>
    <justification jstring="[para(10(a,1),19268(a,2,1,2,2))].">
      <j1 rule="para" parents="10 19268"/>
    </justification>
  </clause>

  <clause id="19270">
    <literal><![CDATA[
      K(x \ ((K(y,z) * L(K(y,u) \ 1,w,v5)) * v6),v7) = K((x * K(z,y)) \ (K(u,y) * v6),v7)
    ]]></literal>
    <justification jstring="[hyper(63,a,17808,a,b,19269,a)].">
      <j1 rule="hyper" parents="63 17808 19269"/>
    </justification>
  </clause>

  <clause id="19273">
    <literal><![CDATA[
      K(x \ ((K(y,z) * L(K(y,u) \ 1,w,v5)) * v6),v7) = K(x \ (K(y,z) * (K(u,y) * v6)),v7)
    ]]></literal>
    <justification jstring="[hyper(333,a,17762,a(flip),b,19270,a),flip(a)].">
      <j1 rule="hyper" parents="333 17762 19270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19274">
    <literal><![CDATA[
      K(x \ ((K(y,z) * L(K(y,z) \ 1,u,w)) * v5),v6) = K(x \ v5,v6)
    ]]></literal>
    <justification jstring="[para(4558(a,1),19273(a,2,1,2))].">
      <j1 rule="para" parents="4558 19273"/>
    </justification>
  </clause>

  <clause id="19275">
    <literal><![CDATA[
      K(x \ ((K(y,z) * L(K(z,y),u,w)) * v5),v6) = K(x \ v5,v6)
    ]]></literal>
    <justification jstring="[para(4367(a,1),19274(a,1,1,2,1,2,1))].">
      <j1 rule="para" parents="4367 19274"/>
    </justification>
  </clause>

  <clause id="19276">
    <literal><![CDATA[
      K(x \ (a(y,z,K(u,w)) * v5),v6) = K(x \ v5,v6)
    ]]></literal>
    <justification jstring="[para(8769(a,1),19275(a,1,1,2,1))].">
      <j1 rule="para" parents="8769 19275"/>
    </justification>
  </clause>

  <clause id="19277">
    <literal><![CDATA[
      K(x \ ((y * z) * K(u,w)),v5) = K(x \ (y * (z * K(u,w))),v5)
    ]]></literal>
    <justification jstring="[para(13589(a,1),19276(a,1,1,2))].">
      <j1 rule="para" parents="13589 19276"/>
    </justification>
  </clause>

  <clause id="19278">
    <literal><![CDATA[
      K((x * K(y,z)) \ (x * (u * K(y,z))),w) = K(u,w)
    ]]></literal>
    <justification jstring="[hyper(18221,a,19277,a),flip(a)].">
      <j1 rule="hyper" parents="18221 19277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19279">
    <literal><![CDATA[
      K(L(T(x,K(y,z)),K(y,z),u),w) = K(x,w)
    ]]></literal>
    <justification jstring="[para(246(a,1),19278(a,1,1))].">
      <j1 rule="para" parents="246 19278"/>
    </justification>
  </clause>

  <clause id="19280">
    <literal><![CDATA[
      K(L(x,K(y,z),u),T(w,K(y,z))) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(6698,a,19279,a)].">
      <j1 rule="hyper" parents="6698 19279"/>
    </justification>
  </clause>

  <clause id="19281">
    <literal><![CDATA[
      K(L(x,K(y,z),u),w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(15516,a,19280,a)].">
      <j1 rule="hyper" parents="15516 19280"/>
    </justification>
  </clause>

  <clause id="19282">
    <literal><![CDATA[
      K(x,L(y,K(z,u),w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(10963,a,19281,a)].">
      <j1 rule="hyper" parents="10963 19281"/>
    </justification>
  </clause>

  <clause id="19283">
    <literal><![CDATA[
      L(K(x,y),K(z,u),w) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(10925,a,19281,a)].">
      <j1 rule="hyper" parents="10925 19281"/>
    </justification>
  </clause>

  <clause id="19287">
    <literal><![CDATA[
      (x * (K(y,z) * K(u,w))) * K(w,u) = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(126,a,19281,a(flip),b,10897,a)].">
      <j1 rule="hyper" parents="126 19281 10897"/>
    </justification>
  </clause>

  <clause id="19290">
    <literal><![CDATA[
      T(x,L(y,K(z,u),w)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(124,a,19282,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 19282 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19291">
    <literal><![CDATA[
      a(x,K(y,z),K(u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(122,a,19282,a,b,13768,a),flip(a)].">
      <j1 rule="hyper" parents="122 19282 13768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19293">
    <literal><![CDATA[
      K(x,(y / z) / K(u,w)) = K(x,y / (K(u,w) * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,13882,a(flip),b,19282,a),flip(a)].">
      <j1 rule="hyper" parents="63 13882 19282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19294">
    <literal><![CDATA[
      K(x,(y \ z) \ K(u,w)) = K(x,z \ (y * K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,10867,a(flip),b,19282,a),flip(a)].">
      <j1 rule="hyper" parents="63 10867 19282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19295">
    <literal><![CDATA[
      K(x,(y * z) \ (y * K(u,w))) = K(x,z \ K(u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,10855,a(flip),b,19282,a)].">
      <j1 rule="hyper" parents="63 10855 19282"/>
    </justification>
  </clause>

  <clause id="19297">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,w) = x * (K(y,z) * K(u,w))
    ]]></literal>
    <justification jstring="[para(19282(a,1),10874(a,1,2))].">
      <j1 rule="para" parents="19282 10874"/>
    </justification>
  </clause>

  <clause id="19298">
    <literal><![CDATA[
      (K(x,y) * K(z,u)) * w = K(x,y) * (K(z,u) * w)
    ]]></literal>
    <justification jstring="[para(19282(a,1),13872(a,1,1)),flip(a)].">
      <j1 rule="para" parents="19282 13872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19302">
    <literal><![CDATA[
      x \ (K(y,z) * (x * K(u,w))) = K(u,w) * T(K(y,z),x * K(u,w))
    ]]></literal>
    <justification jstring="[para(19283(a,1),665(a,1,2,1))].">
      <j1 rule="para" parents="19283 665"/>
    </justification>
  </clause>

  <clause id="19305">
    <literal><![CDATA[
      L(K(x,y),L(K(z,u),w,v5),v6) = K(x,y)
    ]]></literal>
    <justification jstring="[para(5372(a,1),19283(a,1,2))].">
      <j1 rule="para" parents="5372 19283"/>
    </justification>
  </clause>

  <clause id="19306">
    <literal><![CDATA[
      L(K(x,y),a(z,u,K(w,v5)),v6) = K(x,y)
    ]]></literal>
    <justification jstring="[para(13061(a,1),19283(a,1,2))].">
      <j1 rule="para" parents="13061 19283"/>
    </justification>
  </clause>

  <clause id="19308">
    <literal><![CDATA[
      T(x,(y / z) / K(u,w)) = T(x,y / (K(u,w) * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,13912,a(flip),b,19290,a),flip(a)].">
      <j1 rule="hyper" parents="63 13912 19290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19309">
    <literal><![CDATA[
      T(x,a(y,K(z,u),w)) = x
    ]]></literal>
    <justification jstring="[hyper(40,a,13828,a,b,19290,a)].">
      <j1 rule="hyper" parents="40 13828 19290"/>
    </justification>
  </clause>

  <clause id="19310">
    <literal><![CDATA[
      L(x,K(y,z),u) * T(w,x) = w * L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(126,a,19290,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="126 19290 22"/>
    </justification>
  </clause>

  <clause id="19311">
    <literal><![CDATA[
      L(x,K(y,z),K(u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(15937,a,19309,a)].">
      <j1 rule="hyper" parents="15937 19309"/>
    </justification>
  </clause>

  <clause id="19312">
    <literal><![CDATA[
      T(x,a(y,K(z,u),w)) = v5 / (x \ v5)
    ]]></literal>
    <justification jstring="[hyper(333,a,76,a,b,19309,a),flip(a)].">
      <j1 rule="hyper" parents="333 76 19309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19313">
    <literal><![CDATA[
      T(x,y \ R(y,K(z,u),w)) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,12428,a,b,19309,a)].">
      <j1 rule="hyper" parents="63 12428 19309"/>
    </justification>
  </clause>

  <clause id="19314">
    <literal><![CDATA[
      T(x,a(y,K(z,u),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      x = v5
    ]]></literal>
    <justification jstring="[para(19309(a,1),49(a,2))].">
      <j1 rule="para" parents="19309 49"/>
    </justification>
  </clause>

  <clause id="19315">
    <literal><![CDATA[
      (K(x,y) * K(z,u)) \ w = K(z,u) \ (K(x,y) \ w)
    ]]></literal>
    <justification jstring="[hyper(578,a,19311,a),flip(a)].">
      <j1 rule="hyper" parents="578 19311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19317">
    <literal><![CDATA[
      R(x,K(y,z),K(u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,14460,a,b,19311,a)].">
      <j1 rule="hyper" parents="63 14460 19311"/>
    </justification>
  </clause>

  <clause id="19318">
    <literal><![CDATA[
      L(x,K(y,z),T(u,w)) = L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,14513,a(flip),b,19311,a)].">
      <j1 rule="hyper" parents="63 14513 19311"/>
    </justification>
  </clause>

  <clause id="19319">
    <literal><![CDATA[
      (K(x,y) * K(z,u)) \ w = K(u,z) * (K(y,x) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,5158,a(flip),b,19311,a)].">
      <j1 rule="hyper" parents="63 5158 19311"/>
    </justification>
  </clause>

  <clause id="19333">
    <literal><![CDATA[
      T(x,L(y,K(z,u),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = v5
    ]]></literal>
    <justification jstring="[para(13824(a,1),19314(a,1))].">
      <j1 rule="para" parents="13824 19314"/>
    </justification>
  </clause>

  <clause id="19334">
    <literal><![CDATA[
      T(x * K(y,z),a(u,x,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      x * K(y,z) = v5
    ]]></literal>
    <justification jstring="[para(13998(a,1),19314(a,1))].">
      <j1 rule="para" parents="13998 19314"/>
    </justification>
  </clause>

  <clause id="19335">
    <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(63,a,10875,a(flip),b,19305,a)].">
      <j1 rule="hyper" parents="63 10875 19305"/>
    </justification>
  </clause>

  <clause id="19338">
    <literal><![CDATA[
      L(x,K(y,z),(u \ w) \ w) = L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,11835,a,b,19318,a)].">
      <j1 rule="hyper" parents="63 11835 19318"/>
    </justification>
  </clause>

  <clause id="19339">
    <literal><![CDATA[
      L(x,K(y,z),u / w) = L(x,K(y,z),w \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,11834,a(flip),b,19318,a),flip(a)].">
      <j1 rule="hyper" parents="63 11834 19318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19340">
    <literal><![CDATA[
      (x * (K(y,z) * K(u,w))) / (u * w) = (x * K(y,z)) / (w * u)
    ]]></literal>
    <justification jstring="[hyper(123,a,19287,a(flip),b,10358,a),flip(a)].">
      <j1 rule="hyper" parents="123 19287 10358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19341">
    <literal><![CDATA[
      (x * (K(y,z) * K(u,w))) * K(z,y) = x * K(u,w)
    ]]></literal>
    <justification jstring="[para(15499(a,1),19287(a,1,1,2))].">
      <j1 rule="para" parents="15499 19287"/>
    </justification>
  </clause>

  <clause id="19342">
    <literal><![CDATA[
      K(x,(y / z) / K(u,w)) = K(x,y / (K(w,u) \ z))
    ]]></literal>
    <justification jstring="[para(4567(a,2),19293(a,2,2,2))].">
      <j1 rule="para" parents="4567 19293"/>
    </justification>
  </clause>

  <clause id="19343">
    <literal><![CDATA[
      K(x,y / (K(z,u) * w)) = K(x,(y / w) * K(u,z))
    ]]></literal>
    <justification jstring="[para(5994(a,1),19293(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5994 19293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19344">
    <literal><![CDATA[
      K(x,(y \ z) \ K(u,w)) = K(x,K(u,w) * (z \ y))
    ]]></literal>
    <justification jstring="[hyper(333,a,18574,a(flip),b,19294,a),flip(a)].">
      <j1 rule="hyper" parents="333 18574 19294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19345">
    <literal><![CDATA[
      K(x,(y * z) \ (K(u,w) * y)) = K(x,z \ K(u,w))
    ]]></literal>
    <justification jstring="[hyper(16398,a,19295,a)].">
      <j1 rule="hyper" parents="16398 19295"/>
    </justification>
  </clause>

  <clause id="19346">
    <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(123,a,14500,a,b,19297,a)].">
      <j1 rule="hyper" parents="123 14500 19297"/>
    </justification>
  </clause>

  <clause id="19349">
    <literal><![CDATA[
      (K(x,y) * K(z,u)) * w = K(z,u) * (K(x,y) * w)
    ]]></literal>
    <justification jstring="[hyper(333,a,17851,a,b,19298,a),flip(a)].">
      <j1 rule="hyper" parents="333 17851 19298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19352">
    <literal><![CDATA[
      T(x,(y / z) / K(u,w)) = T(x,y / (K(w,u) \ z))
    ]]></literal>
    <justification jstring="[para(4567(a,2),19308(a,2,2,2))].">
      <j1 rule="para" parents="4567 19308"/>
    </justification>
  </clause>

  <clause id="19353">
    <literal><![CDATA[
      (K(x,y) \ K(z,u)) \ w = K(z,u) \ (K(y,x) \ w)
    ]]></literal>
    <justification jstring="[para(4567(a,2),19315(a,1,1))].">
      <j1 rule="para" parents="4567 19315"/>
    </justification>
  </clause>

  <clause id="19354">
    <literal><![CDATA[
      K(x,K(y,z)) \ (K(y,x) \ u) = K(y,T(x,z)) \ u
    ]]></literal>
    <justification jstring="[para(6819(a,1),19315(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6819 19315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19355">
    <literal><![CDATA[
      (K(x,y) \ (K(z,u) \ w)) / w = K(y,x) * K(u,z)
    ]]></literal>
    <justification jstring="[hyper(598,a,19319,a)].">
      <j1 rule="hyper" parents="598 19319"/>
    </justification>
  </clause>

  <clause id="19363">
    <literal><![CDATA[
      x * K(a(y,x,z),L(x,u,w)) = T(x,a(w,u,a(y,x,z)))
    ]]></literal>
    <justification jstring="[hyper(19334,a,15925,a)].">
      <j1 rule="hyper" parents="19334 15925"/>
    </justification>
  </clause>

  <clause id="19364">
    <literal><![CDATA[
      (x * (K(y,z) * K(u,w))) * (K(z,y) * K(w,u)) = x
    ]]></literal>
    <justification jstring="[hyper(35,a,19287,a(flip),b,19341,a),flip(a)].">
      <j1 rule="hyper" parents="35 19287 19341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19365">
    <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(19342(a,1),15599(a,1))].">
      <j1 rule="para" parents="19342 15599"/>
    </justification>
  </clause>

  <clause id="19366">
    <literal><![CDATA[
      K(x,y / (K(z,u) * w)) = K(x,K(u,z) * (y / w))
    ]]></literal>
    <justification jstring="[hyper(333,a,15489,a,b,19343,a),flip(a)].">
      <j1 rule="hyper" parents="333 15489 19343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19367">
    <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(19343(a,2),15533(a,1))].">
      <j1 rule="para" parents="19343 15533"/>
    </justification>
  </clause>

  <clause id="19368">
    <literal><![CDATA[
      K(x,K(y,z) * ((y * (z \ u)) \ u)) = K(x,T((y * (z \ u)) \ u,y))
    ]]></literal>
    <justification jstring="[hyper(16900,a,19344,a),flip(a)].">
      <j1 rule="hyper" parents="16900 19344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19369">
    <literal><![CDATA[
      K(x,(y \ z) \ K(z,u)) = K(x,T(z,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(333,a,14930,a(flip),b,19344,a),flip(a)].">
      <j1 rule="hyper" parents="333 14930 19344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19370">
    <literal><![CDATA[
      T(x,(y \ z) \ K(z,u)) = T(x,T(z,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(124,a,19369,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 19369 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19371">
    <literal><![CDATA[
      K(x,y / (z * K(u,w))) = K(x,(z / y) \ K(w,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,19095,a(flip),b,19345,a)].">
      <j1 rule="hyper" parents="63 19095 19345"/>
    </justification>
  </clause>

  <clause id="19372">
    <literal><![CDATA[
      K(x,L(T(y,z),u,w)) * (K(y,T(x,z)) * (z \ x)) = (z \ T(x,y)) * L(K(y,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,14786,a(flip),b,19349,a),flip(a)].">
      <j1 rule="hyper" parents="63 14786 19349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19375">
    <literal><![CDATA[
      T(x,y / (K(z,u) \ w)) = T(x,K(u,z) \ (y / w))
    ]]></literal>
    <justification jstring="[hyper(15593,a,19352,a),flip(a)].">
      <j1 rule="hyper" parents="15593 19352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19376">
    <literal><![CDATA[
      (L(K(x,y),z,u) \ K(w,v5)) \ v6 = K(L(y,z,u),x) \ (K(w,v5) \ v6)
    ]]></literal>
    <justification jstring="[para(15699(a,2),19353(a,1,1))].">
      <j1 rule="para" parents="15699 19353"/>
    </justification>
  </clause>

  <clause id="19377">
    <literal><![CDATA[
      (x * K(y,z)) * L(u,x,K(y,z)) = K(z,T(y,x)) \ (x * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,18306,a(flip),b,19354,a)].">
      <j1 rule="hyper" parents="63 18306 19354"/>
    </justification>
  </clause>

  <clause id="19378">
    <literal><![CDATA[
      K(K(x,T(y,z)) \ u,w) = K(K(x,y) \ u,w)
    ]]></literal>
    <justification jstring="[para(19354(a,1),16350(a,1,1))].">
      <j1 rule="para" parents="19354 16350"/>
    </justification>
  </clause>

  <clause id="19379">
    <literal><![CDATA[
      K(x,y) \ (K(z,u) \ w) = (K(z,u) \ K(y,x)) * w
    ]]></literal>
    <justification jstring="[hyper(15649,a,19355,a),flip(a)].">
      <j1 rule="hyper" parents="15649 19355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19380">
    <literal><![CDATA[
      K(x,y) \ (K(z,u) \ w) = (K(x,y) \ K(u,z)) * w
    ]]></literal>
    <justification jstring="[hyper(4586,a,19355,a),flip(a)].">
      <j1 rule="hyper" parents="4586 19355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19381">
    <literal><![CDATA[
      (K(x,y) \ (K(z,u) \ w)) / w = K(x,y) \ K(u,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,4567,a,b,19355,a),flip(a)].">
      <j1 rule="hyper" parents="333 4567 19355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19382">
    <literal><![CDATA[
      x / (K(y,z) * K(u,w)) = x * (K(z,y) * K(w,u))
    ]]></literal>
    <justification jstring="[hyper(339,a,19364,a),flip(a)].">
      <j1 rule="hyper" parents="339 19364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19384">
    <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(19364(a,1),268(a,1,1)),flip(b)].">
      <j1 rule="para" parents="19364 268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19385">
    <literal><![CDATA[
      K(x,K(y,z) * (u / (w \ z))) = K(x,u / (w \ T(z,y)))
    ]]></literal>
    <justification jstring="[hyper(16450,a,19366,a),flip(a)].">
      <j1 rule="hyper" parents="16450 19366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19386">
    <literal><![CDATA[
      K(x,K(y,z) * (u / w)) = K(x,u * (w \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(13519,a,19366,a),flip(a)].">
      <j1 rule="hyper" parents="13519 19366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19387">
    <literal><![CDATA[
      K(x,K(y,z) * (u / (w \ z))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,u / (w \ T(z,y))) = v5
    ]]></literal>
    <justification jstring="[para(19366(a,1),16450(a,1))].">
      <j1 rule="para" parents="19366 16450"/>
    </justification>
  </clause>

  <clause id="19388">
    <literal><![CDATA[
      K(x,y / (K(z,u) * w)) = K(x,(w / y) \ K(u,z))
    ]]></literal>
    <justification jstring="[hyper(16449,a,19371,a)].">
      <j1 rule="hyper" parents="16449 19371"/>
    </justification>
  </clause>

  <clause id="19390">
    <literal><![CDATA[
      T(x,y / (z * K(u,w))) = T(x,(z / y) \ K(w,u))
    ]]></literal>
    <justification jstring="[hyper(124,a,19371,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 19371 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19391">
    <literal><![CDATA[
      K(x,(y / z) \ K(z,u)) = K(x,T(z,u) / y)
    ]]></literal>
    <justification jstring="[para(13256(a,1),19371(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13256 19371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19394">
    <literal><![CDATA[
      K(x,(y / (z * K(u,w))) \ K(z,u)) = K(x,T(z * K(u,w),u) / y)
    ]]></literal>
    <justification jstring="[para(7395(a,1),19391(a,1,2,2))].">
      <j1 rule="para" parents="7395 19391"/>
    </justification>
  </clause>

  <clause id="19395">
    <literal><![CDATA[
      K(x,(y / (z * K(u,w))) \ K(z,T(z \ u,w))) = K(x,T(z * K(u,w),z \ u) / y)
    ]]></literal>
    <justification jstring="[para(15656(a,1),19391(a,1,2,2))].">
      <j1 rule="para" parents="15656 19391"/>
    </justification>
  </clause>

  <clause id="19396">
    <literal><![CDATA[
      T(x,(K(y,z) \ u) / w) = T(x,K(y,z) \ (u / w))
    ]]></literal>
    <justification jstring="[hyper(18124,a,19375,a)].">
      <j1 rule="hyper" parents="18124 19375"/>
    </justification>
  </clause>

  <clause id="19397">
    <literal><![CDATA[
      K(x,y) \ (K(z,u) \ w) = K(z,u) \ (K(x,y) \ w)
    ]]></literal>
    <justification jstring="[hyper(333,a,19379,a,b,19380,a)].">
      <j1 rule="hyper" parents="333 19379 19380"/>
    </justification>
  </clause>

  <clause id="19398">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ T(w,u))) = K(x,w * (u \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,18147,a,b,19386,a)].">
      <j1 rule="hyper" parents="63 18147 19386"/>
    </justification>
  </clause>

  <clause id="19399">
    <literal><![CDATA[
      K(x,K(y,z) * (u / y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u / T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(19386(a,2),18107(a,1))].">
      <j1 rule="para" parents="19386 18107"/>
    </justification>
  </clause>

  <clause id="19400">
    <literal><![CDATA[
      K(x,(y / z) \ K(u,w)) = K(x,K(u,w) * (z / y))
    ]]></literal>
    <justification jstring="[hyper(63,a,19366,a(flip),b,19388,a),flip(a)].">
      <j1 rule="hyper" parents="63 19366 19388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19401">
    <literal><![CDATA[
      T(x,(y / z) \ K(u,y)) = T(x,z / T(y,u))
    ]]></literal>
    <justification jstring="[para(4222(a,2),19390(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4222 19390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19402">
    <literal><![CDATA[
      T(x,(y \ z) / T(z,u)) = T(x,y \ K(u,z))
    ]]></literal>
    <justification jstring="[para(76(a,1),19401(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="76 19401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19403">
    <literal><![CDATA[
      T(x,K(y,z) \ ((T(z,y) \ u) / w)) = T(x,(z \ u) / w)
    ]]></literal>
    <justification jstring="[para(4548(a,1),19396(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4548 19396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19404">
    <literal><![CDATA[
      K(x,y) \ (K(z,u) \ y) = K(z,u) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(4233(a,2),19397(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4233 19397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19405">
    <literal><![CDATA[
      K(x,y) \ (K(z,u) \ T(w,K(x,y))) = K(z,u) \ (w * K(y,x))
    ]]></literal>
    <justification jstring="[para(6853(a,1),19397(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6853 19397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19406">
    <literal><![CDATA[
      K(x,(y / z) \ K(y,u)) = K(x,z / T(y,u))
    ]]></literal>
    <justification jstring="[hyper(333,a,15638,a(flip),b,19400,a),flip(a)].">
      <j1 rule="hyper" parents="333 15638 19400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19407">
    <literal><![CDATA[
      K(x,K(y,z) \ (u / y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u / T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(14929(a,2),19399(a,1))].">
      <j1 rule="para" parents="14929 19399"/>
    </justification>
  </clause>

  <clause id="19408">
    <literal><![CDATA[
      K(x,(y / z) \ K(y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,z / T(y,u)) = w
    ]]></literal>
    <justification jstring="[para(19400(a,2),19399(a,1))].">
      <j1 rule="para" parents="19400 19399"/>
    </justification>
  </clause>

  <clause id="19409">
    <literal><![CDATA[
      K(x,y / (z * (u / z))) = K(x,y / T(u,z))
    ]]></literal>
    <justification jstring="[hyper(19407,a,15912,a),flip(a)].">
      <j1 rule="hyper" parents="19407 15912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19411">
    <literal><![CDATA[
      K(x,y / ((z \ 1) * (u / (1 / z)))) = K(x,y / T(u,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,5026,a,b,19409,a)].">
      <j1 rule="hyper" parents="63 5026 19409"/>
    </justification>
  </clause>

  <clause id="19412">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ 1)) / T(z \ 1,u)) = K(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,14651,a(flip),b,19409,a),flip(a)].">
      <j1 rule="hyper" parents="63 14651 19409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19413">
    <literal><![CDATA[
      K(x,y / T(z * u,u)) = K(x,y / (u * z))
    ]]></literal>
    <justification jstring="[para(11(a,1),19409(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="11 19409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19414">
    <literal><![CDATA[
      K(x,y / T(z \ u,u)) = K(x,y / (z \ T(u,z \ 1)))
    ]]></literal>
    <justification jstring="[para(3107(a,2),19409(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3107 19409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19415">
    <literal><![CDATA[
      K(x,y * (((z \ 1) * u) \ K(u,z))) = K(x,y / (u * (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(63,a,18880,a,b,19413,a)].">
      <j1 rule="hyper" parents="63 18880 19413"/>
    </justification>
  </clause>

  <clause id="19416">
    <literal><![CDATA[
      K(x,(y / z) \ K(y,u / (w * v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,z / T(y,L((u / v5) / w,w,v5))) = v6
    ]]></literal>
    <justification jstring="[para(13882(a,1),19408(a,1,2,2))].">
      <j1 rule="para" parents="13882 19408"/>
    </justification>
  </clause>

  <clause id="19417">
    <literal><![CDATA[
      x * a(y,x,K(z,L(x,u,w))) = T(x,a(w,u,a(y,x,z)))
    ]]></literal>
    <justification jstring="[para(13539(a,2),19363(a,1,2))].">
      <j1 rule="para" parents="13539 19363"/>
    </justification>
  </clause>

  <clause id="19418">
    <literal><![CDATA[
      K(x,y / (z \ T(u,K(w,v5)))) = K(x,y / (z \ u))
    ]]></literal>
    <justification jstring="[hyper(16379,a,19385,a),flip(a)].">
      <j1 rule="hyper" parents="16379 19385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19419">
    <literal><![CDATA[
      K(x,y / (z \ (K(u,w) * v5))) = K(x,y / (z \ (v5 * K(u,w))))
    ]]></literal>
    <justification jstring="[para(6019(a,1),19418(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="6019 19418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19420">
    <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),19418(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14912 19418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19421">
    <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(18853,a,19398,a)].">
      <j1 rule="hyper" parents="18853 19398"/>
    </justification>
  </clause>

  <clause id="19422">
    <literal><![CDATA[
      T(x,(((y \ T(z,y)) \ z) \ z) / u) = T(x,(y \ z) / u)
    ]]></literal>
    <justification jstring="[hyper(63,a,15286,a,b,19403,a)].">
      <j1 rule="hyper" parents="63 15286 19403"/>
    </justification>
  </clause>

  <clause id="19423">
    <literal><![CDATA[
      K(x,y / (z \ T(u,z \ 1))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (u / z)) = w
    ]]></literal>
    <justification jstring="[para(19414(a,1),15138(a,1))].">
      <j1 rule="para" parents="19414 15138"/>
    </justification>
  </clause>

  <clause id="19424">
    <literal><![CDATA[
      T(x,a(y,z,a(u,x,w))) = x * 1
    ]]></literal>
    <justification jstring="[para(9537(a,1),19417(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9537 19417"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19425">
    <literal><![CDATA[
      T(x,a(y,z,a(u,x,w))) = x
    ]]></literal>
    <justification jstring="[hyper(333,a,8,a(flip),b,19424,a),flip(a)].">
      <j1 rule="hyper" parents="333 8 19424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19426">
    <literal><![CDATA[
      a(x,y,a(z,x,K(u,w))) = 1
    ]]></literal>
    <justification jstring="[hyper(34,a,13798,a,b,19424,a(flip))].">
      <j1 rule="hyper" parents="34 13798 19424"/>
    </justification>
  </clause>

  <clause id="19428">
    <literal><![CDATA[
      T(x,L(a(y,x,z),u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(14566,a,19425,a)].">
      <j1 rule="hyper" parents="14566 19425"/>
    </justification>
  </clause>

  <clause id="19429">
    <literal><![CDATA[
      L(a(x,y,K(z,u)),w,y) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(52,a,19426,a)].">
      <j1 rule="hyper" parents="52 19426"/>
    </justification>
  </clause>

  <clause id="19430">
    <literal><![CDATA[
      T(a(x,y,z),a(y,u,w)) = (y * a(x,y,z)) / y
    ]]></literal>
    <justification jstring="[para(19428(a,1),13806(a,1,2)),flip(a)].">
      <j1 rule="para" parents="19428 13806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19431">
    <literal><![CDATA[
      a(x,y,K(z,L(u,w,y))) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,13644,a,b,19429,a)].">
      <j1 rule="hyper" parents="63 13644 19429"/>
    </justification>
  </clause>

  <clause id="19432">
    <literal><![CDATA[
      K(x,L(y,z,L(u,w,z))) = K(x,y) * a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[para(19431(a,1),13765(a,1,2)),flip(a)].">
      <j1 rule="para" parents="19431 13765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19433">
    <literal><![CDATA[
      T(a(x,y,z),a(y,u,w)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,13830,a(flip),b,19430,a),flip(a)].">
      <j1 rule="hyper" parents="333 13830 19430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19434">
    <literal><![CDATA[
      T(a(x,y,z),a(u,w,y)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(13812,a,19433,a)].">
      <j1 rule="hyper" parents="13812 19433"/>
    </justification>
  </clause>

  <clause id="19435">
    <literal><![CDATA[
      T(a(x,y,z),a(u,x,w)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(54,a,19433,a)].">
      <j1 rule="hyper" parents="54 19433"/>
    </justification>
  </clause>

  <clause id="19436">
    <literal><![CDATA[
      T(a(x,y,z),a(u,z,w)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(54,a,19434,a)].">
      <j1 rule="hyper" parents="54 19434"/>
    </justification>
  </clause>

  <clause id="19437">
    <literal><![CDATA[
      L(a(x,y,z),x,K(u,w)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(15937,a,19435,a)].">
      <j1 rule="hyper" parents="15937 19435"/>
    </justification>
  </clause>

  <clause id="19438">
    <literal><![CDATA[
      L(a(x,y,z),z,K(u,w)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(15937,a,19436,a)].">
      <j1 rule="hyper" parents="15937 19436"/>
    </justification>
  </clause>

  <clause id="19439">
    <literal><![CDATA[
      R(K(x,y),z,L(a(z,u,w),z,K(x,y))) = (K(x,y) * (z * a(z,u,w))) / (z * a(z,u,w))
    ]]></literal>
    <justification jstring="[para(19437(a,1),500(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="19437 500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19440">
    <literal><![CDATA[
      R(K(x,y),z,L(a(u,w,z),z,K(x,y))) = (K(x,y) * (z * a(u,w,z))) / (z * a(u,w,z))
    ]]></literal>
    <justification jstring="[para(19438(a,1),500(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="19438 500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19441">
    <literal><![CDATA[
      K(x,L(y,z,L(u,w,z))) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(333,a,13765,a(flip),b,19432,a),flip(a)].">
      <j1 rule="hyper" parents="333 13765 19432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19442">
    <literal><![CDATA[
      K(x,L(y,z,(z * u) \ w)) = K(x,L(y,z,u \ (z \ w)))
    ]]></literal>
    <justification jstring="[para(311(a,1),19441(a,1,2,3))].">
      <j1 rule="para" parents="311 19441"/>
    </justification>
  </clause>

  <clause id="19444">
    <literal><![CDATA[
      T(x,T(T(y,z) \ z,y) / u) = T(x,(y \ z) / u)
    ]]></literal>
    <justification jstring="[para(6753(a,1),19422(a,1,2,1))].">
      <j1 rule="para" parents="6753 19422"/>
    </justification>
  </clause>

  <clause id="19445">
    <literal><![CDATA[
      T(x,(y / T(z,y)) / u) = T(x,(z \ y) / u)
    ]]></literal>
    <justification jstring="[hyper(63,a,16418,a(flip),b,19444,a)].">
      <j1 rule="hyper" parents="63 16418 19444"/>
    </justification>
  </clause>

  <clause id="19446">
    <literal><![CDATA[
      T(x,(y \ z) / T(u,y \ z)) = T(x,u \ (z / T(y,z)))
    ]]></literal>
    <justification jstring="[hyper(12691,a,19445,a),flip(a)].">
      <j1 rule="hyper" parents="12691 19445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19447">
    <literal><![CDATA[
      T(x,y \ (z / T(u,z))) = T(x,y \ (u \ z))
    ]]></literal>
    <justification jstring="[hyper(12685,a,19446,a),flip(a)].">
      <j1 rule="hyper" parents="12685 19446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19448">
    <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(19447(a,1),4599(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="19447 4599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19449">
    <literal><![CDATA[
      K(x,K(y \ 1,z * y) \ (u / z)) = K(x,u / ((y \ 1) * (z / (1 / y))))
    ]]></literal>
    <justification jstring="[hyper(19365,a,8583,a)].">
      <j1 rule="hyper" parents="19365 8583"/>
    </justification>
  </clause>

  <clause id="19450">
    <literal><![CDATA[
      K(x,(y / z) \ K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,w) * (z / y)) = v5
    ]]></literal>
    <justification jstring="[para(19388(a,1),19367(a,1))].">
      <j1 rule="para" parents="19388 19367"/>
    </justification>
  </clause>

  <clause id="19451">
    <literal><![CDATA[
      a(x,K(y,T(z,u)) \ (u * (w / u)),x) = a(x,w * K(z,y),x)
    ]]></literal>
    <justification jstring="[para(19377(a,1),14541(a,1,2))].">
      <j1 rule="para" parents="19377 14541"/>
    </justification>
  </clause>

  <clause id="19452">
    <literal><![CDATA[
      K(x,K(y,z) \ (u * w)) \ K(x,K(u,w)) = K(K(y,T(z,w)) \ (w * u),x)
    ]]></literal>
    <justification jstring="[para(19377(a,1),19072(a,1,1)),flip(a)].">
      <j1 rule="para" parents="19377 19072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19453">
    <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(19423,a,14792,a)].">
      <j1 rule="hyper" parents="19423 14792"/>
    </justification>
  </clause>

  <clause id="19454">
    <literal><![CDATA[
      (x * K(y,z)) / (z * y) = x / (T(z,y) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,16776,a(flip),b,19340,a),flip(a)].">
      <j1 rule="hyper" parents="63 16776 19340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19455">
    <literal><![CDATA[
      (x / (y * z)) * K(z,y) = x / (T(y,z) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,10451,a(flip),b,19454,a)].">
      <j1 rule="hyper" parents="63 10451 19454"/>
    </justification>
  </clause>

  <clause id="19456">
    <literal><![CDATA[
      K(x \ (K(y,z) \ u),x) \ (u * K(z,y)) = K(y,z) \ (x * T(u / x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(19161(a,1),19405(a,1,2)),flip(a)].">
      <j1 rule="para" parents="19161 19405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19457">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ 1)) * T(z,u)) = K(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[hyper(18050,a,19412,a)].">
      <j1 rule="hyper" parents="18050 19412"/>
    </justification>
  </clause>

  <clause id="19458">
    <literal><![CDATA[
      K(x,T(y,z * u) * T(u,z)) = K(x,T(u * y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,16932,a(flip),b,19457,a)].">
      <j1 rule="hyper" parents="63 16932 19457"/>
    </justification>
  </clause>

  <clause id="19459">
    <literal><![CDATA[
      K(x,T(y * ((z * y) \ u),z)) = K(x,(u / (y * z)) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,15249,a(flip),b,19458,a),flip(a)].">
      <j1 rule="hyper" parents="63 15249 19458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19460">
    <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(8558(a,1),19458(a,1,2,1))].">
      <j1 rule="para" parents="8558 19458"/>
    </justification>
  </clause>

  <clause id="19461">
    <literal><![CDATA[
      K(x,y * ((z * y) \ T(u,z))) = K(x,(u / (y * z)) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,18355,a(flip),b,19459,a)].">
      <j1 rule="hyper" parents="63 18355 19459"/>
    </justification>
  </clause>

  <clause id="19462">
    <literal><![CDATA[
      K(x,y * ((T(z,u) * y) \ u)) = K(x,(u / (y * z)) * y)
    ]]></literal>
    <justification jstring="[para(13234(a,2),19461(a,1,2,2))].">
      <j1 rule="para" parents="13234 19461"/>
    </justification>
  </clause>

  <clause id="19463">
    <literal><![CDATA[
      K(x,y / ((z \ 1) * T(u,z))) = K(x,y / (u * (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(63,a,18106,a(flip),b,19415,a)].">
      <j1 rule="hyper" parents="63 18106 19415"/>
    </justification>
  </clause>

  <clause id="19464">
    <literal><![CDATA[
      x \ (K(y,z) \ (x * K(u,w))) = K(u,w) * T(K(z,y),x * K(u,w))
    ]]></literal>
    <justification jstring="[para(4567(a,2),19302(a,1,2))].">
      <j1 rule="para" parents="4567 19302"/>
    </justification>
  </clause>

  <clause id="19465">
    <literal><![CDATA[
      K(x,T((y * (z \ u)) \ u,y)) = K(x,(T(y,z) * (z \ u)) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,18625,a(flip),b,19368,a),flip(a)].">
      <j1 rule="hyper" parents="63 18625 19368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19466">
    <literal><![CDATA[
      K(x,T((y * (z \ u)) \ u,y)) = K(x,u / ((u / z) * y))
    ]]></literal>
    <justification jstring="[hyper(333,a,18727,a(flip),b,19465,a),flip(a)].">
      <j1 rule="hyper" parents="333 18727 19465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19467">
    <literal><![CDATA[
      (L(K(x,y),z,u) \ K(w,v5)) \ v6 = L(K(y,x),z,u) \ (K(w,v5) \ v6)
    ]]></literal>
    <justification jstring="[para(10894(a,2),19376(a,2,1))].">
      <j1 rule="para" parents="10894 19376"/>
    </justification>
  </clause>

  <clause id="19468">
    <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(6054(a,2),19420(a,1,2,2))].">
      <j1 rule="para" parents="6054 19420"/>
    </justification>
  </clause>

  <clause id="19469">
    <literal><![CDATA[
      x \ (K(y,z) \ (x * K(u,w))) = K(u,w) * T(K(z,y),K(w,u) \ x)
    ]]></literal>
    <justification jstring="[para(15539(a,2),19464(a,2,2))].">
      <j1 rule="para" parents="15539 19464"/>
    </justification>
  </clause>

  <clause id="19470">
    <literal><![CDATA[
      L(K(x,y),z,u) \ (K(y,x) \ w) = a(K(x,y),z,u) \ w
    ]]></literal>
    <justification jstring="[para(13939(a,1),19467(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13939 19467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19471">
    <literal><![CDATA[
      a(K(x,y),z,u) \ (K(x,y) \ w) = L(K(x,y),z,u) \ w
    ]]></literal>
    <justification jstring="[para(4568(a,1),19470(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4568 19470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19472">
    <literal><![CDATA[
      T(x,K(y,z) \ (u * (K(z,y) \ w))) = T(x,u * (a(K(y,z),v5,v6) \ w))
    ]]></literal>
    <justification jstring="[para(19470(a,1),18291(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="19470 18291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19473">
    <literal><![CDATA[
      x \ (K(y,z) \ (x * K(u,w))) = K(u,w) * K(z,T(y,K(w,u) \ x))
    ]]></literal>
    <justification jstring="[hyper(333,a,6389,a,b,19469,a),flip(a)].">
      <j1 rule="hyper" parents="333 6389 19469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19474">
    <literal><![CDATA[
      K(x,y) \ K(z,T(u,K(x,y) \ w)) = w \ (K(u,z) \ (w * K(y,x)))
    ]]></literal>
    <justification jstring="[hyper(333,a,4567,a,b,19473,a)].">
      <j1 rule="hyper" parents="333 4567 19473"/>
    </justification>
  </clause>

  <clause id="19475">
    <literal><![CDATA[
      x \ (K(y,z) \ (x * K(u,w))) = K(w,u) \ K(z,T(y,x))
    ]]></literal>
    <justification jstring="[para(16534(a,1),19474(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16534 19474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19476">
    <literal><![CDATA[
      K(x,y) \ K(z,T(u,x * y)) = (x * y) \ (K(u,z) \ (y * x))
    ]]></literal>
    <justification jstring="[para(88(a,1),19475(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="88 19475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19478">
    <literal><![CDATA[
      K(x,y) \ K(z,T(u,y \ x)) = (x * y) \ (K(u,z) \ (y * x))
    ]]></literal>
    <justification jstring="[para(15398(a,2),19476(a,1,2))].">
      <j1 rule="para" parents="15398 19476"/>
    </justification>
  </clause>

  <clause id="19479">
    <literal><![CDATA[
      K(x,y) \ (K(T(z,y \ x),u) \ w) = ((x * y) \ (K(z,u) \ (y * x))) * w
    ]]></literal>
    <justification jstring="[hyper(125,a,19478,a(flip),b,19381,a),flip(a)].">
      <j1 rule="hyper" parents="125 19478 19381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19480">
    <literal><![CDATA[
      K(x,y) \ (y * K(z,T(u,y \ x))) = y * ((x * y) \ (K(u,z) \ (y * x)))
    ]]></literal>
    <justification jstring="[para(19478(a,1),4858(a,2,2))].">
      <j1 rule="para" parents="19478 4858"/>
    </justification>
  </clause>

  <clause id="19481">
    <literal><![CDATA[
      T(x,y * (a(K(z,u),w,v5) \ v6)) = T(x,y * v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,17952,a(flip),b,19472,a),flip(a)].">
      <j1 rule="hyper" parents="63 17952 19472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19483">
    <literal><![CDATA[
      K(x,K(y,z) \ (u / y)) = K(x,u / ((z \ 1) * (y / (1 / z))))
    ]]></literal>
    <justification jstring="[hyper(63,a,15037,a(flip),b,19449,a)].">
      <j1 rule="hyper" parents="63 15037 19449"/>
    </justification>
  </clause>

  <clause id="19484">
    <literal><![CDATA[
      K(x,y / ((z \ 1) * (u / (1 / z)))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / T(u,z)) = w
    ]]></literal>
    <justification jstring="[para(19483(a,1),19407(a,1))].">
      <j1 rule="para" parents="19483 19407"/>
    </justification>
  </clause>

  <clause id="19485">
    <literal><![CDATA[
      K(x,y / T(z,u \ 1)) = K(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[hyper(19484,a,19411,a),flip(a)].">
      <j1 rule="hyper" parents="19484 19411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19486">
    <literal><![CDATA[
      K(x,(1 / y) / T(z,y)) = K(x,z \ (1 / y))
    ]]></literal>
    <justification jstring="[hyper(16467,a,19485,a),flip(a)].">
      <j1 rule="hyper" parents="16467 19485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19487">
    <literal><![CDATA[
      K(x,(1 / y) / (z / y)) = K(x,(y \ z) \ (1 / y))
    ]]></literal>
    <justification jstring="[hyper(63,a,15165,a(flip),b,19486,a)].">
      <j1 rule="hyper" parents="63 15165 19486"/>
    </justification>
  </clause>

  <clause id="19488">
    <literal><![CDATA[
      K(x,(y \ 1) / (z / y)) = K(x,(y \ z) \ (1 / y))
    ]]></literal>
    <justification jstring="[hyper(63,a,4794,a(flip),b,19487,a)].">
      <j1 rule="hyper" parents="63 4794 19487"/>
    </justification>
  </clause>

  <clause id="19489">
    <literal><![CDATA[
      K(x,(y \ 1) / (z / y)) = K(x,(y \ z) \ (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(333,a,4800,a(flip),b,19488,a),flip(a)].">
      <j1 rule="hyper" parents="333 4800 19488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19490">
    <literal><![CDATA[
      K(x,K(y,(z \ u) \ (z \ 1)) \ ((u / z) \ w)) = K(x,(T(u,y) / z) \ w)
    ]]></literal>
    <justification jstring="[para(19489(a,1),19129(a,1,2,1))].">
      <j1 rule="para" parents="19489 19129"/>
    </justification>
  </clause>

  <clause id="19491">
    <literal><![CDATA[
      K(x,K(y,z) \ (u * w)) \ K(x,K(u,w)) = K(K(y,z) \ (w * u),x)
    ]]></literal>
    <justification jstring="[hyper(333,a,19378,a(flip),b,19452,a),flip(a)].">
      <j1 rule="hyper" parents="333 19378 19452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19493">
    <literal><![CDATA[
      K(x * (T(y,z) \ (y * u)),w) = K(K(y,z) \ (x * u),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,18876,a,b,19491,a)].">
      <j1 rule="hyper" parents="63 18876 19491"/>
    </justification>
  </clause>

  <clause id="19494">
    <literal><![CDATA[
      K(K(x,y) \ (z * (u / x)),w) = K(z * (u / T(x,T(y,u))),w)
    ]]></literal>
    <justification jstring="[para(7893(a,1),19493(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7893 19493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19495">
    <literal><![CDATA[
      K(K(x,y) \ (z * (u / x)),w) = K(z * (u / T(x,y)),w)
    ]]></literal>
    <justification jstring="[hyper(333,a,16764,a(flip),b,19494,a),flip(a)].">
      <j1 rule="hyper" parents="333 16764 19494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19496">
    <literal><![CDATA[
      K(K(x,y) \ (z * (u / y)),w) = K(z * (u / T(y,x)),w)
    ]]></literal>
    <justification jstring="[hyper(15785,a,19495,a)].">
      <j1 rule="hyper" parents="15785 19495"/>
    </justification>
  </clause>

  <clause id="19498">
    <literal><![CDATA[
      K(x / T(y,z),u) \ K(u * (x / T(y,z)),u) = a(u,y \ (K(y \ 1,z) \ x),u)
    ]]></literal>
    <justification jstring="[para(19496(a,1),17209(a,1,2))].">
      <j1 rule="para" parents="19496 17209"/>
    </justification>
  </clause>

  <clause id="19499">
    <literal><![CDATA[
      K(x,T(T(y,z) \ u,z * y)) = K(x,T(u,y \ (z \ y)) / y)
    ]]></literal>
    <justification jstring="[para(11(a,1),19453(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11 19453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19500">
    <literal><![CDATA[
      K(x,T(T(y,z) \ u,z * y)) = K(x,T(u,z) / y)
    ]]></literal>
    <justification jstring="[hyper(333,a,18520,a(flip),b,19499,a),flip(a)].">
      <j1 rule="hyper" parents="333 18520 19499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19502">
    <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(5033(a,1),19500(a,1,2,1))].">
      <j1 rule="para" parents="5033 19500"/>
    </justification>
  </clause>

  <clause id="19503">
    <literal><![CDATA[
      K(x,y) \ (K(z,T(u,y \ x)) \ w) = ((x * y) \ (K(z,u) \ (y * x))) * w
    ]]></literal>
    <justification jstring="[para(6370(a,1),19479(a,1,2,1))].">
      <j1 rule="para" parents="6370 19479"/>
    </justification>
  </clause>

  <clause id="19504">
    <literal><![CDATA[
      K(x,K(y,z * (z \ u)) \ ((u / z) \ w)) = K(x,(T(u,y) / z) \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,15036,a(flip),b,19490,a)].">
      <j1 rule="hyper" parents="63 15036 19490"/>
    </justification>
  </clause>

  <clause id="19505">
    <literal><![CDATA[
      K(x,K(y,z) \ ((z / u) \ w)) = K(x,(T(z,y) / u) \ w)
    ]]></literal>
    <justification jstring="[para(10(a,1),19504(a,1,2,1,2))].">
      <j1 rule="para" parents="10 19504"/>
    </justification>
  </clause>

  <clause id="19506">
    <literal><![CDATA[
      K(x,K(y,z) \ ((y / u) \ w)) = K(x,(T(y,z) / u) \ w)
    ]]></literal>
    <justification jstring="[hyper(15780,a,19505,a)].">
      <j1 rule="hyper" parents="15780 19505"/>
    </justification>
  </clause>

  <clause id="19507">
    <literal><![CDATA[
      ((x * y) \ (K(z,u) \ (y * x))) * y = K(z,T(u,y \ x)) \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,19404,a(flip),b,19503,a),flip(a)].">
      <j1 rule="hyper" parents="63 19404 19503"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19508">
    <literal><![CDATA[
      K(x,y) \ (z * T(u / z,K(x,y))) = z * ((u * K(y,x)) / z)
    ]]></literal>
    <justification jstring="[hyper(63,a,16471,a(flip),b,19456,a),flip(a)].">
      <j1 rule="hyper" parents="63 16471 19456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19509">
    <literal><![CDATA[
      K(x,T(y,z \ u)) \ (z * (u / z)) = z * ((u * K(y,x)) / z)
    ]]></literal>
    <justification jstring="[hyper(63,a,15953,a,b,19508,a)].">
      <j1 rule="hyper" parents="63 15953 19508"/>
    </justification>
  </clause>

  <clause id="19510">
    <literal><![CDATA[
      K(x,T((y \ z) \ u,y \ z) / y) = K(x,T(y \ ((z / y) \ u),z))
    ]]></literal>
    <justification jstring="[hyper(15723,a,19502,a),flip(a)].">
      <j1 rule="hyper" parents="15723 19502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19512">
    <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(19510(a,2),14303(a,1))].">
      <j1 rule="para" parents="19510 14303"/>
    </justification>
  </clause>

  <clause id="19513">
    <literal><![CDATA[
      K(x,T(y \ ((y / z) * u),z)) = K(x,((((z \ y) * u) \ u) \ u) / y)
    ]]></literal>
    <justification jstring="[hyper(19512,a,19226,a)].">
      <j1 rule="hyper" parents="19512 19226"/>
    </justification>
  </clause>

  <clause id="19514">
    <literal><![CDATA[
      K(x,T(y \ ((y / z) * u),z)) = K(x,T((z \ y) * u,u) / y)
    ]]></literal>
    <justification jstring="[hyper(333,a,12664,a(flip),b,19513,a),flip(a)].">
      <j1 rule="hyper" parents="333 12664 19513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19515">
    <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(19514(a,2),16221(a,1))].">
      <j1 rule="para" parents="19514 16221"/>
    </justification>
  </clause>

  <clause id="19516">
    <literal><![CDATA[
      ((x / T(y,z)) * u) \ T(u * (x / T(y,z)),u) = a(u,y \ (K(y \ 1,z) \ x),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,10028,a(flip),b,19498,a)].">
      <j1 rule="hyper" parents="63 10028 19498"/>
    </justification>
  </clause>

  <clause id="19517">
    <literal><![CDATA[
      a(x,y \ (K(y \ 1,z) \ u),x) = a(x,u / T(y,z),x)
    ]]></literal>
    <justification jstring="[hyper(9276,a,19516,a),flip(a)].">
      <j1 rule="hyper" parents="9276 19516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19518">
    <literal><![CDATA[
      a(x,y \ (K(y \ 1,z) \ u),x) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,T(y,z) \ u,x) = w
    ]]></literal>
    <justification jstring="[para(19517(a,2),12591(a,1))].">
      <j1 rule="para" parents="19517 12591"/>
    </justification>
  </clause>

  <clause id="19519">
    <literal><![CDATA[
      K(x,(y / (z * K(u,w))) \ K(z,z \ u)) = K(x,T(z * K(u,w),z \ u) / y)
    ]]></literal>
    <justification jstring="[hyper(16397,a,19395,a)].">
      <j1 rule="hyper" parents="16397 19395"/>
    </justification>
  </clause>

  <clause id="19520">
    <literal><![CDATA[
      K(x,T(y * K(z,u),y \ z) / w) = K(x,(w / (y * K(z,u))) \ K(y,z))
    ]]></literal>
    <justification jstring="[hyper(12767,a,19519,a),flip(a)].">
      <j1 rule="hyper" parents="12767 19519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19521">
    <literal><![CDATA[
      K(x,T(y * K(z,u),y \ z) / w) = K(x,T(y * K(z,u),z) / w)
    ]]></literal>
    <justification jstring="[hyper(333,a,19394,a(flip),b,19520,a),flip(a)].">
      <j1 rule="hyper" parents="333 19394 19520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19522">
    <literal><![CDATA[
      K(x,(T(y,z) / (y / u)) / w) = K(x,T(u * K(y,z),y) / w)
    ]]></literal>
    <justification jstring="[hyper(63,a,16468,a(flip),b,19521,a)].">
      <j1 rule="hyper" parents="63 16468 19521"/>
    </justification>
  </clause>

  <clause id="19523">
    <literal><![CDATA[
      K(x,(T(y,z) / (y / u)) / w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(u,y) * (w \ K(z,y))) = v5
    ]]></literal>
    <justification jstring="[para(19522(a,2),18779(a,1))].">
      <j1 rule="para" parents="19522 18779"/>
    </justification>
  </clause>

  <clause id="19524">
    <literal><![CDATA[
      K(x,T(y * T(z,u),T(z,u)) / w) = K(x,T(y * z,z) * (w \ K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(19523,a,18809,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="19523 18809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19525">
    <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(333,a,16994,a(flip),b,19524,a),flip(a)].">
      <j1 rule="hyper" parents="333 16994 19524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19526">
    <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(19525(a,1),16221(a,1))].">
      <j1 rule="para" parents="19525 16221"/>
    </justification>
  </clause>

  <clause id="19527">
    <literal><![CDATA[
      K(x,(T(y,z) * (1 / z)) / u) = K(x,((z \ 1) * y) / u)
    ]]></literal>
    <justification jstring="[hyper(19526,a,18805,a)].">
      <j1 rule="hyper" parents="19526 18805"/>
    </justification>
  </clause>

  <clause id="19528">
    <literal><![CDATA[
      K(x,(y * (1 / T(z,y))) / u) = K(x,((z \ 1) * y) / u)
    ]]></literal>
    <justification jstring="[para(4677(a,1),19527(a,1,2,1))].">
      <j1 rule="para" parents="4677 19527"/>
    </justification>
  </clause>

  <clause id="19529">
    <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(63,a,14738,a(flip),b,19528,a)].">
      <j1 rule="hyper" parents="63 14738 19528"/>
    </justification>
  </clause>

  <clause id="19530">
    <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(12757,a,19460,a)].">
      <j1 rule="hyper" parents="12757 19460"/>
    </justification>
  </clause>

  <clause id="19531">
    <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(63,a,18193,a(flip),b,19530,a),flip(a)].">
      <j1 rule="hyper" parents="63 18193 19530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19532">
    <literal><![CDATA[
      K(x,T(y * ((z \ (u * y)) \ 1),u)) = K(x,((u * y) / z) \ T(y,u))
    ]]></literal>
    <justification jstring="[hyper(333,a,14951,a(flip),b,19531,a),flip(a)].">
      <j1 rule="hyper" parents="333 14951 19531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19533">
    <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(19532(a,1),13529(a,1))].">
      <j1 rule="para" parents="19532 13529"/>
    </justification>
  </clause>

  <clause id="19534">
    <literal><![CDATA[
      R(K(x,y),z,L(a(z,u,w),z,K(x,y))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,11,a(flip),b,19439,a),flip(a)].">
      <j1 rule="hyper" parents="333 11 19439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19536">
    <literal><![CDATA[
      R(K(x,y),z,a(z,u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(19437(a,1),19534(a,1,3))].">
      <j1 rule="para" parents="19437 19534"/>
    </justification>
  </clause>

  <clause id="19537">
    <literal><![CDATA[
      K(x,L(y,z,a(z,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(13899,a,19536,a)].">
      <j1 rule="hyper" parents="13899 19536"/>
    </justification>
  </clause>

  <clause id="19539">
    <literal><![CDATA[
      R(K(x,y),z,L(a(u,w,z),z,K(x,y))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,11,a(flip),b,19440,a),flip(a)].">
      <j1 rule="hyper" parents="333 11 19440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19541">
    <literal><![CDATA[
      R(K(x,y),z,a(u,w,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(19438(a,1),19539(a,1,3))].">
      <j1 rule="para" parents="19438 19539"/>
    </justification>
  </clause>

  <clause id="19542">
    <literal><![CDATA[
      K(x,L(y,z,a(u,w,z))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(13899,a,19541,a)].">
      <j1 rule="hyper" parents="13899 19541"/>
    </justification>
  </clause>

  <clause id="19544">
    <literal><![CDATA[
      (K(x,y) * z) / a(u,w,z) = K(x,y) * (z / a(u,w,z))
    ]]></literal>
    <justification jstring="[para(19542(a,1),14063(a,1,1,1))].">
      <j1 rule="para" parents="19542 14063"/>
    </justification>
  </clause>

  <clause id="19545">
    <literal><![CDATA[
      (L(x,y,z) \ x) * (L(x,y,z) * K(u,w)) = x * K(u,w)
    ]]></literal>
    <justification jstring="[para(19542(a,1),14354(a,2,2))].">
      <j1 rule="para" parents="19542 14354"/>
    </justification>
  </clause>

  <clause id="19546">
    <literal><![CDATA[
      R(1 / (L(x,y,z) \ x),L(x,y,z) \ x,L(x,y,z) * K(u,w)) = (L(x,y,z) * K(u,w)) / (x * K(u,w))
    ]]></literal>
    <justification jstring="[hyper(197,a,19545,a(flip),b,398,a),flip(a)].">
      <j1 rule="hyper" parents="197 19545 398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19548">
    <literal><![CDATA[
      K(x,y \ (z / T(u,z))) = K(x,y \ (u \ z))
    ]]></literal>
    <justification jstring="[hyper(333,a,4599,a(flip),b,19448,a),flip(a)].">
      <j1 rule="hyper" parents="333 4599 19448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19549">
    <literal><![CDATA[
      K(x,y \ (T(z,u) / u)) = K(x,y \ (u \ z))
    ]]></literal>
    <justification jstring="[para(3625(a,2),19548(a,1,2,2))].">
      <j1 rule="para" parents="3625 19548"/>
    </justification>
  </clause>

  <clause id="19550">
    <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(12732(a,1),19549(a,1,2,2,1))].">
      <j1 rule="para" parents="12732 19549"/>
    </justification>
  </clause>

  <clause id="19551">
    <literal><![CDATA[
      K(x,y \ (T(z,u / w) / (u / w))) = K(x,y \ ((T(w,u) \ u) \ z))
    ]]></literal>
    <justification jstring="[hyper(18950,a,19550,a)].">
      <j1 rule="hyper" parents="18950 19550"/>
    </justification>
  </clause>

  <clause id="19552">
    <literal><![CDATA[
      K(x,y \ ((T(z,u) \ u) \ w)) = K(x,y \ ((u / z) \ w))
    ]]></literal>
    <justification jstring="[hyper(63,a,19549,a(flip),b,19551,a),flip(a)].">
      <j1 rule="hyper" parents="63 19549 19551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19553">
    <literal><![CDATA[
      K(x,(y \ 1) \ ((z / u) \ w)) = K(x,y * ((u \ T(z,u)) \ w))
    ]]></literal>
    <justification jstring="[hyper(13507,a,19552,a),flip(a)].">
      <j1 rule="hyper" parents="13507 19552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19554">
    <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(19553(a,1),13421(a,1))].">
      <j1 rule="para" parents="19553 13421"/>
    </justification>
  </clause>

  <clause id="19555">
    <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(3628(a,2),19554(a,1,2,2,1))].">
      <j1 rule="para" parents="3628 19554"/>
    </justification>
  </clause>

  <clause id="19556">
    <literal><![CDATA[
      R((L(x,y,z) \ x) \ 1,L(x,y,z) \ x,L(x,y,z) * K(u,w)) = (L(x,y,z) * K(u,w)) / (x * K(u,w))
    ]]></literal>
    <justification jstring="[para(3263(a,1),19546(a,1,1))].">
      <j1 rule="para" parents="3263 19546"/>
    </justification>
  </clause>

  <clause id="19557">
    <literal><![CDATA[
      (K(x,K(y,z)) \ (u * w)) \ ((K(x,K(y,z)) * u) * (w * v5)) = L(v5,L(w,u,K(x,K(y,z))),K(x,K(y,z)) * u)
    ]]></literal>
    <justification jstring="[para(6829(a,2),17594(a,1,1))].">
      <j1 rule="para" parents="6829 17594"/>
    </justification>
  </clause>

  <clause id="19558">
    <literal><![CDATA[
      K(x,y * (z \ ((u / (T(w,v5) \ 1)) \ T(v5,u * T(w,v5))))) = K(x,y * (z \ (T(v5,w) / (u / (w \ 1)))))
    ]]></literal>
    <justification jstring="[para(13325(a,1),18262(a,1,2,2,2,2))].">
      <j1 rule="para" parents="13325 18262"/>
    </justification>
  </clause>

  <clause id="19559">
    <literal><![CDATA[
      K(x,y * (z \ ((u / (T(w,v5) \ 1)) \ T(v5,u * w)))) = K(x,y * (z \ (T(v5,w) / (u / (w \ 1)))))
    ]]></literal>
    <justification jstring="[para(7359(a,1),19558(a,1,2,2,2,2))].">
      <j1 rule="para" parents="7359 19558"/>
    </justification>
  </clause>

  <clause id="19560">
    <literal><![CDATA[
      K(x,y * (z \ ((T(u,w) \ 1) * K(w,w * u)))) = K(x,y * (z \ (T(w,u) / (w / (u \ 1)))))
    ]]></literal>
    <justification jstring="[para(13240(a,1),19559(a,1,2,2,2))].">
      <j1 rule="para" parents="13240 19559"/>
    </justification>
  </clause>

  <clause id="19561">
    <literal><![CDATA[
      K(x,y * (z \ (T(u,w) \ K(w,w * u)))) = K(x,y * (z \ (T(w,u) / (w / (u \ 1)))))
    ]]></literal>
    <justification jstring="[para(13126(a,1),19560(a,1,2,2,2))].">
      <j1 rule="para" parents="13126 19560"/>
    </justification>
  </clause>

  <clause id="19562">
    <literal><![CDATA[
      L(K(x,((y / ((z \ 1) \ 1)) / u) \ x),z \ y,z) \ T(x,(u * z) / y) = R(x,u / (y / ((z \ 1) \ 1)),x)
    ]]></literal>
    <justification jstring="[para(11884(a,2),18343(a,1,1,1))].">
      <j1 rule="para" parents="11884 18343"/>
    </justification>
  </clause>

  <clause id="19563">
    <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(13395(a,1),18475(a,1,2,2))].">
      <j1 rule="para" parents="13395 18475"/>
    </justification>
  </clause>

  <clause id="19564">
    <literal><![CDATA[
      K(x,R(y * z,K(u,L(w,y,z)),K(u,L(w,y,z))) \ v5) = K(x,K(u,w) * (((K(u,w) * y) * z) \ v5))
    ]]></literal>
    <justification jstring="[hyper(333,a,17967,a(flip),b,18607,a),flip(a)].">
      <j1 rule="hyper" parents="333 17967 18607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19566">
    <literal><![CDATA[
      K(x,K(y,z) * (((K(y,z) * u) * w) \ v5)) = K(x,(u * w) \ v5)
    ]]></literal>
    <justification jstring="[para(19317(a,1),19564(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="19317 19564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19567">
    <literal><![CDATA[
      K(x,L(y,z,K(u,w) * v5)) = K(x,(v5 * z) \ (v5 * (z * y)))
    ]]></literal>
    <justification jstring="[hyper(63,a,19178,a(flip),b,19566,a)].">
      <j1 rule="hyper" parents="63 19178 19566"/>
    </justification>
  </clause>

  <clause id="19570">
    <literal><![CDATA[
      K(x,L(y,z,K(u,w) * v5)) = K(x,L(y,z,v5))
    ]]></literal>
    <justification jstring="[para(18(a,2),19567(a,2,2))].">
      <j1 rule="para" parents="18 19567"/>
    </justification>
  </clause>

  <clause id="19571">
    <literal><![CDATA[
      K(x,L(y,z,u * K(w,v5))) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(17744,a,19570,a)].">
      <j1 rule="hyper" parents="17744 19570"/>
    </justification>
  </clause>

  <clause id="19572">
    <literal><![CDATA[
      K(x,L(y,z,K(u,w) * v5)) = K(x,(z * v5) / ((y \ z) * v5))
    ]]></literal>
    <justification jstring="[hyper(333,a,13866,a,b,19570,a),flip(a)].">
      <j1 rule="hyper" parents="333 13866 19570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19573">
    <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(63,a,14004,a,b,19570,a)].">
      <j1 rule="hyper" parents="63 14004 19570"/>
    </justification>
  </clause>

  <clause id="19574">
    <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(19570(a,1),10874(a,1,2))].">
      <j1 rule="para" parents="19570 10874"/>
    </justification>
  </clause>

  <clause id="19575">
    <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(19570(a,1),13872(a,1,1))].">
      <j1 rule="para" parents="19570 13872"/>
    </justification>
  </clause>

  <clause id="19576">
    <literal><![CDATA[
      K(x,L(y,(z \ u) / w,w)) = K(x,L(y,u / z,w * K(z,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,14451,a(flip),b,19571,a),flip(a)].">
      <j1 rule="hyper" parents="63 14451 19571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19577">
    <literal><![CDATA[
      K(x,L(y,z,u * (w / v5))) = K(x,L(y,z,u * (v5 \ w)))
    ]]></literal>
    <justification jstring="[para(5523(a,1),19571(a,1,2,3))].">
      <j1 rule="para" parents="5523 19571"/>
    </justification>
  </clause>

  <clause id="19578">
    <literal><![CDATA[
      a(x,y,K(z * K(u,w),v5)) = K(v5,x) * K(x,L(v5,y,z))
    ]]></literal>
    <justification jstring="[para(19571(a,1),13751(a,1,2)),flip(a)].">
      <j1 rule="para" parents="19571 13751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19579">
    <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(19571(a,1),13872(a,1,1))].">
      <j1 rule="para" parents="19571 13872"/>
    </justification>
  </clause>

  <clause id="19580">
    <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(19571(a,1),15829(a,1,1,1))].">
      <j1 rule="para" parents="19571 15829"/>
    </justification>
  </clause>

  <clause id="19581">
    <literal><![CDATA[
      a(x,y,K(z * K(u,w),v5)) = a(x,y,K(z,v5))
    ]]></literal>
    <justification jstring="[hyper(333,a,13751,a(flip),b,19578,a),flip(a)].">
      <j1 rule="hyper" parents="333 13751 19578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19582">
    <literal><![CDATA[
      a(x,y,K(z * K(u,w),v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(z,v5)) = v6
    ]]></literal>
    <justification jstring="[para(19578(a,2),13842(a,1))].">
      <j1 rule="para" parents="19578 13842"/>
    </justification>
  </clause>

  <clause id="19583">
    <literal><![CDATA[
      a(x * K(y,z),u,K(w,v5)) = a(v5,u,K(x,w))
    ]]></literal>
    <justification jstring="[hyper(13803,a,19581,a)].">
      <j1 rule="hyper" parents="13803 19581"/>
    </justification>
  </clause>

  <clause id="19584">
    <literal><![CDATA[
      a(x \ (y * K(z,u)),w,K(v5,v6)) = a(v5,w,K(y \ x,v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,17957,a,b,19581,a)].">
      <j1 rule="hyper" parents="63 17957 19581"/>
    </justification>
  </clause>

  <clause id="19585">
    <literal><![CDATA[
      a(x,y,K(z \ (u / w),v5)) = a(x,y,K(z \ (w \ u),v5))
    ]]></literal>
    <justification jstring="[para(13414(a,1),19581(a,1,3,1))].">
      <j1 rule="para" parents="13414 19581"/>
    </justification>
  </clause>

  <clause id="19586">
    <literal><![CDATA[
      a(x,y,K((z / u) \ w,v5)) = a(x,y,K((u \ z) \ w,v5))
    ]]></literal>
    <justification jstring="[para(17066(a,1),19581(a,1,3))].">
      <j1 rule="para" parents="17066 19581"/>
    </justification>
  </clause>

  <clause id="19587">
    <literal><![CDATA[
      a(x \ K(y,z),u,K(w,v5)) = a(w,u,K(x,v5))
    ]]></literal>
    <justification jstring="[hyper(17848,a,19583,a)].">
      <j1 rule="hyper" parents="17848 19583"/>
    </justification>
  </clause>

  <clause id="19588">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w) * v5)) = a(z,y,K(v5,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,17699,a(flip),b,19583,a)].">
      <j1 rule="hyper" parents="63 17699 19583"/>
    </justification>
  </clause>

  <clause id="19589">
    <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(19583(a,1),14484(a,2,1))].">
      <j1 rule="para" parents="19583 14484"/>
    </justification>
  </clause>

  <clause id="19590">
    <literal><![CDATA[
      a(x,y,K(z,u * (w * K(v5,v6)))) = a(z,y,K(w * u,x))
    ]]></literal>
    <justification jstring="[hyper(17997,a,19588,a)].">
      <j1 rule="hyper" parents="17997 19588"/>
    </justification>
  </clause>

  <clause id="19591">
    <literal><![CDATA[
      a(x,y,K(z \ T(u,w),v5)) = a(v5,y,K(x,z \ u))
    ]]></literal>
    <justification jstring="[para(4840(a,1),19588(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="4840 19588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19592">
    <literal><![CDATA[
      T(x,a(K(y,z) * u,w,v5)) = x * a(v5,w,K(u,x))
    ]]></literal>
    <justification jstring="[para(19588(a,1),13741(a,1,2)),flip(a)].">
      <j1 rule="para" parents="19588 13741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19593">
    <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(19588(a,1),17047(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="19588 17047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19594">
    <literal><![CDATA[
      a(x,y,K((T(z,u) \ w) \ v5,v6)) = a(v6,y,K(x,(z \ w) \ v5))
    ]]></literal>
    <justification jstring="[para(19132(a,1),19588(a,1,3)),flip(a)].">
      <j1 rule="para" parents="19132 19588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19595">
    <literal><![CDATA[
      a(x,y,K((z / T(u,w)) \ w,v5)) = a(v5,y,K(x,(z / u) \ w))
    ]]></literal>
    <justification jstring="[hyper(63,a,18385,a,b,19591,a)].">
      <j1 rule="hyper" parents="63 18385 19591"/>
    </justification>
  </clause>

  <clause id="19596">
    <literal><![CDATA[
      T(x * y,a(K(z,u) * y,w,v5)) = (x * y) * a(v5,w,K(y,x))
    ]]></literal>
    <justification jstring="[para(11159(a,1),19592(a,2,2))].">
      <j1 rule="para" parents="11159 19592"/>
    </justification>
  </clause>

  <clause id="19597">
    <literal><![CDATA[
      a(x,y,K(z * (u / w),v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(z * (w \ u),v5)) = v6
    ]]></literal>
    <justification jstring="[para(5523(a,1),19582(a,1,3,1))].">
      <j1 rule="para" parents="5523 19582"/>
    </justification>
  </clause>

  <clause id="19598">
    <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(17703(a,2),19582(a,1))].">
      <j1 rule="para" parents="17703 19582"/>
    </justification>
  </clause>

  <clause id="19600">
    <literal><![CDATA[
      x * a(y,z,K(u \ (w \ v5),x)) = T(x,a(u \ (v5 / w),z,y))
    ]]></literal>
    <justification jstring="[para(19585(a,1),13756(a,1,2))].">
      <j1 rule="para" parents="19585 13756"/>
    </justification>
  </clause>

  <clause id="19601">
    <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(19590(a,1),13934(a,1,2)),flip(a)].">
      <j1 rule="para" parents="19590 13934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19602">
    <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(19572(a,2),13922(a,1))].">
      <j1 rule="para" parents="19572 13922"/>
    </justification>
  </clause>

  <clause id="19603">
    <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(4555(a,1),19602(a,1,2,3))].">
      <j1 rule="para" parents="4555 19602"/>
    </justification>
  </clause>

  <clause id="19604">
    <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(6887(a,1),19602(a,1,2,3))].">
      <j1 rule="para" parents="6887 19602"/>
    </justification>
  </clause>

  <clause id="19605">
    <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(10014(a,1),19602(a,1,2,3))].">
      <j1 rule="para" parents="10014 19602"/>
    </justification>
  </clause>

  <clause id="19606">
    <literal><![CDATA[
      K(x,L(y,z,u \ L(T(w,v5),v6,v7))) != v8
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u \ L(w,v6,v7))) = v8
    ]]></literal>
    <justification jstring="[para(13365(a,1),19604(a,1,2,3))].">
      <j1 rule="para" parents="13365 19604"/>
    </justification>
  </clause>

  <clause id="19607">
    <literal><![CDATA[
      K(x,(y \ (z \ u)) \ (y \ u)) = K(x,L(T(z,u),u,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(19603,a,19229,a),flip(a)].">
      <j1 rule="hyper" parents="19603 19229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19608">
    <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(19603,a,14156,a)].">
      <j1 rule="hyper" parents="19603 14156"/>
    </justification>
  </clause>

  <clause id="19609">
    <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(19603,a,9564,a)].">
      <j1 rule="hyper" parents="19603 9564"/>
    </justification>
  </clause>

  <clause id="19610">
    <literal><![CDATA[
      K(x,L(y,(K(z,u) * w) \ v5,w)) = K(x,L(y,v5,w))
    ]]></literal>
    <justification jstring="[hyper(19602,a,19573,a)].">
      <j1 rule="hyper" parents="19602 19573"/>
    </justification>
  </clause>

  <clause id="19613">
    <literal><![CDATA[
      K(x,L(y,z \ (u \ w),z)) = K(x,L(y,w / u,z * K(u,w)))
    ]]></literal>
    <justification jstring="[para(10083(a,1),19576(a,1,2))].">
      <j1 rule="para" parents="10083 19576"/>
    </justification>
  </clause>

  <clause id="19615">
    <literal><![CDATA[
      a(x,y,K((T(z,u) \ w) \ u,v5)) = a(v5,y,K(x,(w / z) \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,19586,a(flip),b,19595,a)].">
      <j1 rule="hyper" parents="63 19586 19595"/>
    </justification>
  </clause>

  <clause id="19616">
    <literal><![CDATA[
      T(x * y,a(K(z,u) * y,w,v5)) = x * T(y,a(v5,w,x))
    ]]></literal>
    <justification jstring="[hyper(333,a,13179,a(flip),b,19596,a),flip(a)].">
      <j1 rule="hyper" parents="333 13179 19596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19617">
    <literal><![CDATA[
      T(x,a(x \ ((y * x) / z),u,w)) = x * a(w,u,K(z \ y,x))
    ]]></literal>
    <justification jstring="[para(10325(a,1),19600(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="10325 19600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19618">
    <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(19600(a,1),13773(a,1))].">
      <j1 rule="para" parents="19600 13773"/>
    </justification>
  </clause>

  <clause id="19619">
    <literal><![CDATA[
      K(x,L(y,z / u,w * K(u,z))) = K(x,L(y,u \ z,w))
    ]]></literal>
    <justification jstring="[hyper(14005,a,19613,a),flip(a)].">
      <j1 rule="hyper" parents="14005 19613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19620">
    <literal><![CDATA[
      K(x,L(y,z / u,w)) = K(x,L(y,u \ z,w))
    ]]></literal>
    <justification jstring="[hyper(19604,a,19619,a)].">
      <j1 rule="hyper" parents="19604 19619"/>
    </justification>
  </clause>

  <clause id="19623">
    <literal><![CDATA[
      K(x,L(T(y,z),u / y,w)) = K(x,L(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(333,a,11037,a(flip),b,19620,a),flip(a)].">
      <j1 rule="hyper" parents="333 11037 19620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19624">
    <literal><![CDATA[
      K(x,L(y,(z * u) / z,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(9(a,1),19620(a,2,2,2))].">
      <j1 rule="para" parents="9 19620"/>
    </justification>
  </clause>

  <clause id="19626">
    <literal><![CDATA[
      K(x,L(y,T(z,u),w)) = K(x,L(y,z,w))
    ]]></literal>
    <justification jstring="[para(239(a,1),19624(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="239 19624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19628">
    <literal><![CDATA[
      K(x,L(y,L(T(z,u),w,v5),v6)) = K(x,L(y,L(z,w,v5),v6))
    ]]></literal>
    <justification jstring="[para(25(a,2),19626(a,1,2,2))].">
      <j1 rule="para" parents="25 19626"/>
    </justification>
  </clause>

  <clause id="19630">
    <literal><![CDATA[
      K(x,L(y \ z,T(y,u),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y \ z,z,w)) = v5
    ]]></literal>
    <justification jstring="[para(19626(a,2),10961(a,1))].">
      <j1 rule="para" parents="19626 10961"/>
    </justification>
  </clause>

  <clause id="19631">
    <literal><![CDATA[
      K(x,L(y,L(z,u,K(w,v5)),v6)) = K(x,L(y,z,v6))
    ]]></literal>
    <justification jstring="[para(14461(a,2),19626(a,1,2,2))].">
      <j1 rule="para" parents="14461 19626"/>
    </justification>
  </clause>

  <clause id="19632">
    <literal><![CDATA[
      K(x,L(y,z * u,w)) = K(x,L(y,u * z,w))
    ]]></literal>
    <justification jstring="[para(14690(a,1),19626(a,1,2))].">
      <j1 rule="para" parents="14690 19626"/>
    </justification>
  </clause>

  <clause id="19633">
    <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(4581(a,1),19631(a,1,2,2))].">
      <j1 rule="para" parents="4581 19631"/>
    </justification>
  </clause>

  <clause id="19634">
    <literal><![CDATA[
      K(x,L(T(y,z),u * y,w)) = K(x,L(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(11(a,1),19623(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11 19623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19635">
    <literal><![CDATA[
      (x * (y / z)) * K(u,L(T(z,w),y,x)) = x * (y / T(z,T(u,w)))
    ]]></literal>
    <justification jstring="[para(19623(a,1),10971(a,1,2))].">
      <j1 rule="para" parents="19623 10971"/>
    </justification>
  </clause>

  <clause id="19636">
    <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(451,a,19634,a(flip),b,19607,a)].">
      <j1 rule="hyper" parents="451 19634 19607"/>
    </justification>
  </clause>

  <clause id="19637">
    <literal><![CDATA[
      K(x,L((y \ 1) \ z,z,u)) = K(x,L(y * z,T(y \ 1,w),u))
    ]]></literal>
    <justification jstring="[hyper(19630,a,13615,a)].">
      <j1 rule="hyper" parents="19630 13615"/>
    </justification>
  </clause>

  <clause id="19638">
    <literal><![CDATA[
      a(x,y,K(z,(u / w) \ v5)) = a(x,y,K(z,(w \ u) \ v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,19594,a(flip),b,19615,a),flip(a)].">
      <j1 rule="hyper" parents="63 19594 19615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19639">
    <literal><![CDATA[
      a(K(x,y) * z,u,K(w,(v5 \ v6) \ v7)) = a((v6 / v5) \ v7,u,K(z,w))
    ]]></literal>
    <justification jstring="[hyper(19598,a,19638,a),flip(a)].">
      <j1 rule="hyper" parents="19598 19638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19641">
    <literal><![CDATA[
      T(x,a(x \ ((y * x) / z),u,w)) = T(x,a(z \ y,u,w))
    ]]></literal>
    <justification jstring="[hyper(333,a,13756,a(flip),b,19617,a),flip(a)].">
      <j1 rule="hyper" parents="333 13756 19617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19642">
    <literal><![CDATA[
      K(x,L(((y / z) \ 1) \ z,z,u)) = K(x,L(y,T((y / z) \ 1,w),u))
    ]]></literal>
    <justification jstring="[para(12(a,1),19637(a,2,2,1))].">
      <j1 rule="para" parents="12 19637"/>
    </justification>
  </clause>

  <clause id="19643">
    <literal><![CDATA[
      a(x,y,K(z * (T(u,x) \ w),v5)) = a(v5,y,K(x,z * (w / u)))
    ]]></literal>
    <justification jstring="[hyper(19597,a,13759,a)].">
      <j1 rule="hyper" parents="19597 13759"/>
    </justification>
  </clause>

  <clause id="19644">
    <literal><![CDATA[
      a(x,y,K(z,u * (w / v5))) = a(x,y,K(z,u * (v5 \ w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,13760,a(flip),b,19643,a),flip(a)].">
      <j1 rule="hyper" parents="63 13760 19643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19645">
    <literal><![CDATA[
      a(K(x,y) * z,u,K(w,v5 * (v6 \ v7))) = a(v5 * (v7 / v6),u,K(z,w))
    ]]></literal>
    <justification jstring="[hyper(19598,a,19644,a),flip(a)].">
      <j1 rule="hyper" parents="19598 19644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19646">
    <literal><![CDATA[
      K(x,L(y,z,(u * w) \ w)) = K(x,L(y,z,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(19605,a,14132,a)].">
      <j1 rule="hyper" parents="19605 14132"/>
    </justification>
  </clause>

  <clause id="19647">
    <literal><![CDATA[
      K(x,L(y,z,u \ (z \ w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,(u * z) \ w)) = v5
    ]]></literal>
    <justification jstring="[para(19442(a,1),19605(a,1))].">
      <j1 rule="para" parents="19442 19605"/>
    </justification>
  </clause>

  <clause id="19648">
    <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(63,a,14715,a(flip),b,19646,a),flip(a)].">
      <j1 rule="hyper" parents="63 14715 19646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19649">
    <literal><![CDATA[
      K(x,L(y,z,u \ (w \ u))) = K(x,L(y,z,w \ 1))
    ]]></literal>
    <justification jstring="[para(10(a,1),19646(a,1,2,3,1))].">
      <j1 rule="para" parents="10 19646"/>
    </justification>
  </clause>

  <clause id="19650">
    <literal><![CDATA[
      K(x,L(y \ (z * u),y,z \ 1)) = K(x,((u / (z * u)) * y) \ u)
    ]]></literal>
    <justification jstring="[para(13618(a,1),19646(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13618 19646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19651">
    <literal><![CDATA[
      ((x * y) \ y) * ((((x * y) \ y) \ z) * K(u,w)) = z * K(u,L(w,z,x \ 1))
    ]]></literal>
    <justification jstring="[para(19646(a,1),14013(a,1,2)),flip(a)].">
      <j1 rule="para" parents="19646 14013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19652">
    <literal><![CDATA[
      (x \ y) * K(z,L(u,y,x \ 1)) = ((x \ y) / y) * (y * K(z,u))
    ]]></literal>
    <justification jstring="[para(19649(a,1),10887(a,1,2))].">
      <j1 rule="para" parents="19649 10887"/>
    </justification>
  </clause>

  <clause id="19653">
    <literal><![CDATA[
      K(x,L(y,z,u \ 1)) * (z * (z \ (z / u))) = (K(x,y) * z) * (z \ (z / u))
    ]]></literal>
    <justification jstring="[para(19649(a,1),13962(a,1,1))].">
      <j1 rule="para" parents="19649 13962"/>
    </justification>
  </clause>

  <clause id="19654">
    <literal><![CDATA[
      T(x,a(x \ (y \ (z * x)),u,w)) = T(x,a(y \ z,u,w))
    ]]></literal>
    <justification jstring="[hyper(19618,a,19641,a)].">
      <j1 rule="hyper" parents="19618 19641"/>
    </justification>
  </clause>

  <clause id="19655">
    <literal><![CDATA[
      T(x,a(y \ (z * x),u,w)) = T(x,a(y \ z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,13943,a(flip),b,19654,a)].">
      <j1 rule="hyper" parents="63 13943 19654"/>
    </justification>
  </clause>

  <clause id="19656">
    <literal><![CDATA[
      T(x,a(y \ 1,z,u)) = T(x,a(y \ x,z,u))
    ]]></literal>
    <justification jstring="[para(7(a,1),19655(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="7 19655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19657">
    <literal><![CDATA[
      T(x,a(y \ x,z,u)) = T(x,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,17864,a(flip),b,19656,a),flip(a)].">
      <j1 rule="hyper" parents="63 17864 19656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19658">
    <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(4550(a,1),19657(a,1,2,1))].">
      <j1 rule="para" parents="4550 19657"/>
    </justification>
  </clause>

  <clause id="19659">
    <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(19658(a,2),17731(a,1))].">
      <j1 rule="para" parents="19658 17731"/>
    </justification>
  </clause>

  <clause id="19660">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (u * (z / y)) = u * (z / T(y,T(x,u * z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,11143,a(flip),b,19635,a)].">
      <j1 rule="hyper" parents="63 11143 19635"/>
    </justification>
  </clause>

  <clause id="19661">
    <literal><![CDATA[
      K(x \ 1,L(y,z,(x * z) \ u)) = K(x \ 1,L(y,z,z \ u))
    ]]></literal>
    <justification jstring="[hyper(19647,a,14242,a)].">
      <j1 rule="hyper" parents="19647 14242"/>
    </justification>
  </clause>

  <clause id="19662">
    <literal><![CDATA[
      K(x \ 1,L(T(y,z),u,u \ z)) = K(z \ (u * ((x * u) \ z)),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,13946,a(flip),b,19661,a),flip(a)].">
      <j1 rule="hyper" parents="63 13946 19661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19663">
    <literal><![CDATA[
      K(x,((y / (z * y)) * u) \ y) = K(x,(z \ u) \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,14192,a(flip),b,19650,a),flip(a)].">
      <j1 rule="hyper" parents="63 14192 19650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19664">
    <literal><![CDATA[
      K(x,((y / z) \ u) \ z) = K(x,((z / y) * u) \ z)
    ]]></literal>
    <justification jstring="[para(12(a,1),19663(a,1,2,1,1,2)),flip(a)].">
      <j1 rule="para" parents="12 19663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19665">
    <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(19664(a,2),14166(a,1))].">
      <j1 rule="para" parents="19664 14166"/>
    </justification>
  </clause>

  <clause id="19666">
    <literal><![CDATA[
      ((x \ y) / y) * (y * K(z,u)) = x \ (y * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,14185,a(flip),b,19652,a),flip(a)].">
      <j1 rule="hyper" parents="63 14185 19652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19667">
    <literal><![CDATA[
      (((T(x,K(y,z)) / u) \ x) / x) * (x * K(y,z)) = (x / u) \ (K(y,z) * x)
    ]]></literal>
    <justification jstring="[hyper(333,a,13480,a(flip),b,19666,a),flip(a)].">
      <j1 rule="hyper" parents="333 13480 19666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19668">
    <literal><![CDATA[
      (x / y) \ (x * K(z,u)) = (y / x) * (x * K(z,u))
    ]]></literal>
    <justification jstring="[para(79(a,1),19666(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="79 19666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19669">
    <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(19666(a,1),7488(a,2,2,1))].">
      <j1 rule="para" parents="19666 7488"/>
    </justification>
  </clause>

  <clause id="19670">
    <literal><![CDATA[
      K(x,y * T(z \ (u * K(w,v5)),u * K(w,v5))) = K(x,y * ((u * K(w,v5)) * ((z \ u) / u)))
    ]]></literal>
    <justification jstring="[para(19666(a,1),16029(a,1,2,2,1))].">
      <j1 rule="para" parents="19666 16029"/>
    </justification>
  </clause>

  <clause id="19671">
    <literal><![CDATA[
      T(x * y,a(z,u,x)) = x * T(y,a(z,u,x))
    ]]></literal>
    <justification jstring="[hyper(19659,a,19616,a)].">
      <j1 rule="hyper" parents="19659 19616"/>
    </justification>
  </clause>

  <clause id="19672">
    <literal><![CDATA[
      T(x * y,a(z,u,x)) = x * L(y,u,K(x,z))
    ]]></literal>
    <justification jstring="[para(14461(a,2),19671(a,2,2))].">
      <j1 rule="para" parents="14461 19671"/>
    </justification>
  </clause>

  <clause id="19673">
    <literal><![CDATA[
      T(x * K(y,z),a(u,w,x)) = x * K(y,z)
    ]]></literal>
    <justification jstring="[para(17538(a,1),19671(a,2,2))].">
      <j1 rule="para" parents="17538 19671"/>
    </justification>
  </clause>

  <clause id="19674">
    <literal><![CDATA[
      T(T(x,y) * K(z,u),a(w,v5,x)) = T(x,y) * K(z,u)
    ]]></literal>
    <justification jstring="[hyper(17731,a,19673,a)].">
      <j1 rule="hyper" parents="17731 19673"/>
    </justification>
  </clause>

  <clause id="19675">
    <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(19673(a,1),13345(a,2,2))].">
      <j1 rule="para" parents="19673 13345"/>
    </justification>
  </clause>

  <clause id="19676">
    <literal><![CDATA[
      L(x * y,z,K(x,u)) = x * L(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(14528,a,19672,a)].">
      <j1 rule="hyper" parents="14528 19672"/>
    </justification>
  </clause>

  <clause id="19677">
    <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(19660(a,1),18174(a,1,2))].">
      <j1 rule="para" parents="19660 18174"/>
    </justification>
  </clause>

  <clause id="19678">
    <literal><![CDATA[
      K(x \ (y * (((z / y) * y) \ x)),u) = K((z * (y \ x)) \ x,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,14205,a(flip),b,19662,a),flip(a)].">
      <j1 rule="hyper" parents="63 14205 19662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19679">
    <literal><![CDATA[
      K((x * (y \ z)) \ z,u) = K(z \ (y * (x \ z)),u)
    ]]></literal>
    <justification jstring="[para(12(a,1),19678(a,1,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="12 19678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19681">
    <literal><![CDATA[
      x / (K(y \ (z * (u \ y)),w) * x) = K(w,(u * (z \ y)) \ y)
    ]]></literal>
    <justification jstring="[para(19679(a,1),4569(a,1,2,1))].">
      <j1 rule="para" parents="19679 4569"/>
    </justification>
  </clause>

  <clause id="19682">
    <literal><![CDATA[
      ((x * y) / x) / ((x * (y * K(z \ (u * (w \ z)),y))) / x) = K(y,T((w * (u \ z)) \ z,x))
    ]]></literal>
    <justification jstring="[para(19679(a,1),7855(a,1,2,1,2,2))].">
      <j1 rule="para" parents="19679 7855"/>
    </justification>
  </clause>

  <clause id="19683">
    <literal><![CDATA[
      K(x,(y * (z \ u)) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u \ (z * (y \ u))) = w
    ]]></literal>
    <justification jstring="[para(19681(a,1),4579(a,1))].">
      <j1 rule="para" parents="19681 4579"/>
    </justification>
  </clause>

  <clause id="19684">
    <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(13250(a,1),19589(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13250 19589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19685">
    <literal><![CDATA[
      R(x,y,K(K(z,u) * w,v5)) = x * a(x,y,K(w,v5))
    ]]></literal>
    <justification jstring="[para(17585(a,1),19593(a,2,2))].">
      <j1 rule="para" parents="17585 19593"/>
    </justification>
  </clause>

  <clause id="19687">
    <literal><![CDATA[
      R(x,y,K(K(z,u) * w,v5)) = L(x,y,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(333,a,14466,a(flip),b,19685,a),flip(a)].">
      <j1 rule="hyper" parents="333 14466 19685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19689">
    <literal><![CDATA[
      L(x,y,K(K(z,u) * w,v5)) = L(x,y,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(14529,a,19687,a)].">
      <j1 rule="hyper" parents="14529 19687"/>
    </justification>
  </clause>

  <clause id="19690">
    <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(14531,a,19689,a)].">
      <j1 rule="hyper" parents="14531 19689"/>
    </justification>
  </clause>

  <clause id="19691">
    <literal><![CDATA[
      L(x,(K(y,z) * u) \ w,K(u,v5)) = L(x,w,K(u,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,19689,a(flip),b,19690,a)].">
      <j1 rule="hyper" parents="63 19689 19690"/>
    </justification>
  </clause>

  <clause id="19693">
    <literal><![CDATA[
      K(x,L(y,z,u / (K(w,v5) / v6))) = K(x,L(y,z,v6 * u))
    ]]></literal>
    <justification jstring="[hyper(333,a,13764,a(flip),b,19601,a),flip(a)].">
      <j1 rule="hyper" parents="333 13764 19601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19695">
    <literal><![CDATA[
      K(x,L(y,z \ (K(u,w) * v5),z)) = K(x,L(y,v5,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,19610,a(flip),b,19633,a),flip(a)].">
      <j1 rule="hyper" parents="63 19610 19633"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19696">
    <literal><![CDATA[
      K(x,L(y,K(z,u) * w,v5)) = K(x,L(y,w,v5))
    ]]></literal>
    <justification jstring="[hyper(14005,a,19695,a)].">
      <j1 rule="hyper" parents="14005 19695"/>
    </justification>
  </clause>

  <clause id="19697">
    <literal><![CDATA[
      a(x,K(y,z) * u,K(w,v5)) = K(w,v5) * K(v5,L(w,u,x))
    ]]></literal>
    <justification jstring="[hyper(126,a,19695,a(flip),b,13993,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="126 19695 13993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19698">
    <literal><![CDATA[
      T(x,L(y,K(z,u) * w,v5)) = T(x,L(y,w,v5))
    ]]></literal>
    <justification jstring="[hyper(124,a,19696,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 19696 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19702">
    <literal><![CDATA[
      K(x,L(y,(K(z,u) * w) * v5,v6)) = K(x,L(y,w * v5,v6))
    ]]></literal>
    <justification jstring="[para(11580(a,1),19696(a,1,2,2))].">
      <j1 rule="para" parents="11580 19696"/>
    </justification>
  </clause>

  <clause id="19703">
    <literal><![CDATA[
      T(x,L(y,z * K(u,w),v5)) = T(x,L(y,z,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,14095,a(flip),b,19698,a)].">
      <j1 rule="hyper" parents="63 14095 19698"/>
    </justification>
  </clause>

  <clause id="19705">
    <literal><![CDATA[
      a(x,K(y,z) * u,K(w,v5)) = a(v5,u,K(x,w))
    ]]></literal>
    <justification jstring="[hyper(333,a,13751,a(flip),b,19697,a),flip(a)].">
      <j1 rule="hyper" parents="333 13751 19697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19706">
    <literal><![CDATA[
      a(x,K(y,z) * u,K(w,v5)) = a(x,u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(333,a,10883,a(flip),b,19697,a),flip(a)].">
      <j1 rule="hyper" parents="333 10883 19697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19707">
    <literal><![CDATA[
      a(x,y * z,K(u,w)) = a(x,z * y,K(u,w))
    ]]></literal>
    <justification jstring="[para(4201(a,1),19706(a,1,2))].">
      <j1 rule="para" parents="4201 19706"/>
    </justification>
  </clause>

  <clause id="19712">
    <literal><![CDATA[
      x * a(x,y * z,K(u,w)) = L(x,z * y,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(126,a,19707,a,b,14471,a)].">
      <j1 rule="hyper" parents="126 19707 14471"/>
    </justification>
  </clause>

  <clause id="19713">
    <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(19712(a,1),14504(a,1))].">
      <j1 rule="para" parents="19712 14504"/>
    </justification>
  </clause>

  <clause id="19714">
    <literal><![CDATA[
      L(x,y * (y \ z),K(u,w)) = L(x,T(z,y),K(u,w))
    ]]></literal>
    <justification jstring="[hyper(19713,a,14697,a)].">
      <j1 rule="hyper" parents="19713 14697"/>
    </justification>
  </clause>

  <clause id="19715">
    <literal><![CDATA[
      L(x,T(y,z),K(u,w)) = L(x,y,K(u,w))
    ]]></literal>
    <justification jstring="[para(10(a,1),19714(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 19714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19717">
    <literal><![CDATA[
      L(x,L(y,z,K(u,w)),K(v5,v6)) = L(x,y,K(v5,v6))
    ]]></literal>
    <justification jstring="[para(14461(a,2),19715(a,1,2))].">
      <j1 rule="para" parents="14461 19715"/>
    </justification>
  </clause>

  <clause id="19718">
    <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(4581(a,1),19717(a,1,2))].">
      <j1 rule="para" parents="4581 19717"/>
    </justification>
  </clause>

  <clause id="19719">
    <literal><![CDATA[
      K(x,L(y,z * (K(u,w) * v5),v6)) = K(x,L(y,v5 * z,v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,19632,a,b,19702,a)].">
      <j1 rule="hyper" parents="63 19632 19702"/>
    </justification>
  </clause>

  <clause id="19720">
    <literal><![CDATA[
      K(x,L(y,z * (u * K(w,v5)),v6)) = K(x,L(y,u * z,v6))
    ]]></literal>
    <justification jstring="[para(6887(a,1),19719(a,1,2,2,2))].">
      <j1 rule="para" parents="6887 19719"/>
    </justification>
  </clause>

  <clause id="19721">
    <literal><![CDATA[
      a((x / y) \ z,u,K(w,v5)) = a((y \ x) \ z,u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(19598,a,19639,a),flip(a)].">
      <j1 rule="hyper" parents="19598 19639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19722">
    <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(19721(a,1),17736(a,1,2))].">
      <j1 rule="para" parents="19721 17736"/>
    </justification>
  </clause>

  <clause id="19723">
    <literal><![CDATA[
      K(x,L(((y / z) \ 1) \ z,z,u)) = K(x,L(y,(y / z) \ 1,u))
    ]]></literal>
    <justification jstring="[hyper(333,a,19626,a(flip),b,19642,a),flip(a)].">
      <j1 rule="hyper" parents="333 19626 19642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19724">
    <literal><![CDATA[
      K(x,L(((y / z) \ 1) \ z,z,u)) = K(x,L(y,(z \ y) \ 1,u))
    ]]></literal>
    <justification jstring="[para(14726(a,1),19723(a,2,2))].">
      <j1 rule="para" parents="14726 19723"/>
    </justification>
  </clause>

  <clause id="19725">
    <literal><![CDATA[
      K(x,L((y / z) * z,z,u)) = K(x,L(y,(z \ y) \ 1,u))
    ]]></literal>
    <justification jstring="[hyper(13616,a,19724,a)].">
      <j1 rule="hyper" parents="13616 19724"/>
    </justification>
  </clause>

  <clause id="19726">
    <literal><![CDATA[
      K(x,L(y,(z \ y) \ 1,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(12(a,1),19725(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12 19725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19727">
    <literal><![CDATA[
      a(x * (y / z),u,K(w,v5)) = a(x * (z \ y),u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(19598,a,19645,a),flip(a)].">
      <j1 rule="hyper" parents="19598 19645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19728">
    <literal><![CDATA[
      a(x * (y \ T(z,y)),u,K(w,v5)) = a(w,u,K(v5,(y \ z) * x))
    ]]></literal>
    <justification jstring="[hyper(63,a,18142,a(flip),b,19727,a),flip(a)].">
      <j1 rule="hyper" parents="63 18142 19727"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19729">
    <literal><![CDATA[
      a(x,y,K(z,(u / w) * v5)) = a(x,y,K(z,(w \ u) * v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,18046,a(flip),b,19728,a)].">
      <j1 rule="hyper" parents="63 18046 19728"/>
    </justification>
  </clause>

  <clause id="19730">
    <literal><![CDATA[
      L(x,y \ (K(z,u) * w),K(y,v5)) = L(x,w,K(y,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,19691,a(flip),b,19718,a),flip(a)].">
      <j1 rule="hyper" parents="63 19691 19718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19731">
    <literal><![CDATA[
      L(x,K(y,z) * u,K(w,v5)) = L(x,u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,14506,a(flip),b,19730,a)].">
      <j1 rule="hyper" parents="63 14506 19730"/>
    </justification>
  </clause>

  <clause id="19732">
    <literal><![CDATA[
      L(x,y * K(z,u),K(w,v5)) = L(x,y,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(19713,a,19731,a)].">
      <j1 rule="hyper" parents="19713 19731"/>
    </justification>
  </clause>

  <clause id="19733">
    <literal><![CDATA[
      K(x,y) * ((K(y,x) * z) * u) = z * L(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(19731(a,1),4575(a,1,2)),flip(a)].">
      <j1 rule="para" parents="19731 4575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19734">
    <literal><![CDATA[
      T(x,K(y,z)) * L(u,x,K(y,z)) = K(y,z) * ((x * K(z,y)) * u)
    ]]></literal>
    <justification jstring="[para(19731(a,1),10229(a,1,2))].">
      <j1 rule="para" parents="19731 10229"/>
    </justification>
  </clause>

  <clause id="19735">
    <literal><![CDATA[
      L(x,K(y,z) * u,a(w,v5,K(v6,v7))) = L(x,u,K(a(w,v5,v6),v7))
    ]]></literal>
    <justification jstring="[para(13539(a,2),19731(a,1,3))].">
      <j1 rule="para" parents="13539 19731"/>
    </justification>
  </clause>

  <clause id="19736">
    <literal><![CDATA[
      T(x,a(y,z * K(u,w),v5)) = L(x,z,K(v5,y))
    ]]></literal>
    <justification jstring="[hyper(14477,a,19732,a)].">
      <j1 rule="hyper" parents="14477 19732"/>
    </justification>
  </clause>

  <clause id="19737">
    <literal><![CDATA[
      L((x * K(y,z)) \ u,x,K(z,y)) = x \ (K(z,T(y,x)) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,10171,a(flip),b,19732,a),flip(a)].">
      <j1 rule="hyper" parents="63 10171 19732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19738">
    <literal><![CDATA[
      L(x,y \ (z * K(u,w)),K(v5,v6)) = L(x,y \ z,K(v5,v6))
    ]]></literal>
    <justification jstring="[para(14185(a,1),19732(a,1,2))].">
      <j1 rule="para" parents="14185 19732"/>
    </justification>
  </clause>

  <clause id="19739">
    <literal><![CDATA[
      T(x,a(y,z * K(u,w),v5)) = T(x,a(y,z,v5))
    ]]></literal>
    <justification jstring="[hyper(333,a,14461,a(flip),b,19736,a),flip(a)].">
      <j1 rule="hyper" parents="333 14461 19736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19740">
    <literal><![CDATA[
      T(x,a(y,z * u,w)) = T(x,a(y,u * z,w))
    ]]></literal>
    <justification jstring="[para(88(a,1),19739(a,1,2,2))].">
      <j1 rule="para" parents="88 19739"/>
    </justification>
  </clause>

  <clause id="19742">
    <literal><![CDATA[
      T(x,a(y,y * z,u)) = L(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(14530,a,19740,a),flip(a)].">
      <j1 rule="hyper" parents="14530 19740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19743">
    <literal><![CDATA[
      L(x,y * z,K(u,y)) = L(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(14528,a,19742,a)].">
      <j1 rule="hyper" parents="14528 19742"/>
    </justification>
  </clause>

  <clause id="19744">
    <literal><![CDATA[
      L(a(x,y,z),z,K(x,y)) = a(x,y,K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,17749,a(flip),b,19743,a),flip(a)].">
      <j1 rule="hyper" parents="63 17749 19743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19745">
    <literal><![CDATA[
      L(a(x,y,z),z,K(x,y)) != u
    ]]></literal>
    <literal><![CDATA[
      a(T(x,y),y,z) = u
    ]]></literal>
    <justification jstring="[para(19744(a,2),10158(a,1))].">
      <j1 rule="para" parents="19744 10158"/>
    </justification>
  </clause>

  <clause id="19746">
    <literal><![CDATA[
      a(T(x,y),y,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(19745,a,19438,a)].">
      <j1 rule="hyper" parents="19745 19438"/>
    </justification>
  </clause>

  <clause id="19747">
    <literal><![CDATA[
      a(x * (y / x),x,z) = a(y,x,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,11956,a(flip),b,19746,a),flip(a)].">
      <j1 rule="hyper" parents="63 11956 19746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19749">
    <literal><![CDATA[
      a(x,y,z) * (x * (T(y,x) * z)) = (y * x) * z
    ]]></literal>
    <justification jstring="[para(19747(a,1),13726(a,1,1))].">
      <j1 rule="para" parents="19747 13726"/>
    </justification>
  </clause>

  <clause id="19750">
    <literal><![CDATA[
      a(x,y,z) \ ((y * x) * z) = x * (T(y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(129,a,19749,a)].">
      <j1 rule="hyper" parents="129 19749"/>
    </justification>
  </clause>

  <clause id="19751">
    <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(333,a,664,a(flip),b,19750,a),flip(a)].">
      <j1 rule="hyper" parents="333 664 19750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19752">
    <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(444,a,19733,a,b,1814,a)].">
      <j1 rule="hyper" parents="444 19733 1814"/>
    </justification>
  </clause>

  <clause id="19753">
    <literal><![CDATA[
      (x * y) * (z * L(u,z,K(y,x))) = (y * x) * ((K(x,y) * z) * u)
    ]]></literal>
    <justification jstring="[hyper(126,a,19733,a(flip),b,10008,a)].">
      <j1 rule="hyper" parents="126 19733 10008"/>
    </justification>
  </clause>

  <clause id="19755">
    <literal><![CDATA[
      L(x,y \ (K(z,u) * w),K(v5,v6)) = L(x,y \ w,K(v5,v6))
    ]]></literal>
    <justification jstring="[para(6355(a,1),19738(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6355 19738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19756">
    <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(63,a,18611,a(flip),b,19755,a),flip(a)].">
      <j1 rule="hyper" parents="63 18611 19755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19758">
    <literal><![CDATA[
      L(x,a(y,z,K(u,w)) * v5,a(v6,v7,K(v8,v9))) = L(x,v5,K(a(v6,v7,v8),v9))
    ]]></literal>
    <justification jstring="[para(13061(a,1),19735(a,1,2,1))].">
      <j1 rule="para" parents="13061 19735"/>
    </justification>
  </clause>

  <clause id="19760">
    <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(19753(a,1),14565(a,1,1))].">
      <j1 rule="para" parents="19753 14565"/>
    </justification>
  </clause>

  <clause id="19761">
    <literal><![CDATA[
      T(x * a(y,x,K(z,u)),y) = y \ (K(z,u) * ((K(u,z) * x) * y))
    ]]></literal>
    <justification jstring="[para(14534(a,1),19752(a,1,1))].">
      <j1 rule="para" parents="14534 19752"/>
    </justification>
  </clause>

  <clause id="19762">
    <literal><![CDATA[
      (K(x,y) * ((K(y,x) * z) * u)) / u = z * a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(262,a,19761,a)].">
      <j1 rule="hyper" parents="262 19761"/>
    </justification>
  </clause>

  <clause id="19763">
    <literal><![CDATA[
      (K(x,y) * ((K(y,x) * z) * (u \ 1))) / (u \ 1) = z * a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[para(13796(a,1),19762(a,2,2))].">
      <j1 rule="para" parents="13796 19762"/>
    </justification>
  </clause>

  <clause id="19764">
    <literal><![CDATA[
      L(x,a(y,z,K(u,w)) * v5,a(v6,v7,K(v8,v9))) = L(x,v5,a(v6,v7,K(v8,v9)))
    ]]></literal>
    <justification jstring="[para(13539(a,2),19758(a,2,3))].">
      <j1 rule="para" parents="13539 19758"/>
    </justification>
  </clause>

  <clause id="19765">
    <literal><![CDATA[
      (K(x,y) * ((K(y,x) * z) / u)) * u = z * a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(18455,a,19763,a)].">
      <j1 rule="hyper" parents="18455 19763"/>
    </justification>
  </clause>

  <clause id="19766">
    <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(13446(a,1),19765(a,1,1,2))].">
      <j1 rule="para" parents="13446 19765"/>
    </justification>
  </clause>

  <clause id="19767">
    <literal><![CDATA[
      ((x * K(K(y,z),u)) / u) * (u * K(y,z)) = (u / x) \ (K(y,z) * u)
    ]]></literal>
    <justification jstring="[para(13253(a,1),19667(a,1,1,1))].">
      <j1 rule="para" parents="13253 19667"/>
    </justification>
  </clause>

  <clause id="19768">
    <literal><![CDATA[
      (x / T(y,K(z,u))) * (y * K(z,u)) = (y / x) \ (K(z,u) * y)
    ]]></literal>
    <justification jstring="[para(5460(a,1),19767(a,1,1))].">
      <j1 rule="para" parents="5460 19767"/>
    </justification>
  </clause>

  <clause id="19769">
    <literal><![CDATA[
      (x / y) \ (K(z,u) * x) = (y / x) * (K(z,u) * x)
    ]]></literal>
    <justification jstring="[hyper(10456,a,19768,a),flip(a)].">
      <j1 rule="hyper" parents="10456 19768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19770">
    <literal><![CDATA[
      ((x \ y) / y) * (K(z,u) * y) = x \ (K(z,u) * y)
    ]]></literal>
    <justification jstring="[para(76(a,1),19769(a,1,1)),flip(a)].">
      <j1 rule="para" parents="76 19769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19771">
    <literal><![CDATA[
      (x \ y) / (K(x,z) * y) = (T(x,z) \ y) / y
    ]]></literal>
    <justification jstring="[hyper(123,a,4530,a(flip),b,19770,a)].">
      <j1 rule="hyper" parents="123 4530 19770"/>
    </justification>
  </clause>

  <clause id="19772">
    <literal><![CDATA[
      ((x \ y) / y) * K(z,x) = (T(x,z) \ y) / y
    ]]></literal>
    <justification jstring="[hyper(63,a,14737,a(flip),b,19771,a)].">
      <j1 rule="hyper" parents="63 14737 19771"/>
    </justification>
  </clause>

  <clause id="19773">
    <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(19772(a,1),4591(a,2,1))].">
      <j1 rule="para" parents="19772 4591"/>
    </justification>
  </clause>

  <clause id="19774">
    <literal><![CDATA[
      K(x,y * (z / T(u,K(w,v5) * v6))) = K(x,y * (z / T(u,v6)))
    ]]></literal>
    <justification jstring="[hyper(16706,a,19677,a),flip(a)].">
      <j1 rule="hyper" parents="16706 19677"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19775">
    <literal><![CDATA[
      K(x,y * ((K(z,u) * w) / T(v5,w))) = K(x,y * (v5 \ (K(z,u) * w)))
    ]]></literal>
    <justification jstring="[hyper(12770,a,19774,a),flip(a)].">
      <j1 rule="hyper" parents="12770 19774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19777">
    <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(19606,a,14155,a)].">
      <j1 rule="hyper" parents="19606 14155"/>
    </justification>
  </clause>

  <clause id="19778">
    <literal><![CDATA[
      (x / (y * x)) * ((y * x) * K(z,u)) = x * K(z,L(u,x,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(5183,a,19651,a)].">
      <j1 rule="hyper" parents="5183 19651"/>
    </justification>
  </clause>

  <clause id="19779">
    <literal><![CDATA[
      K(x,L(y,z,u \ 1)) * (z / u) = (K(x,y) * z) * (z \ (z / u))
    ]]></literal>
    <justification jstring="[hyper(343,a,19653,a)].">
      <j1 rule="hyper" parents="343 19653"/>
    </justification>
  </clause>

  <clause id="19782">
    <literal><![CDATA[
      (K(x,y) * z) \ ((K(x,y) * z) / u) = z \ (z / u)
    ]]></literal>
    <justification jstring="[hyper(121,a,14186,a(flip),b,19779,a(flip))].">
      <j1 rule="hyper" parents="121 14186 19779"/>
    </justification>
  </clause>

  <clause id="19783">
    <literal><![CDATA[
      x * L(y \ 1,y,y \ (K(z,u) * x)) = x / y
    ]]></literal>
    <justification jstring="[hyper(10049,a,19782,a)].">
      <j1 rule="hyper" parents="10049 19782"/>
    </justification>
  </clause>

  <clause id="19784">
    <literal><![CDATA[
      x * L(y \ 1,y,y \ (x * K(z,u))) = x / y
    ]]></literal>
    <justification jstring="[para(6887(a,1),19783(a,1,2,3,2))].">
      <j1 rule="para" parents="6887 19783"/>
    </justification>
  </clause>

  <clause id="19785">
    <literal><![CDATA[
      x * L((y \ (x * K(z,u))) \ 1,y \ (x * K(z,u)),y) = x / (y \ (x * K(z,u)))
    ]]></literal>
    <justification jstring="[para(10098(a,1),19784(a,1,2))].">
      <j1 rule="para" parents="10098 19784"/>
    </justification>
  </clause>

  <clause id="19786">
    <literal><![CDATA[
      (x * K(y,z)) \ (x / u) = x \ ((x * K(z,y)) / u)
    ]]></literal>
    <justification jstring="[para(19784(a,1),19026(a,1,2))].">
      <j1 rule="para" parents="19784 19026"/>
    </justification>
  </clause>

  <clause id="19788">
    <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(18859,a,19669,a)].">
      <j1 rule="hyper" parents="18859 19669"/>
    </justification>
  </clause>

  <clause id="19789">
    <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(471(a,1),19788(a,1,2,2,1))].">
      <j1 rule="para" parents="471 19788"/>
    </justification>
  </clause>

  <clause id="19790">
    <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(10961,a,19609,a),flip(a)].">
      <j1 rule="hyper" parents="10961 19609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19791">
    <literal><![CDATA[
      K(x,((T(y,z) \ 1) * u) \ ((y \ 1) * (z * y))) = K(x,(y \ u) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,14192,a(flip),b,19609,a),flip(a)].">
      <j1 rule="hyper" parents="63 14192 19609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19792">
    <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(14558,a,19756,a)].">
      <j1 rule="hyper" parents="14558 19756"/>
    </justification>
  </clause>

  <clause id="19794">
    <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(63,a,12844,a(flip),b,19773,a)].">
      <j1 rule="hyper" parents="63 12844 19773"/>
    </justification>
  </clause>

  <clause id="19795">
    <literal><![CDATA[
      x / (y \ (x * K(z,u))) = x * ((x * K(z,u)) \ y)
    ]]></literal>
    <justification jstring="[para(388(a,1),19785(a,1,2)),flip(a)].">
      <j1 rule="para" parents="388 19785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19796">
    <literal><![CDATA[
      x / ((y / x) * (x * K(z,u))) = x * ((x * K(z,u)) \ (x / y))
    ]]></literal>
    <justification jstring="[para(19668(a,1),19795(a,1,2))].">
      <j1 rule="para" parents="19668 19795"/>
    </justification>
  </clause>

  <clause id="19797">
    <literal><![CDATA[
      x / ((y / x) * (x * K(z,u))) = x * (x \ ((x * K(u,z)) / y))
    ]]></literal>
    <justification jstring="[para(19786(a,1),19796(a,2,2))].">
      <j1 rule="para" parents="19786 19796"/>
    </justification>
  </clause>

  <clause id="19798">
    <literal><![CDATA[
      x / ((y / x) * (x * K(z,u))) = (x * K(u,z)) / y
    ]]></literal>
    <justification jstring="[hyper(333,a,10,a(flip),b,19797,a),flip(a)].">
      <j1 rule="hyper" parents="333 10 19797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19800">
    <literal><![CDATA[
      x / (((T(y,y \ 1) * (x * K(z,u))) / x) * (x * K(u,z))) = R(y \ 1,y,x * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(333,a,1953,a(flip),b,19798,a),flip(a)].">
      <j1 rule="hyper" parents="333 1953 19798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19801">
    <literal><![CDATA[
      K(x,y) * (((x \ z) / z) \ u) = ((T(x,y) \ z) / z) \ u
    ]]></literal>
    <justification jstring="[hyper(5799,a,19794,a)].">
      <j1 rule="hyper" parents="5799 19794"/>
    </justification>
  </clause>

  <clause id="19803">
    <literal><![CDATA[
      T(x,((T(y,z) \ u) / u) \ w) = T(x,T((y \ u) / u,z) \ w)
    ]]></literal>
    <justification jstring="[para(19801(a,1),15247(a,1,2))].">
      <j1 rule="para" parents="19801 15247"/>
    </justification>
  </clause>

  <clause id="19804">
    <literal><![CDATA[
      T(x,T((y \ z) / z,u) \ w) = T(x,(z \ (z / T(y,u))) \ w)
    ]]></literal>
    <justification jstring="[hyper(18908,a,19803,a),flip(a)].">
      <j1 rule="hyper" parents="18908 19803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19805">
    <literal><![CDATA[
      ((x * y) * ((K(y,x) * z) * u)) / T((y * x) * z,u) = L(u,z,x * y)
    ]]></literal>
    <justification jstring="[para(17558(a,1),19760(a,1,2))].">
      <j1 rule="para" parents="17558 19760"/>
    </justification>
  </clause>

  <clause id="19806">
    <literal><![CDATA[
      L(x,K(y,z) * u,z * y) = L(x,u,z * y)
    ]]></literal>
    <justification jstring="[hyper(13643,a,19805,a)].">
      <j1 rule="hyper" parents="13643 19805"/>
    </justification>
  </clause>

  <clause id="19808">
    <literal><![CDATA[
      L(x,K(y,z / y) * u,z) = L(x,u,(z / y) * y)
    ]]></literal>
    <justification jstring="[para(12(a,1),19806(a,1,3))].">
      <j1 rule="para" parents="12 19806"/>
    </justification>
  </clause>

  <clause id="19809">
    <literal><![CDATA[
      L(x,K(y,y \ z) * u,z) = L(x,u,(z / y) * y)
    ]]></literal>
    <justification jstring="[para(4368(a,1),19808(a,1,2,1))].">
      <j1 rule="para" parents="4368 19808"/>
    </justification>
  </clause>

  <clause id="19810">
    <literal><![CDATA[
      L(x,K(y,z) * u,z) = L(x,u,(z / y) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,14716,a(flip),b,19809,a)].">
      <j1 rule="hyper" parents="63 14716 19809"/>
    </justification>
  </clause>

  <clause id="19811">
    <literal><![CDATA[
      L(x,K(y,z) * u,z) = L(x,u,z)
    ]]></literal>
    <justification jstring="[para(12(a,1),19810(a,2,3))].">
      <j1 rule="para" parents="12 19810"/>
    </justification>
  </clause>

  <clause id="19812">
    <literal><![CDATA[
      L(x,K(y,z) * u,y) = L(x,u,y)
    ]]></literal>
    <justification jstring="[para(4558(a,1),19811(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4558 19811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19816">
    <literal><![CDATA[
      L(x,y \ K(z,u),z) = L(x,y \ 1,z)
    ]]></literal>
    <justification jstring="[para(13659(a,1),19812(a,1,2))].">
      <j1 rule="para" parents="13659 19812"/>
    </justification>
  </clause>

  <clause id="19817">
    <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(19816(a,1),18970(a,1,2,1))].">
      <j1 rule="para" parents="19816 18970"/>
    </justification>
  </clause>

  <clause id="19818">
    <literal><![CDATA[
      T(x,(y * (z \ K(u,z \ 1))) * u) = T(x,u * ((z \ 1) * T(y,u / z)))
    ]]></literal>
    <justification jstring="[para(13327(a,1),19817(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13327 19817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19820">
    <literal><![CDATA[
      T(x,(y * (z \ K(u,z \ 1))) * u) = T(x,u * ((z \ 1) * T(y,z \ u)))
    ]]></literal>
    <justification jstring="[hyper(333,a,16720,a(flip),b,19818,a),flip(a)].">
      <j1 rule="hyper" parents="333 16720 19818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19821">
    <literal><![CDATA[
      T(x,y * ((z \ 1) * T(u,z \ y))) = T(x,(u * (z \ 1)) * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,16283,a(flip),b,19820,a),flip(a)].">
      <j1 rule="hyper" parents="63 16283 19820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19822">
    <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(17539(a,1),19580(a,1,1,1))].">
      <j1 rule="para" parents="17539 19580"/>
    </justification>
  </clause>

  <clause id="19824">
    <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(19384,a,19822,a)].">
      <j1 rule="hyper" parents="19384 19822"/>
    </justification>
  </clause>

  <clause id="19826">
    <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(19382(a,1),19824(a,2,2))].">
      <j1 rule="para" parents="19382 19824"/>
    </justification>
  </clause>

  <clause id="19827">
    <literal><![CDATA[
      L(K(x,y) * K(z,u),w,K(v5,v6)) = K(z,u) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(2942,a,19826,a)].">
      <j1 rule="hyper" parents="2942 19826"/>
    </justification>
  </clause>

  <clause id="19828">
    <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(19827(a,1),19346(a,1,1,1))].">
      <j1 rule="para" parents="19827 19346"/>
    </justification>
  </clause>

  <clause id="19829">
    <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(19298(a,1),19828(a,1,1))].">
      <j1 rule="para" parents="19298 19828"/>
    </justification>
  </clause>

  <clause id="19831">
    <literal><![CDATA[
      T(K(x,y) * a(z,u,w),K(v5,v6)) = a(z,u,w) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6867,a,19829,a)].">
      <j1 rule="hyper" parents="6867 19829"/>
    </justification>
  </clause>

  <clause id="19833">
    <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(63,a,14015,a(flip),b,19648,a)].">
      <j1 rule="hyper" parents="63 14015 19648"/>
    </justification>
  </clause>

  <clause id="19834">
    <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(17078,a,19833,a)].">
      <j1 rule="hyper" parents="17078 19833"/>
    </justification>
  </clause>

  <clause id="19835">
    <literal><![CDATA[
      K(x,(((y * z) \ z) * u) \ T(z,y)) = K(x,L(u \ (y * z),z,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(17082,a,19834,a),flip(a)].">
      <j1 rule="hyper" parents="17082 19834"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19836">
    <literal><![CDATA[
      K(x,L(y \ (z * u),u,z \ 1)) = K(x,(((u * z) \ u) * y) \ u)
    ]]></literal>
    <justification jstring="[para(13315(a,1),19835(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13315 19835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19837">
    <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(13539(a,2),19675(a,1,2,1,2))].">
      <j1 rule="para" parents="13539 19675"/>
    </justification>
  </clause>

  <clause id="19838">
    <literal><![CDATA[
      (x / (1 / y)) * (K(z,T(u,y)) / y) = (x / (y \ 1)) * (y \ K(z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,17735,a(flip),b,19722,a),flip(a)].">
      <j1 rule="hyper" parents="63 17735 19722"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19839">
    <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(333,a,14015,a(flip),b,19790,a),flip(a)].">
      <j1 rule="hyper" parents="333 14015 19790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19840">
    <literal><![CDATA[
      K(x,L(y \ (z * u),u,z \ 1)) = K(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,19791,a(flip),b,19839,a),flip(a)].">
      <j1 rule="hyper" parents="63 19791 19839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19841">
    <literal><![CDATA[
      K(x,(((y * z) \ y) * u) \ y) = K(x,(z \ u) \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,19836,a(flip),b,19840,a)].">
      <j1 rule="hyper" parents="63 19836 19840"/>
    </justification>
  </clause>

  <clause id="19842">
    <literal><![CDATA[
      K(x,y \ (z * (((y * u) \ y) \ y))) = K(x,(u \ (z \ y)) \ y)
    ]]></literal>
    <justification jstring="[hyper(19683,a,19841,a)].">
      <j1 rule="hyper" parents="19683 19841"/>
    </justification>
  </clause>

  <clause id="19843">
    <literal><![CDATA[
      K(x,T(y \ z,K(u,w)) \ v5) = K(x,(((v5 * y) \ v5) * z) \ v5)
    ]]></literal>
    <justification jstring="[hyper(333,a,16330,a,b,19841,a)].">
      <j1 rule="hyper" parents="333 16330 19841"/>
    </justification>
  </clause>

  <clause id="19844">
    <literal><![CDATA[
      K(x,(((y * z) \ y) * T(u,z \ 1)) \ y) = K(x,(u / z) \ y)
    ]]></literal>
    <justification jstring="[hyper(333,a,15142,a(flip),b,19841,a),flip(a)].">
      <j1 rule="hyper" parents="333 15142 19841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19845">
    <literal><![CDATA[
      K(x,((y \ z) \ u) \ y) = K(x,((z \ y) * u) \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),19841(a,1,2,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 19841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19846">
    <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(14044(a,1),19841(a,2,2,1))].">
      <j1 rule="para" parents="14044 19841"/>
    </justification>
  </clause>

  <clause id="19847">
    <literal><![CDATA[
      K(x,((y \ z) * u) \ z) * K(x,K(z,y \ u)) = K(x,z / ((z \ y) \ u))
    ]]></literal>
    <justification jstring="[para(19845(a,1),10389(a,1,1))].">
      <j1 rule="para" parents="19845 10389"/>
    </justification>
  </clause>

  <clause id="19848">
    <literal><![CDATA[
      K(x,y \ (z * T(y * u,y))) = K(x,(u \ (z \ y)) \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,12749,a(flip),b,19842,a)].">
      <j1 rule="hyper" parents="63 12749 19842"/>
    </justification>
  </clause>

  <clause id="19849">
    <literal><![CDATA[
      K(x,(y \ (z \ u)) \ u) = K(x,u \ (z * (y * u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,18698,a(flip),b,19848,a),flip(a)].">
      <j1 rule="hyper" parents="63 18698 19848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19850">
    <literal><![CDATA[
      K(x,y \ ((y / z) * (u * y))) = K(x,(u \ z) \ y)
    ]]></literal>
    <justification jstring="[para(79(a,1),19849(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="79 19849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19851">
    <literal><![CDATA[
      K(x,y \ (R(1 / z,z,y) * (u * y))) = K(x,(u \ (z * y)) \ y)
    ]]></literal>
    <justification jstring="[para(398(a,1),19849(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="398 19849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19852">
    <literal><![CDATA[
      K(x,y \ ((y / z) * (u * y))) = K(x,T(y / (u \ z),y))
    ]]></literal>
    <justification jstring="[hyper(333,a,6368,a,b,19850,a),flip(a)].">
      <j1 rule="hyper" parents="333 6368 19850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19853">
    <literal><![CDATA[
      K(x,((y / z) \ u) \ z) = K(x,z \ ((z / u) * y))
    ]]></literal>
    <justification jstring="[para(12(a,1),19850(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="12 19850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19854">
    <literal><![CDATA[
      K(x * (y * (x \ 1)),z \ ((z / u) * w)) = K(y,T(((z / w) * u) \ z,x))
    ]]></literal>
    <justification jstring="[hyper(19665,a,19853,a),flip(a)].">
      <j1 rule="hyper" parents="19665 19853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19855">
    <literal><![CDATA[
      K(x,y \ ((y / z) * (u * y))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(u \ z) \ y) = w
    ]]></literal>
    <justification jstring="[para(19852(a,2),6413(a,1))].">
      <j1 rule="para" parents="19852 6413"/>
    </justification>
  </clause>

  <clause id="19856">
    <literal><![CDATA[
      K(x,(y * ((z * u) \ z)) \ z) = K(x,(y / u) \ z)
    ]]></literal>
    <justification jstring="[para(5826(a,1),19844(a,1,2,1))].">
      <j1 rule="para" parents="5826 19844"/>
    </justification>
  </clause>

  <clause id="19857">
    <literal><![CDATA[
      K(x,y \ ((y * z) * (u \ y))) = K(x,(u / z) \ y)
    ]]></literal>
    <justification jstring="[hyper(19683,a,19856,a)].">
      <j1 rule="hyper" parents="19683 19856"/>
    </justification>
  </clause>

  <clause id="19858">
    <literal><![CDATA[
      K(x,((y / z) / u) \ y) = K(x,y \ ((y * u) * z))
    ]]></literal>
    <justification jstring="[para(79(a,1),19857(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="79 19857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19859">
    <literal><![CDATA[
      K(x,y \ ((z * y) * (u \ y))) = K(x,(u / T(z,y)) \ y)
    ]]></literal>
    <justification jstring="[para(111(a,1),19857(a,1,2,2,1))].">
      <j1 rule="para" parents="111 19857"/>
    </justification>
  </clause>

  <clause id="19860">
    <literal><![CDATA[
      K(x,((y * ((y * z) / y)) / u) \ z) = K(x,z \ ((z * u) * ((y * z) \ T(z,y))))
    ]]></literal>
    <justification jstring="[para(10072(a,1),19857(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="10072 19857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19861">
    <literal><![CDATA[
      K(x,T(y,z * u) / ((y / z) / u)) = K(x,y \ ((y * u) * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,18526,a,b,19858,a)].">
      <j1 rule="hyper" parents="63 18526 19858"/>
    </justification>
  </clause>

  <clause id="19862">
    <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(3205(a,1),19859(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="3205 19859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19863">
    <literal><![CDATA[
      K(x,(y \ (z * u)) \ u) = K(x,u \ (z \ (y * u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,14300,a(flip),b,19851,a),flip(a)].">
      <j1 rule="hyper" parents="63 14300 19851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19864">
    <literal><![CDATA[
      T(K(x,y \ (z \ (u * y))),y) = K(x,y / (u \ (z * y)))
    ]]></literal>
    <justification jstring="[para(19863(a,1),6893(a,1,1))].">
      <j1 rule="para" parents="19863 6893"/>
    </justification>
  </clause>

  <clause id="19865">
    <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(63,a,14214,a,b,19864,a)].">
      <j1 rule="hyper" parents="63 14214 19864"/>
    </justification>
  </clause>

  <clause id="19866">
    <literal><![CDATA[
      K(x,y / ((y \ z) \ u)) = K(x,y / ((z \ y) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,13569,a(flip),b,19847,a),flip(a)].">
      <j1 rule="hyper" parents="63 13569 19847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19867">
    <literal><![CDATA[
      K(x,T(((y / z) * u) \ y,w)) = K(x,T(y \ ((y / u) * z),w))
    ]]></literal>
    <justification jstring="[hyper(14166,a,19854,a),flip(a)].">
      <j1 rule="hyper" parents="14166 19854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19868">
    <literal><![CDATA[
      K(x,T(y \ ((y / z) * u),z)) = K(x,y / (z * (u \ y)))
    ]]></literal>
    <justification jstring="[hyper(63,a,18527,a(flip),b,19867,a),flip(a)].">
      <j1 rule="hyper" parents="63 18527 19867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19869">
    <literal><![CDATA[
      K(x,(y * (z \ u)) / u) = K(x,u / (z * (y \ u)))
    ]]></literal>
    <justification jstring="[hyper(19515,a,19868,a)].">
      <j1 rule="hyper" parents="19515 19868"/>
    </justification>
  </clause>

  <clause id="19870">
    <literal><![CDATA[
      K(x,(y * T(z,z \ u)) / u) = K(x,u / ((z \ u) * (y \ u)))
    ]]></literal>
    <justification jstring="[para(112(a,2),19869(a,1,2,1,2))].">
      <j1 rule="para" parents="112 19869"/>
    </justification>
  </clause>

  <clause id="19871">
    <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(18286(a,2),19869(a,2,2,2,2))].">
      <j1 rule="para" parents="18286 19869"/>
    </justification>
  </clause>

  <clause id="19872">
    <literal><![CDATA[
      K(x,y / ((z \ y) * (u \ y))) = K(x,(u * T(z,y)) / y)
    ]]></literal>
    <justification jstring="[hyper(63,a,16898,a(flip),b,19870,a),flip(a)].">
      <j1 rule="hyper" parents="63 16898 19870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19873">
    <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(14122(a,1),19872(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14122 19872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19874">
    <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(17713(a,1),19837(a,1,2,1))].">
      <j1 rule="para" parents="17713 19837"/>
    </justification>
  </clause>

  <clause id="19875">
    <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(19674(a,1),19874(a,1,2)),flip(a)].">
      <j1 rule="para" parents="19674 19874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19876">
    <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(333,a,13250,a(flip),b,19875,a),flip(a)].">
      <j1 rule="hyper" parents="333 13250 19875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19878">
    <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(13732(a,2),19876(a,1,1))].">
      <j1 rule="para" parents="13732 19876"/>
    </justification>
  </clause>

  <clause id="19879">
    <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(14461(a,2),19878(a,2,2))].">
      <j1 rule="para" parents="14461 19878"/>
    </justification>
  </clause>

  <clause id="19880">
    <literal><![CDATA[
      L(K(x,y) / z,u,K(w,v5)) = K(x,y) / L(z,u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,19684,a(flip),b,19879,a)].">
      <j1 rule="hyper" parents="63 19684 19879"/>
    </justification>
  </clause>

  <clause id="19881">
    <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(333,a,18163,a(flip),b,19880,a),flip(a)].">
      <j1 rule="hyper" parents="333 18163 19880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19882">
    <literal><![CDATA[
      L(K(x,y) * z,u,K(w,v5)) = K(x,y) * L(z,u,K(w,v5))
    ]]></literal>
    <justification jstring="[para(13307(a,1),19881(a,1,1))].">
      <j1 rule="para" parents="13307 19881"/>
    </justification>
  </clause>

  <clause id="19883">
    <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(333,a,14778,a(flip),b,19882,a),flip(a)].">
      <j1 rule="hyper" parents="333 14778 19882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19884">
    <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(19882(a,2),17179(a,1,2,1))].">
      <j1 rule="para" parents="19882 17179"/>
    </justification>
  </clause>

  <clause id="19885">
    <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(8088(a,1),19883(a,1,1))].">
      <j1 rule="para" parents="8088 19883"/>
    </justification>
  </clause>

  <clause id="19886">
    <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(11459(a,1),19885(a,1,1))].">
      <j1 rule="para" parents="11459 19885"/>
    </justification>
  </clause>

  <clause id="19887">
    <literal><![CDATA[
      T(a(x,y,z) \ u,K(w,v5)) = a(x,y,z) \ T(u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(14494,a,19886,a),flip(a)].">
      <j1 rule="hyper" parents="14494 19886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19888">
    <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(333,a,15672,a(flip),b,19887,a),flip(a)].">
      <j1 rule="hyper" parents="333 15672 19887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19889">
    <literal><![CDATA[
      x * K(y,K(z,x * a(u,w,v5))) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(9(a,1),19888(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 19888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19890">
    <literal><![CDATA[
      T(a(x,y,z) * u,K(w,v5)) = a(x,y,z) * T(u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(126,a,19889,a(flip),b,15672,a),flip(a)].">
      <j1 rule="hyper" parents="126 19889 15672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19891">
    <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(121,a,19890,a,b,6809,a(flip))].">
      <j1 rule="hyper" parents="121 19890 6809"/>
    </justification>
  </clause>

  <clause id="19892">
    <literal><![CDATA[
      K(x,K(y,a(z,u,w) \ v5)) = v5 \ T(v5,K(x,y))
    ]]></literal>
    <justification jstring="[para(10(a,1),19891(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 19891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19893">
    <literal><![CDATA[
      K(x,K(y,a(z,u,w) \ v5)) = K(v5,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(333,a,4215,a,b,19892,a),flip(a)].">
      <j1 rule="hyper" parents="333 4215 19892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19895">
    <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(19893(a,1),15835(a,1,1))].">
      <j1 rule="para" parents="19893 15835"/>
    </justification>
  </clause>

  <clause id="19896">
    <literal><![CDATA[
      K(x,T(y,a(z,u,w) \ v5)) = K(x,T(y,v5))
    ]]></literal>
    <justification jstring="[hyper(16006,a,19895,a),flip(a)].">
      <j1 rule="hyper" parents="16006 19895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19897">
    <literal><![CDATA[
      K(x,T(y,a(z,u,w) * v5)) = K(x,T(y,v5))
    ]]></literal>
    <justification jstring="[hyper(15784,a,19896,a)].">
      <j1 rule="hyper" parents="15784 19896"/>
    </justification>
  </clause>

  <clause id="19898">
    <literal><![CDATA[
      K(x,T(y,z * a(u,w,v5))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(15783,a,19896,a)].">
      <j1 rule="hyper" parents="15783 19896"/>
    </justification>
  </clause>

  <clause id="19899">
    <literal><![CDATA[
      K(x,T(y,(z * u) * w)) = K(x,T(y,z * (u * w)))
    ]]></literal>
    <justification jstring="[para(13589(a,1),19897(a,1,2,2))].">
      <j1 rule="para" parents="13589 19897"/>
    </justification>
  </clause>

  <clause id="19900">
    <literal><![CDATA[
      T(x * K(y,T(x,z)),y) = T(x,K(y,z * a(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(19898(a,1),7126(a,1,1,2))].">
      <j1 rule="para" parents="19898 7126"/>
    </justification>
  </clause>

  <clause id="19901">
    <literal><![CDATA[
      K(x,T(y,T(z * u,w) * v5)) = K(x,T(y,u * (z * v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,16712,a,b,19899,a)].">
      <j1 rule="hyper" parents="63 16712 19899"/>
    </justification>
  </clause>

  <clause id="19903">
    <literal><![CDATA[
      T(x,K(y,z * a(u,w,v5))) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(7258,a,19900,a),flip(a)].">
      <j1 rule="hyper" parents="7258 19900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19904">
    <literal><![CDATA[
      T(x,K(y,(z * u) * w)) = T(x,K(y,z * (u * w)))
    ]]></literal>
    <justification jstring="[para(84(a,1),19903(a,1,2,2))].">
      <j1 rule="para" parents="84 19903"/>
    </justification>
  </clause>

  <clause id="19906">
    <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(19903(a,1),14912(a,1,2,1,2))].">
      <j1 rule="para" parents="19903 14912"/>
    </justification>
  </clause>

  <clause id="19907">
    <literal><![CDATA[
      K(x,T(y,T(z * a(u,w,v5),v6) * v7)) = K(x,T(y,z * v7))
    ]]></literal>
    <justification jstring="[hyper(333,a,19897,a(flip),b,19901,a),flip(a)].">
      <j1 rule="hyper" parents="333 19897 19901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19908">
    <literal><![CDATA[
      K(x,T(y,(z * a(u,w,v5)) * v6)) = K(x,T(y,z * v6))
    ]]></literal>
    <justification jstring="[hyper(16570,a,19907,a)].">
      <j1 rule="hyper" parents="16570 19907"/>
    </justification>
  </clause>

  <clause id="19909">
    <literal><![CDATA[
      K(x,T(y,z * (a(u,w,v5) * v6))) = K(x,T(y,z * v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,19899,a(flip),b,19908,a)].">
      <j1 rule="hyper" parents="63 19899 19908"/>
    </justification>
  </clause>

  <clause id="19910">
    <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(63,a,17683,a(flip),b,19909,a),flip(a)].">
      <j1 rule="hyper" parents="63 17683 19909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19912">
    <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(19903(a,1),19906(a,1,2)),flip(a)].">
      <j1 rule="para" parents="19903 19906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19913">
    <literal><![CDATA[
      T(x,K(y * a(z,u,w),v5) * v6) = T(x,K(y,v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(333,a,14912,a(flip),b,19912,a),flip(a)].">
      <j1 rule="hyper" parents="333 14912 19912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19915">
    <literal><![CDATA[
      T(x,T(y,z * a(u,w,v5)) \ v6) = T(x,K(z,y) * (y \ v6))
    ]]></literal>
    <justification jstring="[para(4555(a,1),19913(a,1,2))].">
      <j1 rule="para" parents="4555 19913"/>
    </justification>
  </clause>

  <clause id="19916">
    <literal><![CDATA[
      T(x,T(y,z * a(u,w,v5)) \ v6) = T(x,T(y,z) \ v6)
    ]]></literal>
    <justification jstring="[para(4555(a,1),19915(a,2,2))].">
      <j1 rule="para" parents="4555 19915"/>
    </justification>
  </clause>

  <clause id="19917">
    <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(18309,a,19916,a),flip(a)].">
      <j1 rule="hyper" parents="18309 19916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19918">
    <literal><![CDATA[
      T(x,y / T(z,T(a(u,w,v5),v6) * v7)) = T(x,y / T(z,v7))
    ]]></literal>
    <justification jstring="[hyper(15592,a,19917,a),flip(a)].">
      <j1 rule="hyper" parents="15592 19917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19919">
    <literal><![CDATA[
      T(x,y / T(z,u * a(w,v5,v6))) = T(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(12268(a,1),19918(a,1,2,2))].">
      <j1 rule="para" parents="12268 19918"/>
    </justification>
  </clause>

  <clause id="19920">
    <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(19919(a,1),6724(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="19919 6724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19921">
    <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(19920(a,2),7309(a,1))].">
      <j1 rule="para" parents="19920 7309"/>
    </justification>
  </clause>

  <clause id="19922">
    <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(19921,a,19910,a)].">
      <j1 rule="hyper" parents="19921 19910"/>
    </justification>
  </clause>

  <clause id="19923">
    <literal><![CDATA[
      K(x,y \ T(z,a(u,w,v5) * v6)) = K(x,y \ T(z,v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,16812,a(flip),b,19922,a),flip(a)].">
      <j1 rule="hyper" parents="63 16812 19922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19924">
    <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(25(a,2),19884(a,1,2))].">
      <j1 rule="para" parents="25 19884"/>
    </justification>
  </clause>

  <clause id="19925">
    <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(14486(a,1),19924(a,1,2))].">
      <j1 rule="para" parents="14486 19924"/>
    </justification>
  </clause>

  <clause id="19926">
    <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(63,a,15827,a(flip),b,19925,a),flip(a)].">
      <j1 rule="hyper" parents="63 15827 19925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19927">
    <literal><![CDATA[
      K(x,T(y,L(z,u,w) * v5)) = K(x,T(y,z * v5))
    ]]></literal>
    <justification jstring="[hyper(17639,a,19926,a),flip(a)].">
      <j1 rule="hyper" parents="17639 19926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19929">
    <literal><![CDATA[
      K(x,T(y,(z \ u) * (z * w))) = K(x,T(y,w * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,16579,a(flip),b,19927,a)].">
      <j1 rule="hyper" parents="63 16579 19927"/>
    </justification>
  </clause>

  <clause id="19930">
    <literal><![CDATA[
      K(x,T(y,(z * u) * (z \ w))) = K(x,T(y,u * w))
    ]]></literal>
    <justification jstring="[hyper(15608,a,19929,a)].">
      <j1 rule="hyper" parents="15608 19929"/>
    </justification>
  </clause>

  <clause id="19932">
    <literal><![CDATA[
      K(x,T(y,(z \ u) * w)) = K(x,T(y,u * (z \ w)))
    ]]></literal>
    <justification jstring="[para(10(a,1),19930(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10 19930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19933">
    <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(63,a,17040,a(flip),b,19932,a),flip(a)].">
      <j1 rule="hyper" parents="63 17040 19932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19934">
    <literal><![CDATA[
      K(x,y * ((z * K(u,w)) * ((v5 \ z) / z))) = K(x,y * T(v5 \ (z * K(u,w)),z))
    ]]></literal>
    <justification jstring="[hyper(16787,a,19670,a),flip(a)].">
      <j1 rule="hyper" parents="16787 19670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19935">
    <literal><![CDATA[
      K(x,y * ((z * K(u,w)) * ((v5 \ z) / z))) = K(x,y * (z / (K(w,u) * v5)))
    ]]></literal>
    <justification jstring="[hyper(333,a,18739,a(flip),b,19934,a),flip(a)].">
      <j1 rule="hyper" parents="333 18739 19934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19936">
    <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(19682(a,1),7856(a,1))].">
      <j1 rule="para" parents="19682 7856"/>
    </justification>
  </clause>

  <clause id="19937">
    <literal><![CDATA[
      K(x,T(y \ (z * (u \ y)),u)) = K(x,y / ((y / z) * u))
    ]]></literal>
    <justification jstring="[hyper(19936,a,19466,a)].">
      <j1 rule="hyper" parents="19936 19466"/>
    </justification>
  </clause>

  <clause id="19938">
    <literal><![CDATA[
      K(x,((y / z) * u) / y) = K(x,y / ((y / u) * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,16851,a(flip),b,19937,a)].">
      <j1 rule="hyper" parents="63 16851 19937"/>
    </justification>
  </clause>

  <clause id="19939">
    <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(63,a,19649,a(flip),b,19608,a)].">
      <j1 rule="hyper" parents="63 19649 19608"/>
    </justification>
  </clause>

  <clause id="19940">
    <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(14027,a,19939,a),flip(a)].">
      <j1 rule="hyper" parents="14027 19939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19942">
    <literal><![CDATA[
      K(x,(y \ z) / (u * T(z \ (y \ z),z))) = K(x,((y \ 1) * z) / (u * (y \ 1)))
    ]]></literal>
    <justification jstring="[hyper(333,a,18181,a(flip),b,19940,a),flip(a)].">
      <j1 rule="hyper" parents="333 18181 19940"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19943">
    <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(6787(a,1),19766(a,1,1,2,1))].">
      <j1 rule="para" parents="6787 19766"/>
    </justification>
  </clause>

  <clause id="19944">
    <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(15584(a,1),19943(a,1,1))].">
      <j1 rule="para" parents="15584 19943"/>
    </justification>
  </clause>

  <clause id="19945">
    <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(6190(a,1),19944(a,1,1,2,1))].">
      <j1 rule="para" parents="6190 19944"/>
    </justification>
  </clause>

  <clause id="19946">
    <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(4556(a,1),19945(a,1,1))].">
      <j1 rule="para" parents="4556 19945"/>
    </justification>
  </clause>

  <clause id="19947">
    <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(19015,a,19946,a),flip(a)].">
      <j1 rule="hyper" parents="19015 19946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19948">
    <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(16564(a,1),19947(a,2,2))].">
      <j1 rule="para" parents="16564 19947"/>
    </justification>
  </clause>

  <clause id="19949">
    <literal><![CDATA[
      x * a(y,x,K(x \ z,u)) = z * ((K(y,u) * z) \ (K(y,u) * x))
    ]]></literal>
    <justification jstring="[para(19584(a,1),19948(a,1,2))].">
      <j1 rule="para" parents="19584 19948"/>
    </justification>
  </clause>

  <clause id="19950">
    <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(7714(a,1),19949(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7714 19949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19952">
    <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(13795(a,1),19950(a,2,2))].">
      <j1 rule="para" parents="13795 19950"/>
    </justification>
  </clause>

  <clause id="19953">
    <literal><![CDATA[
      (x * y) * L((x * y) \ z,x,K(y,u)) = z * a(u,z,K(y,z \ x))
    ]]></literal>
    <justification jstring="[para(17750(a,1),19952(a,1,2))].">
      <j1 rule="para" parents="17750 19952"/>
    </justification>
  </clause>

  <clause id="19954">
    <literal><![CDATA[
      x * a(y,x,K(z,x \ u)) = u * (z * L(z \ (u \ x),u,K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(1032,a,19953,a),flip(a)].">
      <j1 rule="hyper" parents="1032 19953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19955">
    <literal><![CDATA[
      x * L(y * (y \ (x \ z)),x,K(y,u)) = z * a(u,z,K(y,z \ x))
    ]]></literal>
    <justification jstring="[para(19676(a,2),19954(a,2,2)),flip(a)].">
      <j1 rule="para" parents="19676 19954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19956">
    <literal><![CDATA[
      x * L(x \ y,x,K(z,u)) = y * a(u,y,K(z,y \ x))
    ]]></literal>
    <justification jstring="[para(10(a,1),19955(a,1,2,1))].">
      <j1 rule="para" parents="10 19955"/>
    </justification>
  </clause>

  <clause id="19958">
    <literal><![CDATA[
      x * L(x \ y,x,K(z,u)) = y * a(u,y,K(x \ y,z))
    ]]></literal>
    <justification jstring="[para(11163(a,2),19956(a,2,2))].">
      <j1 rule="para" parents="11163 19956"/>
    </justification>
  </clause>

  <clause id="19959">
    <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(10077(a,1),19751(a,2,1))].">
      <j1 rule="para" parents="10077 19751"/>
    </justification>
  </clause>

  <clause id="19960">
    <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="[hyper(333,a,235,a(flip),b,19959,a),flip(a)].">
      <j1 rule="hyper" parents="333 235 19959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19961">
    <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(111(a,1),19960(a,1,1,3,2))].">
      <j1 rule="para" parents="111 19960"/>
    </justification>
  </clause>

  <clause id="19962">
    <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(7041(a,1),19865(a,1,1))].">
      <j1 rule="para" parents="7041 19865"/>
    </justification>
  </clause>

  <clause id="19963">
    <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(15810(a,1),19962(a,1,1))].">
      <j1 rule="para" parents="15810 19962"/>
    </justification>
  </clause>

  <clause id="19964">
    <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(19904(a,1),19963(a,1,1))].">
      <j1 rule="para" parents="19904 19963"/>
    </justification>
  </clause>

  <clause id="19965">
    <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(15949(a,1),19964(a,1,1))].">
      <j1 rule="para" parents="15949 19964"/>
    </justification>
  </clause>

  <clause id="19966">
    <literal><![CDATA[
      T(x,K(y,z)) \ (u \ ((K(y,z) * u) * x)) = K(y,x / ((z * u) \ (u * x)))
    ]]></literal>
    <justification jstring="[para(15818(a,1),19965(a,1,1))].">
      <j1 rule="para" parents="15818 19965"/>
    </justification>
  </clause>

  <clause id="19967">
    <literal><![CDATA[
      x \ (y \ ((K(z,u) * y) * T(x,K(z,u)))) = K(z,x / ((u * y) \ (y * x)))
    ]]></literal>
    <justification jstring="[hyper(63,a,18477,a(flip),b,19966,a)].">
      <j1 rule="hyper" parents="63 18477 19966"/>
    </justification>
  </clause>

  <clause id="19969">
    <literal><![CDATA[
      K(x,y * (R(z,z \ (a(u,w,K(v5,v6)) * v7),a(v6,w,K(v5,u))) \ v7)) = K(x,y * (z \ (v7 / a(v6,w,K(v5,u)))))
    ]]></literal>
    <justification jstring="[para(17674(a,1),18675(a,1,2,2,1,2,2))].">
      <j1 rule="para" parents="17674 18675"/>
    </justification>
  </clause>

  <clause id="19970">
    <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(333,a,18373,a(flip),b,19222,a),flip(a)].">
      <j1 rule="hyper" parents="333 18373 19222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19972">
    <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(333,a,12660,a(flip),b,19970,a),flip(a)].">
      <j1 rule="hyper" parents="333 12660 19970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19973">
    <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(19250(a,1),19972(a,1,2,2,2))].">
      <j1 rule="para" parents="19250 19972"/>
    </justification>
  </clause>

  <clause id="19974">
    <literal><![CDATA[
      K(x,((y \ z) \ z) \ (u * ((w * y) \ y))) = K(x,T(y,z) \ (u / T(w,y)))
    ]]></literal>
    <justification jstring="[hyper(17871,a,19973,a)].">
      <j1 rule="hyper" parents="17871 19973"/>
    </justification>
  </clause>

  <clause id="19975">
    <literal><![CDATA[
      K(x,T(y,z) \ (u * ((w * y) \ y))) = K(x,T(y,z) \ (u / T(w,y)))
    ]]></literal>
    <justification jstring="[hyper(12787,a,19974,a)].">
      <j1 rule="hyper" parents="12787 19974"/>
    </justification>
  </clause>

  <clause id="19977">
    <literal><![CDATA[
      K(x,y \ (z * ((u * y) \ T(y,w)))) = K(x,T(y,w) \ (z / T(u,y)))
    ]]></literal>
    <justification jstring="[hyper(63,a,19193,a(flip),b,19975,a)].">
      <j1 rule="hyper" parents="63 19193 19975"/>
    </justification>
  </clause>

  <clause id="19978">
    <literal><![CDATA[
      K(x,T(y,z) \ ((y * u) / T(z,y))) = K(x,((z * ((z * y) / z)) / u) \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,19860,a,b,19977,a),flip(a)].">
      <j1 rule="hyper" parents="63 19860 19977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19979">
    <literal><![CDATA[
      K(x,T(y \ ((y * z) / u),K(y,u))) = K(x,((u * ((u * y) / u)) / z) \ y)
    ]]></literal>
    <justification jstring="[para(6176(a,2),19978(a,1,2))].">
      <j1 rule="para" parents="6176 19978"/>
    </justification>
  </clause>

  <clause id="19980">
    <literal><![CDATA[
      K(x,((y * ((y * z) / y)) / u) \ z) = K(x,z \ ((z * u) / y))
    ]]></literal>
    <justification jstring="[hyper(15516,a,19979,a),flip(a)].">
      <j1 rule="hyper" parents="15516 19979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19982">
    <literal><![CDATA[
      K(x,((y * z) / u) \ T(z,y)) = K(x,z \ ((z * u) / y))
    ]]></literal>
    <justification jstring="[para(14170(a,1),19980(a,1,2))].">
      <j1 rule="para" parents="14170 19980"/>
    </justification>
  </clause>

  <clause id="19983">
    <literal><![CDATA[
      K(x,T(y / (z \ (u * y)),u)) = K(x,y \ ((y * z) / u))
    ]]></literal>
    <justification jstring="[hyper(19533,a,19982,a)].">
      <j1 rule="hyper" parents="19533 19982"/>
    </justification>
  </clause>

  <clause id="19984">
    <literal><![CDATA[
      K(x,y / (T(z,u) \ (u * y))) = K(x,y \ ((y * z) / u))
    ]]></literal>
    <justification jstring="[hyper(18797,a,19983,a)].">
      <j1 rule="hyper" parents="18797 19983"/>
    </justification>
  </clause>

  <clause id="19985">
    <literal><![CDATA[
      K(x,y / ((z * u) \ (u * y))) = K(x,y \ ((y * (u * z)) / u))
    ]]></literal>
    <justification jstring="[hyper(63,a,18982,a(flip),b,19984,a)].">
      <j1 rule="hyper" parents="63 18982 19984"/>
    </justification>
  </clause>

  <clause id="19986">
    <literal><![CDATA[
      K(x,y / (z \ (T(u,z) * y))) = K(x,y \ ((y * z) / u))
    ]]></literal>
    <justification jstring="[para(4706(a,1),19984(a,1,2,2))].">
      <j1 rule="para" parents="4706 19984"/>
    </justification>
  </clause>

  <clause id="19987">
    <literal><![CDATA[
      (K(x,K(y,z)) \ (u * w)) \ ((K(K(y,z),x) \ u) * (w * v5)) = L(v5,L(w,u,K(x,K(y,z))),K(x,K(y,z)) * u)
    ]]></literal>
    <justification jstring="[para(4567(a,2),19557(a,1,2,1))].">
      <j1 rule="para" parents="4567 19557"/>
    </justification>
  </clause>

  <clause id="19988">
    <literal><![CDATA[
      L(K(x,((y / T(z,1)) / u) \ x),z \ y,z) \ T(x,(u * z) / y) = R(x,u / (y / ((z \ 1) \ 1)),x)
    ]]></literal>
    <justification jstring="[para(19032(a,1),19562(a,1,1,1))].">
      <j1 rule="para" parents="19032 19562"/>
    </justification>
  </clause>

  <clause id="19989">
    <literal><![CDATA[
      L(K(x,((y / z) / u) \ x),z \ y,z) \ T(x,(u * z) / y) = R(x,u / (y / ((z \ 1) \ 1)),x)
    ]]></literal>
    <justification jstring="[para(199(a,1),19988(a,1,1,1,2,1,1,2))].">
      <j1 rule="para" parents="199 19988"/>
    </justification>
  </clause>

  <clause id="19990">
    <literal><![CDATA[
      K(x,((x * y) * z) / u) \ T(x,(y * z) / u) = R(x,y / (u / ((z \ 1) \ 1)),x)
    ]]></literal>
    <justification jstring="[para(14069(a,1),19989(a,1,1))].">
      <j1 rule="para" parents="14069 19989"/>
    </justification>
  </clause>

  <clause id="19991">
    <literal><![CDATA[
      K(x,((x * y) * z) / u) \ T(x,(y * z) / u) = R(x,(u / ((z \ 1) \ 1)) \ y,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,12564,a(flip),b,19990,a),flip(a)].">
      <j1 rule="hyper" parents="333 12564 19990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19992">
    <literal><![CDATA[
      K(x,((x * y) * z) / u) \ T(x,(y * z) / u) = R(x,(u / z) \ y,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,14413,a(flip),b,19991,a),flip(a)].">
      <j1 rule="hyper" parents="333 14413 19991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19993">
    <literal><![CDATA[
      K(x,(y / (z * u)) \ x) \ T(x,(z * u) / y) = R(x,(y / u) \ z,x)
    ]]></literal>
    <justification jstring="[para(11564(a,1),19992(a,1,1))].">
      <j1 rule="para" parents="11564 19992"/>
    </justification>
  </clause>

  <clause id="19994">
    <literal><![CDATA[
      R(x,(y / z) \ u,x) = R(x,y \ (u * z),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,12583,a(flip),b,19993,a),flip(a)].">
      <j1 rule="hyper" parents="63 12583 19993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19995">
    <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(9440(a,1),19563(a,1,2,2))].">
      <j1 rule="para" parents="9440 19563"/>
    </justification>
  </clause>

  <clause id="19996">
    <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(9037(a,1),19995(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9037 19995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19998">
    <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(333,a,13247,a(flip),b,19996,a),flip(a)].">
      <j1 rule="hyper" parents="333 13247 19996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19999">
    <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(333,a,12707,a(flip),b,19998,a),flip(a)].">
      <j1 rule="hyper" parents="333 12707 19998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20000">
    <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(333,a,18472,a(flip),b,19999,a),flip(a)].">
      <j1 rule="hyper" parents="333 18472 19999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20001">
    <literal><![CDATA[
      K(x,y * L((z / (y \ 1)) / y,u,w)) = K(x,y * L(z,u,w))
    ]]></literal>
    <justification jstring="[para(8598(a,1),20000(a,1,2,2,1))].">
      <j1 rule="para" parents="8598 20000"/>
    </justification>
  </clause>

  <clause id="20002">
    <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(333,a,5766,a(flip),b,19873,a),flip(a)].">
      <j1 rule="hyper" parents="333 5766 19873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20003">
    <literal><![CDATA[
      K(x,y * (L(z,z \ (a(u,w,K(v5,v6)) * v7),a(v6,w,K(v5,u))) \ v7)) = K(x,y * (z \ (v7 / a(v6,w,K(v5,u)))))
    ]]></literal>
    <justification jstring="[para(14533(a,1),19969(a,1,2,2,1))].">
      <j1 rule="para" parents="14533 19969"/>
    </justification>
  </clause>

  <clause id="20004">
    <literal><![CDATA[
      (K(x,K(y,z)) \ (u * w)) \ ((K(y,K(x,z)) \ u) * (w * v5)) = L(v5,L(w,u,K(x,K(y,z))),K(x,K(y,z)) * u)
    ]]></literal>
    <justification jstring="[para(6796(a,1),19987(a,1,2,1,1))].">
      <j1 rule="para" parents="6796 19987"/>
    </justification>
  </clause>

  <clause id="20005">
    <literal><![CDATA[
      K(x,y * (L(z,a(u,w,K(v5,v6)) * v7,a(v6,w,K(v5,u))) \ v7)) = K(x,y * (z \ (v7 / a(v6,w,K(v5,u)))))
    ]]></literal>
    <justification jstring="[para(14559(a,1),20003(a,1,2,2,1))].">
      <j1 rule="para" parents="14559 20003"/>
    </justification>
  </clause>

  <clause id="20006">
    <literal><![CDATA[
      K(x,y * (L(z,u,a(w,v5,K(v6,v7))) \ u)) = K(x,y * (z \ (u / a(w,v5,K(v6,v7)))))
    ]]></literal>
    <justification jstring="[para(19764(a,1),20005(a,1,2,2,1))].">
      <j1 rule="para" parents="19764 20005"/>
    </justification>
  </clause>

  <clause id="20007">
    <literal><![CDATA[
      K(x,y * (L(z,u,a(w,v5,K(v6,v7))) \ u)) = K(x,y * (z \ (a(v7,v5,K(v6,w)) * u)))
    ]]></literal>
    <justification jstring="[para(17674(a,1),20006(a,2,2,2,2))].">
      <j1 rule="para" parents="17674 20006"/>
    </justification>
  </clause>

  <clause id="20009">
    <literal><![CDATA[
      K(x,y * (z \ (a(u,w,K(v5,v6)) * v7))) = K(x,y * (z \ v7))
    ]]></literal>
    <justification jstring="[hyper(63,a,18679,a(flip),b,20007,a),flip(a)].">
      <j1 rule="hyper" parents="63 18679 20007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20011">
    <literal><![CDATA[
      K(x,y * (z \ ((u * w) * K(v5,v6)))) = K(x,y * (z \ (u * (w * K(v5,v6)))))
    ]]></literal>
    <justification jstring="[para(13589(a,1),20009(a,1,2,2,2))].">
      <j1 rule="para" parents="13589 20009"/>
    </justification>
  </clause>

  <clause id="20012">
    <literal><![CDATA[
      (K(x,K(y,z)) \ (u * w)) \ (K(x,K(y,z)) \ (u * (w * v5))) = L(v5,L(w,u,K(x,K(y,z))),K(x,K(y,z)) * u)
    ]]></literal>
    <justification jstring="[para(17780(a,2),20004(a,1,2))].">
      <j1 rule="para" parents="17780 20004"/>
    </justification>
  </clause>

  <clause id="20013">
    <literal><![CDATA[
      L(x,L(y,z,K(u,K(w,v5))),K(u,K(w,v5)) * z) = (z * y) \ (z * (y * x))
    ]]></literal>
    <justification jstring="[hyper(63,a,17776,a(flip),b,20012,a),flip(a)].">
      <j1 rule="hyper" parents="63 17776 20012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20015">
    <literal><![CDATA[
      L(x,L(y,z,K(u,K(w,v5))),K(u,K(w,v5)) * z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,18,a,b,20013,a),flip(a)].">
      <j1 rule="hyper" parents="333 18 20013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20016">
    <literal><![CDATA[
      L(x,y,K(z,K(u,w)) * v5) = L(x,y,v5)
    ]]></literal>
    <justification jstring="[para(17577(a,1),20015(a,1,2))].">
      <j1 rule="para" parents="17577 20015"/>
    </justification>
  </clause>

  <clause id="20017">
    <literal><![CDATA[
      L(x,y,T(z,K(u,w)) \ v5) = L(x,y,z \ v5)
    ]]></literal>
    <justification jstring="[para(4518(a,1),20016(a,1,3)),flip(a)].">
      <j1 rule="para" parents="4518 20016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20018">
    <literal><![CDATA[
      L(x,y,z * T(u,K(w,v5))) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(4967(a,1),20016(a,1,3))].">
      <j1 rule="para" parents="4967 20016"/>
    </justification>
  </clause>

  <clause id="20019">
    <literal><![CDATA[
      L(x,y,z / T(u,K(w,v5))) = L(x,y,z / u)
    ]]></literal>
    <justification jstring="[para(15628(a,1),20016(a,1,3))].">
      <j1 rule="para" parents="15628 20016"/>
    </justification>
  </clause>

  <clause id="20020">
    <literal><![CDATA[
      L(x,y,z * K(u,T(w,v5))) = L(x,y,z * K(u,w))
    ]]></literal>
    <justification jstring="[para(15835(a,1),20016(a,1,3))].">
      <j1 rule="para" parents="15835 20016"/>
    </justification>
  </clause>

  <clause id="20021">
    <literal><![CDATA[
      L(x,y,((1 / z) * K(u,w)) \ v5) = L(x,y,(K(u,w) / z) \ v5)
    ]]></literal>
    <justification jstring="[para(13309(a,1),20017(a,1,3,1))].">
      <j1 rule="para" parents="13309 20017"/>
    </justification>
  </clause>

  <clause id="20022">
    <literal><![CDATA[
      L(x,y,z * (T(u,T(w,v5)) / v5)) = L(x,y,z * (T(u,w) / v5))
    ]]></literal>
    <justification jstring="[para(7319(a,1),20018(a,1,3,2))].">
      <j1 rule="para" parents="7319 20018"/>
    </justification>
  </clause>

  <clause id="20023">
    <literal><![CDATA[
      L(x,y,z / ((1 / u) * K(w,v5))) = L(x,y,z / (K(w,v5) / u))
    ]]></literal>
    <justification jstring="[para(13309(a,1),20019(a,1,3,2))].">
      <j1 rule="para" parents="13309 20019"/>
    </justification>
  </clause>

  <clause id="20024">
    <literal><![CDATA[
      L(x,y,T(K(z,u) * w,v5)) = L(x,y,T(w,v5) * K(z,u))
    ]]></literal>
    <justification jstring="[para(14103(a,1),20020(a,1,3))].">
      <j1 rule="para" parents="14103 20020"/>
    </justification>
  </clause>

  <clause id="20025">
    <literal><![CDATA[
      L(x,y,T(K(z,u) * w,v5)) = L(x,y,K(z,u) * T(w,v5))
    ]]></literal>
    <justification jstring="[hyper(333,a,17596,a,b,20024,a),flip(a)].">
      <j1 rule="hyper" parents="333 17596 20024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20026">
    <literal><![CDATA[
      L(x,y,(K(z,u) / w) \ v5) = L(x,y,(w \ K(z,u)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,13700,a(flip),b,20021,a),flip(a)].">
      <j1 rule="hyper" parents="63 13700 20021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20027">
    <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(20026(a,1),14193(a,1,2,2,2))].">
      <j1 rule="para" parents="20026 14193"/>
    </justification>
  </clause>

  <clause id="20028">
    <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(20026(a,1),17059(a,1,2,2))].">
      <j1 rule="para" parents="20026 17059"/>
    </justification>
  </clause>

  <clause id="20029">
    <literal><![CDATA[
      L(x,y,z / (K(u,w) / v5)) = L(x,y,z / (v5 \ K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,13699,a(flip),b,20023,a),flip(a)].">
      <j1 rule="hyper" parents="63 13699 20023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20030">
    <literal><![CDATA[
      K(x,L(y,z,u / (w \ K(v5,v6)))) = K(x,L(y,z,w * u))
    ]]></literal>
    <justification jstring="[para(20029(a,1),19693(a,1,2))].">
      <j1 rule="para" parents="20029 19693"/>
    </justification>
  </clause>

  <clause id="20031">
    <literal><![CDATA[
      K(x,L(y,z,(u \ K(w,v5)) \ v6)) = K(x,L(y,z,u * v6))
    ]]></literal>
    <justification jstring="[hyper(17863,a,20030,a)].">
      <j1 rule="hyper" parents="17863 20030"/>
    </justification>
  </clause>

  <clause id="20032">
    <literal><![CDATA[
      K(x,L(y,z,(u \ K(w,v5)) \ v6)) = K(x,L(y,z,v6 * u))
    ]]></literal>
    <justification jstring="[hyper(17744,a,20031,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="17744 20031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20033">
    <literal><![CDATA[
      K(x,L(y,z,(u \ 1) * w)) = K(x,L(y,z,u \ w))
    ]]></literal>
    <justification jstring="[para(359(a,1),20031(a,1,2,3,1)),flip(a)].">
      <j1 rule="para" parents="359 20031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20034">
    <literal><![CDATA[
      K(x,L(y,z,u * (w \ 1))) = K(x,L(y,z,w \ u))
    ]]></literal>
    <justification jstring="[hyper(17744,a,20033,a)].">
      <j1 rule="hyper" parents="17744 20033"/>
    </justification>
  </clause>

  <clause id="20035">
    <literal><![CDATA[
      K(x,L(y,z,L(u,w,w \ 1))) = K(x,L(y,z,w \ (w * u)))
    ]]></literal>
    <justification jstring="[hyper(18178,a,20034,a)].">
      <j1 rule="hyper" parents="18178 20034"/>
    </justification>
  </clause>

  <clause id="20036">
    <literal><![CDATA[
      K(x,L(y,z,u \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,(u \ 1) * w)) = v5
    ]]></literal>
    <justification jstring="[para(20034(a,1),17744(a,1))].">
      <j1 rule="para" parents="20034 17744"/>
    </justification>
  </clause>

  <clause id="20037">
    <literal><![CDATA[
      K(x,L(y,z,(u \ 1) \ w)) = K(x,L(y,z,w * u))
    ]]></literal>
    <justification jstring="[para(171(a,1),20032(a,1,2,3,1,2))].">
      <j1 rule="para" parents="171 20032"/>
    </justification>
  </clause>

  <clause id="20038">
    <literal><![CDATA[
      K(x,L((y \ 1) \ z,u,u * y)) = K(x,u \ ((u / (y \ 1)) * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,14018,a(flip),b,20037,a),flip(a)].">
      <j1 rule="hyper" parents="63 14018 20037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20039">
    <literal><![CDATA[
      K(x,L(y,z,L(u,w,w \ 1))) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(9(a,1),20035(a,2,2,3))].">
      <j1 rule="para" parents="9 20035"/>
    </justification>
  </clause>

  <clause id="20040">
    <literal><![CDATA[
      K(x,L(y,a(z \ 1,z,u),u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,14290,a(flip),b,20039,a),flip(a)].">
      <j1 rule="hyper" parents="63 14290 20039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20042">
    <literal><![CDATA[
      K(x,(y * z) / a(u \ 1,u,z)) = K(x,y / (a(u \ 1,u,z) / z))
    ]]></literal>
    <justification jstring="[hyper(63,a,14066,a(flip),b,20040,a)].">
      <j1 rule="hyper" parents="63 14066 20040"/>
    </justification>
  </clause>

  <clause id="20043">
    <literal><![CDATA[
      K(x,L(y * z,u,u * y)) = K(x,u \ ((u / (y \ 1)) * z))
    ]]></literal>
    <justification jstring="[hyper(13616,a,20038,a)].">
      <j1 rule="hyper" parents="13616 20038"/>
    </justification>
  </clause>

  <clause id="20044">
    <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(111(a,1),20043(a,1,2,3))].">
      <j1 rule="para" parents="111 20043"/>
    </justification>
  </clause>

  <clause id="20045">
    <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(20042(a,1),17638(a,1))].">
      <j1 rule="para" parents="20042 17638"/>
    </justification>
  </clause>

  <clause id="20046">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,z,y * z)) = K(x,z \ (((y \ 1) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(333,a,19206,a(flip),b,20044,a),flip(a)].">
      <j1 rule="hyper" parents="333 19206 20044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20047">
    <literal><![CDATA[
      K(x,y / (z \ a(u \ 1,u,z))) = K(x,a(u \ 1,u,z) \ (y * z))
    ]]></literal>
    <justification jstring="[hyper(20045,a,18561,a),flip(a)].">
      <j1 rule="hyper" parents="20045 18561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20048">
    <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(20047(a,1),15317(a,1))].">
      <j1 rule="para" parents="20047 15317"/>
    </justification>
  </clause>

  <clause id="20049">
    <literal><![CDATA[
      K(x,(y * z) * a(z,u,u \ 1)) = K(x,y * L(z,u,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(20048,a,18312,a),flip(a)].">
      <j1 rule="hyper" parents="20048 18312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20050">
    <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(8597(a,2),20049(a,1,2,1))].">
      <j1 rule="para" parents="8597 20049"/>
    </justification>
  </clause>

  <clause id="20051">
    <literal><![CDATA[
      x * K(y,L(T(z,u \ 1),x,u * x)) = (x / (K(z,y) / u)) * (1 / u)
    ]]></literal>
    <justification jstring="[para(20031(a,1),20028(a,1,2))].">
      <j1 rule="para" parents="20031 20028"/>
    </justification>
  </clause>

  <clause id="20052">
    <literal><![CDATA[
      x * K(y,L(T(z,u),x,u * x)) = (x / (K(z,y) / u)) * (1 / u)
    ]]></literal>
    <justification jstring="[para(15983(a,1),20051(a,1,2))].">
      <j1 rule="para" parents="15983 20051"/>
    </justification>
  </clause>

  <clause id="20054">
    <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(14129(a,1),20027(a,1,2,2))].">
      <j1 rule="para" parents="14129 20027"/>
    </justification>
  </clause>

  <clause id="20055">
    <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(4458(a,1),20054(a,1,2,2,2,3))].">
      <j1 rule="para" parents="4458 20054"/>
    </justification>
  </clause>

  <clause id="20056">
    <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(11867(a,1),20055(a,1,2,2,2))].">
      <j1 rule="para" parents="11867 20055"/>
    </justification>
  </clause>

  <clause id="20057">
    <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(17642(a,1),20056(a,1,2,2))].">
      <j1 rule="para" parents="17642 20056"/>
    </justification>
  </clause>

  <clause id="20059">
    <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(10873(a,1),20057(a,1,2))].">
      <j1 rule="para" parents="10873 20057"/>
    </justification>
  </clause>

  <clause id="20060">
    <literal><![CDATA[
      L(x * K(y,z),u,u \ 1) = L(x,u,u \ 1) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(5350,a,20059,a)].">
      <j1 rule="hyper" parents="5350 20059"/>
    </justification>
  </clause>

  <clause id="20061">
    <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(20060(a,2),14561(a,1,2))].">
      <j1 rule="para" parents="20060 14561"/>
    </justification>
  </clause>

  <clause id="20062">
    <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(20060(a,2),18466(a,1,1))].">
      <j1 rule="para" parents="20060 18466"/>
    </justification>
  </clause>

  <clause id="20063">
    <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(2560,a,20061,a)].">
      <j1 rule="hyper" parents="2560 20061"/>
    </justification>
  </clause>

  <clause id="20064">
    <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(20063(a,1),3208(a,1))].">
      <j1 rule="para" parents="20063 3208"/>
    </justification>
  </clause>

  <clause id="20065">
    <literal><![CDATA[
      a(x \ 1,x,y * K(z,u)) = a(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(20064,a,19438,a)].">
      <j1 rule="hyper" parents="20064 19438"/>
    </justification>
  </clause>

  <clause id="20066">
    <literal><![CDATA[
      a(x \ 1,x,K(y,z) * u) = a(x \ 1,x,u)
    ]]></literal>
    <justification jstring="[para(6355(a,1),20065(a,1,3)),flip(a)].">
      <j1 rule="para" parents="6355 20065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20067">
    <literal><![CDATA[
      a(x \ 1,x,y) \ (K(z,u) * y) = L(K(z,u) * y,x,x \ 1)
    ]]></literal>
    <justification jstring="[para(20066(a,1),3207(a,1,1))].">
      <j1 rule="para" parents="20066 3207"/>
    </justification>
  </clause>

  <clause id="20068">
    <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(13254(a,1),20062(a,1,1,1))].">
      <j1 rule="para" parents="13254 20062"/>
    </justification>
  </clause>

  <clause id="20070">
    <literal><![CDATA[
      L(x \ y,z,z \ 1) / L(x \ T(y,u),z,z \ 1) != w
    ]]></literal>
    <literal><![CDATA[
      K(u,T(y,x)) = w
    ]]></literal>
    <justification jstring="[para(20068(a,2),13558(a,1))].">
      <j1 rule="para" parents="20068 13558"/>
    </justification>
  </clause>

  <clause id="20071">
    <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(18458(a,1),20050(a,1,2,2))].">
      <j1 rule="para" parents="18458 20050"/>
    </justification>
  </clause>

  <clause id="20072">
    <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(18462(a,1),20071(a,1,2,2))].">
      <j1 rule="para" parents="18462 20071"/>
    </justification>
  </clause>

  <clause id="20073">
    <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(63,a,19006,a(flip),b,20072,a)].">
      <j1 rule="hyper" parents="63 19006 20072"/>
    </justification>
  </clause>

  <clause id="20074">
    <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(333,a,20001,a(flip),b,20073,a),flip(a)].">
      <j1 rule="hyper" parents="333 20001 20073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20075">
    <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(14043(a,1),17661(a,2,2))].">
      <j1 rule="para" parents="14043 17661"/>
    </justification>
  </clause>

  <clause id="20076">
    <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(333,a,16499,a(flip),b,20075,a),flip(a)].">
      <j1 rule="hyper" parents="333 16499 20075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20078">
    <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(333,a,25,a,b,20076,a),flip(a)].">
      <j1 rule="hyper" parents="333 25 20076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20079">
    <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(17642(a,1),20078(a,1,1,2,1))].">
      <j1 rule="para" parents="17642 20078"/>
    </justification>
  </clause>

  <clause id="20080">
    <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(14043(a,1),20079(a,1,1))].">
      <j1 rule="para" parents="14043 20079"/>
    </justification>
  </clause>

  <clause id="20081">
    <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(11(a,1),20080(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11 20080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20082">
    <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(333,a,17225,a(flip),b,20081,a),flip(a)].">
      <j1 rule="hyper" parents="333 17225 20081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20083">
    <literal><![CDATA[
      (K(x,y) * (z \ (K(y,x) * u))) \ u = ((z \ u) * K(x,y)) \ (u * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,19792,a(flip),b,20082,a)].">
      <j1 rule="hyper" parents="63 19792 20082"/>
    </justification>
  </clause>

  <clause id="20084">
    <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(20083(a,1),14502(a,1,1))].">
      <j1 rule="para" parents="20083 14502"/>
    </justification>
  </clause>

  <clause id="20085">
    <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(63,a,19755,a(flip),b,20084,a)].">
      <j1 rule="hyper" parents="63 19755 20084"/>
    </justification>
  </clause>

  <clause id="20087">
    <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(63,a,19737,a(flip),b,20085,a)].">
      <j1 rule="hyper" parents="63 19737 20085"/>
    </justification>
  </clause>

  <clause id="20088">
    <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(15398(a,1),20087(a,1,2,1))].">
      <j1 rule="para" parents="15398 20087"/>
    </justification>
  </clause>

  <clause id="20089">
    <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(8198(a,2),20088(a,1,2))].">
      <j1 rule="para" parents="8198 20088"/>
    </justification>
  </clause>

  <clause id="20090">
    <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(6788(a,2),20089(a,1,2,1,1))].">
      <j1 rule="para" parents="6788 20089"/>
    </justification>
  </clause>

  <clause id="20091">
    <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(18119,a,20090,a)].">
      <j1 rule="hyper" parents="18119 20090"/>
    </justification>
  </clause>

  <clause id="20092">
    <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(15811,a,20091,a)].">
      <j1 rule="hyper" parents="15811 20091"/>
    </justification>
  </clause>

  <clause id="20093">
    <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(20092(a,2),14408(a,1,3,2))].">
      <j1 rule="para" parents="20092 14408"/>
    </justification>
  </clause>

  <clause id="20094">
    <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(14920(a,1),20093(a,2,3,2))].">
      <j1 rule="para" parents="14920 20093"/>
    </justification>
  </clause>

  <clause id="20095">
    <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(10851(a,1),17879(a,1,2))].">
      <j1 rule="para" parents="10851 17879"/>
    </justification>
  </clause>

  <clause id="20096">
    <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(14726(a,1),20095(a,1,2,2))].">
      <j1 rule="para" parents="14726 20095"/>
    </justification>
  </clause>

  <clause id="20097">
    <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(20037(a,1),20096(a,1,2))].">
      <j1 rule="para" parents="20037 20096"/>
    </justification>
  </clause>

  <clause id="20098">
    <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(20022(a,1),20097(a,1,2,2))].">
      <j1 rule="para" parents="20022 20097"/>
    </justification>
  </clause>

  <clause id="20099">
    <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(19577(a,1),20098(a,1,2))].">
      <j1 rule="para" parents="19577 20098"/>
    </justification>
  </clause>

  <clause id="20100">
    <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(18251(a,1),20099(a,1,2))].">
      <j1 rule="para" parents="18251 20099"/>
    </justification>
  </clause>

  <clause id="20102">
    <literal><![CDATA[
      x / K(y,L(z,u,u \ x)) = (x / (((z / u) \ 1) * K(y,z))) * ((z / u) \ 1)
    ]]></literal>
    <justification jstring="[para(19726(a,1),20100(a,1,2))].">
      <j1 rule="para" parents="19726 20100"/>
    </justification>
  </clause>

  <clause id="20103">
    <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(20102(a,1),13657(a,1))].">
      <j1 rule="para" parents="20102 13657"/>
    </justification>
  </clause>

  <clause id="20104">
    <literal><![CDATA[
      (K(x,K(y,z)) \ (u * (w * v5))) \ ((u * (K(x,K(y,z)) * w)) * v5) = a(u,K(x,K(y,z)) * w,L(v5,w,K(x,K(y,z))))
    ]]></literal>
    <justification jstring="[para(17826(a,2),17595(a,1,1))].">
      <j1 rule="para" parents="17826 17595"/>
    </justification>
  </clause>

  <clause id="20105">
    <literal><![CDATA[
      (K(x,y) * (z * (K(y,x) * L(K(x,y),u,w)))) * a(x,z,K(K(x,y) * K(y,x),y)) = L(K(x,y),u,w) * z
    ]]></literal>
    <justification jstring="[para(17963(a,1),18979(a,1,2,3))].">
      <j1 rule="para" parents="17963 18979"/>
    </justification>
  </clause>

  <clause id="20106">
    <literal><![CDATA[
      (K(x,y) * (z * (K(y,x) * L(K(x,y),u,w)))) * a(x,z,K(1,y)) = L(K(x,y),u,w) * z
    ]]></literal>
    <justification jstring="[para(4373(a,1),20105(a,1,2,3,1))].">
      <j1 rule="para" parents="4373 20105"/>
    </justification>
  </clause>

  <clause id="20108">
    <literal><![CDATA[
      (K(x,y) * (z * (K(y,x) * L(K(x,y),u,w)))) * 1 = L(K(x,y),u,w) * z
    ]]></literal>
    <justification jstring="[para(381(a,1),20106(a,1,2))].">
      <j1 rule="para" parents="381 20106"/>
    </justification>
  </clause>

  <clause id="20110">
    <literal><![CDATA[
      K(x,y) * (z * (K(y,x) * L(K(x,y),u,w))) = L(K(x,y),u,w) * z
    ]]></literal>
    <justification jstring="[hyper(135,a,20108,a)].">
      <j1 rule="hyper" parents="135 20108"/>
    </justification>
  </clause>

  <clause id="20112">
    <literal><![CDATA[
      K(x,y) * (z * a(x,u,K(w,y))) = L(K(x,y),u,w) * z
    ]]></literal>
    <justification jstring="[para(13752(a,1),20110(a,1,2,2))].">
      <j1 rule="para" parents="13752 20110"/>
    </justification>
  </clause>

  <clause id="20113">
    <literal><![CDATA[
      L(K(x,y),z * a(x,u,K(w,y)),v5) \ ((L(K(x,y),u,w) * z) * v5) = (z * a(x,u,K(w,y))) * v5
    ]]></literal>
    <justification jstring="[para(20112(a,1),13892(a,1,2,1))].">
      <j1 rule="para" parents="20112 13892"/>
    </justification>
  </clause>

  <clause id="20114">
    <literal><![CDATA[
      K(x,y) \ ((L(K(x,y),z,u) * w) * K(v5,v6)) = (w * a(x,z,K(u,y))) * K(v5,v6)
    ]]></literal>
    <justification jstring="[para(17537(a,1),20113(a,1,1))].">
      <j1 rule="para" parents="17537 20113"/>
    </justification>
  </clause>

  <clause id="20115">
    <literal><![CDATA[
      K(x,y) \ (L(K(x,y),z,u) * (w * K(v5,v6))) = (w * a(x,z,K(u,y))) * K(v5,v6)
    ]]></literal>
    <justification jstring="[para(17550(a,1),20114(a,1,2))].">
      <j1 rule="para" parents="17550 20114"/>
    </justification>
  </clause>

  <clause id="20116">
    <literal><![CDATA[
      T(x * a(y,z,K(u,w)),K(y,w)) = L(K(y,w),z,u) * (x * K(w,y))
    ]]></literal>
    <justification jstring="[hyper(7102,a,20115,a)].">
      <j1 rule="hyper" parents="7102 20115"/>
    </justification>
  </clause>

  <clause id="20118">
    <literal><![CDATA[
      (K(x,K(y,z)) \ (u * (w * v5))) \ ((K(x,K(y,z)) \ (u * w)) * v5) = a(u,K(x,K(y,z)) * w,L(v5,w,K(x,K(y,z))))
    ]]></literal>
    <justification jstring="[para(17826(a,2),20104(a,1,2,1))].">
      <j1 rule="para" parents="17826 20104"/>
    </justification>
  </clause>

  <clause id="20119">
    <literal><![CDATA[
      (K(x,K(y,z)) \ (u * (w * v5))) \ (K(x,K(y,z)) \ ((u * w) * v5)) = a(u,K(x,K(y,z)) * w,L(v5,w,K(x,K(y,z))))
    ]]></literal>
    <justification jstring="[para(17593(a,2),20118(a,1,2))].">
      <j1 rule="para" parents="17593 20118"/>
    </justification>
  </clause>

  <clause id="20120">
    <literal><![CDATA[
      a(x,K(y,K(z,u)) * w,L(v5,w,K(y,K(z,u)))) = (x * (w * v5)) \ ((x * w) * v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,17776,a(flip),b,20119,a),flip(a)].">
      <j1 rule="hyper" parents="63 17776 20119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20122">
    <literal><![CDATA[
      a(x,K(y,K(z,u)) * w,L(v5,w,K(y,K(z,u)))) = a(x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(333,a,14,a,b,20120,a),flip(a)].">
      <j1 rule="hyper" parents="333 14 20120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20123">
    <literal><![CDATA[
      a(x,K(y,K(z,u)),w) = 1
    ]]></literal>
    <justification jstring="[hyper(63,a,508,a(flip),b,20122,a),flip(a)].">
      <j1 rule="hyper" parents="63 508 20122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20124">
    <literal><![CDATA[
      a(x,K(y,K(z,u)) * w,v5) = a(x,w,v5)
    ]]></literal>
    <justification jstring="[para(17577(a,1),20122(a,1,3))].">
      <j1 rule="para" parents="17577 20122"/>
    </justification>
  </clause>

  <clause id="20125">
    <literal><![CDATA[
      L(x,K(y,K(z,u)),w) = x
    ]]></literal>
    <justification jstring="[hyper(52,a,20123,a)].">
      <j1 rule="hyper" parents="52 20123"/>
    </justification>
  </clause>

  <clause id="20126">
    <literal><![CDATA[
      (x * K(y,K(z,u))) * w = x * (K(y,K(z,u)) * w)
    ]]></literal>
    <justification jstring="[hyper(1170,a,20125,a),flip(a)].">
      <j1 rule="hyper" parents="1170 20125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20127">
    <literal><![CDATA[
      (x * K(y,K(z,u))) \ w = K(y,K(z,u)) \ (x \ w)
    ]]></literal>
    <justification jstring="[hyper(578,a,20125,a),flip(a)].">
      <j1 rule="hyper" parents="578 20125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20128">
    <literal><![CDATA[
      (x * (y * K(z,K(u,w)))) \ v5 = K(z,K(u,w)) * ((x * y) \ v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,18937,a(flip),b,20125,a)].">
      <j1 rule="hyper" parents="63 18937 20125"/>
    </justification>
  </clause>

  <clause id="20129">
    <literal><![CDATA[
      (x / (K(y,K(z,u)) * w)) * K(y,K(z,u)) = x / w
    ]]></literal>
    <justification jstring="[hyper(197,a,20125,a(flip),b,102,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="197 20125 102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20130">
    <literal><![CDATA[
      a(x,K(y,K(z,u)) \ w,v5) = a(x,w,v5)
    ]]></literal>
    <justification jstring="[para(10(a,1),20124(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 20124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20131">
    <literal><![CDATA[
      a(x,y \ T(z,K(u,w)),v5) = a(x,y \ z,v5)
    ]]></literal>
    <justification jstring="[para(4963(a,1),20124(a,1,2))].">
      <j1 rule="para" parents="4963 20124"/>
    </justification>
  </clause>

  <clause id="20132">
    <literal><![CDATA[
      a(x,K(y,T(z,u)),w) = a(x,K(y,z),w)
    ]]></literal>
    <justification jstring="[para(6376(a,1),20124(a,1,2))].">
      <j1 rule="para" parents="6376 20124"/>
    </justification>
  </clause>

  <clause id="20133">
    <literal><![CDATA[
      a(x,K(y,T(z,u)) \ w,v5) = a(x,K(y,z) \ w,v5)
    ]]></literal>
    <justification jstring="[para(19354(a,1),20130(a,1,2))].">
      <j1 rule="para" parents="19354 20130"/>
    </justification>
  </clause>

  <clause id="20134">
    <literal><![CDATA[
      a(x,y \ (K(z,u) \ w),v5) = a(x,y \ (w * K(u,z)),v5)
    ]]></literal>
    <justification jstring="[para(6020(a,1),20131(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6020 20131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20135">
    <literal><![CDATA[
      a(x,y \ T(z,T(u,w)),v5) = a(x,y \ T(z,u),v5)
    ]]></literal>
    <justification jstring="[para(6191(a,1),20131(a,1,2,2))].">
      <j1 rule="para" parents="6191 20131"/>
    </justification>
  </clause>

  <clause id="20136">
    <literal><![CDATA[
      a(x,K(y,z) \ u,w) = a(x,u * K(z,y),w)
    ]]></literal>
    <justification jstring="[para(6853(a,1),20131(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6853 20131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20137">
    <literal><![CDATA[
      a(x,K(y,T(z,u)) \ (u * (w / u)),x) = a(x,K(y,z) \ w,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,19451,a,b,20136,a)].">
      <j1 rule="hyper" parents="333 19451 20136"/>
    </justification>
  </clause>

  <clause id="20138">
    <literal><![CDATA[
      R(x,K(y,K(z,u)),w) = x
    ]]></literal>
    <justification jstring="[hyper(1924,a,20126,a)].">
      <j1 rule="hyper" parents="1924 20126"/>
    </justification>
  </clause>

  <clause id="20139">
    <literal><![CDATA[
      (x * (K(y,K(z,u)) * (w * v5))) \ (((x * K(y,K(z,u))) * w) * v5) = a(x * K(y,K(z,u)),w,v5)
    ]]></literal>
    <justification jstring="[para(20126(a,1),14(a,2,1)),flip(a)].">
      <j1 rule="para" parents="20126 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20140">
    <literal><![CDATA[
      (x * K(y,K(z,u))) * w = x * (w * K(y,K(z,u)))
    ]]></literal>
    <justification jstring="[para(15475(a,1),20126(a,2,2))].">
      <j1 rule="para" parents="15475 20126"/>
    </justification>
  </clause>

  <clause id="20141">
    <literal><![CDATA[
      K(x,y * ((z * (K(u,K(w,v5)) * v6)) * ((v6 * (z * K(u,K(w,v5)))) / v6))) = K(x,y * ((v6 * (z * K(u,K(w,v5)))) * z))
    ]]></literal>
    <justification jstring="[para(20126(a,1),16515(a,1,2,2,1))].">
      <j1 rule="para" parents="20126 16515"/>
    </justification>
  </clause>

  <clause id="20142">
    <literal><![CDATA[
      (x * (y * K(z,K(u,w)))) * v5 = (x * y) * (K(z,K(u,w)) * v5)
    ]]></literal>
    <justification jstring="[para(17519(a,1),20126(a,1,1))].">
      <j1 rule="para" parents="17519 20126"/>
    </justification>
  </clause>

  <clause id="20143">
    <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(20138(a,1),542(a,1,1,1,2))].">
      <j1 rule="para" parents="20138 542"/>
    </justification>
  </clause>

  <clause id="20144">
    <literal><![CDATA[
      (K(x,K(y,z)) \ u) \ w = K(x,K(y,z)) \ (u \ w)
    ]]></literal>
    <justification jstring="[para(15626(a,2),20127(a,1,1))].">
      <j1 rule="para" parents="15626 20127"/>
    </justification>
  </clause>

  <clause id="20145">
    <literal><![CDATA[
      x / (K(y,K(z,u)) * w) = K(y,K(z,u)) \ (x / w)
    ]]></literal>
    <justification jstring="[hyper(121,a,20129,a(flip),b,15475,a),flip(a)].">
      <j1 rule="hyper" parents="121 20129 15475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20146">
    <literal><![CDATA[
      x / (y * K(z,K(u,w))) = (x / y) * K(z,K(u,w))
    ]]></literal>
    <justification jstring="[para(15627(a,1),20129(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="15627 20129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20147">
    <literal><![CDATA[
      a(x,T(y \ z,u) \ T(w,z \ y),x) = a(x,T(y \ z,u) \ w,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,13033,a(flip),b,20135,a),flip(a)].">
      <j1 rule="hyper" parents="63 13033 20135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20148">
    <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(20140(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="20140 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20149">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * w = u * (w * K(x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(15475(a,2),20140(a,1,1))].">
      <j1 rule="para" parents="15475 20140"/>
    </justification>
  </clause>

  <clause id="20150">
    <literal><![CDATA[
      T(x * K(y,K(z,u)),w) * v5 = T(x,w) * (v5 * K(y,K(z,u)))
    ]]></literal>
    <justification jstring="[para(15831(a,2),20140(a,1,1))].">
      <j1 rule="para" parents="15831 20140"/>
    </justification>
  </clause>

  <clause id="20151">
    <literal><![CDATA[
      K(x,K(y,z)) \ (u \ w) = u \ (K(x,K(y,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,17777,a(flip),b,20144,a),flip(a)].">
      <j1 rule="hyper" parents="63 17777 20144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20152">
    <literal><![CDATA[
      K(x,K(y,z)) \ (u / (K(x,K(y,z)) \ w)) = u / w
    ]]></literal>
    <justification jstring="[para(10(a,1),20145(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 20145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20153">
    <literal><![CDATA[
      T(x,K(K(y,z) * u,w) * ((v5 / w) * K(y,K(z,u)))) = T(x,v5 / (u \ T(w * u,K(y,z))))
    ]]></literal>
    <justification jstring="[para(20146(a,1),17239(a,1,2,2))].">
      <j1 rule="para" parents="20146 17239"/>
    </justification>
  </clause>

  <clause id="20154">
    <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(20149(a,1),14(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="20149 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20155">
    <literal><![CDATA[
      (x * (K(y,K(z,u)) * w)) * v5 = (x * w) * (v5 * K(y,K(z,u)))
    ]]></literal>
    <justification jstring="[para(17794(a,1),20149(a,1,1))].">
      <j1 rule="para" parents="17794 20149"/>
    </justification>
  </clause>

  <clause id="20156">
    <literal><![CDATA[
      a(x,y \ (K(z,K(u,w)) \ v5),v6) = a(x,y \ v5,v6)
    ]]></literal>
    <justification jstring="[para(20151(a,1),20130(a,1,2))].">
      <j1 rule="para" parents="20151 20130"/>
    </justification>
  </clause>

  <clause id="20157">
    <literal><![CDATA[
      a(x,y \ (T(z,K(u,w)) \ v5),v6) = a(x,y \ (z \ v5),v6)
    ]]></literal>
    <justification jstring="[para(4511(a,1),20156(a,1,2,2))].">
      <j1 rule="para" parents="4511 20156"/>
    </justification>
  </clause>

  <clause id="20158">
    <literal><![CDATA[
      a(x,y \ (z * T(u,K(w,v5))),v6) = a(x,y \ (z * u),v6)
    ]]></literal>
    <justification jstring="[para(15692(a,1),20156(a,1,2,2))].">
      <j1 rule="para" parents="15692 20156"/>
    </justification>
  </clause>

  <clause id="20159">
    <literal><![CDATA[
      a(x,y \ (T(z,z \ u) \ w),v5) = a(x,y \ (((z \ u) \ u) \ w),v5)
    ]]></literal>
    <justification jstring="[para(2720(a,1),20157(a,1,2,2,1))].">
      <j1 rule="para" parents="2720 20157"/>
    </justification>
  </clause>

  <clause id="20160">
    <literal><![CDATA[
      a(x,y \ (z * (K(u,w) \ v5)),v6) = a(x,y \ (z * (v5 * K(w,u))),v6)
    ]]></literal>
    <justification jstring="[para(6020(a,1),20158(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="6020 20158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20162">
    <literal><![CDATA[
      (x * (K(y,K(z,u)) * w)) \ v5 = K(y,K(z,u)) * ((x * w) \ v5)
    ]]></literal>
    <justification jstring="[para(15475(a,2),20128(a,1,1,2))].">
      <j1 rule="para" parents="15475 20128"/>
    </justification>
  </clause>

  <clause id="20163">
    <literal><![CDATA[
      a(x,K(y,z) \ (u * (w / u)),x) = a(x,K(y,z) \ w,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,20133,a(flip),b,20137,a)].">
      <j1 rule="hyper" parents="63 20133 20137"/>
    </justification>
  </clause>

  <clause id="20165">
    <literal><![CDATA[
      a(x,K(y,z) \ T(u,w),x) = a(x,K(y,z) \ u,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,13035,a(flip),b,20163,a),flip(a)].">
      <j1 rule="hyper" parents="63 13035 20163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20166">
    <literal><![CDATA[
      a(x,y \ (K(z,u) \ T(y * T(w,v5),y)),x) = a(x,K(z,u) \ w,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,13038,a,b,20165,a)].">
      <j1 rule="hyper" parents="63 13038 20165"/>
    </justification>
  </clause>

  <clause id="20167">
    <literal><![CDATA[
      (x * (K(y,K(z,u)) * w)) * v5 = (x * w) * (K(y,K(z,u)) * v5)
    ]]></literal>
    <justification jstring="[para(15475(a,2),20142(a,1,1,2))].">
      <j1 rule="para" parents="15475 20142"/>
    </justification>
  </clause>

  <clause id="20168">
    <literal><![CDATA[
      K(x,y * ((z * (u * K(w,K(v5,v6)))) * v7)) != v8
    ]]></literal>
    <literal><![CDATA[
      K(x,y * ((z * u) * v7)) = v8
    ]]></literal>
    <justification jstring="[para(20142(a,2),17831(a,1,2,2))].">
      <j1 rule="para" parents="20142 17831"/>
    </justification>
  </clause>

  <clause id="20169">
    <literal><![CDATA[
      K(x,y) * (T(K(y,L(x,z,u)),w) * (v5 * K(x,K(y,w)))) = a(y,z,K(u,x)) * v5
    ]]></literal>
    <justification jstring="[para(20150(a,1),18439(a,1,2))].">
      <j1 rule="para" parents="20150 18439"/>
    </justification>
  </clause>

  <clause id="20171">
    <literal><![CDATA[
      a(x,y \ ((z * (1 / z)) \ (z \ u)),w) = a(x,y \ (((z \ 1) \ 1) \ u),w)
    ]]></literal>
    <justification jstring="[para(4682(a,2),20159(a,1,2,2))].">
      <j1 rule="para" parents="4682 20159"/>
    </justification>
  </clause>

  <clause id="20172">
    <literal><![CDATA[
      a(x,T(y,z) \ T(y * T(u,w),y),x) = a(x,K(y \ 1,z) \ u,x)
    ]]></literal>
    <justification jstring="[hyper(19518,a,20166,a)].">
      <j1 rule="hyper" parents="19518 20166"/>
    </justification>
  </clause>

  <clause id="20173">
    <literal><![CDATA[
      a(x,K(y \ 1,z) \ u,x) = a(x,K(y,z) \ T(u,w),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,13039,a(flip),b,20172,a),flip(a)].">
      <j1 rule="hyper" parents="63 13039 20172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20174">
    <literal><![CDATA[
      a(x,K(y \ 1,z) \ u,x) = a(x,K(y,z) \ u,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,20165,a(flip),b,20173,a),flip(a)].">
      <j1 rule="hyper" parents="333 20165 20173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20175">
    <literal><![CDATA[
      a(x,T(T(y \ (y / z),u),z \ 1) * w,x) = a(x,K(z,u) \ ((y \ (y / z)) * w),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,19097,a(flip),b,20174,a)].">
      <j1 rule="hyper" parents="63 19097 20174"/>
    </justification>
  </clause>

  <clause id="20176">
    <literal><![CDATA[
      a(x,y \ (((z \ 1) \ 1) \ u),w) = a(x,y \ (z \ u),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,13031,a(flip),b,20171,a),flip(a)].">
      <j1 rule="hyper" parents="63 13031 20171"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20178">
    <literal><![CDATA[
      K(x,y) * (K(y,L(T(x,z),u,w)) * (v5 * K(x,K(y,z)))) = a(y,u,K(w,x)) * v5
    ]]></literal>
    <justification jstring="[para(6396(a,2),20169(a,1,2,1))].">
      <j1 rule="para" parents="6396 20169"/>
    </justification>
  </clause>

  <clause id="20179">
    <literal><![CDATA[
      K(x,L(T(y,z),u,w)) * (K(y,T(x,z)) * v5) = a(x,u,K(w,y)) * v5
    ]]></literal>
    <justification jstring="[hyper(63,a,17855,a(flip),b,20178,a)].">
      <j1 rule="hyper" parents="63 17855 20178"/>
    </justification>
  </clause>

  <clause id="20180">
    <literal><![CDATA[
      (x \ T(y,z)) * L(K(z,y),u,w) = a(y,u,K(w,z)) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,19372,a(flip),b,20179,a)].">
      <j1 rule="hyper" parents="63 19372 20179"/>
    </justification>
  </clause>

  <clause id="20182">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (w \ x) = w \ L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,14552,a(flip),b,20180,a),flip(a)].">
      <j1 rule="hyper" parents="63 14552 20180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20183">
    <literal><![CDATA[
      K(x,y \ L(z,u,K(w,v5))) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(20182(a,1),18555(a,1,2))].">
      <j1 rule="para" parents="20182 18555"/>
    </justification>
  </clause>

  <clause id="20184">
    <literal><![CDATA[
      K(x,(y \ L(z,u,K(w,v5))) * v6) = K(x,(y \ z) * v6)
    ]]></literal>
    <justification jstring="[para(20182(a,1),18680(a,1,2,1))].">
      <j1 rule="para" parents="20182 18680"/>
    </justification>
  </clause>

  <clause id="20185">
    <literal><![CDATA[
      K(x,y \ ((K(z,u) * w) \ v5)) = K(x,y \ (w \ (K(u,z) * v5)))
    ]]></literal>
    <justification jstring="[para(4581(a,1),20183(a,1,2,2))].">
      <j1 rule="para" parents="4581 20183"/>
    </justification>
  </clause>

  <clause id="20186">
    <literal><![CDATA[
      K(x,y \ T(z,L(u,w,v5))) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(14486(a,1),20183(a,1,2,2))].">
      <j1 rule="para" parents="14486 20183"/>
    </justification>
  </clause>

  <clause id="20187">
    <literal><![CDATA[
      K(x,y \ T(z,L(u / w,v5,v6))) = K(x,y \ T(z,w \ u))
    ]]></literal>
    <justification jstring="[hyper(16442,a,20186,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="16442 20186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20188">
    <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(4429(a,1),20184(a,1,2,1,2))].">
      <j1 rule="para" parents="4429 20184"/>
    </justification>
  </clause>

  <clause id="20189">
    <literal><![CDATA[
      K(x,y \ T(z,u / (w * v5))) = K(x,y \ T(z,w \ (u / v5)))
    ]]></literal>
    <justification jstring="[para(13912(a,1),20187(a,1,2,2))].">
      <j1 rule="para" parents="13912 20187"/>
    </justification>
  </clause>

  <clause id="20190">
    <literal><![CDATA[
      K(x,y \ ((z \ u) \ (K(z,w) * v5))) = K(x,y \ ((T(z,w) \ u) \ v5))
    ]]></literal>
    <justification jstring="[para(4555(a,1),20185(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4555 20185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20191">
    <literal><![CDATA[
      K(x,y \ T(z,(u * w) \ v5)) = K(x,y \ T(z,u \ (v5 / w)))
    ]]></literal>
    <justification jstring="[hyper(16442,a,20189,a)].">
      <j1 rule="hyper" parents="16442 20189"/>
    </justification>
  </clause>

  <clause id="20192">
    <literal><![CDATA[
      K(x,y \ T(z,u \ (w / v5))) = K(x,y \ T(z,(u * v5) * w))
    ]]></literal>
    <justification jstring="[hyper(16196,a,20191,a),flip(a)].">
      <j1 rule="hyper" parents="16196 20191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20193">
    <literal><![CDATA[
      K(x,y \ T(z,(u * w) * v5)) = K(x,y \ T(z,u * (v5 / w)))
    ]]></literal>
    <justification jstring="[hyper(16196,a,20192,a),flip(a)].">
      <j1 rule="hyper" parents="16196 20192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20194">
    <literal><![CDATA[
      K(x,y \ T(z,(u * w) * v5)) = K(x,y \ T(z,u * (w \ v5)))
    ]]></literal>
    <justification jstring="[hyper(333,a,19145,a(flip),b,20193,a),flip(a)].">
      <j1 rule="hyper" parents="333 19145 20193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20195">
    <literal><![CDATA[
      K(x,y \ ((z \ y) * (K(y,u) * w))) = K(x,y \ ((T(y,u) \ z) \ w))
    ]]></literal>
    <justification jstring="[hyper(63,a,19208,a(flip),b,20190,a)].">
      <j1 rule="hyper" parents="63 19208 20190"/>
    </justification>
  </clause>

  <clause id="20196">
    <literal><![CDATA[
      K(x,K(y,z) * (z \ ((u \ z) * w))) = K(x,z \ ((T(z,y) \ u) \ w))
    ]]></literal>
    <justification jstring="[hyper(19183,a,20195,a)].">
      <j1 rule="hyper" parents="19183 20195"/>
    </justification>
  </clause>

  <clause id="20197">
    <literal><![CDATA[
      K(x,T(y,z) \ ((u \ y) * w)) = K(x,y \ ((T(y,z) \ u) \ w))
    ]]></literal>
    <justification jstring="[para(4555(a,1),20196(a,1,2))].">
      <j1 rule="para" parents="4555 20196"/>
    </justification>
  </clause>

  <clause id="20198">
    <literal><![CDATA[
      K(x,T(y,z) \ ((u \ y) * w)) = K(x,y \ ((u \ T(y,z)) * w))
    ]]></literal>
    <justification jstring="[hyper(333,a,19214,a(flip),b,20197,a),flip(a)].">
      <j1 rule="hyper" parents="333 19214 20197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20199">
    <literal><![CDATA[
      a(x,T(T(y \ (y / z),u),z \ 1) * w,x) = a(x,(y \ (y / T(z,u))) * w,x)
    ]]></literal>
    <justification jstring="[para(11058(a,1),20175(a,2,2))].">
      <j1 rule="para" parents="11058 20175"/>
    </justification>
  </clause>

  <clause id="20200">
    <literal><![CDATA[
      a(x,T(y \ (y / z),u) * w,x) = a(x,(y \ (y / T(z,u))) * w,x)
    ]]></literal>
    <justification jstring="[para(5836(a,1),20199(a,1,2,1))].">
      <j1 rule="para" parents="5836 20199"/>
    </justification>
  </clause>

  <clause id="20201">
    <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="[hyper(63,a,20128,a(flip),b,20148,a)].">
      <j1 rule="hyper" parents="63 20128 20148"/>
    </justification>
  </clause>

  <clause id="20202">
    <literal><![CDATA[
      K(x,K(y,z)) * L(u * K(x,K(y,z)),w,v5) = L(u,w * K(x,K(y,z)),v5)
    ]]></literal>
    <justification jstring="[para(18(a,2),20201(a,1,2))].">
      <j1 rule="para" parents="18 20201"/>
    </justification>
  </clause>

  <clause id="20203">
    <literal><![CDATA[
      K(x,K(y,z)) * L(K(x,K(y,z)) * u,w,v5) = L(u,w * K(x,K(y,z)),v5)
    ]]></literal>
    <justification jstring="[para(15475(a,2),20202(a,1,2,1))].">
      <j1 rule="para" parents="15475 20202"/>
    </justification>
  </clause>

  <clause id="20204">
    <literal><![CDATA[
      L(K(x,K(y,z)) * (u * K(x,K(y,z))),w,v5) = L(u,w * K(x,K(y,z)),v5)
    ]]></literal>
    <justification jstring="[hyper(34,a,18318,a(flip),b,20203,a),flip(a)].">
      <j1 rule="hyper" parents="34 18318 20203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20205">
    <literal><![CDATA[
      L(x,y * K(z,K(u,w)),v5) = L(x,y,v5)
    ]]></literal>
    <justification jstring="[para(15627(a,1),20204(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15627 20204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20206">
    <literal><![CDATA[
      L(x,K(y,z) * u,w) = L(x,u * K(y,z),w)
    ]]></literal>
    <justification jstring="[para(88(a,1),20205(a,1,2)),flip(a)].">
      <j1 rule="para" parents="88 20205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20207">
    <literal><![CDATA[
      L(x,T(y,K(z,u)),w) = L(x,y,w)
    ]]></literal>
    <justification jstring="[para(4222(a,2),20205(a,1,2))].">
      <j1 rule="para" parents="4222 20205"/>
    </justification>
  </clause>

  <clause id="20208">
    <literal><![CDATA[
      L(x,K(y,T(z,u)),w) = L(x,K(y,z),w)
    ]]></literal>
    <justification jstring="[para(6377(a,1),20205(a,1,2))].">
      <j1 rule="para" parents="6377 20205"/>
    </justification>
  </clause>

  <clause id="20210">
    <literal><![CDATA[
      L(x,K(y,z) * (u * K(y,z)),w) = L(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,8053,a,b,20207,a)].">
      <j1 rule="hyper" parents="63 8053 20207"/>
    </justification>
  </clause>

  <clause id="20211">
    <literal><![CDATA[
      L(x,K(y,z) * (u * y),w) = L(x,u * T(y,z),w)
    ]]></literal>
    <justification jstring="[para(7097(a,1),20207(a,1,2))].">
      <j1 rule="para" parents="7097 20207"/>
    </justification>
  </clause>

  <clause id="20212">
    <literal><![CDATA[
      L(x,K(y,T(z,u)),w) = L(x,K(z,y),w)
    ]]></literal>
    <justification jstring="[hyper(333,a,4390,a,b,20208,a),flip(a)].">
      <j1 rule="hyper" parents="333 4390 20208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20213">
    <literal><![CDATA[
      R(x,K(y,z),u) = L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,19069,a(flip),b,20208,a)].">
      <j1 rule="hyper" parents="63 19069 20208"/>
    </justification>
  </clause>

  <clause id="20214">
    <literal><![CDATA[
      L((x / y) * K(z,u),K(u,z),y) = x / (K(u,z) * y)
    ]]></literal>
    <justification jstring="[hyper(6028,a,20213,a),flip(a)].">
      <j1 rule="hyper" parents="6028 20213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20216">
    <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(63,a,15576,a,b,20213,a)].">
      <j1 rule="hyper" parents="63 15576 20213"/>
    </justification>
  </clause>

  <clause id="20217">
    <literal><![CDATA[
      L(x * K(y,T(z,u)),K(z,y),u * K(y,z)) = (x * (u * K(y,z))) / u
    ]]></literal>
    <justification jstring="[hyper(63,a,10550,a(flip),b,20213,a),flip(a)].">
      <j1 rule="hyper" parents="63 10550 20213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20218">
    <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(63,a,8308,a(flip),b,20213,a),flip(a)].">
      <j1 rule="hyper" parents="63 8308 20213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20219">
    <literal><![CDATA[
      L(x,K(y,z),u) * (K(y,z) * u) = (x * K(y,z)) * u
    ]]></literal>
    <justification jstring="[hyper(125,a,20213,a(flip),b,20,a(flip))].">
      <j1 rule="hyper" parents="125 20213 20"/>
    </justification>
  </clause>

  <clause id="20220">
    <literal><![CDATA[
      L(x,K(y,z),u * K(z,y)) * u = (x * K(y,z)) * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(20213(a,1),8764(a,1,1))].">
      <j1 rule="para" parents="20213 8764"/>
    </justification>
  </clause>

  <clause id="20221">
    <literal><![CDATA[
      L(x \ L(x,K(y,z),u),x,K(y,z) * u) = a(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[para(20213(a,1),14051(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="20213 14051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20222">
    <literal><![CDATA[
      T(x,y \ L(y,K(z,u),w)) = x
    ]]></literal>
    <justification jstring="[para(20213(a,1),19313(a,1,2,2))].">
      <j1 rule="para" parents="20213 19313"/>
    </justification>
  </clause>

  <clause id="20223">
    <literal><![CDATA[
      T(x \ L(x,K(y,z),u),w) = x \ L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(54,a,20222,a)].">
      <j1 rule="hyper" parents="54 20222"/>
    </justification>
  </clause>

  <clause id="20224">
    <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(20212(a,2),4391(a,1))].">
      <j1 rule="para" parents="20212 4391"/>
    </justification>
  </clause>

  <clause id="20225">
    <literal><![CDATA[
      L(x,K(y,y \ z) * (u * z),w) = L(x,u * (y * (z / y)),w)
    ]]></literal>
    <justification jstring="[para(10324(a,1),20206(a,2,2))].">
      <j1 rule="para" parents="10324 20206"/>
    </justification>
  </clause>

  <clause id="20227">
    <literal><![CDATA[
      L(x,K(y,z) * (u * z),w) = L(x,u * T(z,y),w)
    ]]></literal>
    <justification jstring="[para(5455(a,1),20210(a,1,2,2))].">
      <j1 rule="para" parents="5455 20210"/>
    </justification>
  </clause>

  <clause id="20228">
    <literal><![CDATA[
      R(x,K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,K(y,z),u) = w
    ]]></literal>
    <justification jstring="[para(19069(a,1),20224(a,1))].">
      <j1 rule="para" parents="19069 20224"/>
    </justification>
  </clause>

  <clause id="20229">
    <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(17765(a,2),20228(a,1))].">
      <j1 rule="para" parents="17765 20228"/>
    </justification>
  </clause>

  <clause id="20230">
    <literal><![CDATA[
      L(x,K(y,z) * (u * y),w) = L(x,u * T(y,y * z),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,14711,a(flip),b,20211,a)].">
      <j1 rule="hyper" parents="63 14711 20211"/>
    </justification>
  </clause>

  <clause id="20231">
    <literal><![CDATA[
      L(x * K(y,z),K(z,y),u) = (x * u) / (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(11(a,1),20214(a,1,1,1))].">
      <j1 rule="para" parents="11 20214"/>
    </justification>
  </clause>

  <clause id="20232">
    <literal><![CDATA[
      (x * y) \ (L(x,K(z,u),K(z,u) \ y) * (K(z,u) * (K(z,u) \ y))) = a(x,K(z,u),K(z,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(121,a,20219,a,b,749,a)].">
      <j1 rule="hyper" parents="121 20219 749"/>
    </justification>
  </clause>

  <clause id="20233">
    <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(20231(a,1),6114(a,1,1)),flip(a)].">
      <j1 rule="para" parents="20231 6114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20234">
    <literal><![CDATA[
      T(x,L(K(y,z) * u,K(z,y),w)) = T(x,(u * w) / (K(z,y) * w))
    ]]></literal>
    <justification jstring="[para(20231(a,1),16289(a,2,2))].">
      <j1 rule="para" parents="20231 16289"/>
    </justification>
  </clause>

  <clause id="20235">
    <literal><![CDATA[
      L(x,y * T(z,z * u),w) = L(x,y * T(z,u),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,20211,a(flip),b,20230,a),flip(a)].">
      <j1 rule="hyper" parents="63 20211 20230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20236">
    <literal><![CDATA[
      L(x \ L(x,K(y,z),u),x,u * K(y,z)) = a(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(17668,a,20221,a)].">
      <j1 rule="hyper" parents="17668 20221"/>
    </justification>
  </clause>

  <clause id="20237">
    <literal><![CDATA[
      L(x \ L(x,K(y,z),u),x,K(y,z) * T(u,w)) = a(x,K(y,z),T(u,w))
    ]]></literal>
    <justification jstring="[para(19318(a,1),20221(a,1,1,2))].">
      <j1 rule="para" parents="19318 20221"/>
    </justification>
  </clause>

  <clause id="20238">
    <literal><![CDATA[
      (x * ((y * K(z,u)) * w)) \ (x * ((y * K(z,u)) * L(w,K(z,u),y))) = L(a(w,K(z,u),y),(y * K(z,u)) * w,x)
    ]]></literal>
    <justification jstring="[para(20236(a,1),526(a,1,1)),flip(a)].">
      <j1 rule="para" parents="20236 526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20239">
    <literal><![CDATA[
      L(x,K(y,z) * (u * z),w) = L(x,u * (y * (z / y)),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,14716,a(flip),b,20225,a)].">
      <j1 rule="hyper" parents="63 14716 20225"/>
    </justification>
  </clause>

  <clause id="20240">
    <literal><![CDATA[
      L(x,(y * (z / y)) * T(u,z),w) = L(x,u * (y * (z / y)),w)
    ]]></literal>
    <justification jstring="[para(10127(a,1),20225(a,1,2))].">
      <j1 rule="para" parents="10127 20225"/>
    </justification>
  </clause>

  <clause id="20241">
    <literal><![CDATA[
      L(x,y * (z * (u / z)),w) = L(x,y * T(u,z),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,20227,a(flip),b,20239,a),flip(a)].">
      <j1 rule="hyper" parents="63 20227 20239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20242">
    <literal><![CDATA[
      L(x,y * ((z \ u) * z),w) = L(x,y * (z * (u / z)),w)
    ]]></literal>
    <justification jstring="[hyper(16783,a,20240,a)].">
      <j1 rule="hyper" parents="16783 20240"/>
    </justification>
  </clause>

  <clause id="20243">
    <literal><![CDATA[
      L(x,y * (T(z * u,u \ 1) * ((z * u) \ z)),w) = L(x,y * (((z * u) \ z) * (z / ((z * u) \ z))),w)
    ]]></literal>
    <justification jstring="[para(5824(a,2),20242(a,1,2,2,1))].">
      <j1 rule="para" parents="5824 20242"/>
    </justification>
  </clause>

  <clause id="20244">
    <literal><![CDATA[
      L(x * K(y,T(z,u)),K(z,y),u) = (x * u) / (u * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(20224,a,20218,a)].">
      <j1 rule="hyper" parents="20224 20218"/>
    </justification>
  </clause>

  <clause id="20246">
    <literal><![CDATA[
      (K(x,y) * z) \ (z * T(u,K(x,y))) = (u * z) / (z * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,15833,a,b,20244,a)].">
      <j1 rule="hyper" parents="63 15833 20244"/>
    </justification>
  </clause>

  <clause id="20247">
    <literal><![CDATA[
      x \ ((K(y,z) * x) * T(u,K(z,y))) = (u * x) / (x * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,19016,a(flip),b,20246,a)].">
      <j1 rule="hyper" parents="63 19016 20246"/>
    </justification>
  </clause>

  <clause id="20248">
    <literal><![CDATA[
      x \ ((K(y,z) * x) * T(u,K(y,z))) = (u * x) / (x * K(z,y))
    ]]></literal>
    <justification jstring="[para(6840(a,1),20247(a,1,2,2))].">
      <j1 rule="para" parents="6840 20247"/>
    </justification>
  </clause>

  <clause id="20249">
    <literal><![CDATA[
      x \ ((K(y,z) * (x * K(u,K(y,z)))) * u) = (u * x) / (x * K(z,y))
    ]]></literal>
    <justification jstring="[para(6217(a,2),20248(a,1,2))].">
      <j1 rule="para" parents="6217 20248"/>
    </justification>
  </clause>

  <clause id="20250">
    <literal><![CDATA[
      K(x,y / ((z * u) \ (u * y))) = y \ ((y * u) / (u * K(z,x)))
    ]]></literal>
    <justification jstring="[para(20248(a,1),19967(a,1,2)),flip(a)].">
      <j1 rule="para" parents="20248 19967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20251">
    <literal><![CDATA[
      L(x,K(y,z),u) * u = (x * K(y,z)) * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(19019(a,1),20220(a,1,1))].">
      <j1 rule="para" parents="19019 20220"/>
    </justification>
  </clause>

  <clause id="20252">
    <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(6015(a,1),20251(a,2,1))].">
      <j1 rule="para" parents="6015 20251"/>
    </justification>
  </clause>

  <clause id="20253">
    <literal><![CDATA[
      L(x,K(y,z),L(u,x,K(y,z))) * L(K(K(y,z),x) * u,x,K(y,z)) = (x * K(y,z)) * (K(z,y) * L(K(K(y,z),x) * u,x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(17847(a,1),20251(a,1,1))].">
      <j1 rule="para" parents="17847 20251"/>
    </justification>
  </clause>

  <clause id="20254">
    <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(20234(a,1),19333(a,1))].">
      <j1 rule="para" parents="20234 19333"/>
    </justification>
  </clause>

  <clause id="20255">
    <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(13328(a,1),20254(a,1))].">
      <j1 rule="para" parents="13328 20254"/>
    </justification>
  </clause>

  <clause id="20256">
    <literal><![CDATA[
      x \ ((K(y,z) * (x * K(y,K(z,u)))) * u) = (u * x) / (x * K(z,y))
    ]]></literal>
    <justification jstring="[para(6788(a,2),20249(a,1,2,1,2,2))].">
      <j1 rule="para" parents="6788 20249"/>
    </justification>
  </clause>

  <clause id="20257">
    <literal><![CDATA[
      x \ ((K(y,T(z,u)) * x) * u) = (u * x) / (x * K(z,y))
    ]]></literal>
    <justification jstring="[para(15634(a,1),20256(a,1,2,1))].">
      <j1 rule="para" parents="15634 20256"/>
    </justification>
  </clause>

  <clause id="20258">
    <literal><![CDATA[
      (x * y) / (y * K(z,T(u,x))) = y \ ((K(u,z) * y) * x)
    ]]></literal>
    <justification jstring="[para(6901(a,1),20257(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="6901 20257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20259">
    <literal><![CDATA[
      L(x * K(y,T(z,u)),K(z,y),u) = (x * (u * K(y,z))) / u
    ]]></literal>
    <justification jstring="[hyper(63,a,19019,a(flip),b,20217,a)].">
      <j1 rule="hyper" parents="63 19019 20217"/>
    </justification>
  </clause>

  <clause id="20260">
    <literal><![CDATA[
      (x * (y * K(z,u))) / y = (x * y) / (y * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,20244,a(flip),b,20259,a),flip(a)].">
      <j1 rule="hyper" parents="63 20244 20259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20261">
    <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(444,a,20260,a,b,19455,a),flip(a)].">
      <j1 rule="hyper" parents="444 20260 19455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20262">
    <literal><![CDATA[
      (x / (y * K(z,u))) * y = (x / y) * (y * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(125,a,156,a(flip),b,20260,a)].">
      <j1 rule="hyper" parents="125 156 20260"/>
    </justification>
  </clause>

  <clause id="20263">
    <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(20260(a,1),14063(a,2,2))].">
      <j1 rule="para" parents="20260 14063"/>
    </justification>
  </clause>

  <clause id="20264">
    <literal><![CDATA[
      x / (((T(y,y \ 1) * x) / (x * K(z,u))) * (x * K(z,u))) = R(y \ 1,y,x * K(u,z))
    ]]></literal>
    <justification jstring="[para(20260(a,1),19800(a,1,2,1))].">
      <j1 rule="para" parents="20260 19800"/>
    </justification>
  </clause>

  <clause id="20265">
    <literal><![CDATA[
      (x / y) * (y * K(z,T(u,y))) = (x / (K(u,z) * y)) * y
    ]]></literal>
    <justification jstring="[para(6357(a,1),20262(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6357 20262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20266">
    <literal><![CDATA[
      (x / ((y \ 1) * K(z,u))) * (y \ 1) = (x / (y \ 1)) * (y \ K(u,z))
    ]]></literal>
    <justification jstring="[para(13126(a,1),20262(a,2,2))].">
      <j1 rule="para" parents="13126 20262"/>
    </justification>
  </clause>

  <clause id="20267">
    <literal><![CDATA[
      (x / (K(y,z) * u)) * u = (x / u) * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(6401,a,20265,a),flip(a)].">
      <j1 rule="hyper" parents="6401 20265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20268">
    <literal><![CDATA[
      (x / (K(y,z) * (1 / u))) * (1 / u) = (x / (1 / u)) * (K(z,y) / u)
    ]]></literal>
    <justification jstring="[para(13230(a,1),20267(a,2,2))].">
      <j1 rule="para" parents="13230 20267"/>
    </justification>
  </clause>

  <clause id="20269">
    <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(20266(a,1),20103(a,1))].">
      <j1 rule="para" parents="20266 20103"/>
    </justification>
  </clause>

  <clause id="20270">
    <literal><![CDATA[
      (x / (K(y,z) / u)) * (1 / u) = (x / (1 / u)) * (K(z,y) / u)
    ]]></literal>
    <justification jstring="[para(13230(a,1),20268(a,1,1,2))].">
      <j1 rule="para" parents="13230 20268"/>
    </justification>
  </clause>

  <clause id="20271">
    <literal><![CDATA[
      x * K(y,L(T(z,u),x,u * x)) = (x / (1 / u)) * (K(y,z) / u)
    ]]></literal>
    <justification jstring="[hyper(63,a,20052,a,b,20270,a)].">
      <j1 rule="hyper" parents="63 20052 20270"/>
    </justification>
  </clause>

  <clause id="20272">
    <literal><![CDATA[
      L(x \ L(x,K(y,z),u),x,T(K(y,z) * u,w)) = a(x,K(y,z),T(u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,20025,a,b,20237,a)].">
      <j1 rule="hyper" parents="63 20025 20237"/>
    </justification>
  </clause>

  <clause id="20273">
    <literal><![CDATA[
      ((K(x,y) * z) * u) / (u * K(x,T(y,z))) != w
    ]]></literal>
    <literal><![CDATA[
      L(z * K(x,K(y,u)),K(x,y),u) = w
    ]]></literal>
    <justification jstring="[para(20216(a,2),20224(a,1))].">
      <j1 rule="para" parents="20216 20224"/>
    </justification>
  </clause>

  <clause id="20274">
    <literal><![CDATA[
      R(x \ 1,x,y * K(z,u)) = y / (T(x,x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(12(a,1),20264(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12 20264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20276">
    <literal><![CDATA[
      R(x \ 1,x,y * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      R(x \ 1,x,y) = w
    ]]></literal>
    <justification jstring="[para(20274(a,2),1955(a,1))].">
      <j1 rule="para" parents="20274 1955"/>
    </justification>
  </clause>

  <clause id="20277">
    <literal><![CDATA[
      R((L(x,y,z) \ x) \ 1,L(x,y,z) \ x,L(x,y,z)) = (L(x,y,z) * K(u,w)) / (x * K(u,w))
    ]]></literal>
    <justification jstring="[hyper(20276,a,19556,a)].">
      <j1 rule="hyper" parents="20276 19556"/>
    </justification>
  </clause>

  <clause id="20278">
    <literal><![CDATA[
      R(x \ 1,x,T(y,z)) = R(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(20276,a,4560,a),flip(a)].">
      <j1 rule="hyper" parents="20276 4560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20279">
    <literal><![CDATA[
      T(x,y / (z \ T(u * z,K(w,v5)))) = T(x,K(K(w,v5) * z,u) * (y / u))
    ]]></literal>
    <justification jstring="[hyper(16400,a,20153,a),flip(a)].">
      <j1 rule="hyper" parents="16400 20153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20280">
    <literal><![CDATA[
      T(x,y / (z \ T(u * z,K(w,v5)))) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,y / T(u,K(w,v5) * z)) = v6
    ]]></literal>
    <justification jstring="[para(20279(a,2),15596(a,1))].">
      <j1 rule="para" parents="20279 15596"/>
    </justification>
  </clause>

  <clause id="20281">
    <literal><![CDATA[
      T(x,y / T(z,K(u,w) * v5)) = T(x,y / (v5 \ (z * v5)))
    ]]></literal>
    <justification jstring="[hyper(20280,a,18283,a)].">
      <j1 rule="hyper" parents="20280 18283"/>
    </justification>
  </clause>

  <clause id="20282">
    <literal><![CDATA[
      T(x,y / T(z,K(u,w) * v5)) = T(x,y / T(z,v5))
    ]]></literal>
    <justification jstring="[para(22(a,2),20281(a,2,2,2))].">
      <j1 rule="para" parents="22 20281"/>
    </justification>
  </clause>

  <clause id="20283">
    <literal><![CDATA[
      T(x,y \ K(K(z,u) * w,v5)) = T(x,(y \ v5) / T(v5,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,19402,a(flip),b,20282,a)].">
      <j1 rule="hyper" parents="63 19402 20282"/>
    </justification>
  </clause>

  <clause id="20284">
    <literal><![CDATA[
      T(x,y / T(z,u * T(w,v5))) = T(x,y / T(z,u * w))
    ]]></literal>
    <justification jstring="[para(4967(a,1),20282(a,1,2,2,2))].">
      <j1 rule="para" parents="4967 20282"/>
    </justification>
  </clause>

  <clause id="20285">
    <literal><![CDATA[
      T(x,y \ K(K(z,u) * w,v5)) = T(x,y \ K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(333,a,19402,a(flip),b,20283,a),flip(a)].">
      <j1 rule="hyper" parents="333 19402 20283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20286">
    <literal><![CDATA[
      T(x,y \ K(K(z,u) \ w,v5)) = T(x,y \ K(w,v5))
    ]]></literal>
    <justification jstring="[para(10(a,1),20285(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10 20285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20287">
    <literal><![CDATA[
      T(x,y \ K(z / u,w)) = T(x,y \ K(u \ z,w))
    ]]></literal>
    <justification jstring="[para(4312(a,1),20285(a,1,2,2,1))].">
      <j1 rule="para" parents="4312 20285"/>
    </justification>
  </clause>

  <clause id="20288">
    <literal><![CDATA[
      T(x,y \ K(T(z,u) \ w,v5)) = T(x,y \ K(z \ w,v5))
    ]]></literal>
    <justification jstring="[para(4518(a,1),20285(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4518 20285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20289">
    <literal><![CDATA[
      T(x,y \ T(K(z,u) \ y,w)) = T(x,K(z,u) \ K(y,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,18662,a(flip),b,20286,a)].">
      <j1 rule="hyper" parents="63 18662 20286"/>
    </justification>
  </clause>

  <clause id="20290">
    <literal><![CDATA[
      T(x,(y \ (z / u)) \ K(u \ z,w)) = T(x,T(z / u,w) \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,19370,a(flip),b,20287,a),flip(a)].">
      <j1 rule="hyper" parents="63 19370 20287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20291">
    <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(20284(a,1),16419(a,1))].">
      <j1 rule="para" parents="20284 16419"/>
    </justification>
  </clause>

  <clause id="20292">
    <literal><![CDATA[
      T(x,T(y * (z * K(u,z)),w) / T(v5,y * z)) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,v5 \ T(y * (z * K(u,z)),w)) = v6
    ]]></literal>
    <justification jstring="[para(20284(a,1),16504(a,1))].">
      <j1 rule="para" parents="20284 16504"/>
    </justification>
  </clause>

  <clause id="20294">
    <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(63,a,20288,a(flip),b,20290,a)].">
      <j1 rule="hyper" parents="63 20288 20290"/>
    </justification>
  </clause>

  <clause id="20295">
    <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(63,a,19804,a,b,20294,a)].">
      <j1 rule="hyper" parents="63 19804 20294"/>
    </justification>
  </clause>

  <clause id="20296">
    <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(17046,a,20295,a)].">
      <j1 rule="hyper" parents="17046 20295"/>
    </justification>
  </clause>

  <clause id="20297">
    <literal><![CDATA[
      T(x,T(y / T(z \ y,u),w)) = T(x,T(y / T(z,w),u) \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,15280,a(flip),b,20296,a)].">
      <j1 rule="hyper" parents="63 15280 20296"/>
    </justification>
  </clause>

  <clause id="20298">
    <literal><![CDATA[
      T(x,T(T(y / z,u) \ y,w)) = T(x,T(y / T(z,w),u) \ y)
    ]]></literal>
    <justification jstring="[para(6641(a,1),20297(a,1,2,1))].">
      <j1 rule="para" parents="6641 20297"/>
    </justification>
  </clause>

  <clause id="20299">
    <literal><![CDATA[
      T(x,T(T(y / z,u) \ y,w)) = T(x,y * T(y \ T(z,w),u))
    ]]></literal>
    <justification jstring="[hyper(333,a,18305,a(flip),b,20298,a),flip(a)].">
      <j1 rule="hyper" parents="333 18305 20298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20300">
    <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(333,a,12363,a,b,20299,a)].">
      <j1 rule="hyper" parents="333 12363 20299"/>
    </justification>
  </clause>

  <clause id="20301">
    <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(18770,a,20300,a)].">
      <j1 rule="hyper" parents="18770 20300"/>
    </justification>
  </clause>

  <clause id="20302">
    <literal><![CDATA[
      T(x,T(T(y / z,u) \ y,w)) = T(x,T(T(z / y,u) * y,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,12356,a(flip),b,20301,a),flip(a)].">
      <j1 rule="hyper" parents="63 12356 20301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20303">
    <literal><![CDATA[
      T(x,T(T(y / z,u) \ y,w)) = T(x,T(y * T(y \ z,u),w))
    ]]></literal>
    <justification jstring="[para(471(a,1),20302(a,2,2,1))].">
      <j1 rule="para" parents="471 20302"/>
    </justification>
  </clause>

  <clause id="20304">
    <literal><![CDATA[
      T(x,T(y * T(y \ z,u),w)) = T(x,y * T(y \ T(z,w),u))
    ]]></literal>
    <justification jstring="[hyper(63,a,20299,a(flip),b,20303,a),flip(a)].">
      <j1 rule="hyper" parents="63 20299 20303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20305">
    <literal><![CDATA[
      (x * (K(y,K(z,u)) * (w * v5))) \ ((x * (K(y,K(z,u)) * w)) * v5) = a(x * K(y,K(z,u)),w,v5)
    ]]></literal>
    <justification jstring="[para(20126(a,1),20139(a,1,2,1))].">
      <j1 rule="para" parents="20126 20139"/>
    </justification>
  </clause>

  <clause id="20306">
    <literal><![CDATA[
      (x * (y * (z * K(u,K(w,v5))))) \ ((x * y) * (z * K(u,K(w,v5)))) = a(x,K(u,K(w,v5)) * y,z)
    ]]></literal>
    <justification jstring="[para(20155(a,1),20154(a,1,2))].">
      <j1 rule="para" parents="20155 20154"/>
    </justification>
  </clause>

  <clause id="20307">
    <literal><![CDATA[
      T((L(x,y,z) / x) \ 1,L(x,y,z)) \ 1 = (L(x,y,z) * K(u,w)) / (x * K(u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,14235,a(flip),b,20277,a)].">
      <j1 rule="hyper" parents="63 14235 20277"/>
    </justification>
  </clause>

  <clause id="20308">
    <literal><![CDATA[
      T((x \ L(x,y,z)) \ 1,L(x,y,z)) \ 1 = (L(x,y,z) * K(u,w)) / (x * K(u,w))
    ]]></literal>
    <justification jstring="[para(2516(a,1),20307(a,1,1,1,1))].">
      <j1 rule="para" parents="2516 20307"/>
    </justification>
  </clause>

  <clause id="20309">
    <literal><![CDATA[
      (L(x,y,z) * K(u,w)) / (x * K(u,w)) = ((x \ L(x,y,z)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(5965(a,1),20308(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5965 20308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20310">
    <literal><![CDATA[
      (L(x,y,z) * K(u,w)) / (x * K(u,w)) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,3009,a(flip),b,20309,a),flip(a)].">
      <j1 rule="hyper" parents="333 3009 20309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20312">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,K(u,w)) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(14532,a,20310,a)].">
      <j1 rule="hyper" parents="14532 20310"/>
    </justification>
  </clause>

  <clause id="20313">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,T(u,w)) = L(x \ L(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[para(20312(a,1),14514(a,1,1)),flip(a)].">
      <j1 rule="para" parents="20312 14514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20314">
    <literal><![CDATA[
      L(x \ L(x,K(y,z),u),x,K(y,z) * u) = a(x,K(y,z),T(u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,20272,a(flip),b,20313,a),flip(a)].">
      <j1 rule="hyper" parents="63 20272 20313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20316">
    <literal><![CDATA[
      a(x,K(y,z),T(u,w)) = a(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,20221,a(flip),b,20314,a),flip(a)].">
      <j1 rule="hyper" parents="63 20221 20314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20317">
    <literal><![CDATA[
      a(x,K(y,z),L(u,w,K(v5,v6))) = a(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[para(14461(a,2),20316(a,1,3))].">
      <j1 rule="para" parents="14461 20316"/>
    </justification>
  </clause>

  <clause id="20318">
    <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(20292,a,19007,a),flip(a)].">
      <j1 rule="hyper" parents="20292 19007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20320">
    <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(20318(a,1),20291(a,1))].">
      <j1 rule="para" parents="20318 20291"/>
    </justification>
  </clause>

  <clause id="20321">
    <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(17286(a,1),20320(a,1))].">
      <j1 rule="para" parents="17286 20320"/>
    </justification>
  </clause>

  <clause id="20322">
    <literal><![CDATA[
      (x * (K(y,K(z,u)) * (w * v5))) \ ((x * w) * (K(y,K(z,u)) * v5)) = a(x * K(y,K(z,u)),w,v5)
    ]]></literal>
    <justification jstring="[para(20167(a,1),20305(a,1,2))].">
      <j1 rule="para" parents="20167 20305"/>
    </justification>
  </clause>

  <clause id="20323">
    <literal><![CDATA[
      a(x,K(y,K(z,u)) * w,v5) = a(x,w,v5 * K(y,K(z,u)))
    ]]></literal>
    <justification jstring="[hyper(752,a,20306,a),flip(a)].">
      <j1 rule="hyper" parents="752 20306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20324">
    <literal><![CDATA[
      a(x,y,z * K(u,K(w,v5))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,20124,a(flip),b,20323,a),flip(a)].">
      <j1 rule="hyper" parents="63 20124 20323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20326">
    <literal><![CDATA[
      a(x,y,z * K(u,K(w,v5))) = a(x,y,z) * 1
    ]]></literal>
    <justification jstring="[hyper(333,a,8,a,b,20324,a),flip(a)].">
      <j1 rule="hyper" parents="333 8 20324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20327">
    <literal><![CDATA[
      a(x,y,T(z,K(u,w))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(4222(a,2),20324(a,1,3))].">
      <j1 rule="para" parents="4222 20324"/>
    </justification>
  </clause>

  <clause id="20328">
    <literal><![CDATA[
      a(x,y,L(z / K(u,w),v5,v6) * K(v7,K(u,w))) = a(x,y,L(K(u,w) \ z,v5,v6) * K(v7,K(u,w)))
    ]]></literal>
    <justification jstring="[para(6662(a,1),20327(a,1,3)),flip(a)].">
      <j1 rule="para" parents="6662 20327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20329">
    <literal><![CDATA[
      a(x,y,z * K(u,K(w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = v6
    ]]></literal>
    <justification jstring="[para(20326(a,2),134(a,1)),flip(b)].">
      <j1 rule="para" parents="20326 134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20330">
    <literal><![CDATA[
      a(x,y,T(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = v5
    ]]></literal>
    <justification jstring="[para(4222(a,2),20329(a,1,3))].">
      <j1 rule="para" parents="4222 20329"/>
    </justification>
  </clause>

  <clause id="20331">
    <literal><![CDATA[
      a(x,K(y,K(z,u)) * w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,w,v5) = v6
    ]]></literal>
    <justification jstring="[para(20323(a,2),20329(a,1))].">
      <j1 rule="para" parents="20323 20329"/>
    </justification>
  </clause>

  <clause id="20332">
    <literal><![CDATA[
      a(x,y,T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,T(z,T(u,v5))) = w
    ]]></literal>
    <justification jstring="[para(6863(a,1),20330(a,1,3))].">
      <j1 rule="para" parents="6863 20330"/>
    </justification>
  </clause>

  <clause id="20333">
    <literal><![CDATA[
      a(x,T(y,K(z,u)) \ w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y \ w,v5) = v6
    ]]></literal>
    <justification jstring="[para(6778(a,1),20331(a,1,2))].">
      <j1 rule="para" parents="6778 20331"/>
    </justification>
  </clause>

  <clause id="20334">
    <literal><![CDATA[
      a(x,y,T(z,T(x * y,u))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(20332,a,14588,a)].">
      <j1 rule="hyper" parents="20332 14588"/>
    </justification>
  </clause>

  <clause id="20335">
    <literal><![CDATA[
      a(x,y,T(z,y * x)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(12225(a,1),20334(a,1,3))].">
      <j1 rule="para" parents="12225 20334"/>
    </justification>
  </clause>

  <clause id="20336">
    <literal><![CDATA[
      a(x,y,z) \ ((y * x) * T(z,x * T(y,x))) = L(z,y,x) * (y * x)
    ]]></literal>
    <justification jstring="[para(20335(a,1),19961(a,1,1))].">
      <j1 rule="para" parents="20335 19961"/>
    </justification>
  </clause>

  <clause id="20337">
    <literal><![CDATA[
      a(x,K(y,z) \ (u \ ((w / u) \ v5)),x) = a(x,w \ (u * ((K(z,y) \ u) \ v5)),x)
    ]]></literal>
    <justification jstring="[hyper(20333,a,19071,a),flip(a)].">
      <j1 rule="hyper" parents="20333 19071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20338">
    <literal><![CDATA[
      a(x,K(y,z) \ (u \ w),x) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,u \ (K(y,z) \ w),x) = v5
    ]]></literal>
    <justification jstring="[para(12895(a,1),20333(a,1))].">
      <j1 rule="para" parents="12895 20333"/>
    </justification>
  </clause>

  <clause id="20339">
    <literal><![CDATA[
      a(x,y,z) \ ((y * x) * T(z,y * x)) = L(z,y,x) * (y * x)
    ]]></literal>
    <justification jstring="[para(111(a,1),20336(a,1,2,2,2))].">
      <j1 rule="para" parents="111 20336"/>
    </justification>
  </clause>

  <clause id="20340">
    <literal><![CDATA[
      a(x,y,z) \ (z * (y * x)) = L(z,y,x) * (y * x)
    ]]></literal>
    <justification jstring="[para(111(a,1),20339(a,1,2))].">
      <j1 rule="para" parents="111 20339"/>
    </justification>
  </clause>

  <clause id="20341">
    <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(20340(a,1),16195(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="20340 16195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20342">
    <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(18967(a,1),20341(a,2,2,2))].">
      <j1 rule="para" parents="18967 20341"/>
    </justification>
  </clause>

  <clause id="20343">
    <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(333,a,20194,a(flip),b,20342,a),flip(a)].">
      <j1 rule="hyper" parents="333 20194 20342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20344">
    <literal><![CDATA[
      K(x,y \ T(z,u * (w \ v5))) = K(x,y \ T(z,u * (w * v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,19923,a(flip),b,20343,a),flip(a)].">
      <j1 rule="hyper" parents="63 19923 20343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20346">
    <literal><![CDATA[
      ((x * (K(y,K(z,u)) * (w * v5))) \ ((x * w) * v5)) * K(y,K(z,u)) = a(x * K(y,K(z,u)),w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,18120,a(flip),b,20322,a)].">
      <j1 rule="hyper" parents="63 18120 20322"/>
    </justification>
  </clause>

  <clause id="20347">
    <literal><![CDATA[
      (K(x,K(y,z)) * ((u * (w * v5)) \ ((u * w) * v5))) * K(x,K(y,z)) = a(u * K(x,K(y,z)),w,v5)
    ]]></literal>
    <justification jstring="[para(20162(a,1),20346(a,1,1))].">
      <j1 rule="para" parents="20162 20346"/>
    </justification>
  </clause>

  <clause id="20348">
    <literal><![CDATA[
      (K(x,K(y,z)) * a(u,w,v5)) * K(x,K(y,z)) = a(u * K(x,K(y,z)),w,v5)
    ]]></literal>
    <justification jstring="[para(14(a,2),20347(a,1,1,2))].">
      <j1 rule="para" parents="14 20347"/>
    </justification>
  </clause>

  <clause id="20349">
    <literal><![CDATA[
      a(x * K(y,K(z,u)),w,v5) = a(x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(15694,a,20348,a),flip(a)].">
      <j1 rule="hyper" parents="15694 20348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20351">
    <literal><![CDATA[
      a(T(x,K(y,z)),u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[para(4222(a,2),20349(a,1,1))].">
      <j1 rule="para" parents="4222 20349"/>
    </justification>
  </clause>

  <clause id="20352">
    <literal><![CDATA[
      a(T(x,T(y,z)),u,w) = a(T(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(6191(a,1),20351(a,1,1))].">
      <j1 rule="para" parents="6191 20351"/>
    </justification>
  </clause>

  <clause id="20354">
    <literal><![CDATA[
      a(T(x * ((x / y) / x),x),z,u) = a(x * ((y \ x) / x),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,11990,a(flip),b,20352,a),flip(a)].">
      <j1 rule="hyper" parents="63 11990 20352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20356">
    <literal><![CDATA[
      a(x * ((y \ x) / x),z,u) = a(x / y,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,11956,a(flip),b,20354,a),flip(a)].">
      <j1 rule="hyper" parents="63 11956 20354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20358">
    <literal><![CDATA[
      a(T(x,y) * ((z \ x) / x),u,w) = a(T(x,y) / z,u,w)
    ]]></literal>
    <justification jstring="[para(13353(a,1),20356(a,1,1,2))].">
      <j1 rule="para" parents="13353 20356"/>
    </justification>
  </clause>

  <clause id="20359">
    <literal><![CDATA[
      a(T(x,y) * ((z \ x) / x),u,w) = a(T(x,x \ y) / z,u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,11959,a(flip),b,20358,a)].">
      <j1 rule="hyper" parents="63 11959 20358"/>
    </justification>
  </clause>

  <clause id="20360">
    <literal><![CDATA[
      a(T(x,x \ y) / z,u,w) = a(T(x,y) / z,u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,20358,a(flip),b,20359,a),flip(a)].">
      <j1 rule="hyper" parents="63 20358 20359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20361">
    <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(20360(a,1),13032(a,1,2))].">
      <j1 rule="para" parents="20360 13032"/>
    </justification>
  </clause>

  <clause id="20362">
    <literal><![CDATA[
      (x * y) / a(z \ x,T(z,x),y) = (x / ((x \ z) * x)) * (((x \ z) * x) * y)
    ]]></literal>
    <justification jstring="[para(11955(a,1),20361(a,1,2))].">
      <j1 rule="para" parents="11955 20361"/>
    </justification>
  </clause>

  <clause id="20363">
    <literal><![CDATA[
      (x * y) / a(x / z,z,y) = (x / ((x \ z) * x)) * (((x \ z) * x) * y)
    ]]></literal>
    <justification jstring="[para(13678(a,1),20362(a,1,2))].">
      <j1 rule="para" parents="13678 20362"/>
    </justification>
  </clause>

  <clause id="20364">
    <literal><![CDATA[
      (x / ((x \ y) * x)) * (((x \ y) * x) * z) = (x / y) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(927,a,20363,a),flip(a)].">
      <j1 rule="hyper" parents="927 20363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20365">
    <literal><![CDATA[
      ((x / ((x \ y) * x)) * (((x \ y) * x) * z)) * u = ((x / y) * (y * z)) * u
    ]]></literal>
    <justification jstring="[hyper(125,a,20364,a,b,11,a)].">
      <j1 rule="hyper" parents="125 20364 11"/>
    </justification>
  </clause>

  <clause id="20366">
    <literal><![CDATA[
      ((x / y) * (y * K(z,u))) * w = (x * K(z,L(u,x,(x \ y) \ 1))) * w
    ]]></literal>
    <justification jstring="[para(19778(a,1),20365(a,1,1)),flip(a)].">
      <j1 rule="para" parents="19778 20365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20367">
    <literal><![CDATA[
      ((x / y) * (y * K(z,u))) * w = (x * K(z,L(u,x,y \ x))) * w
    ]]></literal>
    <justification jstring="[para(14131(a,1),20366(a,2,1,2))].">
      <j1 rule="para" parents="14131 20366"/>
    </justification>
  </clause>

  <clause id="20368">
    <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(333,a,19297,a(flip),b,20367,a),flip(a)].">
      <j1 rule="hyper" parents="333 19297 20367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20369">
    <literal><![CDATA[
      ((x / y) * (y * K(z,u))) * K(u,z) = x * a(z,x,K(y \ x,u))
    ]]></literal>
    <justification jstring="[para(13750(a,1),20368(a,2,2))].">
      <j1 rule="para" parents="13750 20368"/>
    </justification>
  </clause>

  <clause id="20370">
    <literal><![CDATA[
      (x * y) \ (L(x,K(z,u),K(u,z) * y) * (K(z,u) * (K(z,u) \ y))) = a(x,K(z,u),K(z,u) \ y)
    ]]></literal>
    <justification jstring="[para(4567(a,1),20232(a,1,2,1,3))].">
      <j1 rule="para" parents="4567 20232"/>
    </justification>
  </clause>

  <clause id="20371">
    <literal><![CDATA[
      a(x,y,L(z / K(u,w),v5,v6) * K(v7,K(u,w))) = a(x,y,L(K(w,u) * z,v5,v6) * K(v7,K(u,w)))
    ]]></literal>
    <justification jstring="[para(4567(a,1),20328(a,2,3,1,1))].">
      <j1 rule="para" parents="4567 20328"/>
    </justification>
  </clause>

  <clause id="20372">
    <literal><![CDATA[
      (x * y) \ (L(x,K(z,u),y) * (K(z,u) * (K(z,u) \ y))) = a(x,K(z,u),K(z,u) \ y)
    ]]></literal>
    <justification jstring="[para(19021(a,1),20370(a,1,2,1))].">
      <j1 rule="para" parents="19021 20370"/>
    </justification>
  </clause>

  <clause id="20373">
    <literal><![CDATA[
      a(x,K(y,z),K(y,z) \ u) = (x * u) \ (L(x,K(y,z),u) * u)
    ]]></literal>
    <justification jstring="[para(10(a,1),20372(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 20372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20375">
    <literal><![CDATA[
      a(x,K(y,z),K(z,y) * u) = (x * u) \ (L(x,K(y,z),u) * u)
    ]]></literal>
    <justification jstring="[para(4567(a,1),20373(a,1,3))].">
      <j1 rule="para" parents="4567 20373"/>
    </justification>
  </clause>

  <clause id="20376">
    <literal><![CDATA[
      (x * L(K(K(y,z),x) * u,x,K(y,z))) \ (L(x,K(y,z),L(u,x,K(y,z))) * L(K(K(y,z),x) * u,x,K(y,z))) = a(x,K(y,z),K(z,y) * L(K(K(y,z),x) * u,x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(17847(a,1),20375(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="17847 20375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20377">
    <literal><![CDATA[
      a(x,y,L(z / K(u,w),v5,v6) * K(v7,K(u,w))) = a(x,y,L(K(w,u) * z,v5,v6) * K(u,K(w,v7)))
    ]]></literal>
    <justification jstring="[para(6788(a,2),20371(a,2,3,2))].">
      <j1 rule="para" parents="6788 20371"/>
    </justification>
  </clause>

  <clause id="20378">
    <literal><![CDATA[
      a(x,y,L(K(z,K(u,w)) * (K(u,z) * v5),v6,v7)) = a(x,y,L(v5 / K(z,u),v6,v7) * K(w,K(z,u)))
    ]]></literal>
    <justification jstring="[para(18324(a,2),20377(a,2,3)),flip(a)].">
      <j1 rule="para" parents="18324 20377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20379">
    <literal><![CDATA[
      a(x,y,L(z * (T(T(z,u),K(u,w)) \ v5),v6,v7)) = a(x,y,L(v5 / K(z,u),v6,v7) * K(w,K(z,u)))
    ]]></literal>
    <justification jstring="[para(16047(a,1),20378(a,1,3,1))].">
      <j1 rule="para" parents="16047 20378"/>
    </justification>
  </clause>

  <clause id="20380">
    <literal><![CDATA[
      a(x,y,L(z / K(u,w),v5,v6) * K(v7,K(u,w))) = a(x,y,L(u * (T(u,T(w,v7)) \ z),v5,v6))
    ]]></literal>
    <justification jstring="[para(6191(a,1),20379(a,1,3,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6191 20379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20381">
    <literal><![CDATA[
      a(x,y,L(z / K(u,w),v5,v6) * K(v7,K(u,w))) = a(x,y,L(K(T(w,v7),u) * z,v5,v6))
    ]]></literal>
    <justification jstring="[para(4556(a,1),20380(a,2,3,1))].">
      <j1 rule="para" parents="4556 20380"/>
    </justification>
  </clause>

  <clause id="20382">
    <literal><![CDATA[
      a(x,y,L(z / K(u,w),v5,v6) * K(v7,K(u,w))) = a(x,y,L(K(w,T(u,v7)) * z,v5,v6))
    ]]></literal>
    <justification jstring="[para(6370(a,1),20381(a,2,3,1,1))].">
      <j1 rule="para" parents="6370 20381"/>
    </justification>
  </clause>

  <clause id="20383">
    <literal><![CDATA[
      a(x,y,L(z * K(u,w),v5,v6) * K(v7,K(w,u))) = a(x,y,L(K(u,T(w,v7)) * z,v5,v6))
    ]]></literal>
    <justification jstring="[para(5994(a,1),20382(a,1,3,1,1))].">
      <j1 rule="para" parents="5994 20382"/>
    </justification>
  </clause>

  <clause id="20384">
    <literal><![CDATA[
      a(x,y,L(K(z,T(u,w)) * v5,v6,v7)) = a(x,y,L(v5 * K(z,u),v6,v7))
    ]]></literal>
    <justification jstring="[hyper(20329,a,20383,a),flip(a)].">
      <j1 rule="hyper" parents="20329 20383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20386">
    <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(19720(a,1),20263(a,1,1,1))].">
      <j1 rule="para" parents="19720 20263"/>
    </justification>
  </clause>

  <clause id="20387">
    <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(14008(a,1),20386(a,1,1,1))].">
      <j1 rule="para" parents="14008 20386"/>
    </justification>
  </clause>

  <clause id="20389">
    <literal><![CDATA[
      ((K(x,y) * z) * (u * K(w,v5))) / u = K(x,y) * ((z * u) / (u * K(v5,w)))
    ]]></literal>
    <justification jstring="[para(19579(a,1),20387(a,1,1))].">
      <j1 rule="para" parents="19579 20387"/>
    </justification>
  </clause>

  <clause id="20390">
    <literal><![CDATA[
      ((K(x,y) * z) * u) / (u * K(w,v5)) = K(x,y) * ((z * u) / (u * K(w,v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,20260,a(flip),b,20389,a)].">
      <j1 rule="hyper" parents="63 20260 20389"/>
    </justification>
  </clause>

  <clause id="20391">
    <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(20273,a,20390,a),flip(a)].">
      <j1 rule="hyper" parents="20273 20390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20392">
    <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(20258(a,1),20391(a,1,2))].">
      <j1 rule="para" parents="20258 20391"/>
    </justification>
  </clause>

  <clause id="20394">
    <literal><![CDATA[
      L(x,y * (((z * u) \ z) * (z / ((z * u) \ z))),w) = L(x,y * (K(z * u,u \ 1) * z),w)
    ]]></literal>
    <justification jstring="[para(4242(a,1),20243(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4242 20243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20396">
    <literal><![CDATA[
      L(x,y * (((z * u) \ z) * (z / ((z * u) \ z))),w) = L(x,y * (z * K(u * z,u \ 1)),w)
    ]]></literal>
    <justification jstring="[para(12199(a,1),20394(a,2,2,2))].">
      <j1 rule="para" parents="12199 20394"/>
    </justification>
  </clause>

  <clause id="20397">
    <literal><![CDATA[
      L(x,y * (((z * u) \ z) * (z * u)),w) = L(x,y * (z * K(u * z,u \ 1)),w)
    ]]></literal>
    <justification jstring="[para(76(a,1),20396(a,1,2,2,2))].">
      <j1 rule="para" parents="76 20396"/>
    </justification>
  </clause>

  <clause id="20399">
    <literal><![CDATA[
      L(x,y * ((z * u) * (z / (z * u))),w) = L(x,y * (z * K(u * z,u \ 1)),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,20242,a(flip),b,20397,a)].">
      <j1 rule="hyper" parents="63 20242 20397"/>
    </justification>
  </clause>

  <clause id="20400">
    <literal><![CDATA[
      L(x,y * (z * K(u * z,u \ 1)),w) = L(x,y * T(z,z * u),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,20241,a(flip),b,20399,a),flip(a)].">
      <j1 rule="hyper" parents="63 20241 20399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20401">
    <literal><![CDATA[
      L(x,y * (z * K(u * z,u \ 1)),w) = L(x,y * T(z,u),w)
    ]]></literal>
    <justification jstring="[hyper(333,a,20235,a(flip),b,20400,a),flip(a)].">
      <j1 rule="hyper" parents="333 20235 20400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20402">
    <literal><![CDATA[
      L(x,y * T(z,u \ 1),w) = L(x,y * T(z,u),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,14781,a(flip),b,20401,a)].">
      <j1 rule="hyper" parents="63 14781 20401"/>
    </justification>
  </clause>

  <clause id="20403">
    <literal><![CDATA[
      L(x,(y / z) * T(z,u),w) = L(x,y * K(z,u \ 1),w)
    ]]></literal>
    <justification jstring="[para(5974(a,1),20402(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5974 20402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20404">
    <literal><![CDATA[
      L(x,y * K(z,u \ 1),w) = L(x,y * K(z,u),w)
    ]]></literal>
    <justification jstring="[para(5974(a,1),20403(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5974 20403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20405">
    <literal><![CDATA[
      L(x,T(y \ 1,z),u) = L(x,y * K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(5095,a,20404,a)].">
      <j1 rule="hyper" parents="5095 20404"/>
    </justification>
  </clause>

  <clause id="20406">
    <literal><![CDATA[
      L(x,T(y \ 1,z),u) = L(x,T(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(333,a,4562,a(flip),b,20405,a),flip(a)].">
      <j1 rule="hyper" parents="333 4562 20405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20407">
    <literal><![CDATA[
      L(x,T((y * z) \ z,z),u) = L(x,((z * y) \ z) \ 1,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,11207,a(flip),b,20406,a),flip(a)].">
      <j1 rule="hyper" parents="63 11207 20406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20408">
    <literal><![CDATA[
      L(x,((y * z) \ y) \ 1,u) = L(x,y / (z * y),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,14703,a(flip),b,20407,a),flip(a)].">
      <j1 rule="hyper" parents="63 14703 20407"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20409">
    <literal><![CDATA[
      L(x,y / (z * y),u) = L(x,(y * z) \ y,u)
    ]]></literal>
    <justification jstring="[hyper(2631,a,20408,a),flip(a)].">
      <j1 rule="hyper" parents="2631 20408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20410">
    <literal><![CDATA[
      K(x,L((y / T(z,u \ 1)) / (w / (u * w)),(w * u) \ w,T(z,u \ 1))) = K(x,y / (z * (w / (u * w))))
    ]]></literal>
    <justification jstring="[para(20409(a,1),13969(a,1,2))].">
      <j1 rule="para" parents="20409 13969"/>
    </justification>
  </clause>

  <clause id="20411">
    <literal><![CDATA[
      K(x,L((y / T(z,u \ 1)) / (w / (u * w)),(w * u) \ w,z)) = K(x,y / (z * (w / (u * w))))
    ]]></literal>
    <justification jstring="[hyper(17657,a,20410,a)].">
      <j1 rule="hyper" parents="17657 20410"/>
    </justification>
  </clause>

  <clause id="20413">
    <literal><![CDATA[
      K(x,L((y / T(z,u \ 1)) / ((w * u) \ w),(w * u) \ w,z)) = K(x,y / (z * (w / (u * w))))
    ]]></literal>
    <justification jstring="[hyper(63,a,18914,a(flip),b,20411,a)].">
      <j1 rule="hyper" parents="63 18914 20411"/>
    </justification>
  </clause>

  <clause id="20414">
    <literal><![CDATA[
      K(x,y / (((z * u) \ z) * T(w,u \ 1))) = K(x,y / (w * (z / (u * z))))
    ]]></literal>
    <justification jstring="[hyper(63,a,17643,a(flip),b,20413,a)].">
      <j1 rule="hyper" parents="63 17643 20413"/>
    </justification>
  </clause>

  <clause id="20415">
    <literal><![CDATA[
      K(x,y / (z * (u / (w * u)))) = K(x,y / (z * ((u * w) \ u)))
    ]]></literal>
    <justification jstring="[para(5826(a,1),20414(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5826 20414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20416">
    <literal><![CDATA[
      K(x,y / (z * ((y * u) \ y))) = K(x,y / (z / u))
    ]]></literal>
    <justification jstring="[hyper(63,a,18941,a(flip),b,20415,a),flip(a)].">
      <j1 rule="hyper" parents="63 18941 20415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20417">
    <literal><![CDATA[
      K(x,((y / ((y * z) \ y)) * u) / y) = K(x,y / ((y / u) / z))
    ]]></literal>
    <justification jstring="[hyper(63,a,19938,a,b,20416,a)].">
      <j1 rule="hyper" parents="63 19938 20416"/>
    </justification>
  </clause>

  <clause id="20418">
    <literal><![CDATA[
      K(x,((y * z) * u) / y) = K(x,y / ((y / u) / z))
    ]]></literal>
    <justification jstring="[para(76(a,1),20417(a,1,2,1,1))].">
      <j1 rule="para" parents="76 20417"/>
    </justification>
  </clause>

  <clause id="20420">
    <literal><![CDATA[
      K(x,T(y,z) / ((T(y,z) / u) / (K(z,y) * w))) = K(x,((y * w) * u) / T(y,z))
    ]]></literal>
    <justification jstring="[para(4250(a,1),20418(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="4250 20418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20421">
    <literal><![CDATA[
      K(x,((y * z) * (u * K(y,w))) / y) = K(x,y / ((K(w,y) * (y / u)) / z))
    ]]></literal>
    <justification jstring="[para(13322(a,1),20418(a,2,2,2,1))].">
      <j1 rule="para" parents="13322 20418"/>
    </justification>
  </clause>

  <clause id="20422">
    <literal><![CDATA[
      K(x,y / ((K(z,y) * (y / u)) / w)) = K(x,((y * w) * u) * (y \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(18422,a,20421,a),flip(a)].">
      <j1 rule="hyper" parents="18422 20421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20423">
    <literal><![CDATA[
      K(x,y / ((K(z,y) * (y / u)) / w)) = K(x,((y * w) * u) / T(y,z))
    ]]></literal>
    <justification jstring="[hyper(333,a,18105,a(flip),b,20422,a),flip(a)].">
      <j1 rule="hyper" parents="333 18105 20422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20424">
    <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(17826(a,2),20143(a,1,1))].">
      <j1 rule="para" parents="17826 20143"/>
    </justification>
  </clause>

  <clause id="20425">
    <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(15626(a,2),20424(a,1,2,1))].">
      <j1 rule="para" parents="15626 20424"/>
    </justification>
  </clause>

  <clause id="20426">
    <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(17593(a,2),20425(a,1,2))].">
      <j1 rule="para" parents="17593 20425"/>
    </justification>
  </clause>

  <clause id="20427">
    <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(17820,a,20426,a)].">
      <j1 rule="hyper" parents="17820 20426"/>
    </justification>
  </clause>

  <clause id="20428">
    <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(63,a,20152,a(flip),b,20427,a),flip(a)].">
      <j1 rule="hyper" parents="63 20152 20427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20430">
    <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(333,a,20,a,b,20428,a),flip(a)].">
      <j1 rule="hyper" parents="333 20 20428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20431">
    <literal><![CDATA[
      R(x,y,K(z,K(u,w)) * v5) = R(x,y,v5)
    ]]></literal>
    <justification jstring="[para(20138(a,1),20430(a,1,2))].">
      <j1 rule="para" parents="20138 20430"/>
    </justification>
  </clause>

  <clause id="20432">
    <literal><![CDATA[
      R(x,y,z \ T(u,K(w,v5))) = R(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(4963(a,1),20431(a,1,3))].">
      <j1 rule="para" parents="4963 20431"/>
    </justification>
  </clause>

  <clause id="20434">
    <literal><![CDATA[
      R(x,y,z \ K(u,T(w,v5))) = R(x,y,z \ K(u,w))
    ]]></literal>
    <justification jstring="[para(17797(a,1),20431(a,1,3))].">
      <j1 rule="para" parents="17797 20431"/>
    </justification>
  </clause>

  <clause id="20435">
    <literal><![CDATA[
      R(x,y,z \ (u \ K(w,K(v5,v6)))) = R(x,y,z \ (u \ 1))
    ]]></literal>
    <justification jstring="[para(17798(a,1),20431(a,1,3))].">
      <j1 rule="para" parents="17798 20431"/>
    </justification>
  </clause>

  <clause id="20436">
    <literal><![CDATA[
      R(x,y,z \ ((u \ T(K(w,v5),v6)) \ T(K(w,v5),u))) = R(x,y,z \ ((u \ T(K(w,v5),v6)) \ K(w,v5)))
    ]]></literal>
    <justification jstring="[para(13672(a,1),20432(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="13672 20432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20437">
    <literal><![CDATA[
      R(x,y,(z * u) \ (K(w,v5) \ (u * z))) = R(x,y,K(z,u) \ K(v5,w))
    ]]></literal>
    <justification jstring="[para(19476(a,1),20434(a,1,3))].">
      <j1 rule="para" parents="19476 20434"/>
    </justification>
  </clause>

  <clause id="20438">
    <literal><![CDATA[
      R(x,y,K(x,y) \ K(z,u)) \ (K(u,z) \ (y * x)) = y * ((x * y) \ (K(u,z) \ (y * x)))
    ]]></literal>
    <justification jstring="[para(20437(a,1),364(a,1,1))].">
      <j1 rule="para" parents="20437 364"/>
    </justification>
  </clause>

  <clause id="20439">
    <literal><![CDATA[
      R(x,y,K(z,u)) \ (K(u,z) \ (y * x)) = y * ((x * y) \ (K(u,z) \ (y * x)))
    ]]></literal>
    <justification jstring="[para(14284(a,1),20438(a,1,1))].">
      <j1 rule="para" parents="14284 20438"/>
    </justification>
  </clause>

  <clause id="20440">
    <literal><![CDATA[
      L(x,y,K(z,u)) \ (K(u,z) \ (y * x)) = y * ((x * y) \ (K(u,z) \ (y * x)))
    ]]></literal>
    <justification jstring="[para(14460(a,1),20439(a,1,1))].">
      <j1 rule="para" parents="14460 20439"/>
    </justification>
  </clause>

  <clause id="20441">
    <literal><![CDATA[
      (x * y) \ (K(z,u) \ (y * x)) = y \ T(K(z,u) \ y,x)
    ]]></literal>
    <justification jstring="[hyper(17899,a,20440,a),flip(a)].">
      <j1 rule="hyper" parents="17899 20440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20442">
    <literal><![CDATA[
      x * ((y * x) \ (K(z,u) \ (x * y))) != w
    ]]></literal>
    <literal><![CDATA[
      T(K(z,u) \ x,y) = w
    ]]></literal>
    <justification jstring="[para(20441(a,2),273(a,1,2)),flip(b)].">
      <j1 rule="para" parents="20441 273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20443">
    <literal><![CDATA[
      K(x,T(y,z \ u)) \ T(z,u) = (z \ T(K(x,y) \ z,u)) * z
    ]]></literal>
    <justification jstring="[para(20441(a,1),19507(a,1,1)),flip(a)].">
      <j1 rule="para" parents="20441 19507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20444">
    <literal><![CDATA[
      K(x,y) \ (y * K(z,T(u,y \ x))) = T(K(u,z) \ y,x)
    ]]></literal>
    <justification jstring="[hyper(20442,a,19480,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="20442 19480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20445">
    <literal><![CDATA[
      T(x,y) * K(z,T(u,x \ y)) = T(K(u,z) \ x,y)
    ]]></literal>
    <justification jstring="[hyper(4715,a,20444,a)].">
      <j1 rule="hyper" parents="4715 20444"/>
    </justification>
  </clause>

  <clause id="20446">
    <literal><![CDATA[
      T(x,y) * K(z,T(u,y \ x)) = T(K(u,z) \ x,y)
    ]]></literal>
    <justification jstring="[para(7271(a,1),20445(a,1,2))].">
      <j1 rule="para" parents="7271 20445"/>
    </justification>
  </clause>

  <clause id="20447">
    <literal><![CDATA[
      K(x,T(K(y,z) \ u,w)) = K(x,K(y,z) \ T(u,w))
    ]]></literal>
    <justification jstring="[para(20445(a,1),16410(a,1,2))].">
      <j1 rule="para" parents="20445 16410"/>
    </justification>
  </clause>

  <clause id="20448">
    <literal><![CDATA[
      T(K(x,T(y,z \ u)) \ u,z) = T(u,z) * K(y,x)
    ]]></literal>
    <justification jstring="[para(6901(a,1),20446(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6901 20446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20449">
    <literal><![CDATA[
      T(x,T(K(y,z) \ u,w)) = T(x,K(y,z) \ T(u,w))
    ]]></literal>
    <justification jstring="[hyper(124,a,20447,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 20447 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20450">
    <literal><![CDATA[
      T(K(x,T(y,(((z / u) \ 1) * z) \ z)) \ (u * (z / u)),((u \ z) \ 1) * z) = T(u * (z / u),((u \ z) \ 1) * z) * K(y,x)
    ]]></literal>
    <justification jstring="[para(11983(a,1),20448(a,1,1,1,2,2))].">
      <j1 rule="para" parents="11983 20448"/>
    </justification>
  </clause>

  <clause id="20451">
    <literal><![CDATA[
      T(T(x,K(y,z) \ T(x,u)),x \ T(K(y,z) \ x,u)) = (x \ T(x * K(z,y),u)) \ T(K(y,z) \ x,u)
    ]]></literal>
    <justification jstring="[para(20449(a,1),12970(a,1,1))].">
      <j1 rule="para" parents="20449 12970"/>
    </justification>
  </clause>

  <clause id="20452">
    <literal><![CDATA[
      R(x,y,z \ ((u \ T(K(w,v5),v6)) \ T(K(w,v5),u))) = R(x,y,z \ ((u \ K(w,v5)) \ K(w,T(v5,v6))))
    ]]></literal>
    <justification jstring="[para(17832(a,1),20436(a,2,3,2))].">
      <j1 rule="para" parents="17832 20436"/>
    </justification>
  </clause>

  <clause id="20453">
    <literal><![CDATA[
      R(x,y,z \ ((u \ K(w,T(v5,v6))) \ T(K(w,v5),u))) = R(x,y,z \ ((u \ K(w,v5)) \ K(w,T(v5,v6))))
    ]]></literal>
    <justification jstring="[para(6365(a,2),20452(a,1,3,2,1,2))].">
      <j1 rule="para" parents="6365 20452"/>
    </justification>
  </clause>

  <clause id="20454">
    <literal><![CDATA[
      R(x,y,z \ ((u \ K(w,T(v5,v6))) \ K(w,T(v5,u)))) = R(x,y,z \ ((u \ K(w,v5)) \ K(w,T(v5,v6))))
    ]]></literal>
    <justification jstring="[para(6365(a,2),20453(a,1,3,2,2))].">
      <j1 rule="para" parents="6365 20453"/>
    </justification>
  </clause>

  <clause id="20455">
    <literal><![CDATA[
      R(x,y,z \ ((u \ K(w,v5)) \ K(w,T(T(v5,v6),u)))) = R(x,y,z \ ((u \ K(w,v5)) \ K(w,T(v5,v6))))
    ]]></literal>
    <justification jstring="[para(18882(a,1),20454(a,1,3,2))].">
      <j1 rule="para" parents="18882 20454"/>
    </justification>
  </clause>

  <clause id="20456">
    <literal><![CDATA[
      R(x,y,z \ ((u \ K(w,v5)) \ K(w,T(v5,v6)))) = R(x,y,z \ ((u \ 1) \ K(w,K(v5,v6))))
    ]]></literal>
    <justification jstring="[para(17023(a,1),20455(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="17023 20455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20457">
    <literal><![CDATA[
      R(x,y,z \ ((u \ K(w,v5)) \ K(w,T(v5,v6)))) = R(x,y,z \ ((u \ 1) \ 1))
    ]]></literal>
    <justification jstring="[hyper(333,a,20435,a(flip),b,20456,a),flip(a)].">
      <j1 rule="hyper" parents="333 20435 20456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20459">
    <literal><![CDATA[
      R(x,y,z \ ((u \ K(w,v5)) \ K(w,T(v5,v6)))) = R(x,y,z \ T(u,1))
    ]]></literal>
    <justification jstring="[hyper(333,a,14408,a(flip),b,20457,a),flip(a)].">
      <j1 rule="hyper" parents="333 14408 20457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20460">
    <literal><![CDATA[
      R(x,y,z \ ((u \ K(w,v5)) \ K(w,T(v5,v6)))) = R(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(199(a,1),20459(a,2,3,2))].">
      <j1 rule="para" parents="199 20459"/>
    </justification>
  </clause>

  <clause id="20461">
    <literal><![CDATA[
      R(x,y,z \ T(T(u,K(w,v5)) \ v6,K(w,T(v5,u)))) = R(x,y,z \ (u \ v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,14411,a,b,20460,a)].">
      <j1 rule="hyper" parents="63 14411 20460"/>
    </justification>
  </clause>

  <clause id="20463">
    <literal><![CDATA[
      R(x,y,z \ (T(u,K(w,v5)) \ v6)) = R(x,y,z \ (u \ v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,20432,a(flip),b,20461,a)].">
      <j1 rule="hyper" parents="63 20432 20461"/>
    </justification>
  </clause>

  <clause id="20465">
    <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(63,a,20094,a(flip),b,20463,a),flip(a)].">
      <j1 rule="hyper" parents="63 20094 20463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20467">
    <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(63,a,14415,a,b,20465,a)].">
      <j1 rule="hyper" parents="63 14415 20465"/>
    </justification>
  </clause>

  <clause id="20468">
    <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(17800(a,1),20467(a,1,3))].">
      <j1 rule="para" parents="17800 20467"/>
    </justification>
  </clause>

  <clause id="20469">
    <literal><![CDATA[
      R(x,y,z \ T(u,K(w,v5) * v6)) = R(x,y,z \ T(u,v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,20431,a(flip),b,20468,a),flip(a)].">
      <j1 rule="hyper" parents="63 20431 20468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20471">
    <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(20469(a,1),19148(a,1,2,1))].">
      <j1 rule="para" parents="20469 19148"/>
    </justification>
  </clause>

  <clause id="20472">
    <literal><![CDATA[
      K(x,y * (z \ T(u,K(w,v5) * v6))) = K(x,y * (z \ T(u,v6)))
    ]]></literal>
    <justification jstring="[para(527(a,1),20471(a,1,2)),flip(a)].">
      <j1 rule="para" parents="527 20471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20474">
    <literal><![CDATA[
      T(T(x,K(y,z) \ x),x \ T(K(y,z) \ x,u)) = (x \ T(x * K(z,y),u)) \ T(K(y,z) \ x,u)
    ]]></literal>
    <justification jstring="[para(9598(a,1),20451(a,1,1))].">
      <j1 rule="para" parents="9598 20451"/>
    </justification>
  </clause>

  <clause id="20476">
    <literal><![CDATA[
      (x \ T(x * K(y,z),u)) \ T(K(z,y) \ x,u) = T(T(x,K(z,y)),x \ T(K(z,y) \ x,u))
    ]]></literal>
    <justification jstring="[para(15707(a,1),20474(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15707 20474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20477">
    <literal><![CDATA[
      (x \ T(x * K(y,z),u)) \ T(K(z,y) \ x,u) = T(T(x,K(z,y)),K(z,y) \ K(x,u))
    ]]></literal>
    <justification jstring="[hyper(333,a,20289,a(flip),b,20476,a),flip(a)].">
      <j1 rule="hyper" parents="333 20289 20476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20478">
    <literal><![CDATA[
      (x \ T(x * K(y,z),u)) \ T(K(z,y) \ x,u) = T(T(x,K(z,y) \ 1),K(z,y))
    ]]></literal>
    <justification jstring="[hyper(333,a,7650,a(flip),b,20477,a),flip(a)].">
      <j1 rule="hyper" parents="333 7650 20477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20480">
    <literal><![CDATA[
      (x \ T(x * K(y,z),u)) \ T(K(z,y) \ x,u) = T(T(x,K(y,z)),K(z,y))
    ]]></literal>
    <justification jstring="[para(4367(a,1),20478(a,2,1,2))].">
      <j1 rule="para" parents="4367 20478"/>
    </justification>
  </clause>

  <clause id="20481">
    <literal><![CDATA[
      (x \ T(x * K(y,z),u)) \ T(K(z,y) \ x,u) = x
    ]]></literal>
    <justification jstring="[hyper(333,a,5303,a(flip),b,20480,a),flip(a)].">
      <j1 rule="hyper" parents="333 5303 20480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20483">
    <literal><![CDATA[
      (x * T(K(y,z) \ x,u)) / x = (x \ T(K(y,z) \ x,u)) * x
    ]]></literal>
    <justification jstring="[para(20481(a,1),12971(a,1,2)),flip(a)].">
      <j1 rule="para" parents="20481 12971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20484">
    <literal><![CDATA[
      (x \ T(K(y,z) \ x,u)) * x = T(x * K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,15756,a(flip),b,20483,a),flip(a)].">
      <j1 rule="hyper" parents="63 15756 20483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20485">
    <literal><![CDATA[
      K(x,T(y,z \ u)) \ T(z,u) = T(z * K(y,x),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,20443,a,b,20484,a)].">
      <j1 rule="hyper" parents="63 20443 20484"/>
    </justification>
  </clause>

  <clause id="20486">
    <literal><![CDATA[
      K(x,T(y,z \ u)) \ T(u,z) = T(u * K(y,x),z)
    ]]></literal>
    <justification jstring="[para(7271(a,1),20485(a,1,1))].">
      <j1 rule="para" parents="7271 20485"/>
    </justification>
  </clause>

  <clause id="20487">
    <literal><![CDATA[
      K(x,T(y,z)) \ T(u,z \ u) = T(u * K(y,x),z \ u)
    ]]></literal>
    <justification jstring="[para(15436(a,1),20485(a,1,1))].">
      <j1 rule="para" parents="15436 20485"/>
    </justification>
  </clause>

  <clause id="20488">
    <literal><![CDATA[
      K(x,T(y,L(T(z,z \ 1),z \ 1,u))) \ T(u,u * (z \ 1)) = T(u * K(y,x),u * (z \ 1))
    ]]></literal>
    <justification jstring="[para(396(a,2),20486(a,1,1,2,2))].">
      <j1 rule="para" parents="396 20486"/>
    </justification>
  </clause>

  <clause id="20489">
    <literal><![CDATA[
      K(x,T(y,L(z,z \ 1,u))) \ T(u,u * (z \ 1)) = T(u * K(y,x),u * (z \ 1))
    ]]></literal>
    <justification jstring="[para(3179(a,1),20488(a,1,1,2))].">
      <j1 rule="para" parents="3179 20488"/>
    </justification>
  </clause>

  <clause id="20490">
    <literal><![CDATA[
      K(x,T(y,z)) \ T(u,u * (z \ 1)) = T(u * K(y,x),u * (z \ 1))
    ]]></literal>
    <justification jstring="[para(6706(a,1),20489(a,1,1,2))].">
      <j1 rule="para" parents="6706 20489"/>
    </justification>
  </clause>

  <clause id="20491">
    <literal><![CDATA[
      T(x * K(y,z),x * (u \ 1)) = K(z,T(y,u)) \ T(x,u \ x)
    ]]></literal>
    <justification jstring="[para(1686(a,1),20490(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1686 20490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20494">
    <literal><![CDATA[
      T(x * K(y,z),x * (u \ 1)) = T(x * K(y,z),u \ x)
    ]]></literal>
    <justification jstring="[hyper(333,a,20487,a(flip),b,20491,a),flip(a)].">
      <j1 rule="hyper" parents="333 20487 20491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20495">
    <literal><![CDATA[
      (x * ((y * K(z,u)) * w)) \ (x * (y * (K(z,u) * w))) = L(a(w,K(z,u),y),(y * K(z,u)) * w,x)
    ]]></literal>
    <justification jstring="[para(97(a,1),20238(a,1,2,2))].">
      <j1 rule="para" parents="97 20238"/>
    </justification>
  </clause>

  <clause id="20496">
    <literal><![CDATA[
      K(x,y * ((z * (K(u,K(w,v5)) * v6)) * (K(u,K(w,v5)) * ((v6 * z) / v6)))) = K(x,y * ((v6 * (z * K(u,K(w,v5)))) * z))
    ]]></literal>
    <justification jstring="[para(17795(a,1),20141(a,1,2,2,2))].">
      <j1 rule="para" parents="17795 20141"/>
    </justification>
  </clause>

  <clause id="20497">
    <literal><![CDATA[
      K(x,y * ((z * (K(u,K(w,v5)) * v6)) * ((v6 * z) / v6))) = K(x,y * ((v6 * (z * K(u,K(w,v5)))) * z))
    ]]></literal>
    <justification jstring="[hyper(17831,a,20496,a)].">
      <j1 rule="hyper" parents="17831 20496"/>
    </justification>
  </clause>

  <clause id="20498">
    <literal><![CDATA[
      K(x,y * ((z * (K(u,K(w,v5)) * v6)) * T(z,v6))) = K(x,y * ((v6 * (z * K(u,K(w,v5)))) * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,18989,a(flip),b,20497,a)].">
      <j1 rule="hyper" parents="63 18989 20497"/>
    </justification>
  </clause>

  <clause id="20499">
    <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(15541(a,1),18007(a,1,2,1,1))].">
      <j1 rule="para" parents="15541 18007"/>
    </justification>
  </clause>

  <clause id="20500">
    <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(12320(a,2),20499(a,1,2,1,1))].">
      <j1 rule="para" parents="12320 20499"/>
    </justification>
  </clause>

  <clause id="20501">
    <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(20026(a,1),20500(a,1,2))].">
      <j1 rule="para" parents="20026 20500"/>
    </justification>
  </clause>

  <clause id="20502">
    <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(63,a,20031,a(flip),b,20501,a)].">
      <j1 rule="hyper" parents="63 20031 20501"/>
    </justification>
  </clause>

  <clause id="20504">
    <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(63,a,18326,a(flip),b,20502,a)].">
      <j1 rule="hyper" parents="63 18326 20502"/>
    </justification>
  </clause>

  <clause id="20505">
    <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(18209,a,20504,a)].">
      <j1 rule="hyper" parents="18209 20504"/>
    </justification>
  </clause>

  <clause id="20507">
    <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(3678(a,1),20505(a,1,2,1,1))].">
      <j1 rule="para" parents="3678 20505"/>
    </justification>
  </clause>

  <clause id="20508">
    <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(12910,a,20507,a)].">
      <j1 rule="hyper" parents="12910 20507"/>
    </justification>
  </clause>

  <clause id="20509">
    <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(333,a,18581,a(flip),b,20508,a),flip(a)].">
      <j1 rule="hyper" parents="333 18581 20508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20510">
    <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(333,a,14930,a(flip),b,20509,a),flip(a)].">
      <j1 rule="hyper" parents="333 14930 20509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20511">
    <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(333,a,20198,a(flip),b,20510,a),flip(a)].">
      <j1 rule="hyper" parents="333 20198 20510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20512">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,u,y * z)) = K(x,z \ (((1 / y) \ z) * u))
    ]]></literal>
    <justification jstring="[para(11181(a,1),20511(a,2,2,2,1))].">
      <j1 rule="para" parents="11181 20511"/>
    </justification>
  </clause>

  <clause id="20513">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,u,y * z)) = K(x,z \ (((y \ 1) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(333,a,15255,a(flip),b,20512,a),flip(a)].">
      <j1 rule="hyper" parents="333 15255 20512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20514">
    <literal><![CDATA[
      K(x,((y * z) * (y \ 1)) \ ((((y * z) \ z) \ z) * u)) = K(x,z \ (((y \ 1) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,19165,a(flip),b,20513,a)].">
      <j1 rule="hyper" parents="63 19165 20513"/>
    </justification>
  </clause>

  <clause id="20515">
    <literal><![CDATA[
      K(x,((y * z) * (y \ 1)) \ (T(y * z,z) * u)) = K(x,z \ (((y \ 1) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,12751,a(flip),b,20514,a)].">
      <j1 rule="hyper" parents="63 12751 20514"/>
    </justification>
  </clause>

  <clause id="20516">
    <literal><![CDATA[
      K(x,((y * z) * (y \ 1)) \ ((z * y) * u)) = K(x,z \ (((y \ 1) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,18719,a(flip),b,20515,a)].">
      <j1 rule="hyper" parents="63 18719 20515"/>
    </justification>
  </clause>

  <clause id="20517">
    <literal><![CDATA[
      T(x,K(y,z)) / (z * (a(u,w,K(v5,v6)) * T(a(u,w,K(v5,v6)) \ (z \ x),y))) = K(y,(x \ (z * a(u,w,K(v5,v6)))) \ 1)
    ]]></literal>
    <justification jstring="[para(940(a,1),18560(a,1,2))].">
      <j1 rule="para" parents="940 18560"/>
    </justification>
  </clause>

  <clause id="20518">
    <literal><![CDATA[
      L(K(x,K(y,z * L(u \ 1,u,w))),(w * u) \ w,w * u) = w \ (w * (u * (z \ T(z * (u \ 1),K(x,y)))))
    ]]></literal>
    <justification jstring="[para(97(a,1),19056(a,2,2))].">
      <j1 rule="para" parents="97 19056"/>
    </justification>
  </clause>

  <clause id="20519">
    <literal><![CDATA[
      L(K(x,K(y,z * L(u \ 1,u,w))),(w * u) \ w,w * u) = w \ (w * K((u * (z \ 1)) \ 1,K(x,y)))
    ]]></literal>
    <justification jstring="[para(5121(a,1),20518(a,2,2,2))].">
      <j1 rule="para" parents="5121 20518"/>
    </justification>
  </clause>

  <clause id="20520">
    <literal><![CDATA[
      L(K(x,K(y,z * L(u \ 1,u,w))),(w * u) \ w,w * u) = w \ (w * K(x,K(y,u * (z \ 1))))
    ]]></literal>
    <justification jstring="[para(7163(a,1),20519(a,2,2,2))].">
      <j1 rule="para" parents="7163 20519"/>
    </justification>
  </clause>

  <clause id="20521">
    <literal><![CDATA[
      L(K(x,K(y,z * L(u \ 1,u,w))),(w * u) \ w,w * u) = w \ (w * K(x,K(y,z \ u)))
    ]]></literal>
    <justification jstring="[para(15667(a,1),20520(a,2,2,2))].">
      <j1 rule="para" parents="15667 20520"/>
    </justification>
  </clause>

  <clause id="20522">
    <literal><![CDATA[
      L(K(x,K(y,z * L(u \ 1,u,w))),(w * u) \ w,w * u) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(333,a,9,a(flip),b,20521,a),flip(a)].">
      <j1 rule="hyper" parents="333 9 20521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20524">
    <literal><![CDATA[
      K(x,K(y,z * L(u \ 1,u,w))) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,17509,a(flip),b,20522,a)].">
      <j1 rule="hyper" parents="63 17509 20522"/>
    </justification>
  </clause>

  <clause id="20526">
    <literal><![CDATA[
      K(x,K(y,z * (u \ (u / w)))) = K(x,K(y,z \ w))
    ]]></literal>
    <justification jstring="[para(393(a,1),20524(a,1,2,2,2))].">
      <j1 rule="para" parents="393 20524"/>
    </justification>
  </clause>

  <clause id="20527">
    <literal><![CDATA[
      K(x,K(y,(z \ (z / u)) * w)) = K(x,K(y,w \ u))
    ]]></literal>
    <justification jstring="[hyper(15681,a,20526,a)].">
      <j1 rule="hyper" parents="15681 20526"/>
    </justification>
  </clause>

  <clause id="20528">
    <literal><![CDATA[
      K(x,K(y,z \ (u \ w))) = K(x,K(y,(w \ u) * z))
    ]]></literal>
    <justification jstring="[para(76(a,1),20527(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="76 20527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20529">
    <literal><![CDATA[
      K(x,K(y,(z \ T(u,w)) * v5)) = K(x,K(y,u \ (v5 \ z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,18246,a(flip),b,20528,a),flip(a)].">
      <j1 rule="hyper" parents="63 18246 20528"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20530">
    <literal><![CDATA[
      K(x,K(y,z \ (u \ w))) = K(x,K(y,u * (w \ z)))
    ]]></literal>
    <justification jstring="[hyper(16717,a,20529,a),flip(a)].">
      <j1 rule="hyper" parents="16717 20529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20531">
    <literal><![CDATA[
      T(x,K(y,z \ (u \ w))) = T(x,K(y,u * (w \ z)))
    ]]></literal>
    <justification jstring="[hyper(124,a,20530,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 20530 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20533">
    <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(63,a,15027,a(flip),b,20531,a),flip(a)].">
      <j1 rule="hyper" parents="63 15027 20531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20534">
    <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(63,a,16668,a(flip),b,20533,a)].">
      <j1 rule="hyper" parents="63 16668 20533"/>
    </justification>
  </clause>

  <clause id="20536">
    <literal><![CDATA[
      x * K(y,T(x,z \ (T(u,z) \ w))) = x * K(y,T(x,u * (w \ z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,7134,a(flip),b,20534,a),flip(a)].">
      <j1 rule="hyper" parents="63 7134 20534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20537">
    <literal><![CDATA[
      x * K(y,T(x,z \ (u \ w))) = x * K(y,T(x,u * (w \ z)))
    ]]></literal>
    <justification jstring="[para(18659(a,1),20536(a,1,2))].">
      <j1 rule="para" parents="18659 20536"/>
    </justification>
  </clause>

  <clause id="20538">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ w))) = K(x,T(y,u * (w \ z)))
    ]]></literal>
    <justification jstring="[hyper(297,a,20537,a),flip(a)].">
      <j1 rule="hyper" parents="297 20537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20541">
    <literal><![CDATA[
      K(x,T(y,z * ((u * w) \ w))) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,17886,a(flip),b,20538,a),flip(a)].">
      <j1 rule="hyper" parents="63 17886 20538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20542">
    <literal><![CDATA[
      K(x * K(y \ (z \ x),y),T(u,x \ z)) = K(((z * y) \ x) * (y * z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,19933,a(flip),b,20541,a),flip(a)].">
      <j1 rule="hyper" parents="63 19933 20541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20544">
    <literal><![CDATA[
      K(K(x \ (y \ z),x) * z,T(u,y)) = K(((y * x) \ z) * (x * y),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,18234,a(flip),b,20542,a)].">
      <j1 rule="hyper" parents="63 18234 20542"/>
    </justification>
  </clause>

  <clause id="20545">
    <literal><![CDATA[
      K(x * K(y \ (x / z),y),T(u,z)) = K(((z * y) \ x) * (y * z),u)
    ]]></literal>
    <justification jstring="[para(10516(a,1),20544(a,1,1))].">
      <j1 rule="para" parents="10516 20544"/>
    </justification>
  </clause>

  <clause id="20546">
    <literal><![CDATA[
      K(K(x / y,z) * x,T(u,y)) = K(((y * z) \ x) * (z * y),u)
    ]]></literal>
    <justification jstring="[hyper(15659,a,20545,a)].">
      <j1 rule="hyper" parents="15659 20545"/>
    </justification>
  </clause>

  <clause id="20547">
    <literal><![CDATA[
      K(((x * y) \ z) * (y * x),u) = K(z * K(x \ z,y),T(u,x))
    ]]></literal>
    <justification jstring="[para(5908(a,1),20546(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5908 20546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20548">
    <literal><![CDATA[
      K(((x * y) \ z) * (y * x),u) = K(x * T(z / x,y),u)
    ]]></literal>
    <justification jstring="[hyper(333,a,12218,a(flip),b,20547,a),flip(a)].">
      <j1 rule="hyper" parents="333 12218 20547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20549">
    <literal><![CDATA[
      K(K(x,y) * z,T(u,x * y)) = K(y * T(z / y,x),u)
    ]]></literal>
    <justification jstring="[hyper(12276,a,20548,a)].">
      <j1 rule="hyper" parents="12276 20548"/>
    </justification>
  </clause>

  <clause id="20550">
    <literal><![CDATA[
      K(x \ T(y * x,z),u) = K(x * T(y / x,z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,16682,a(flip),b,20549,a)].">
      <j1 rule="hyper" parents="63 16682 20549"/>
    </justification>
  </clause>

  <clause id="20551">
    <literal><![CDATA[
      K(x * K(x * y,z),T(u,y)) = K(y * T(x / y,z),u)
    ]]></literal>
    <justification jstring="[hyper(16518,a,20550,a)].">
      <j1 rule="hyper" parents="16518 20550"/>
    </justification>
  </clause>

  <clause id="20552">
    <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(20551(a,1),13690(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="20551 13690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20553">
    <literal><![CDATA[
      T(x,T(y * z,u) / T(z,y)) = T(x,z * T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(333,a,4549,a(flip),b,20552,a),flip(a)].">
      <j1 rule="hyper" parents="333 4549 20552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20554">
    <literal><![CDATA[
      T(x,T(y * K(y * z,u),z)) = T(x,z * T(y / z,u))
    ]]></literal>
    <justification jstring="[para(13689(a,1),20553(a,1,2))].">
      <j1 rule="para" parents="13689 20553"/>
    </justification>
  </clause>

  <clause id="20555">
    <literal><![CDATA[
      T(x,y \ T(z * y,u)) = T(x,y * T(z / y,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,16417,a(flip),b,20554,a)].">
      <j1 rule="hyper" parents="63 16417 20554"/>
    </justification>
  </clause>

  <clause id="20556">
    <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(63,a,16112,a(flip),b,20555,a),flip(a)].">
      <j1 rule="hyper" parents="63 16112 20555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20557">
    <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(18770,a,20556,a)].">
      <j1 rule="hyper" parents="18770 20556"/>
    </justification>
  </clause>

  <clause id="20558">
    <literal><![CDATA[
      T(x,T(y * T(z / y,u),y)) = T(x,T(y,z) \ T(z * y,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,17027,a(flip),b,20557,a)].">
      <j1 rule="hyper" parents="63 17027 20557"/>
    </justification>
  </clause>

  <clause id="20559">
    <literal><![CDATA[
      T(x,T(y,z) \ T(z * y,u)) = T(x,T(z / y,u) * y)
    ]]></literal>
    <justification jstring="[hyper(12232,a,20558,a),flip(a)].">
      <j1 rule="hyper" parents="12232 20558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20560">
    <literal><![CDATA[
      T(x,T(y,z) \ T(z * y,u)) = T(x,y * T(y \ z,u))
    ]]></literal>
    <justification jstring="[para(471(a,1),20559(a,2,2))].">
      <j1 rule="para" parents="471 20559"/>
    </justification>
  </clause>

  <clause id="20561">
    <literal><![CDATA[
      T(x,y \ T(z * T(y,z),u)) = T(x,y * T(y \ z,u))
    ]]></literal>
    <justification jstring="[hyper(20321,a,20560,a)].">
      <j1 rule="hyper" parents="20321 20560"/>
    </justification>
  </clause>

  <clause id="20562">
    <literal><![CDATA[
      T(x,y \ T(y * z,u)) = T(x,y * T(y \ z,u))
    ]]></literal>
    <justification jstring="[para(111(a,1),20561(a,1,2,2,1))].">
      <j1 rule="para" parents="111 20561"/>
    </justification>
  </clause>

  <clause id="20563">
    <literal><![CDATA[
      T(x,K(y,z)) / (z * (a(u,w,K(v5,v6)) * T(a(v6,w,K(v5,u)) * (z \ x),y))) = K(y,(x \ (z * a(u,w,K(v5,v6)))) \ 1)
    ]]></literal>
    <justification jstring="[para(13763(a,1),20517(a,1,2,2,2,1))].">
      <j1 rule="para" parents="13763 20517"/>
    </justification>
  </clause>

  <clause id="20564">
    <literal><![CDATA[
      T(x,K(y,z)) / (z * T((a(u,w,K(v5,v6)) * (z \ x)) * a(v6,w,K(v5,u)),y)) = K(y,(x \ (z * a(v6,w,K(v5,u)))) \ 1)
    ]]></literal>
    <justification jstring="[para(18127(a,2),20563(a,1,2,2))].">
      <j1 rule="para" parents="18127 20563"/>
    </justification>
  </clause>

  <clause id="20565">
    <literal><![CDATA[
      K(x,(y \ (z * a(u,w,K(v5,v6)))) \ 1) = T(y,K(x,z)) / (z * T(z \ y,x))
    ]]></literal>
    <justification jstring="[para(17675(a,1),20564(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="17675 20564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20566">
    <literal><![CDATA[
      K(x,(y \ (z * a(u,w,K(v5,v6)))) \ 1) = K(x,(y \ z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(333,a,8882,a(flip),b,20565,a),flip(a)].">
      <j1 rule="hyper" parents="333 8882 20565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20568">
    <literal><![CDATA[
      K(x,(y \ (a(z,u,K(w,v5)) * v6)) \ 1) = K(x,(y \ v6) \ 1)
    ]]></literal>
    <justification jstring="[para(17584(a,2),20566(a,1,2,1,2))].">
      <j1 rule="para" parents="17584 20566"/>
    </justification>
  </clause>

  <clause id="20569">
    <literal><![CDATA[
      K(x,(a(y,z,K(u,w)) * v5) \ v6) = K(x,(v6 \ v5) \ 1)
    ]]></literal>
    <justification jstring="[hyper(5853,a,20568,a)].">
      <j1 rule="hyper" parents="5853 20568"/>
    </justification>
  </clause>

  <clause id="20570">
    <literal><![CDATA[
      K(x,(a(y,z,K(u,w)) * v5) \ v6) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,v5 \ v6) = v7
    ]]></literal>
    <justification jstring="[para(20569(a,2),5853(a,1))].">
      <j1 rule="para" parents="20569 5853"/>
    </justification>
  </clause>

  <clause id="20571">
    <literal><![CDATA[
      K(x,(K(y,z) \ u) \ (L(K(z,y),w,v5) * v6)) = K(x,u \ v6)
    ]]></literal>
    <justification jstring="[hyper(20570,a,19254,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="20570 19254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20572">
    <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(13937(a,1),20570(a,1,2,1))].">
      <j1 rule="para" parents="13937 20570"/>
    </justification>
  </clause>

  <clause id="20573">
    <literal><![CDATA[
      K(x,(y * L(K(z,u),w,v5)) \ v6) = K(x,K(z,u) \ (y \ v6))
    ]]></literal>
    <justification jstring="[hyper(20572,a,19335,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="20572 19335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20574">
    <literal><![CDATA[
      K(x,L(K(y,z),u,w) \ v5) = K(x,K(y,z) \ v5)
    ]]></literal>
    <justification jstring="[hyper(20572,a,xx),flip(a)].">
      <j1 rule="hyper" parents="20572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20575">
    <literal><![CDATA[
      K(x,K(L(y,z,u),w) \ v5) = K(x,K(w,y) \ v5)
    ]]></literal>
    <justification jstring="[hyper(15796,a,20574,a)].">
      <j1 rule="hyper" parents="15796 20574"/>
    </justification>
  </clause>

  <clause id="20576">
    <literal><![CDATA[
      K(x,y \ (K(L(z,u,w),v5) \ v6)) = K(x,K(v5,z) \ (y \ v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,19111,a(flip),b,20575,a)].">
      <j1 rule="hyper" parents="63 19111 20575"/>
    </justification>
  </clause>

  <clause id="20577">
    <literal><![CDATA[
      K(x,y * (z * L(K(u,w),v5,v6))) = K(x,K(u,w) \ (y * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,18024,a(flip),b,20575,a)].">
      <j1 rule="hyper" parents="63 18024 20575"/>
    </justification>
  </clause>

  <clause id="20578">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ (L(K(y,z),w,v5) * v6)) = K(x,u \ v6)
    ]]></literal>
    <justification jstring="[para(4567(a,1),20571(a,1,2,1))].">
      <j1 rule="para" parents="4567 20571"/>
    </justification>
  </clause>

  <clause id="20580">
    <literal><![CDATA[
      K(x,(y * (z * K(u,w))) \ v5) = K(x,K(u,w) \ ((y * z) \ v5))
    ]]></literal>
    <justification jstring="[para(97(a,1),20573(a,1,2,1))].">
      <j1 rule="para" parents="97 20573"/>
    </justification>
  </clause>

  <clause id="20581">
    <literal><![CDATA[
      K(x,(L(K(y,z),u,w) \ v5) \ v6) = K(x,K(y,z) \ (v5 \ v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,17805,a,b,20576,a)].">
      <j1 rule="hyper" parents="63 17805 20576"/>
    </justification>
  </clause>

  <clause id="20583">
    <literal><![CDATA[
      K(x,K(y,z) \ (u * T(w,y))) = K(x,u * (y \ (w * T(y,z))))
    ]]></literal>
    <justification jstring="[para(6675(a,1),20577(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6675 20577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20584">
    <literal><![CDATA[
      K(x,y \ ((L(K(z,u),w,v5) * v6) * K(u,z))) = K(x,y \ v6)
    ]]></literal>
    <justification jstring="[hyper(17770,a,20578,a)].">
      <j1 rule="hyper" parents="17770 20578"/>
    </justification>
  </clause>

  <clause id="20586">
    <literal><![CDATA[
      K(x,y \ (L(K(z,u),w,v5) * (v6 * K(u,z)))) = K(x,y \ v6)
    ]]></literal>
    <justification jstring="[para(17550(a,1),20584(a,1,2,2))].">
      <j1 rule="para" parents="17550 20584"/>
    </justification>
  </clause>

  <clause id="20587">
    <literal><![CDATA[
      K(x,y \ T(z * a(u,w,K(v5,v6)),K(u,v6))) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(20116(a,2),20586(a,1,2,2))].">
      <j1 rule="para" parents="20116 20586"/>
    </justification>
  </clause>

  <clause id="20588">
    <literal><![CDATA[
      K(x,y \ (z * a(u,w,K(v5,v6)))) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(16377,a,20587,a)].">
      <j1 rule="hyper" parents="16377 20587"/>
    </justification>
  </clause>

  <clause id="20590">
    <literal><![CDATA[
      K(x,y \ K(z,L(u,w,v5))) = K(x,y \ K(z,u))
    ]]></literal>
    <justification jstring="[para(10860(a,1),20588(a,1,2,2))].">
      <j1 rule="para" parents="10860 20588"/>
    </justification>
  </clause>

  <clause id="20591">
    <literal><![CDATA[
      K(x,a(K(y,z),u,w) \ v5) = K(x,v5)
    ]]></literal>
    <justification jstring="[para(17671(a,1),20588(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17671 20588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20592">
    <literal><![CDATA[
      K(x,y) \ T(x,(a(K(z,u),w,v5) \ y) * x) = L(x,a(K(z,u),w,v5) \ T(y,x),x)
    ]]></literal>
    <justification jstring="[para(20591(a,1),11028(a,1,1))].">
      <j1 rule="para" parents="20591 11028"/>
    </justification>
  </clause>

  <clause id="20593">
    <literal><![CDATA[
      K(x,y \ K(z,(u / w) / v5)) = K(x,y \ K(z,u / (v5 * w)))
    ]]></literal>
    <justification jstring="[para(13882(a,1),20590(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13882 20590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20594">
    <literal><![CDATA[
      K(x,(y * (K(z,u) \ w)) \ v5) = K(x,K(u,z) \ ((y * w) \ v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,18636,a,b,20580,a)].">
      <j1 rule="hyper" parents="63 18636 20580"/>
    </justification>
  </clause>

  <clause id="20595">
    <literal><![CDATA[
      K(x,(y * (z * K(u,w))) \ v5) = K(x,K(w,u) * ((y * z) \ v5))
    ]]></literal>
    <justification jstring="[para(4567(a,1),20580(a,2,2))].">
      <j1 rule="para" parents="4567 20580"/>
    </justification>
  </clause>

  <clause id="20596">
    <literal><![CDATA[
      K(x,K(y,z) \ (x * T(y \ u,y))) \ T(x,u / T(y,z)) = R(x,y \ ((y \ u) * T(y,z)),x)
    ]]></literal>
    <justification jstring="[para(20583(a,2),16231(a,1,1))].">
      <j1 rule="para" parents="20583 16231"/>
    </justification>
  </clause>

  <clause id="20597">
    <literal><![CDATA[
      K(x,y \ K(z,u / (w * v5))) = K(x,y \ K(z,w \ (u / v5)))
    ]]></literal>
    <justification jstring="[hyper(16494,a,20593,a),flip(a)].">
      <j1 rule="hyper" parents="16494 20593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20598">
    <literal><![CDATA[
      K(x,K(y,z) \ (((z \ u) * z) \ w)) = K(x,(z * (u / T(z,y))) \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,18638,a(flip),b,20594,a),flip(a)].">
      <j1 rule="hyper" parents="63 18638 20594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20599">
    <literal><![CDATA[
      T(x,(y * (z * K(u,w))) \ v5) = T(x,K(w,u) * ((y * z) \ v5))
    ]]></literal>
    <justification jstring="[hyper(124,a,20595,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 20595 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20600">
    <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(63,a,19843,a,b,20595,a)].">
      <j1 rule="hyper" parents="63 19843 20595"/>
    </justification>
  </clause>

  <clause id="20601">
    <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(63,a,19846,a(flip),b,20595,a),flip(a)].">
      <j1 rule="hyper" parents="63 19846 20595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20602">
    <literal><![CDATA[
      K(x,(y / z) \ K(y,u \ (w / v5))) = K(x,z / T(y,L((w / v5) / u,u,v5)))
    ]]></literal>
    <justification jstring="[hyper(19416,a,20597,a),flip(a)].">
      <j1 rule="hyper" parents="19416 20597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20603">
    <literal><![CDATA[
      T(x,L(L(K(y,z) \ u,K(y,z),w),w * K(y,z),v5)) = T(x,K(z,y) * ((v5 * w) \ (v5 * (w * u))))
    ]]></literal>
    <justification jstring="[para(526(a,2),20599(a,1,2))].">
      <j1 rule="para" parents="526 20599"/>
    </justification>
  </clause>

  <clause id="20604">
    <literal><![CDATA[
      K(x,((y \ z) * T(y,u)) \ w) = K(x,(y * (z / T(y,u))) \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,18634,a(flip),b,20598,a)].">
      <j1 rule="hyper" parents="63 18634 20598"/>
    </justification>
  </clause>

  <clause id="20605">
    <literal><![CDATA[
      K(x,(y * (z / T(y,u))) \ w) = K(x,K(u,y) \ (T(z,y) \ w))
    ]]></literal>
    <justification jstring="[hyper(19138,a,20604,a),flip(a)].">
      <j1 rule="hyper" parents="19138 20604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20606">
    <literal><![CDATA[
      K(x,T((T(y,z) \ 1) \ z,u) \ w) = K(x,K(K(v5,v6),y) \ (T(T((y \ 1) \ z,u),y) \ w))
    ]]></literal>
    <justification jstring="[hyper(63,a,19154,a,b,20605,a)].">
      <j1 rule="hyper" parents="63 19154 20605"/>
    </justification>
  </clause>

  <clause id="20607">
    <literal><![CDATA[
      K(x,y / T(z,L((u / w) / v5,v5,w))) = K(x,y / T(z,v5 \ (u / w)))
    ]]></literal>
    <justification jstring="[hyper(19408,a,20602,a),flip(a)].">
      <j1 rule="hyper" parents="19408 20602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20608">
    <literal><![CDATA[
      K(x,y * T(z,L((u / w) / v5,v5,w))) = K(x,y / T(z \ 1,v5 \ (u / w)))
    ]]></literal>
    <justification jstring="[hyper(18050,a,20607,a)].">
      <j1 rule="hyper" parents="18050 20607"/>
    </justification>
  </clause>

  <clause id="20609">
    <literal><![CDATA[
      K(x,y * T(z,L((u / w) / v5,v5,w))) = K(x,y * T(z,v5 \ (u / w)))
    ]]></literal>
    <justification jstring="[hyper(333,a,18049,a(flip),b,20608,a),flip(a)].">
      <j1 rule="hyper" parents="333 18049 20608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20610">
    <literal><![CDATA[
      K(x,y * T(z,u / (w * v5))) = K(x,y * T(z,w \ (u / v5)))
    ]]></literal>
    <justification jstring="[para(13912(a,1),20609(a,1,2,2))].">
      <j1 rule="para" parents="13912 20609"/>
    </justification>
  </clause>

  <clause id="20611">
    <literal><![CDATA[
      K(x,y * T(z,(u * w) \ v5)) = K(x,y * T(z,u \ (v5 / w)))
    ]]></literal>
    <justification jstring="[hyper(16437,a,20610,a)].">
      <j1 rule="hyper" parents="16437 20610"/>
    </justification>
  </clause>

  <clause id="20612">
    <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(20611(a,2),16788(a,1))].">
      <j1 rule="para" parents="20611 16788"/>
    </justification>
  </clause>

  <clause id="20613">
    <literal><![CDATA[
      K(x,y) \ T(x,x * (a(K(z,u),w,v5) \ y)) = L(x,a(K(z,u),w,v5) \ T(y,x),x)
    ]]></literal>
    <justification jstring="[para(3678(a,1),20592(a,1,2))].">
      <j1 rule="para" parents="3678 20592"/>
    </justification>
  </clause>

  <clause id="20614">
    <literal><![CDATA[
      K(x,K(y,z) * ((((u * w) \ u) * v5) \ u)) = K(x,((w \ v5) * K(z,y)) \ u)
    ]]></literal>
    <justification jstring="[hyper(18036,a,20601,a)].">
      <j1 rule="hyper" parents="18036 20601"/>
    </justification>
  </clause>

  <clause id="20616">
    <literal><![CDATA[
      K(x,K(y,z) * ((((u * w) \ u) * v5) \ u)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z) * ((w \ v5) \ u)) = v6
    ]]></literal>
    <justification jstring="[para(20614(a,2),18652(a,1))].">
      <j1 rule="para" parents="20614 18652"/>
    </justification>
  </clause>

  <clause id="20617">
    <literal><![CDATA[
      L(x,a(K(y,z),u,w) \ T(v5,x),x) = K(x,v5) \ T(x,x * v5)
    ]]></literal>
    <justification jstring="[para(19481(a,1),20613(a,1,2)),flip(a)].">
      <j1 rule="para" parents="19481 20613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20618">
    <literal><![CDATA[
      L(x,a(K(y,z),u,w) \ T(v5,x),x) = L(x,v5,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,4734,a(flip),b,20617,a),flip(a)].">
      <j1 rule="hyper" parents="333 4734 20617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20620">
    <literal><![CDATA[
      L(x,a(K(y,z),u,w) \ v5,x) = L(x,v5,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,11021,a(flip),b,20618,a)].">
      <j1 rule="hyper" parents="63 11021 20618"/>
    </justification>
  </clause>

  <clause id="20622">
    <literal><![CDATA[
      a(x,a(K(y,z),u,w) \ v5,x) = (v6 / x) \ (v6 / L(x,v5,x))
    ]]></literal>
    <justification jstring="[para(20620(a,1),8269(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="20620 8269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20623">
    <literal><![CDATA[
      a(x,a(K(y,z),u,w) \ v5,x) = a(x,v5,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,8269,a(flip),b,20622,a),flip(a)].">
      <j1 rule="hyper" parents="333 8269 20622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20624">
    <literal><![CDATA[
      a(x,(y * a(K(z,u),w,v5)) \ v6,x) = a(x,y \ v6,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,12882,a,b,20623,a)].">
      <j1 rule="hyper" parents="63 12882 20623"/>
    </justification>
  </clause>

  <clause id="20625">
    <literal><![CDATA[
      a(x,L(K(y,z),u,w) \ v5,x) = a(x,K(y,z) \ v5,x)
    ]]></literal>
    <justification jstring="[para(19471(a,1),20623(a,1,2))].">
      <j1 rule="para" parents="19471 20623"/>
    </justification>
  </clause>

  <clause id="20626">
    <literal><![CDATA[
      a(x,(a(K(y,z),u,w) \ v5) \ v6,x) = a(x,v5 \ v6,x)
    ]]></literal>
    <justification jstring="[para(17579(a,1),20624(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="17579 20624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20627">
    <literal><![CDATA[
      a(x,K(y,(z \ u) \ w) \ v5,x) = a(x,K(y,u \ (z * w)) \ v5,x)
    ]]></literal>
    <justification jstring="[para(9513(a,1),20625(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9513 20625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20628">
    <literal><![CDATA[
      a(x,y \ (a(K(z,u),w,v5) * v6),x) = a(x,y \ v6,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,12883,a(flip),b,20626,a)].">
      <j1 rule="hyper" parents="63 12883 20626"/>
    </justification>
  </clause>

  <clause id="20629">
    <literal><![CDATA[
      a(x,y \ (a(K(z,u),w,v5) \ v6),x) = a(x,y \ v6,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),20628(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 20628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20630">
    <literal><![CDATA[
      a(x,y \ (z * a(u,w,K(v5,v6))),x) = a(x,y \ z,x)
    ]]></literal>
    <justification jstring="[para(17671(a,1),20629(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="17671 20629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20631">
    <literal><![CDATA[
      a(x,y \ (L(K(z,u),w,v5) \ v6),x) = a(x,y \ (K(z,u) \ v6),x)
    ]]></literal>
    <justification jstring="[para(19471(a,1),20629(a,1,2,2))].">
      <j1 rule="para" parents="19471 20629"/>
    </justification>
  </clause>

  <clause id="20632">
    <literal><![CDATA[
      a(x,y \ ((z * u) * K(w,v5)),x) = a(x,y \ (z * (u * K(w,v5))),x)
    ]]></literal>
    <justification jstring="[para(84(a,1),20630(a,1,2,2))].">
      <j1 rule="para" parents="84 20630"/>
    </justification>
  </clause>

  <clause id="20633">
    <literal><![CDATA[
      a(x,y \ (z * ((K(u,w) \ z) \ v5)),x) = a(x,y \ (K(w,u) \ v5),x)
    ]]></literal>
    <justification jstring="[para(13985(a,1),20631(a,1,2,2))].">
      <j1 rule="para" parents="13985 20631"/>
    </justification>
  </clause>

  <clause id="20634">
    <literal><![CDATA[
      a(x,T(y \ (y / (z \ u)),w) * T(y,(z \ u) \ 1),x) = a(x,K(w,u \ (z * 1)) \ (y / (z \ u)),x)
    ]]></literal>
    <justification jstring="[para(8695(a,2),20627(a,1,2))].">
      <j1 rule="para" parents="8695 20627"/>
    </justification>
  </clause>

  <clause id="20635">
    <literal><![CDATA[
      a(x,y \ ((z * u) * K(w,v5)),x) = a(x,y \ (z * (K(v5,w) \ u)),x)
    ]]></literal>
    <justification jstring="[hyper(333,a,20160,a,b,20632,a),flip(a)].">
      <j1 rule="hyper" parents="333 20160 20632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20636">
    <literal><![CDATA[
      a(x,K(y,z) \ (u \ ((w / u) \ v5)),x) = a(x,w \ (K(y,z) \ v5),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,20337,a,b,20633,a)].">
      <j1 rule="hyper" parents="63 20337 20633"/>
    </justification>
  </clause>

  <clause id="20637">
    <literal><![CDATA[
      a(x,y \ (K(z,u) \ (w * v5)),x) = a(x,y \ (w * (K(z,u) \ v5)),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,20134,a,b,20635,a)].">
      <j1 rule="hyper" parents="63 20134 20635"/>
    </justification>
  </clause>

  <clause id="20638">
    <literal><![CDATA[
      a(x,y \ (K(z,u) \ ((w / y) \ v5)),x) = a(x,w \ (K(z,u) \ v5),x)
    ]]></literal>
    <justification jstring="[hyper(20338,a,20636,a)].">
      <j1 rule="hyper" parents="20338 20636"/>
    </justification>
  </clause>

  <clause id="20640">
    <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(20616,a,20600,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="20616 20600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20641">
    <literal><![CDATA[
      K(x,(y \ (z * K(u,w))) \ v5) = K(x,K(w,u) * ((y \ z) \ v5))
    ]]></literal>
    <justification jstring="[hyper(16381,a,20640,a)].">
      <j1 rule="hyper" parents="16381 20640"/>
    </justification>
  </clause>

  <clause id="20642">
    <literal><![CDATA[
      K(x,K(y,z) * ((u \ w) \ T(v5,u * w))) = K(x,v5 / (u \ (w * K(z,y))))
    ]]></literal>
    <justification jstring="[hyper(19153,a,20641,a),flip(a)].">
      <j1 rule="hyper" parents="19153 20641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20643">
    <literal><![CDATA[
      K(x,y / (z \ (u * K(w,v5)))) = K(x,y * ((z \ u) \ K(v5,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,19421,a(flip),b,20642,a),flip(a)].">
      <j1 rule="hyper" parents="63 19421 20642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20644">
    <literal><![CDATA[
      K(x,y / (z \ (K(u,w) * v5))) = K(x,y * ((z \ v5) \ K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,19419,a,b,20643,a)].">
      <j1 rule="hyper" parents="63 19419 20643"/>
    </justification>
  </clause>

  <clause id="20646">
    <literal><![CDATA[
      K(x,T(T((y \ 1) \ z,u),y) \ w) = K(x,T((T(y,z) \ 1) \ z,u) \ w)
    ]]></literal>
    <justification jstring="[hyper(333,a,16331,a(flip),b,20606,a)].">
      <j1 rule="hyper" parents="333 16331 20606"/>
    </justification>
  </clause>

  <clause id="20647">
    <literal><![CDATA[
      K(x,T((T(x,y) \ 1) \ y,z) \ u) = K(x,T((x \ 1) \ y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(7455,a,20646,a),flip(a)].">
      <j1 rule="hyper" parents="7455 20646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20649">
    <literal><![CDATA[
      K(x,T((T(y,z) \ 1) \ z,u) \ w) = K(x,T(z / (y \ 1),u) \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,16184,a(flip),b,20646,a),flip(a)].">
      <j1 rule="hyper" parents="63 16184 20646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20650">
    <literal><![CDATA[
      K(x,T((T(x,y) \ 1) \ y,z) \ u) = K(x,T(x * y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(333,a,9981,a(flip),b,20647,a),flip(a)].">
      <j1 rule="hyper" parents="333 9981 20647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20651">
    <literal><![CDATA[
      K(x,T(y / (x \ 1),z) \ u) = K(x,T(x * y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,20650,a(flip),b,20649,a),flip(a)].">
      <j1 rule="hyper" parents="63 20650 20649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20652">
    <literal><![CDATA[
      K(x,K(y,x * z) \ ((z / (x \ 1)) \ u)) = K(x,T(x * z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,16721,a,b,20651,a)].">
      <j1 rule="hyper" parents="63 16721 20651"/>
    </justification>
  </clause>

  <clause id="20653">
    <literal><![CDATA[
      K(x,K(y,z) \ (x * (u / y))) \ T(x,u / T(y,z)) = R(x,y \ ((y \ u) * T(y,z)),x)
    ]]></literal>
    <justification jstring="[para(19134(a,1),20596(a,1,1))].">
      <j1 rule="para" parents="19134 20596"/>
    </justification>
  </clause>

  <clause id="20654">
    <literal><![CDATA[
      R(x,y \ ((y \ z) * T(y,u)),x) = K(x,x * (z / T(y,u))) \ T(x,z / T(y,u))
    ]]></literal>
    <justification jstring="[para(18023(a,1),20653(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18023 20653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20655">
    <literal><![CDATA[
      R(x,y \ ((y \ z) * T(y,u)),x) = R(x,z / T(y,u),x)
    ]]></literal>
    <justification jstring="[hyper(333,a,4737,a(flip),b,20654,a),flip(a)].">
      <j1 rule="hyper" parents="333 4737 20654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20656">
    <literal><![CDATA[
      R(x,y \ ((y \ z) * T(y,u)),x) = R(x,T(y,u) \ z,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,12564,a(flip),b,20655,a),flip(a)].">
      <j1 rule="hyper" parents="333 12564 20655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20657">
    <literal><![CDATA[
      R(x,y \ (y \ (T(y,z) * u)),x) = R(x,T(y,z) \ u,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,12566,a,b,20656,a)].">
      <j1 rule="hyper" parents="63 12566 20656"/>
    </justification>
  </clause>

  <clause id="20658">
    <literal><![CDATA[
      R(x,(K(y,z) \ y) \ u,x) = R(x,T(y,z) \ u,x)
    ]]></literal>
    <justification jstring="[para(4904(a,1),20657(a,1,2))].">
      <j1 rule="para" parents="4904 20657"/>
    </justification>
  </clause>

  <clause id="20659">
    <literal><![CDATA[
      R(x,((y * z) / y) \ u,x) = R(x,T(z,y) \ u,x)
    ]]></literal>
    <justification jstring="[para(4358(a,1),20658(a,1,2,1))].">
      <j1 rule="para" parents="4358 20658"/>
    </justification>
  </clause>

  <clause id="20660">
    <literal><![CDATA[
      R(x,(y * z) \ (u * y),x) = R(x,T(z,y) \ u,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,19994,a(flip),b,20659,a)].">
      <j1 rule="hyper" parents="63 19994 20659"/>
    </justification>
  </clause>

  <clause id="20661">
    <literal><![CDATA[
      R(x,y \ (z \ (u * z)),x) = R(x,T(y,z) \ u,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,12887,a(flip),b,20660,a)].">
      <j1 rule="hyper" parents="63 12887 20660"/>
    </justification>
  </clause>

  <clause id="20662">
    <literal><![CDATA[
      R(x,T(y,z) \ u,x) = R(x,y \ T(u,z),x)
    ]]></literal>
    <justification jstring="[para(22(a,2),20661(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="22 20661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20663">
    <literal><![CDATA[
      R(x,x \ T(y,z),x) = R(x,x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,12590,a(flip),b,20662,a),flip(a)].">
      <j1 rule="hyper" parents="63 12590 20662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20664">
    <literal><![CDATA[
      x \ R(x,y \ T(z,u),x) = a(x,T(y,u) \ z,x)
    ]]></literal>
    <justification jstring="[hyper(121,a,20662,a(flip),b,8214,a)].">
      <j1 rule="hyper" parents="121 20662 8214"/>
    </justification>
  </clause>

  <clause id="20665">
    <literal><![CDATA[
      a(x,x \ T(y,z),x) = x \ R(x,x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(121,a,20663,a(flip),b,8214,a),flip(a)].">
      <j1 rule="hyper" parents="121 20663 8214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20666">
    <literal><![CDATA[
      a(x,x \ T(y,z),x) = a(x,x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,8210,a(flip),b,20665,a),flip(a)].">
      <j1 rule="hyper" parents="333 8210 20665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20667">
    <literal><![CDATA[
      a(x,x \ T(y,z),x) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,x \ y,x) = u
    ]]></literal>
    <justification jstring="[para(20665(a,2),8237(a,1))].">
      <j1 rule="para" parents="20665 8237"/>
    </justification>
  </clause>

  <clause id="20668">
    <literal><![CDATA[
      a(x,x \ (y * z),x) = a(x,x \ (z * y),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,13036,a(flip),b,20666,a)].">
      <j1 rule="hyper" parents="63 13036 20666"/>
    </justification>
  </clause>

  <clause id="20669">
    <literal><![CDATA[
      a(x,x \ (y / z),x) = a(x,x \ (z \ y),x)
    ]]></literal>
    <justification jstring="[para(113(a,1),20666(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="113 20666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20670">
    <literal><![CDATA[
      a(x,x \ (y / ((z / x) * u)),x) = a(x,x \ (((x \ z) * u) \ y),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,14796,a,b,20669,a)].">
      <j1 rule="hyper" parents="63 14796 20669"/>
    </justification>
  </clause>

  <clause id="20671">
    <literal><![CDATA[
      a(x,x \ (y * z),x) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,x \ (z * y),x) = u
    ]]></literal>
    <justification jstring="[para(13036(a,1),20667(a,1))].">
      <j1 rule="para" parents="13036 20667"/>
    </justification>
  </clause>

  <clause id="20672">
    <literal><![CDATA[
      a(x,T(y,z) \ u,x) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y \ T(u,z),x) = w
    ]]></literal>
    <justification jstring="[para(20664(a,1),8237(a,1))].">
      <j1 rule="para" parents="20664 8237"/>
    </justification>
  </clause>

  <clause id="20673">
    <literal><![CDATA[
      a(x,y \ (z \ (y * u)),x) = a(x,z \ T(u,y),x)
    ]]></literal>
    <justification jstring="[hyper(20672,a,12894,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="20672 12894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20674">
    <literal><![CDATA[
      a(x,x \ (y / ((z / x) * u)),x) = a(x,x \ (u \ ((x \ z) \ y)),x)
    ]]></literal>
    <justification jstring="[hyper(333,a,12937,a(flip),b,20670,a),flip(a)].">
      <j1 rule="hyper" parents="333 12937 20670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20675">
    <literal><![CDATA[
      a(x,x \ (((y / x) * z) \ u),x) = a(x,x \ (z \ ((x \ y) \ u)),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,20669,a(flip),b,20674,a)].">
      <j1 rule="hyper" parents="63 20669 20674"/>
    </justification>
  </clause>

  <clause id="20676">
    <literal><![CDATA[
      a(x,x \ (y \ ((z / x) \ u)),x) = a(x,x \ (y \ ((x \ z) \ u)),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,12937,a(flip),b,20675,a)].">
      <j1 rule="hyper" parents="63 12937 20675"/>
    </justification>
  </clause>

  <clause id="20677">
    <literal><![CDATA[
      a(x,x \ (K(y,z) \ ((x \ u) \ w)),x) = a(x,u \ (K(y,z) \ w),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,20638,a(flip),b,20676,a),flip(a)].">
      <j1 rule="hyper" parents="63 20638 20676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20678">
    <literal><![CDATA[
      T(x,L(L(K(y,z) * u,K(z,y),w),w * K(z,y),v5)) = T(x,K(y,z) * ((v5 * w) \ (v5 * (w * u))))
    ]]></literal>
    <justification jstring="[para(4567(a,1),20603(a,1,2,1,1))].">
      <j1 rule="para" parents="4567 20603"/>
    </justification>
  </clause>

  <clause id="20679">
    <literal><![CDATA[
      a(x,T(y \ (y / (z \ u)),w) * T(y,u \ z),x) = a(x,K(w,u \ (z * 1)) \ (y / (z \ u)),x)
    ]]></literal>
    <justification jstring="[para(5772(a,1),20634(a,1,2,2))].">
      <j1 rule="para" parents="5772 20634"/>
    </justification>
  </clause>

  <clause id="20680">
    <literal><![CDATA[
      a(x,(y \ (y / T(z \ u,w))) * T(y,u \ z),x) = a(x,K(w,u \ (z * 1)) \ (y / (z \ u)),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,20200,a(flip),b,20679,a)].">
      <j1 rule="hyper" parents="63 20200 20679"/>
    </justification>
  </clause>

  <clause id="20681">
    <literal><![CDATA[
      a(x,y \ ((y / T(z \ u,w)) * T(y,u \ z)),x) = a(x,K(w,u \ (z * 1)) \ (y / (z \ u)),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,13048,a,b,20680,a)].">
      <j1 rule="hyper" parents="63 13048 20680"/>
    </justification>
  </clause>

  <clause id="20682">
    <literal><![CDATA[
      a(x,K(y \ z,u) \ (u / T(z \ y,w)),x) = a(x,K(w,y \ (z * 1)) \ (u / (z \ y)),x)
    ]]></literal>
    <justification jstring="[hyper(12772,a,20681,a)].">
      <j1 rule="hyper" parents="12772 20681"/>
    </justification>
  </clause>

  <clause id="20683">
    <literal><![CDATA[
      a(x,K(y,z \ (u * 1)) \ (w / (u \ z)),x) = a(x,T(w,z \ u) / T(u \ z,y),x)
    ]]></literal>
    <justification jstring="[para(13299(a,1),20682(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13299 20682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20684">
    <literal><![CDATA[
      a(x,K(y,z \ (u * 1)) \ (w / (u \ z)),x) = a(x,T(u \ z,y) \ T(w,z \ u),x)
    ]]></literal>
    <justification jstring="[hyper(333,a,12549,a(flip),b,20683,a),flip(a)].">
      <j1 rule="hyper" parents="333 12549 20683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20685">
    <literal><![CDATA[
      a(x,K(y,z \ (u * 1)) \ (w / (u \ z)),x) = a(x,T(u \ z,y) \ w,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,20147,a(flip),b,20684,a),flip(a)].">
      <j1 rule="hyper" parents="333 20147 20684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20686">
    <literal><![CDATA[
      a(x,K(y,z \ u) \ (w / (u \ z)),x) = a(x,T(u \ z,y) \ w,x)
    ]]></literal>
    <justification jstring="[para(8(a,1),20685(a,1,2,1,2,2))].">
      <j1 rule="para" parents="8 20685"/>
    </justification>
  </clause>

  <clause id="20687">
    <literal><![CDATA[
      a(x,(y \ z) \ (K(u,z \ y) \ w),x) = a(x,T(y \ z,u) \ w,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,12892,a,b,20686,a)].">
      <j1 rule="hyper" parents="63 12892 20686"/>
    </justification>
  </clause>

  <clause id="20688">
    <literal><![CDATA[
      a(x,y \ (z * (K(u,y \ z) \ w)),x) = a(x,T(z \ y,u) \ w,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,12883,a(flip),b,20687,a)].">
      <j1 rule="hyper" parents="63 12883 20687"/>
    </justification>
  </clause>

  <clause id="20689">
    <literal><![CDATA[
      a(x,y \ (z * (K(u,y \ z) \ w)),x) = a(x,(z \ y) \ T(w,u),x)
    ]]></literal>
    <justification jstring="[hyper(20672,a,20688,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="20672 20688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20690">
    <literal><![CDATA[
      a(x,y \ (z * (K(u,y \ z) \ w)),x) = a(x,y \ (z * T(w,u)),x)
    ]]></literal>
    <justification jstring="[hyper(333,a,12883,a(flip),b,20689,a),flip(a)].">
      <j1 rule="hyper" parents="333 12883 20689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20691">
    <literal><![CDATA[
      a(x,y \ (K(z,y \ u) \ (u * w)),x) = a(x,y \ (u * T(w,z)),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,20637,a,b,20690,a)].">
      <j1 rule="hyper" parents="63 20637 20690"/>
    </justification>
  </clause>

  <clause id="20692">
    <literal><![CDATA[
      L(K(x,K(y,x \ z) \ (z * u)),w,v5) \ L(K(x,x \ (K(y,x \ z) \ (z * u))),w,v5) = a(x,x \ (z * T(u,y)),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,12932,a,b,20691,a)].">
      <j1 rule="hyper" parents="63 12932 20691"/>
    </justification>
  </clause>

  <clause id="20693">
    <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(63,a,15171,a(flip),b,18058,a),flip(a)].">
      <j1 rule="hyper" parents="63 15171 18058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20694">
    <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(65(a,1),20693(a,1,2,1))].">
      <j1 rule="para" parents="65 20693"/>
    </justification>
  </clause>

  <clause id="20695">
    <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(19290(a,1),19025(a,1,2,2,2))].">
      <j1 rule="para" parents="19290 19025"/>
    </justification>
  </clause>

  <clause id="20696">
    <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(63,a,20472,a(flip),b,20695,a)].">
      <j1 rule="hyper" parents="63 20472 20695"/>
    </justification>
  </clause>

  <clause id="20699">
    <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(63,a,18211,a(flip),b,20696,a),flip(a)].">
      <j1 rule="hyper" parents="63 18211 20696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20700">
    <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(10378(a,1),20261(a,2,1))].">
      <j1 rule="para" parents="10378 20261"/>
    </justification>
  </clause>

  <clause id="20701">
    <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(333,a,15473,a(flip),b,20700,a),flip(a)].">
      <j1 rule="hyper" parents="333 15473 20700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20703">
    <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(6799(a,1),20701(a,1,1))].">
      <j1 rule="para" parents="6799 20701"/>
    </justification>
  </clause>

  <clause id="20704">
    <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(5304(a,1),20703(a,1,2,1,2))].">
      <j1 rule="para" parents="5304 20703"/>
    </justification>
  </clause>

  <clause id="20705">
    <literal><![CDATA[
      (x * (K(y,z) * u)) / u = (x * u) / (K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(15695,a,20704,a)].">
      <j1 rule="hyper" parents="15695 20704"/>
    </justification>
  </clause>

  <clause id="20706">
    <literal><![CDATA[
      (x * (y / z)) / (K(u,y) * (y / z)) = (x * (T(y,u) / z)) / (y / z)
    ]]></literal>
    <justification jstring="[para(13229(a,1),20705(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="13229 20705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20707">
    <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(20705(a,1),14063(a,2,2))].">
      <j1 rule="para" parents="20705 14063"/>
    </justification>
  </clause>

  <clause id="20708">
    <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(19719(a,1),20707(a,1,1,1))].">
      <j1 rule="para" parents="19719 20707"/>
    </justification>
  </clause>

  <clause id="20709">
    <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(14008(a,1),20708(a,1,1,1))].">
      <j1 rule="para" parents="14008 20708"/>
    </justification>
  </clause>

  <clause id="20711">
    <literal><![CDATA[
      ((K(x,y) * z) * (K(u,w) * v5)) / v5 = K(x,y) * ((z * v5) / (K(w,u) * v5))
    ]]></literal>
    <justification jstring="[para(19575(a,1),20709(a,1,1))].">
      <j1 rule="para" parents="19575 20709"/>
    </justification>
  </clause>

  <clause id="20712">
    <literal><![CDATA[
      ((K(x,y) * z) * u) / (K(w,v5) * u) = K(x,y) * ((z * u) / (K(w,v5) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,20705,a(flip),b,20711,a)].">
      <j1 rule="hyper" parents="63 20705 20711"/>
    </justification>
  </clause>

  <clause id="20713">
    <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(20229,a,20712,a),flip(a)].">
      <j1 rule="hyper" parents="20229 20712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20714">
    <literal><![CDATA[
      L(K(x,y) * z,K(u,w),v5) = K(x,y) * R(z,K(u,w),v5)
    ]]></literal>
    <justification jstring="[para(20(a,2),20713(a,1,2)),flip(a)].">
      <j1 rule="para" parents="20 20713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20715">
    <literal><![CDATA[
      L(K(x,y) * z,K(u,w),v5) = K(x,y) * L(z,K(u,w),v5)
    ]]></literal>
    <justification jstring="[para(20213(a,1),20714(a,2,2))].">
      <j1 rule="para" parents="20213 20714"/>
    </justification>
  </clause>

  <clause id="20716">
    <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(333,a,20233,a(flip),b,20715,a),flip(a)].">
      <j1 rule="hyper" parents="333 20233 20715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20717">
    <literal><![CDATA[
      ((x * y) / (K(z,u) * y)) * K(z,u) = L(x,K(z,u),y)
    ]]></literal>
    <justification jstring="[para(4558(a,1),20716(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4558 20716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20718">
    <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(13300(a,1),20717(a,1,1,2))].">
      <j1 rule="para" parents="13300 20717"/>
    </justification>
  </clause>

  <clause id="20719">
    <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(333,a,19339,a(flip),b,20718,a),flip(a)].">
      <j1 rule="hyper" parents="333 19339 20718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20720">
    <literal><![CDATA[
      ((x * (T(y,z) / u)) / (y / u)) * K(z,y) = L(x,K(z,y),u \ y)
    ]]></literal>
    <justification jstring="[hyper(333,a,19022,a(flip),b,20719,a),flip(a)].">
      <j1 rule="hyper" parents="333 19022 20719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20721">
    <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(18080(a,1),18218(a,1,1,3))].">
      <j1 rule="para" parents="18080 18218"/>
    </justification>
  </clause>

  <clause id="20722">
    <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(19586(a,1),20721(a,1,1))].">
      <j1 rule="para" parents="19586 20721"/>
    </justification>
  </clause>

  <clause id="20723">
    <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="[para(19705(a,1),20722(a,1,1))].">
      <j1 rule="para" parents="19705 20722"/>
    </justification>
  </clause>

  <clause id="20724">
    <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(18424(a,1),20723(a,1,2))].">
      <j1 rule="para" parents="18424 20723"/>
    </justification>
  </clause>

  <clause id="20726">
    <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(13444(a,1),20724(a,1,2))].">
      <j1 rule="para" parents="13444 20724"/>
    </justification>
  </clause>

  <clause id="20727">
    <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(18647(a,1),20726(a,1,2))].">
      <j1 rule="para" parents="18647 20726"/>
    </justification>
  </clause>

  <clause id="20728">
    <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(333,a,17810,a(flip),b,20727,a),flip(a)].">
      <j1 rule="hyper" parents="333 17810 20727"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20729">
    <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(98(a,1),18533(a,1,2,2))].">
      <j1 rule="para" parents="98 18533"/>
    </justification>
  </clause>

  <clause id="20730">
    <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(15030,a,20729,a)].">
      <j1 rule="hyper" parents="15030 20729"/>
    </justification>
  </clause>

  <clause id="20731">
    <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(15140,a,20730,a)].">
      <j1 rule="hyper" parents="15140 20730"/>
    </justification>
  </clause>

  <clause id="20732">
    <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(18532(a,1),20731(a,2,3,1))].">
      <j1 rule="para" parents="18532 20731"/>
    </justification>
  </clause>

  <clause id="20733">
    <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(12208(a,1),20732(a,2,3))].">
      <j1 rule="para" parents="12208 20732"/>
    </justification>
  </clause>

  <clause id="20734">
    <literal><![CDATA[
      K(x,(y * (z \ u)) \ L(y / (u \ z),u \ z,u)) = a(x,u,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(333,a,17690,a(flip),b,20733,a),flip(a)].">
      <j1 rule="hyper" parents="333 17690 20733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20736">
    <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(63,a,17518,a,b,20734,a)].">
      <j1 rule="hyper" parents="63 17518 20734"/>
    </justification>
  </clause>

  <clause id="20737">
    <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(18549(a,1),20736(a,1,1,2))].">
      <j1 rule="para" parents="18549 20736"/>
    </justification>
  </clause>

  <clause id="20738">
    <literal><![CDATA[
      K(x,L(y / (z \ u),z \ u,z) / (y * (u \ z))) = a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(214,a,20737,a)].">
      <j1 rule="hyper" parents="214 20737"/>
    </justification>
  </clause>

  <clause id="20740">
    <literal><![CDATA[
      T(K(x,L(T(y,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(3678(a,1),19636(a,1,1,2,1))].">
      <j1 rule="para" parents="3678 19636"/>
    </justification>
  </clause>

  <clause id="20741">
    <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(8295(a,1),20740(a,1,1))].">
      <j1 rule="para" parents="8295 20740"/>
    </justification>
  </clause>

  <clause id="20742">
    <literal><![CDATA[
      K(x,(y \ (z \ (u * z))) \ (y \ (u * z))) = K(x,L(T(z,u),u,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(15512,a,20741,a),flip(a)].">
      <j1 rule="hyper" parents="15512 20741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20744">
    <literal><![CDATA[
      K(x,(y \ T(z,u)) \ (y \ (z * u))) = K(x,L(T(u,z),z,y \ 1))
    ]]></literal>
    <justification jstring="[para(22(a,2),20742(a,1,2,1,2))].">
      <j1 rule="para" parents="22 20742"/>
    </justification>
  </clause>

  <clause id="20745">
    <literal><![CDATA[
      T(K(x,T(y,T(1 \ (z / u),z))) \ (u * (z / u)),((u \ z) \ 1) * z) = T(u * (z / u),((u \ z) \ 1) * z) * K(y,x)
    ]]></literal>
    <justification jstring="[para(7972(a,1),20450(a,1,1,1,2))].">
      <j1 rule="para" parents="7972 20450"/>
    </justification>
  </clause>

  <clause id="20746">
    <literal><![CDATA[
      T(K(x,T(y,T(z / u,z))) \ (u * (z / u)),((u \ z) \ 1) * z) = T(u * (z / u),((u \ z) \ 1) * z) * K(y,x)
    ]]></literal>
    <justification jstring="[para(65(a,1),20745(a,1,1,1,2,2,1))].">
      <j1 rule="para" parents="65 20745"/>
    </justification>
  </clause>

  <clause id="20747">
    <literal><![CDATA[
      T(K(x,T(y,z \ u)) \ (z * (u / z)),((z \ u) \ 1) * u) = T(z * (u / z),((z \ u) \ 1) * u) * K(y,x)
    ]]></literal>
    <justification jstring="[para(6466(a,1),20746(a,1,1,1,2))].">
      <j1 rule="para" parents="6466 20746"/>
    </justification>
  </clause>

  <clause id="20748">
    <literal><![CDATA[
      T(x * ((y * K(z,u)) / x),((x \ y) \ 1) * y) = T(x * (y / x),((x \ y) \ 1) * y) * K(z,u)
    ]]></literal>
    <justification jstring="[para(19509(a,1),20747(a,1,1))].">
      <j1 rule="para" parents="19509 20747"/>
    </justification>
  </clause>

  <clause id="20749">
    <literal><![CDATA[
      T(x * ((y * K(z,u)) / x),y * ((y / x) \ 1)) = T(x * (y / x),((x \ y) \ 1) * y) * K(z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,12255,a(flip),b,20748,a)].">
      <j1 rule="hyper" parents="63 12255 20748"/>
    </justification>
  </clause>

  <clause id="20750">
    <literal><![CDATA[
      T(x * (y / x),((x \ y) \ 1) * y) * K(z,u) = x * (T(y * K(z,u),y * ((y / x) \ 1)) / x)
    ]]></literal>
    <justification jstring="[hyper(63,a,4083,a(flip),b,20749,a),flip(a)].">
      <j1 rule="hyper" parents="63 4083 20749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20751">
    <literal><![CDATA[
      T(x * (y / x),((x \ y) \ 1) * y) * K(z,u) = x * (T(y * K(z,u),(y / x) \ y) / x)
    ]]></literal>
    <justification jstring="[para(20494(a,1),20750(a,2,2,1))].">
      <j1 rule="para" parents="20494 20750"/>
    </justification>
  </clause>

  <clause id="20752">
    <literal><![CDATA[
      T(x * (y / x),((x \ y) \ 1) * y) * K(z,u) = x * (T(y * K(z,u),x) / x)
    ]]></literal>
    <justification jstring="[para(79(a,1),20751(a,2,2,1,2))].">
      <j1 rule="para" parents="79 20751"/>
    </justification>
  </clause>

  <clause id="20753">
    <literal><![CDATA[
      T(x * (y / x),y * ((y / x) \ 1)) * K(z,u) = x * (T(y * K(z,u),x) / x)
    ]]></literal>
    <justification jstring="[para(12255(a,1),20752(a,1,1))].">
      <j1 rule="para" parents="12255 20752"/>
    </justification>
  </clause>

  <clause id="20754">
    <literal><![CDATA[
      (x * (T(y,y * ((y / x) \ 1)) / x)) * K(z,u) = x * (T(y * K(z,u),x) / x)
    ]]></literal>
    <justification jstring="[para(4083(a,1),20753(a,1,1))].">
      <j1 rule="para" parents="4083 20753"/>
    </justification>
  </clause>

  <clause id="20755">
    <literal><![CDATA[
      (x * (T(y,(y / x) \ y) / x)) * K(z,u) = x * (T(y * K(z,u),x) / x)
    ]]></literal>
    <justification jstring="[para(1686(a,1),20754(a,1,1,2,1))].">
      <j1 rule="para" parents="1686 20754"/>
    </justification>
  </clause>

  <clause id="20756">
    <literal><![CDATA[
      (x * (T(y,x) / x)) * K(z,u) = x * (T(y * K(z,u),x) / x)
    ]]></literal>
    <justification jstring="[para(79(a,1),20755(a,1,1,2,1,2))].">
      <j1 rule="para" parents="79 20755"/>
    </justification>
  </clause>

  <clause id="20757">
    <literal><![CDATA[
      (x * (T((y * z) * K(z,u),x) / x)) / (y * T(z,u)) = a(x,x \ (y * z),x)
    ]]></literal>
    <justification jstring="[para(20756(a,1),14752(a,1,1))].">
      <j1 rule="para" parents="20756 14752"/>
    </justification>
  </clause>

  <clause id="20758">
    <literal><![CDATA[
      (x * (T(y * T(z,u),x) / x)) / (y * T(z,u)) = a(x,x \ (y * z),x)
    ]]></literal>
    <justification jstring="[para(5984(a,1),20757(a,1,1,2,1,1))].">
      <j1 rule="para" parents="5984 20757"/>
    </justification>
  </clause>

  <clause id="20759">
    <literal><![CDATA[
      (x * T(y,z)) \ (u * (T(x * T(y,z),u) / u)) = a(u,u \ (x * y),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,15997,a(flip),b,20758,a)].">
      <j1 rule="hyper" parents="63 15997 20758"/>
    </justification>
  </clause>

  <clause id="20760">
    <literal><![CDATA[
      a(x,x \ (y * T(z,u)),x) = a(x,x \ (y * z),x)
    ]]></literal>
    <justification jstring="[hyper(9243,a,20759,a)].">
      <j1 rule="hyper" parents="9243 20759"/>
    </justification>
  </clause>

  <clause id="20761">
    <literal><![CDATA[
      a(x,x \ (y * T(z,u)),x) = a(x,x \ (z * y),x)
    ]]></literal>
    <justification jstring="[hyper(333,a,20668,a,b,20760,a),flip(a)].">
      <j1 rule="hyper" parents="333 20668 20760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20762">
    <literal><![CDATA[
      a(x,x \ (1 \ (y * z)),x) = a(x,x \ (z * T(y,u)),x)
    ]]></literal>
    <justification jstring="[para(65(a,2),20761(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="65 20761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20763">
    <literal><![CDATA[
      a(x,x \ (y * T(z,u)),x) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,x \ (y * z),x) = w
    ]]></literal>
    <justification jstring="[para(20761(a,2),20671(a,1))].">
      <j1 rule="para" parents="20761 20671"/>
    </justification>
  </clause>

  <clause id="20764">
    <literal><![CDATA[
      a(x,x \ ((y \ 1) \ z),x) = a(x,x \ (z * T(y,u)),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,12938,a,b,20762,a)].">
      <j1 rule="hyper" parents="63 12938 20762"/>
    </justification>
  </clause>

  <clause id="20765">
    <literal><![CDATA[
      a(x,x \ ((y \ 1) \ z),x) = a(x,x \ (z * y),x)
    ]]></literal>
    <justification jstring="[hyper(333,a,20760,a(flip),b,20764,a),flip(a)].">
      <j1 rule="hyper" parents="333 20760 20764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20766">
    <literal><![CDATA[
      a(x,x \ (y * (z \ 1)),x) = a(x,x \ (z \ y),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,20176,a(flip),b,20765,a),flip(a)].">
      <j1 rule="hyper" parents="63 20176 20765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20767">
    <literal><![CDATA[
      a(x,x \ ((y \ 1) * z),x) = a(x,x \ (y \ z),x)
    ]]></literal>
    <justification jstring="[hyper(20671,a,20766,a)].">
      <j1 rule="hyper" parents="20671 20766"/>
    </justification>
  </clause>

  <clause id="20768">
    <literal><![CDATA[
      a(x,x \ (((T(y,z) \ 1) \ 1) * ((y \ 1) * u)),x) = a(x,x \ (K(z,y) \ u),x)
    ]]></literal>
    <justification jstring="[para(9161(a,1),20767(a,2,2,2))].">
      <j1 rule="para" parents="9161 20767"/>
    </justification>
  </clause>

  <clause id="20769">
    <literal><![CDATA[
      a(x,x \ (T(y,z) * ((1 / y) * u)),x) = a(x,x \ (K(z,y) \ u),x)
    ]]></literal>
    <justification jstring="[para(10160(a,1),20768(a,1,2,2))].">
      <j1 rule="para" parents="10160 20768"/>
    </justification>
  </clause>

  <clause id="20770">
    <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(16448,a,19871,a),flip(a)].">
      <j1 rule="hyper" parents="16448 19871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20771">
    <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(333,a,18314,a(flip),b,20770,a),flip(a)].">
      <j1 rule="hyper" parents="333 18314 20770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20772">
    <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(18286(a,1),20771(a,1,2,2,2))].">
      <j1 rule="para" parents="18286 20771"/>
    </justification>
  </clause>

  <clause id="20773">
    <literal><![CDATA[
      L(x,K(y,z),u) * L(K(K(y,z),x) * u,x,K(y,z)) = (x * K(y,z)) * (K(z,y) * L(K(K(y,z),x) * u,x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(14811(a,1),20253(a,1,1))].">
      <j1 rule="para" parents="14811 20253"/>
    </justification>
  </clause>

  <clause id="20774">
    <literal><![CDATA[
      L(x,K(y,z),u) * L(K(x,K(y,z)) * u,x,K(y,z)) = (x * K(y,z)) * (K(z,y) * L(K(K(y,z),x) * u,x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(6799(a,1),20773(a,1,2,1,1))].">
      <j1 rule="para" parents="6799 20773"/>
    </justification>
  </clause>

  <clause id="20776">
    <literal><![CDATA[
      L(T(x,K(y,z)),K(y,z),u) * L(u,x,K(y,z)) = (x * K(y,z)) * (K(z,y) * L(K(K(y,z),x) * u,x,K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,10418,a(flip),b,20774,a)].">
      <j1 rule="hyper" parents="63 10418 20774"/>
    </justification>
  </clause>

  <clause id="20777">
    <literal><![CDATA[
      L(T(x,K(y,z)),K(y,z),u) * L(u,x,K(y,z)) = (x * K(y,z)) * (K(z,y) * L(K(x,K(y,z)) * u,x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(6799(a,1),20776(a,2,2,2,1,1))].">
      <j1 rule="para" parents="6799 20776"/>
    </justification>
  </clause>

  <clause id="20778">
    <literal><![CDATA[
      L(T(x,K(y,z)),K(y,z),u) * L(u,x,K(y,z)) = (x * K(y,z)) * L(K(z,y) * (K(x,K(y,z)) * u),x,K(y,z))
    ]]></literal>
    <justification jstring="[para(19882(a,2),20777(a,2,2))].">
      <j1 rule="para" parents="19882 20777"/>
    </justification>
  </clause>

  <clause id="20779">
    <literal><![CDATA[
      L(T(x,K(y,z)),K(y,z),u) * L(u,x,K(y,z)) = (x * K(y,z)) * L(y * (T(T(y,K(x,z)),z) \ u),x,K(y,z))
    ]]></literal>
    <justification jstring="[para(15584(a,1),20778(a,2,2,1))].">
      <j1 rule="para" parents="15584 20778"/>
    </justification>
  </clause>

  <clause id="20780">
    <literal><![CDATA[
      L(T(x,K(y,z)),K(y,z),u) * L(u,x,K(y,z)) = (x * K(y,z)) * L(y * (T(y,T(z,x)) \ u),x,K(y,z))
    ]]></literal>
    <justification jstring="[para(6859(a,1),20779(a,2,2,1,2,1))].">
      <j1 rule="para" parents="6859 20779"/>
    </justification>
  </clause>

  <clause id="20781">
    <literal><![CDATA[
      L(T(x,K(y,z)),K(y,z),u) * L(u,x,K(y,z)) = (x * K(y,z)) * L(K(T(z,x),y) * u,x,K(y,z))
    ]]></literal>
    <justification jstring="[para(4556(a,1),20780(a,2,2,1))].">
      <j1 rule="para" parents="4556 20780"/>
    </justification>
  </clause>

  <clause id="20782">
    <literal><![CDATA[
      L(T(x,K(y,z)),K(y,z),u) * L(u,x,K(y,z)) = (x * K(y,z)) * L(K(z,T(y,x)) * u,x,K(y,z))
    ]]></literal>
    <justification jstring="[para(6370(a,1),20781(a,2,2,1,1))].">
      <j1 rule="para" parents="6370 20781"/>
    </justification>
  </clause>

  <clause id="20783">
    <literal><![CDATA[
      L(T(x,K(y,z)),K(y,z),u) * L(u,x,K(y,z)) = K(y,z) * (T(x,K(y,z)) * (K(z,T(y,x)) * u))
    ]]></literal>
    <justification jstring="[hyper(333,a,10085,a(flip),b,20782,a),flip(a)].">
      <j1 rule="hyper" parents="333 10085 20782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20784">
    <literal><![CDATA[
      L(T(x,K(y,z)),K(y,z),u) * L(u,x,K(y,z)) = K(y,z) * (x * (K(z,y) * u))
    ]]></literal>
    <justification jstring="[para(7767(a,1),20783(a,2,2))].">
      <j1 rule="para" parents="7767 20783"/>
    </justification>
  </clause>

  <clause id="20785">
    <literal><![CDATA[
      L(K(x,(y / (z * K(u,w))) \ 1),a(u,v5,K(v6,w)),z * K(u,w)) = K(x,T((z * L(K(u,w),v5,v6)) / y,a(u,v5,K(v6,w))))
    ]]></literal>
    <justification jstring="[para(18552(a,1),17865(a,1,1))].">
      <j1 rule="para" parents="18552 17865"/>
    </justification>
  </clause>

  <clause id="20786">
    <literal><![CDATA[
      L(K(x,y / (z * K(u,w))),a(w,v5,K(v6,u)),y * K(w,u)) = K(x,T((y * L(K(w,u),v5,v6)) / z,a(w,v5,K(v6,u))))
    ]]></literal>
    <justification jstring="[para(17772(a,1),20785(a,1,1))].">
      <j1 rule="para" parents="17772 20785"/>
    </justification>
  </clause>

  <clause id="20788">
    <literal><![CDATA[
      L(K(x,y / (z * K(u,w))),a(w,v5,K(v6,u)),y * K(w,u)) = K(x,(y * L(K(w,u),v5,v6)) / z)
    ]]></literal>
    <justification jstring="[hyper(333,a,17553,a(flip),b,20786,a),flip(a)].">
      <j1 rule="hyper" parents="333 17553 20786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20790">
    <literal><![CDATA[
      L(K(x,y / (z * K(u,w))),a(w,v5,K(v6,u)),y * K(w,u)) = K(x,y / (z * L(K(u,w),v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(333,a,18346,a(flip),b,20788,a),flip(a)].">
      <j1 rule="hyper" parents="333 18346 20788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20791">
    <literal><![CDATA[
      K(x,y / (z * L(K(u,w),v5,v6))) = K(x,y / (z * K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,19306,a(flip),b,20790,a),flip(a)].">
      <j1 rule="hyper" parents="63 19306 20790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20793">
    <literal><![CDATA[
      K(x,y / ((z * u) * K(w,v5))) = K(x,y / (z * (u * K(w,v5))))
    ]]></literal>
    <justification jstring="[para(97(a,1),20791(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="97 20791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20794">
    <literal><![CDATA[
      K(x,y / (z * (u * K(w,v5)))) = K(x,y * ((z * u) \ K(v5,w)))
    ]]></literal>
    <justification jstring="[hyper(16465,a,20793,a),flip(a)].">
      <j1 rule="hyper" parents="16465 20793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20795">
    <literal><![CDATA[
      K(x,y * ((z * T(u,z)) \ K(w,v5))) = K(x,y / ((K(v5,w) * u) * z))
    ]]></literal>
    <justification jstring="[hyper(18171,a,20794,a),flip(a)].">
      <j1 rule="hyper" parents="18171 20794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20796">
    <literal><![CDATA[
      K(x,y / (z * (u * K(w,u)))) = K(x,y / (z * T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(333,a,18106,a(flip),b,20794,a),flip(a)].">
      <j1 rule="hyper" parents="333 18106 20794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20797">
    <literal><![CDATA[
      K(x,y / (z * T(T(u,w),w))) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[para(4271(a,1),20796(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4271 20796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20798">
    <literal><![CDATA[
      K(x,y / (z * T(u \ w,u))) = K(x,y / (z * (w / u)))
    ]]></literal>
    <justification jstring="[para(4292(a,1),20796(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4292 20796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20799">
    <literal><![CDATA[
      K(x,y / (T(z,u) * (u \ 1))) = K(x,y / ((u \ 1) * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,19463,a(flip),b,20797,a)].">
      <j1 rule="hyper" parents="63 19463 20797"/>
    </justification>
  </clause>

  <clause id="20800">
    <literal><![CDATA[
      K(x,(y \ z) / (u * ((y \ z) / z))) = K(x,((y \ 1) * z) / (u * (y \ 1)))
    ]]></literal>
    <justification jstring="[hyper(63,a,19942,a(flip),b,20798,a),flip(a)].">
      <j1 rule="hyper" parents="63 19942 20798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20801">
    <literal><![CDATA[
      K(x,y / ((K(z,u) * w) * v5)) = K(x,y * ((w * v5) \ K(u,z)))
    ]]></literal>
    <justification jstring="[para(111(a,1),20795(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="111 20795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20802">
    <literal><![CDATA[
      K(x,y / (((z \ K(u,w)) \ 1) * v5)) = K(x,y * ((z * v5) \ K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,13269,a,b,20801,a)].">
      <j1 rule="hyper" parents="63 13269 20801"/>
    </justification>
  </clause>

  <clause id="20803">
    <literal><![CDATA[
      K(x,y / (((T(z,u) / (z / (u \ 1))) \ 1) * w)) = K(x,y * ((T(u,z) * w) \ K(u * z,u \ 1)))
    ]]></literal>
    <justification jstring="[para(13441(a,1),20802(a,1,2,2,1,1))].">
      <j1 rule="para" parents="13441 20802"/>
    </justification>
  </clause>

  <clause id="20804">
    <literal><![CDATA[
      K(x,((y \ 1) * z) / (u * (y \ 1))) = K(x,(y \ z) / (u / y))
    ]]></literal>
    <justification jstring="[hyper(63,a,18942,a(flip),b,20800,a),flip(a)].">
      <j1 rule="hyper" parents="63 18942 20800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20805">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,y,z \ 1)) = K(x,(z \ y) / ((u \ 1) / z))
    ]]></literal>
    <justification jstring="[hyper(63,a,19529,a,b,20804,a)].">
      <j1 rule="hyper" parents="63 19529 20804"/>
    </justification>
  </clause>

  <clause id="20806">
    <literal><![CDATA[
      K(x,y / (((T(z,u) / (z / (u \ 1))) \ 1) * w)) = K(x,y * ((T(u,z) * w) \ K(u * z,u)))
    ]]></literal>
    <justification jstring="[hyper(333,a,18786,a(flip),b,20803,a),flip(a)].">
      <j1 rule="hyper" parents="333 18786 20803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20807">
    <literal><![CDATA[
      K(x,y / (((T(z,u) / (z / (u \ 1))) \ 1) * w)) = K(x,y * ((T(u,z) * w) \ K(z * u,u)))
    ]]></literal>
    <justification jstring="[para(4543(a,2),20806(a,2,2,2,2))].">
      <j1 rule="para" parents="4543 20806"/>
    </justification>
  </clause>

  <clause id="20808">
    <literal><![CDATA[
      K(x,y / (((T(z,u) / (z / (u \ 1))) \ 1) * w)) = K(x,y * ((T(u,z) * w) \ K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(333,a,18792,a(flip),b,20807,a),flip(a)].">
      <j1 rule="hyper" parents="333 18792 20807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20809">
    <literal><![CDATA[
      K(x,y / (((T(z,u) / (z / (u \ 1))) \ 1) * w)) = K(x,y * ((u * w) \ 1))
    ]]></literal>
    <justification jstring="[para(13268(a,1),20808(a,2,2,2))].">
      <j1 rule="para" parents="13268 20808"/>
    </justification>
  </clause>

  <clause id="20811">
    <literal><![CDATA[
      K(x,y / (((T(z,u) / (z / (u \ 1))) \ 1) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (u * w)) = v5
    ]]></literal>
    <justification jstring="[para(20809(a,2),13528(a,1))].">
      <j1 rule="para" parents="20809 13528"/>
    </justification>
  </clause>

  <clause id="20812">
    <literal><![CDATA[
      K(x,L(y \ (L(T(z,K(u,w)),v5,v6) * v7),y,L(K(v7,T(z,K(u,w))),v5,v6))) = K(x,(K(L(T(z,K(u,w)),v5,v6),v7) \ y) \ (v7 * L(z,v5,v6)))
    ]]></literal>
    <justification jstring="[para(10851(a,2),18252(a,1,2,3))].">
      <j1 rule="para" parents="10851 18252"/>
    </justification>
  </clause>

  <clause id="20813">
    <literal><![CDATA[
      L(T(x \ L(x,K(y,z),T(u * K(z,y),w)),v5),T(x,v5),T(u * K(u * K(z,y),w),K(z,y))) = a(T(x,v5),K(y,z),T(u * K(z,y),w))
    ]]></literal>
    <justification jstring="[para(20213(a,1),18543(a,1,1,1,2))].">
      <j1 rule="para" parents="20213 18543"/>
    </justification>
  </clause>

  <clause id="20814">
    <literal><![CDATA[
      K(x,L(y \ (L(T(z,K(u,w)),v5,v6) * v7),y,L(K(v7,z),v5,v6))) = K(x,(K(L(T(z,K(u,w)),v5,v6),v7) \ y) \ (v7 * L(z,v5,v6)))
    ]]></literal>
    <justification jstring="[para(15472(a,1),20812(a,1,2,3,1))].">
      <j1 rule="para" parents="15472 20812"/>
    </justification>
  </clause>

  <clause id="20815">
    <literal><![CDATA[
      L(K(x,y \ (L(T(z,K(u,w)),v5,v6) * v7)),y,L(K(v7,z),v5,v6)) = K(x,(K(L(T(z,K(u,w)),v5,v6),v7) \ y) \ (v7 * L(z,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(10893,a,20814,a)].">
      <j1 rule="hyper" parents="10893 20814"/>
    </justification>
  </clause>

  <clause id="20817">
    <literal><![CDATA[
      L(K(x,y \ (L(z,u,w) * v5)),y,L(K(v5,z),u,w)) = K(x,(K(L(T(z,K(v6,v7)),u,w),v5) \ y) \ (v5 * L(z,u,w)))
    ]]></literal>
    <justification jstring="[para(17875(a,1),20815(a,1,1))].">
      <j1 rule="para" parents="17875 20815"/>
    </justification>
  </clause>

  <clause id="20818">
    <literal><![CDATA[
      K(x,(K(L(T(y,K(z,u)),w,v5),v6) \ v7) \ (v6 * L(y,w,v5))) = K(x,v7 \ (L(y,w,v5) * v6))
    ]]></literal>
    <justification jstring="[hyper(17662,a,20817,a),flip(a)].">
      <j1 rule="hyper" parents="17662 20817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20820">
    <literal><![CDATA[
      K(x,(L(K(T(y,K(z,u)),w),v5,v6) \ v7) \ (w * L(y,v5,v6))) = K(x,v7 \ (L(y,v5,v6) * w))
    ]]></literal>
    <justification jstring="[para(10894(a,2),20818(a,1,2,1,1))].">
      <j1 rule="para" parents="10894 20818"/>
    </justification>
  </clause>

  <clause id="20821">
    <literal><![CDATA[
      K(x,(L(K(y,z),u,w) \ v5) \ (z * L(y,u,w))) = K(x,v5 \ (L(y,u,w) * z))
    ]]></literal>
    <justification jstring="[para(1242(a,1),20820(a,1,2,1,1,1,1))].">
      <j1 rule="para" parents="1242 20820"/>
    </justification>
  </clause>

  <clause id="20822">
    <literal><![CDATA[
      K(x,K(y,z) \ (u \ (z * L(y,w,v5)))) = K(x,u \ (L(y,w,v5) * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,20581,a(flip),b,20821,a)].">
      <j1 rule="hyper" parents="63 20581 20821"/>
    </justification>
  </clause>

  <clause id="20823">
    <literal><![CDATA[
      K(x,y \ (L(x,z,u) * w)) = K(x,y \ (w * L(x,z,u)))
    ]]></literal>
    <justification jstring="[hyper(7531,a,20822,a),flip(a)].">
      <j1 rule="hyper" parents="7531 20822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20825">
    <literal><![CDATA[
      K(x,y \ (L(x,z,u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (w * L(x,z,u))) = v5
    ]]></literal>
    <justification jstring="[para(20822(a,1),7531(a,1))].">
      <j1 rule="para" parents="20822 7531"/>
    </justification>
  </clause>

  <clause id="20826">
    <literal><![CDATA[
      L(K(x,(y \ z) \ L(x,u,w)),y \ z,y) = K(x,z \ (L(x,u,w) * y))
    ]]></literal>
    <justification jstring="[hyper(333,a,10876,a,b,20823,a)].">
      <j1 rule="hyper" parents="333 10876 20823"/>
    </justification>
  </clause>

  <clause id="20827">
    <literal><![CDATA[
      L(K(x,(y \ z) \ x),y \ z,y) = K(x,z \ (L(x,u,w) * y))
    ]]></literal>
    <justification jstring="[para(13494(a,1),20826(a,1,1))].">
      <j1 rule="para" parents="13494 20826"/>
    </justification>
  </clause>

  <clause id="20828">
    <literal><![CDATA[
      K(x,y \ (L(x,z,u) * w)) = K(x,y \ (w * x))
    ]]></literal>
    <justification jstring="[hyper(63,a,10876,a(flip),b,20827,a),flip(a)].">
      <j1 rule="hyper" parents="63 10876 20827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20830">
    <literal><![CDATA[
      K(x,y \ (z * L(x,u,w))) = K(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[hyper(20825,a,20828,a)].">
      <j1 rule="hyper" parents="20825 20828"/>
    </justification>
  </clause>

  <clause id="20832">
    <literal><![CDATA[
      K(x,y \ ((z * u) * x)) = K(x,y \ (z * (u * x)))
    ]]></literal>
    <justification jstring="[para(97(a,1),20830(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="97 20830"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20833">
    <literal><![CDATA[
      K(x,y \ (z * ((z \ u) * x))) = K(x,y \ (u * x))
    ]]></literal>
    <justification jstring="[para(463(a,1),20830(a,1,2,2))].">
      <j1 rule="para" parents="463 20830"/>
    </justification>
  </clause>

  <clause id="20835">
    <literal><![CDATA[
      K(x,y \ ((z \ u) * (z * x))) = K(x,y \ (T(u,z) * x))
    ]]></literal>
    <justification jstring="[hyper(63,a,19195,a(flip),b,20832,a),flip(a)].">
      <j1 rule="hyper" parents="63 19195 20832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20836">
    <literal><![CDATA[
      K(x,y \ ((x * z) * u)) = K(x,y \ (z * (u * x)))
    ]]></literal>
    <justification jstring="[hyper(63,a,11400,a(flip),b,20832,a)].">
      <j1 rule="hyper" parents="63 11400 20832"/>
    </justification>
  </clause>

  <clause id="20837">
    <literal><![CDATA[
      K(x,L(y \ (((z \ u) * x) * z),y,K(z,(z \ u) * x))) = K(x,(K((z \ u) * x,z) \ y) \ (u * x))
    ]]></literal>
    <justification jstring="[para(5184(a,2),20833(a,1,2))].">
      <j1 rule="para" parents="5184 20833"/>
    </justification>
  </clause>

  <clause id="20838">
    <literal><![CDATA[
      K(x,y \ ((z * x) * u)) = K(x,y \ (z * (u * x)))
    ]]></literal>
    <justification jstring="[hyper(10113,a,20836,a)].">
      <j1 rule="hyper" parents="10113 20836"/>
    </justification>
  </clause>

  <clause id="20839">
    <literal><![CDATA[
      K(x,L(y \ (((z \ u) * x) * z),y,K(z,z \ (u * x)))) = K(x,(K((z \ u) * x,z) \ y) \ (u * x))
    ]]></literal>
    <justification jstring="[para(10660(a,2),20837(a,1,2,3))].">
      <j1 rule="para" parents="10660 20837"/>
    </justification>
  </clause>

  <clause id="20840">
    <literal><![CDATA[
      K(x,L(y \ (((z \ u) * x) * z),y,K(z,u * x))) = K(x,(K((z \ u) * x,z) \ y) \ (u * x))
    ]]></literal>
    <justification jstring="[para(11826(a,1),20839(a,1,2))].">
      <j1 rule="para" parents="11826 20839"/>
    </justification>
  </clause>

  <clause id="20841">
    <literal><![CDATA[
      L(K(x,y \ (((z \ u) * x) * z)),y,K(z,u * x)) = K(x,(K((z \ u) * x,z) \ y) \ (u * x))
    ]]></literal>
    <justification jstring="[hyper(10893,a,20840,a)].">
      <j1 rule="hyper" parents="10893 20840"/>
    </justification>
  </clause>

  <clause id="20842">
    <literal><![CDATA[
      L(K(x,y \ ((z \ u) * (z * x))),y,K(z,u * x)) = K(x,(K((z \ u) * x,z) \ y) \ (u * x))
    ]]></literal>
    <justification jstring="[para(20838(a,1),20841(a,1,1))].">
      <j1 rule="para" parents="20838 20841"/>
    </justification>
  </clause>

  <clause id="20843">
    <literal><![CDATA[
      L(K(x,y \ (T(z,u) * x)),y,K(u,z * x)) = K(x,(K((u \ z) * x,u) \ y) \ (z * x))
    ]]></literal>
    <justification jstring="[para(20835(a,1),20842(a,1,1))].">
      <j1 rule="para" parents="20835 20842"/>
    </justification>
  </clause>

  <clause id="20844">
    <literal><![CDATA[
      K(x,(K((y \ z) * x,y) \ u) \ (z * x)) = K(x,u \ (T(z,y) * x))
    ]]></literal>
    <justification jstring="[hyper(17647,a,20843,a),flip(a)].">
      <j1 rule="hyper" parents="17647 20843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20846">
    <literal><![CDATA[
      K(x,(K(y \ (z * x),y) \ u) \ (z * x)) = K(x,u \ (T(z,y) * x))
    ]]></literal>
    <justification jstring="[para(13662(a,2),20844(a,1,2,1,1))].">
      <j1 rule="para" parents="13662 20844"/>
    </justification>
  </clause>

  <clause id="20847">
    <literal><![CDATA[
      K(x,y \ (K(z,z \ (u * x)) \ (u * x))) = K(x,y \ (T(u,z) * x))
    ]]></literal>
    <justification jstring="[hyper(63,a,17760,a(flip),b,20846,a)].">
      <j1 rule="hyper" parents="63 17760 20846"/>
    </justification>
  </clause>

  <clause id="20848">
    <literal><![CDATA[
      K(x,y \ ((z \ (u * x)) * z)) = K(x,y \ (T(u,z) * x))
    ]]></literal>
    <justification jstring="[para(4203(a,1),20847(a,1,2,2))].">
      <j1 rule="para" parents="4203 20847"/>
    </justification>
  </clause>

  <clause id="20849">
    <literal><![CDATA[
      K(x,y \ T(z * x,u)) = K(x,y \ (T(z,u) * x))
    ]]></literal>
    <justification jstring="[hyper(63,a,12726,a(flip),b,20848,a)].">
      <j1 rule="hyper" parents="63 12726 20848"/>
    </justification>
  </clause>

  <clause id="20850">
    <literal><![CDATA[
      K(x,((y * x) / z) \ (T(y,u) * x)) = K(x,K(u,y * x) \ z)
    ]]></literal>
    <justification jstring="[hyper(15777,a,20849,a),flip(a)].">
      <j1 rule="hyper" parents="15777 20849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20851">
    <literal><![CDATA[
      K(x,K(y,z * x) \ u) = K(x,K(y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,18641,a(flip),b,20850,a),flip(a)].">
      <j1 rule="hyper" parents="63 18641 20850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20853">
    <literal><![CDATA[
      K(x,y * K(x * z,u)) = K(x,K(u,z) \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,16430,a(flip),b,20851,a)].">
      <j1 rule="hyper" parents="63 16430 20851"/>
    </justification>
  </clause>

  <clause id="20854">
    <literal><![CDATA[
      K(x,K(y,x * z) \ u) = K(x,K(y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(15601,a,20853,a)].">
      <j1 rule="hyper" parents="15601 20853"/>
    </justification>
  </clause>

  <clause id="20855">
    <literal><![CDATA[
      K(x,K(y,x * z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y) \ u) = w
    ]]></literal>
    <justification jstring="[para(20854(a,2),15780(a,1))].">
      <j1 rule="para" parents="20854 15780"/>
    </justification>
  </clause>

  <clause id="20856">
    <literal><![CDATA[
      K(x,K(y,z) \ ((y / (x \ 1)) \ u)) = K(x,T(x * y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(20855,a,20652,a)].">
      <j1 rule="hyper" parents="20855 20652"/>
    </justification>
  </clause>

  <clause id="20857">
    <literal><![CDATA[
      K(x,(T(y,z) / (x \ 1)) \ u) = K(x,T(x * y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,19506,a(flip),b,20856,a)].">
      <j1 rule="hyper" parents="63 19506 20856"/>
    </justification>
  </clause>

  <clause id="20858">
    <literal><![CDATA[
      K(x,T(x * y,z) \ u) = K(x,T(y,z) \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,9979,a(flip),b,20857,a),flip(a)].">
      <j1 rule="hyper" parents="63 9979 20857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20859">
    <literal><![CDATA[
      K(x,T(x \ y,z) \ (x \ u)) = K(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(10(a,1),20858(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="10 20858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20860">
    <literal><![CDATA[
      K(x,T(y,z) \ (y * u)) = K(x,K(z,x \ y) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,19139,a(flip),b,20859,a),flip(a)].">
      <j1 rule="hyper" parents="63 19139 20859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20861">
    <literal><![CDATA[
      K(x,K(y,x \ z) \ u) = K(x,K(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(4510(a,1),20860(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4510 20860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20862">
    <literal><![CDATA[
      K(x,y \ (K(z,x \ u) \ w)) = K(x,K(u,z) \ (y \ w))
    ]]></literal>
    <justification jstring="[hyper(63,a,19111,a(flip),b,20861,a)].">
      <j1 rule="hyper" parents="63 19111 20861"/>
    </justification>
  </clause>

  <clause id="20863">
    <literal><![CDATA[
      L(K(x,K(y,z) \ (y * u)),w,v5) \ L(K(x,x \ (K(z,x \ y) \ (y * u))),w,v5) = a(x,x \ (y * T(u,z)),x)
    ]]></literal>
    <justification jstring="[para(20861(a,1),20692(a,1,1,1))].">
      <j1 rule="para" parents="20861 20692"/>
    </justification>
  </clause>

  <clause id="20864">
    <literal><![CDATA[
      L(K(x,T(y,z) * u),w,v5) \ L(K(x,x \ (K(z,x \ y) \ (y * u))),w,v5) = a(x,x \ (y * T(u,z)),x)
    ]]></literal>
    <justification jstring="[para(14935(a,1),20863(a,1,1,1))].">
      <j1 rule="para" parents="14935 20863"/>
    </justification>
  </clause>

  <clause id="20865">
    <literal><![CDATA[
      L(K(x,T(y,z) * u),w,v5) \ L(K(x,K(y,z) \ (x \ (y * u))),w,v5) = a(x,x \ (y * T(u,z)),x)
    ]]></literal>
    <justification jstring="[para(20862(a,1),20864(a,1,2,1))].">
      <j1 rule="para" parents="20862 20864"/>
    </justification>
  </clause>

  <clause id="20866">
    <literal><![CDATA[
      L(K(x,T(y,z) * u),w,v5) \ L(K(x,x \ (T(y,z) * u)),w,v5) = a(x,x \ (y * T(u,z)),x)
    ]]></literal>
    <justification jstring="[para(18627(a,1),20865(a,1,2,1))].">
      <j1 rule="para" parents="18627 20865"/>
    </justification>
  </clause>

  <clause id="20867">
    <literal><![CDATA[
      a(x,x \ (T(y,z) * u),x) = a(x,x \ (y * T(u,z)),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,12932,a(flip),b,20866,a)].">
      <j1 rule="hyper" parents="63 12932 20866"/>
    </justification>
  </clause>

  <clause id="20868">
    <literal><![CDATA[
      a(x,x \ (y * T((1 / y) * z,u)),x) = a(x,x \ (K(u,y) \ z),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,20769,a(flip),b,20867,a),flip(a)].">
      <j1 rule="hyper" parents="63 20769 20867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20869">
    <literal><![CDATA[
      a(x,x \ (K(y,z) \ u),x) = a(x,x \ (z * ((1 / z) * u)),x)
    ]]></literal>
    <justification jstring="[hyper(20763,a,20868,a),flip(a)].">
      <j1 rule="hyper" parents="20763 20868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20871">
    <literal><![CDATA[
      a(x,x \ L(y,z \ 1,z),x) = a(x,x \ (K(u,z) \ y),x)
    ]]></literal>
    <justification jstring="[hyper(333,a,13044,a(flip),b,20869,a)].">
      <j1 rule="hyper" parents="333 13044 20869"/>
    </justification>
  </clause>

  <clause id="20872">
    <literal><![CDATA[
      a(x,x \ (K(y,z) \ u),x) = a(x,x \ u,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,12935,a(flip),b,20871,a),flip(a)].">
      <j1 rule="hyper" parents="63 12935 20871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20874">
    <literal><![CDATA[
      a(x,y \ (K(z,u) \ w),x) = a(x,x \ ((x \ y) \ w),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,20677,a(flip),b,20872,a)].">
      <j1 rule="hyper" parents="63 20677 20872"/>
    </justification>
  </clause>

  <clause id="20876">
    <literal><![CDATA[
      a(x,y \ (K(z,u) \ w),x) = a(x,x \ (y \ (x * w)),x)
    ]]></literal>
    <justification jstring="[hyper(333,a,12938,a(flip),b,20874,a),flip(a)].">
      <j1 rule="hyper" parents="333 12938 20874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20877">
    <literal><![CDATA[
      a(x,y \ T(z,x),x) = a(x,y \ (K(u,w) \ z),x)
    ]]></literal>
    <justification jstring="[hyper(333,a,20673,a(flip),b,20876,a)].">
      <j1 rule="hyper" parents="333 20673 20876"/>
    </justification>
  </clause>

  <clause id="20878">
    <literal><![CDATA[
      a(x,y \ (K(z,u) \ w),x) = a(x,y \ w,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,8488,a(flip),b,20877,a),flip(a)].">
      <j1 rule="hyper" parents="63 8488 20877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20884">
    <literal><![CDATA[
      a(x,y \ (z / u),x) = a(x,y \ (u \ z),x)
    ]]></literal>
    <justification jstring="[para(4315(a,1),20878(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4315 20878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20885">
    <literal><![CDATA[
      a(x,y \ (T(z,u) \ w),x) = a(x,y \ (z \ w),x)
    ]]></literal>
    <justification jstring="[para(4511(a,1),20878(a,1,2,2))].">
      <j1 rule="para" parents="4511 20878"/>
    </justification>
  </clause>

  <clause id="20886">
    <literal><![CDATA[
      a(x,y \ (((z * u) * w) / (z * w)),x) = a(x,y \ R(u,z,w),x)
    ]]></literal>
    <justification jstring="[para(14870(a,1),20878(a,1,2,2))].">
      <j1 rule="para" parents="14870 20878"/>
    </justification>
  </clause>

  <clause id="20887">
    <literal><![CDATA[
      a(x,y \ (z \ u),x) = a(x,z \ (y \ u),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,12892,a,b,20884,a)].">
      <j1 rule="hyper" parents="63 12892 20884"/>
    </justification>
  </clause>

  <clause id="20888">
    <literal><![CDATA[
      a(x,y \ ((z * u) \ w),x) = a(x,u \ (z \ (y \ w)),x)
    ]]></literal>
    <justification jstring="[hyper(333,a,12882,a(flip),b,20887,a),flip(a)].">
      <j1 rule="hyper" parents="333 12882 20887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20890">
    <literal><![CDATA[
      a(x,y \ ((z * u) \ w),x) = a(x,z \ (u \ (y \ w)),x)
    ]]></literal>
    <justification jstring="[hyper(333,a,20887,a,b,20888,a),flip(a)].">
      <j1 rule="hyper" parents="333 20887 20888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20891">
    <literal><![CDATA[
      a(x,y \ (z \ (u \ (z * (y * w)))),x) = a(x,u \ L(w,y,z),x)
    ]]></literal>
    <justification jstring="[para(18(a,2),20888(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="18 20888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20892">
    <literal><![CDATA[
      a(x,y \ ((z * T(u,w)) \ v5),x) = a(x,z \ (u \ (y \ v5)),x)
    ]]></literal>
    <justification jstring="[hyper(333,a,20885,a(flip),b,20890,a),flip(a)].">
      <j1 rule="hyper" parents="333 20885 20890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20893">
    <literal><![CDATA[
      a(x,y \ ((z * u) \ ((z * w) * u)),x) = a(x,y \ R(w,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,20884,a(flip),b,20886,a)].">
      <j1 rule="hyper" parents="63 20884 20886"/>
    </justification>
  </clause>

  <clause id="20894">
    <literal><![CDATA[
      a(x,y \ R(z,u,T(w,T(u * z,v5))),x) = a(x,y \ ((u * T(w,u * z)) \ (w * (u * z))),x)
    ]]></literal>
    <justification jstring="[para(18545(a,1),20893(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="18545 20893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20895">
    <literal><![CDATA[
      a(x,y \ R(z,u,T(w,T(u * z,v5))),x) = a(x,u \ (w \ (y \ (w * (u * z)))),x)
    ]]></literal>
    <justification jstring="[hyper(333,a,20892,a(flip),b,20894,a),flip(a)].">
      <j1 rule="hyper" parents="333 20892 20894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20897">
    <literal><![CDATA[
      a(x,y \ R(z,u,T(w,T(u * z,v5))),x) = a(x,y \ L(z,u,w),x)
    ]]></literal>
    <justification jstring="[hyper(333,a,20891,a(flip),b,20895,a),flip(a)].">
      <j1 rule="hyper" parents="333 20891 20895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20898">
    <literal><![CDATA[
      a(x,y \ L(y,z,u),x) = 1
    ]]></literal>
    <justification jstring="[hyper(13607,a,20897,a),flip(a)].">
      <j1 rule="hyper" parents="13607 20897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20899">
    <literal><![CDATA[
      K(x,y \ L(y,z,u)) = 1 * a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[para(20898(a,1),14157(a,1,1)),flip(a)].">
      <j1 rule="para" parents="20898 14157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20900">
    <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(119,a,20899,a(flip),b,20002,a),flip(a)].">
      <j1 rule="hyper" parents="119 20899 20002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20902">
    <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(333,a,19587,a(flip),b,20900,a),flip(a)].">
      <j1 rule="hyper" parents="333 19587 20900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20904">
    <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(5994(a,1),20902(a,1,2))].">
      <j1 rule="para" parents="5994 20902"/>
    </justification>
  </clause>

  <clause id="20905">
    <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(18010,a,20904,a)].">
      <j1 rule="hyper" parents="18010 20904"/>
    </justification>
  </clause>

  <clause id="20906">
    <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(5304(a,1),20905(a,1,2,2))].">
      <j1 rule="para" parents="5304 20905"/>
    </justification>
  </clause>

  <clause id="20907">
    <literal><![CDATA[
      L(T(x \ L(x,K(y,z),u * K(z,y)),w),T(x,w),T(u * K(u * K(z,y),v5),K(z,y))) = a(T(x,w),K(y,z),T(u * K(z,y),v5))
    ]]></literal>
    <justification jstring="[para(19318(a,1),20813(a,1,1,1,2))].">
      <j1 rule="para" parents="19318 20813"/>
    </justification>
  </clause>

  <clause id="20908">
    <literal><![CDATA[
      L(T(x \ L(x,K(y,z),u),w),T(x,w),T(u * K(u * K(z,y),v5),K(z,y))) = a(T(x,w),K(y,z),T(u * K(z,y),v5))
    ]]></literal>
    <justification jstring="[para(19019(a,1),20907(a,1,1,1,2))].">
      <j1 rule="para" parents="19019 20907"/>
    </justification>
  </clause>

  <clause id="20910">
    <literal><![CDATA[
      L(x \ L(x,K(y,z),u),T(x,w),T(u * K(u * K(z,y),v5),K(z,y))) = a(T(x,w),K(y,z),T(u * K(z,y),v5))
    ]]></literal>
    <justification jstring="[para(20223(a,1),20908(a,1,1))].">
      <j1 rule="para" parents="20223 20908"/>
    </justification>
  </clause>

  <clause id="20911">
    <literal><![CDATA[
      L(x \ L(x,K(y,z),u),T(x,w),K(y,z) * T(u * K(z,y),v5)) = a(T(x,w),K(y,z),T(u * K(z,y),v5))
    ]]></literal>
    <justification jstring="[para(16093(a,1),20910(a,1,3))].">
      <j1 rule="para" parents="16093 20910"/>
    </justification>
  </clause>

  <clause id="20913">
    <literal><![CDATA[
      L(x \ L(x,K(y,z),u),T(x,w),T(K(y,z) * (u * K(z,y)),v5)) = a(T(x,w),K(y,z),T(u * K(z,y),v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,20025,a,b,20911,a)].">
      <j1 rule="hyper" parents="63 20025 20911"/>
    </justification>
  </clause>

  <clause id="20914">
    <literal><![CDATA[
      L(x \ L(x,K(y,z),u),T(x,w),T(T(u,K(y,z)),v5)) = a(T(x,w),K(y,z),T(u * K(z,y),v5))
    ]]></literal>
    <justification jstring="[para(6849(a,1),20913(a,1,3,1))].">
      <j1 rule="para" parents="6849 20913"/>
    </justification>
  </clause>

  <clause id="20915">
    <literal><![CDATA[
      a(T(x,y),K(z,u),T(w * K(u,z),v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x \ L(x,K(z,u),w),T(x,y),T(w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(20914(a,1),17666(a,1))].">
      <j1 rule="para" parents="20914 17666"/>
    </justification>
  </clause>

  <clause id="20916">
    <literal><![CDATA[
      a(T(x,y),K(z,u),w * K(u,z)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x \ L(x,K(z,u),w),T(x,y),T(w,v6)) = v5
    ]]></literal>
    <justification jstring="[para(20316(a,1),20915(a,1))].">
      <j1 rule="para" parents="20316 20915"/>
    </justification>
  </clause>

  <clause id="20918">
    <literal><![CDATA[
      T((K(x,L(x \ K(y,z),u,w)) \ K(x,x \ K(y,z))) * L(K(x,x \ K(y,z)),u,w),K(K(z,y) * x,x \ 1)) = K(K(z,y) * x,x \ 1)
    ]]></literal>
    <justification jstring="[para(10851(a,1),15733(a,1,1,1,1))].">
      <j1 rule="para" parents="10851 15733"/>
    </justification>
  </clause>

  <clause id="20919">
    <literal><![CDATA[
      K(x,y * (((z * K(u,K(w,v5))) * (v6 * K(z * K(u,K(w,v5)),v7))) * z)) = K(x,y * ((z * (K(u,K(w,v5)) * v6)) * T(z * K(u,K(w,v5)),v7)))
    ]]></literal>
    <justification jstring="[para(20126(a,1),16514(a,2,2,2,1))].">
      <j1 rule="para" parents="20126 16514"/>
    </justification>
  </clause>

  <clause id="20920">
    <literal><![CDATA[
      L(a(x,K(y,z),u),x * (K(y,z) * u),K(L(z,u,x),T(y,u))) = (x * u) \ (K(z,(x * u) / (x * (y \ u))) * ((x * K(y,z)) * u))
    ]]></literal>
    <justification jstring="[para(10895(a,1),17849(a,1,3))].">
      <j1 rule="para" parents="10895 17849"/>
    </justification>
  </clause>

  <clause id="20921">
    <literal><![CDATA[
      L(a(x,K(y,z),u),x * (K(y,z) * u),K(L(z,u,x),y)) = (x * u) \ (K(z,(x * u) / (x * (y \ u))) * ((x * K(y,z)) * u))
    ]]></literal>
    <justification jstring="[hyper(17725,a,20920,a)].">
      <j1 rule="hyper" parents="17725 20920"/>
    </justification>
  </clause>

  <clause id="20923">
    <literal><![CDATA[
      L(a(x,K(y,z),u),x * (K(y,z) * u),K(z,L(y,u,x))) = (x * u) \ (K(z,(x * u) / (x * (y \ u))) * ((x * K(y,z)) * u))
    ]]></literal>
    <justification jstring="[para(10898(a,1),20921(a,1,3))].">
      <j1 rule="para" parents="10898 20921"/>
    </justification>
  </clause>

  <clause id="20924">
    <literal><![CDATA[
      L(a(x,K(y,z),u),x * (K(y,z) * u),K(z,L(y,u,x))) = ((x * u) \ (K(z,(x * u) / (x * (y \ u))) * ((x * K(y,z)) * u))) / 1
    ]]></literal>
    <justification jstring="[hyper(333,a,74,a,b,20923,a),flip(a)].">
      <j1 rule="hyper" parents="333 74 20923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20925">
    <literal><![CDATA[
      ((x * y) \ (K(z,(x * y) / (x * (u \ y))) * ((x * K(u,z)) * y))) / a(z,x * (K(u,z) * y),K(L(u,y,x),a(x,K(u,z),y))) = a(x,K(u,z),y)
    ]]></literal>
    <justification jstring="[hyper(123,a,20923,a(flip),b,14480,a)].">
      <j1 rule="hyper" parents="123 20923 14480"/>
    </justification>
  </clause>

  <clause id="20926">
    <literal><![CDATA[
      (x * y) \ (((x * K(z,u)) * y) * K(u,T((x * y) / (x * (z \ y)),(x * K(z,u)) * y))) = L(a(x,K(z,u),y),x * (K(z,u) * y),K(u,L(z,y,x)))
    ]]></literal>
    <justification jstring="[para(6390(a,2),20923(a,2,2)),flip(a)].">
      <j1 rule="para" parents="6390 20923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20927">
    <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(14947(a,1),17994(a,1,1))].">
      <j1 rule="para" parents="14947 17994"/>
    </justification>
  </clause>

  <clause id="20928">
    <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(6691,a,20927,a)].">
      <j1 rule="hyper" parents="6691 20927"/>
    </justification>
  </clause>

  <clause id="20929">
    <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(16572,a,20928,a)].">
      <j1 rule="hyper" parents="16572 20928"/>
    </justification>
  </clause>

  <clause id="20931">
    <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(9(a,1),20929(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 20929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20932">
    <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(333,a,16530,a(flip),b,20931,a),flip(a)].">
      <j1 rule="hyper" parents="333 16530 20931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20935">
    <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(12811(a,1),17995(a,1,1))].">
      <j1 rule="para" parents="12811 17995"/>
    </justification>
  </clause>

  <clause id="20936">
    <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(6691,a,20935,a)].">
      <j1 rule="hyper" parents="6691 20935"/>
    </justification>
  </clause>

  <clause id="20937">
    <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(16572,a,20936,a)].">
      <j1 rule="hyper" parents="16572 20936"/>
    </justification>
  </clause>

  <clause id="20939">
    <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(9(a,1),20937(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 20937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20941">
    <literal><![CDATA[
      (x \ T(x * (y * K(z,z \ u)),w)) \ ((y / z) * ((z \ u) \ u)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(w,T(K(u,z) * (y * x),y)) = v5
    ]]></literal>
    <justification jstring="[para(20939(a,2),16574(a,1))].">
      <j1 rule="para" parents="20939 16574"/>
    </justification>
  </clause>

  <clause id="20942">
    <literal><![CDATA[
      K(x,T(K(y,z) * (u * w),u)) = K(x,w * (K(z,y) * u))
    ]]></literal>
    <justification jstring="[hyper(20941,a,17015,a)].">
      <j1 rule="hyper" parents="20941 17015"/>
    </justification>
  </clause>

  <clause id="20943">
    <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(63,a,20932,a,b,20942,a)].">
      <j1 rule="hyper" parents="63 20932 20942"/>
    </justification>
  </clause>

  <clause id="20944">
    <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(6165(a,1),20943(a,1,2))].">
      <j1 rule="para" parents="6165 20943"/>
    </justification>
  </clause>

  <clause id="20945">
    <literal><![CDATA[
      K(x,y * (z * K(u \ w,u))) = K(x,y * (K(w,u) * z))
    ]]></literal>
    <justification jstring="[hyper(13429,a,20944,a)].">
      <j1 rule="hyper" parents="13429 20944"/>
    </justification>
  </clause>

  <clause id="20946">
    <literal><![CDATA[
      K(x,y * (z \ ((u \ w) * u))) = K(x,y * (K(w,u) * (z \ w)))
    ]]></literal>
    <justification jstring="[para(14579(a,1),20945(a,1,2,2))].">
      <j1 rule="para" parents="14579 20945"/>
    </justification>
  </clause>

  <clause id="20947">
    <literal><![CDATA[
      K(x,y * (z \ ((u \ w) * u))) = K(x,y * (z \ T(w,u)))
    ]]></literal>
    <justification jstring="[hyper(333,a,16363,a(flip),b,20946,a),flip(a)].">
      <j1 rule="hyper" parents="333 16363 20946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20948">
    <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(63,a,18028,a(flip),b,20947,a)].">
      <j1 rule="hyper" parents="63 18028 20947"/>
    </justification>
  </clause>

  <clause id="20949">
    <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(13484(a,1),20948(a,2,2,2,2))].">
      <j1 rule="para" parents="13484 20948"/>
    </justification>
  </clause>

  <clause id="20950">
    <literal><![CDATA[
      K(x,T(y * (z \ u),((z \ u) * y) \ u)) = K(x,y * (z \ T(u,z \ y)))
    ]]></literal>
    <justification jstring="[hyper(333,a,12832,a(flip),b,20949,a),flip(a)].">
      <j1 rule="hyper" parents="333 12832 20949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20951">
    <literal><![CDATA[
      K(x,T(y * (z \ u),y \ ((z \ u) \ u))) = K(x,y * (z \ T(u,z \ y)))
    ]]></literal>
    <justification jstring="[hyper(17688,a,20950,a)].">
      <j1 rule="hyper" parents="17688 20950"/>
    </justification>
  </clause>

  <clause id="20952">
    <literal><![CDATA[
      K(x,T(y * (z \ u),y \ T(z,u))) = K(x,y * (z \ T(u,z \ y)))
    ]]></literal>
    <justification jstring="[para(15083(a,1),20951(a,1,2))].">
      <j1 rule="para" parents="15083 20951"/>
    </justification>
  </clause>

  <clause id="20953">
    <literal><![CDATA[
      K(x,T(y * (z \ u),y \ z)) = K(x,y * (z \ T(u,z \ y)))
    ]]></literal>
    <justification jstring="[hyper(16572,a,20952,a)].">
      <j1 rule="hyper" parents="16572 20952"/>
    </justification>
  </clause>

  <clause id="20955">
    <literal><![CDATA[
      K(x,y * (z \ T(u,z \ y))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y * (z \ u),z * y)) = w
    ]]></literal>
    <justification jstring="[para(20953(a,1),15783(a,1))].">
      <j1 rule="para" parents="20953 15783"/>
    </justification>
  </clause>

  <clause id="20956">
    <literal><![CDATA[
      K(x,T(y * (z \ u),z * y)) = K(x,y * (z \ T(u,z * y)))
    ]]></literal>
    <justification jstring="[hyper(20955,a,18264,a)].">
      <j1 rule="hyper" parents="20955 18264"/>
    </justification>
  </clause>

  <clause id="20957">
    <literal><![CDATA[
      K(x,y * (z \ T(u,z * y))) = K(x,(u / z) * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,18974,a(flip),b,20956,a),flip(a)].">
      <j1 rule="hyper" parents="63 18974 20956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20958">
    <literal><![CDATA[
      K(x,(y / z) * T(L(z,u,w),z)) = K(x,y * (z \ L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,16207,a(flip),b,20957,a),flip(a)].">
      <j1 rule="hyper" parents="63 16207 20957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20959">
    <literal><![CDATA[
      K(x,(y / z) * L(z,u,w)) = K(x,y * (z \ L(z,u,w)))
    ]]></literal>
    <justification jstring="[para(180(a,1),20958(a,1,2,2))].">
      <j1 rule="para" parents="180 20958"/>
    </justification>
  </clause>

  <clause id="20960">
    <literal><![CDATA[
      T((K(L(x \ K(y,z),u,w),x) * K(x,x \ K(y,z))) * L(K(x,x \ K(y,z)),u,w),K(K(z,y) * x,x \ 1)) = K(K(z,y) * x,x \ 1)
    ]]></literal>
    <justification jstring="[para(4567(a,1),20918(a,1,1,1))].">
      <j1 rule="para" parents="4567 20918"/>
    </justification>
  </clause>

  <clause id="20961">
    <literal><![CDATA[
      K(x,y * (((z * K(u,K(w,v5))) * (v6 * K(z * K(u,K(w,v5)),v7))) * z)) = K(x,y * ((z * (K(u,K(w,v5)) * v6)) * T(z,v7)))
    ]]></literal>
    <justification jstring="[hyper(333,a,16517,a(flip),b,20919,a),flip(a)].">
      <j1 rule="hyper" parents="333 16517 20919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20963">
    <literal><![CDATA[
      K(x,y * (((z * K(u,K(w,v5))) * (v6 * K(z,v7))) * z)) = K(x,y * ((z * (K(u,K(w,v5)) * v6)) * T(z,v7)))
    ]]></literal>
    <justification jstring="[para(16347(a,1),20961(a,1,2,2,1,2,2))].">
      <j1 rule="para" parents="16347 20961"/>
    </justification>
  </clause>

  <clause id="20965">
    <literal><![CDATA[
      K(x,y * ((z * (K(u,K(w,v5)) * (v6 * K(z,v7)))) * z)) = K(x,y * ((z * (K(u,K(w,v5)) * v6)) * T(z,v7)))
    ]]></literal>
    <justification jstring="[para(20126(a,1),20963(a,1,2,2,1))].">
      <j1 rule="para" parents="20126 20963"/>
    </justification>
  </clause>

  <clause id="20966">
    <literal><![CDATA[
      K(x,y * (z * ((K(u,K(w,v5)) * (v6 * K(z,v7))) * z))) = K(x,y * ((z * (K(u,K(w,v5)) * v6)) * T(z,v7)))
    ]]></literal>
    <justification jstring="[hyper(12753,a,20965,a)].">
      <j1 rule="hyper" parents="12753 20965"/>
    </justification>
  </clause>

  <clause id="20967">
    <literal><![CDATA[
      K(x,y * (z * ((u * K(z,w)) * (z * K(v5,K(v6,v7)))))) = K(x,y * ((z * (K(v5,K(v6,v7)) * u)) * T(z,w)))
    ]]></literal>
    <justification jstring="[para(20149(a,1),20966(a,1,2,2,2))].">
      <j1 rule="para" parents="20149 20966"/>
    </justification>
  </clause>

  <clause id="20968">
    <literal><![CDATA[
      K(x,y * ((z * (K(u,K(w,v5)) * v6)) * T(z,v7))) = K(x,y * (z * (v6 * T(z * K(u,K(w,v5)),v7))))
    ]]></literal>
    <justification jstring="[para(16354(a,1),20967(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="16354 20967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20969">
    <literal><![CDATA[
      K(x,y * (z * (u * T(z * K(w,K(v5,v6)),u)))) = K(x,y * ((u * (z * K(w,K(v5,v6)))) * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,20498,a(flip),b,20968,a),flip(a)].">
      <j1 rule="hyper" parents="63 20498 20968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20970">
    <literal><![CDATA[
      K(x,y * ((z * (u * K(w,K(v5,v6)))) * u)) = K(x,y * (u * ((u * K(w,K(v5,v6))) * z)))
    ]]></literal>
    <justification jstring="[para(111(a,1),20969(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="111 20969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20971">
    <literal><![CDATA[
      K(x,y * ((z * (u * K(w,K(v5,v6)))) * u)) = K(x,y * (u * (u * (K(w,K(v5,v6)) * z))))
    ]]></literal>
    <justification jstring="[para(20126(a,1),20970(a,2,2,2,2))].">
      <j1 rule="para" parents="20126 20970"/>
    </justification>
  </clause>

  <clause id="20972">
    <literal><![CDATA[
      K(x,y * ((z * (u * K(w,K(v5,v6)))) * u)) = K(x,y * (u * (u * z)))
    ]]></literal>
    <justification jstring="[hyper(333,a,16767,a(flip),b,20971,a),flip(a)].">
      <j1 rule="hyper" parents="333 16767 20971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20973">
    <literal><![CDATA[
      K(x,y * ((z * u) * u)) = K(x,y * (u * (u * z)))
    ]]></literal>
    <justification jstring="[hyper(20168,a,20972,a)].">
      <j1 rule="hyper" parents="20168 20972"/>
    </justification>
  </clause>

  <clause id="20975">
    <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(6604(a,2),20973(a,2,2,2,2))].">
      <j1 rule="para" parents="6604 20973"/>
    </justification>
  </clause>

  <clause id="20976">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (K(z,u) * (w \ (1 / u))))) = K(x,y * ((w \ (1 / T(u,z))) * K(z,u)))
    ]]></literal>
    <justification jstring="[para(14049(a,1),20973(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="14049 20973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20977">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (K(z,u) * (w \ (1 / u))))) = K(x,y * (w \ (K(z,u) / T(u,z))))
    ]]></literal>
    <justification jstring="[para(14247(a,1),20976(a,2,2,2))].">
      <j1 rule="para" parents="14247 20976"/>
    </justification>
  </clause>

  <clause id="20978">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (K(z,u) * (w \ (1 / u))))) = K(x,y * (w \ (T(u,z) \ K(z,u))))
    ]]></literal>
    <justification jstring="[hyper(16753,a,20977,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="16753 20977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20979">
    <literal><![CDATA[
      K(x,y * (z \ (T(u,w) \ K(w,u)))) = K(x,y * (z \ (1 / u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,18852,a(flip),b,20978,a),flip(a)].">
      <j1 rule="hyper" parents="63 18852 20978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20981">
    <literal><![CDATA[
      K(x,y * (z \ (T(u,w) \ K(w,u)))) = K(x,y * (z \ (u \ 1)))
    ]]></literal>
    <justification jstring="[hyper(333,a,5019,a(flip),b,20979,a),flip(a)].">
      <j1 rule="hyper" parents="333 5019 20979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20982">
    <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(6524(a,1),20975(a,1,2,2,1))].">
      <j1 rule="para" parents="6524 20975"/>
    </justification>
  </clause>

  <clause id="20983">
    <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(63,a,18674,a(flip),b,20982,a),flip(a)].">
      <j1 rule="hyper" parents="63 18674 20982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20984">
    <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(3546(a,1),20983(a,2,2,2,2))].">
      <j1 rule="para" parents="3546 20983"/>
    </justification>
  </clause>

  <clause id="20985">
    <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(15232(a,2),20984(a,2,2,2,2))].">
      <j1 rule="para" parents="15232 20984"/>
    </justification>
  </clause>

  <clause id="20986">
    <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(7223(a,1),20985(a,2,2,2,2,1))].">
      <j1 rule="para" parents="7223 20985"/>
    </justification>
  </clause>

  <clause id="20987">
    <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(6604(a,1),20986(a,1,2,2,2))].">
      <j1 rule="para" parents="6604 20986"/>
    </justification>
  </clause>

  <clause id="20988">
    <literal><![CDATA[
      K(x,y * (z * T((T(u,w) * w) / u,v5))) = K(x,y * (z * T(w,v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,18852,a(flip),b,20987,a),flip(a)].">
      <j1 rule="hyper" parents="63 18852 20987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20990">
    <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(4320(a,2),20988(a,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4320 20988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20991">
    <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(333,a,18897,a(flip),b,20990,a),flip(a)].">
      <j1 rule="hyper" parents="333 18897 20990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20992">
    <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(333,a,20988,a(flip),b,20991,a),flip(a)].">
      <j1 rule="hyper" parents="333 20988 20991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20993">
    <literal><![CDATA[
      K(x,y * (z * T(u,w \ v5))) = K(x,y * (z * T(u,v5 * w)))
    ]]></literal>
    <justification jstring="[para(4239(a,1),20992(a,1,2,2,2,1))].">
      <j1 rule="para" parents="4239 20992"/>
    </justification>
  </clause>

  <clause id="20994">
    <literal><![CDATA[
      K(x,y * (z * T(u,w / v5))) = K(x,y * (z * T(u,w * v5)))
    ]]></literal>
    <justification jstring="[hyper(18216,a,20993,a)].">
      <j1 rule="hyper" parents="18216 20993"/>
    </justification>
  </clause>

  <clause id="20995">
    <literal><![CDATA[
      T(x,y * (z * T(u,w \ v5))) = T(x,y * (z * T(u,v5 * w)))
    ]]></literal>
    <justification jstring="[hyper(124,a,20993,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 20993 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20996">
    <literal><![CDATA[
      T(x,y * (z * T(u,w / v5))) = T(x,y * (z * T(u,w * v5)))
    ]]></literal>
    <justification jstring="[hyper(124,a,20994,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 20994 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20997">
    <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(63,a,16761,a,b,20994,a)].">
      <j1 rule="hyper" parents="63 16761 20994"/>
    </justification>
  </clause>

  <clause id="20998">
    <literal><![CDATA[
      T(x,y * ((z \ 1) * T(u,y * z))) = T(x,(u * (z \ 1)) * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,19821,a(flip),b,20995,a),flip(a)].">
      <j1 rule="hyper" parents="63 19821 20995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20999">
    <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(20996(a,1),18282(a,1,2,2))].">
      <j1 rule="para" parents="20996 18282"/>
    </justification>
  </clause>

  <clause id="21000">
    <literal><![CDATA[
      K(x,y * (T(z,T(u \ w,u)) * v5)) = K(x,y * (T(z,w * u) * v5))
    ]]></literal>
    <justification jstring="[hyper(333,a,16760,a(flip),b,20997,a),flip(a)].">
      <j1 rule="hyper" parents="333 16760 20997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21001">
    <literal><![CDATA[
      K(x,y * (T(z,u \ w) * v5)) = K(x,y * (T(z,w * u) * v5))
    ]]></literal>
    <justification jstring="[hyper(16509,a,21000,a)].">
      <j1 rule="hyper" parents="16509 21000"/>
    </justification>
  </clause>

  <clause id="21002">
    <literal><![CDATA[
      K(x,y * (T(z,u * w) * (u / w))) = K(x,y * (T(w \ u,w) * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,18993,a(flip),b,21001,a),flip(a)].">
      <j1 rule="hyper" parents="63 18993 21001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21003">
    <literal><![CDATA[
      K(x,y * (T(z,u * w) * (u / w))) = K(x,y * ((u / w) * z))
    ]]></literal>
    <justification jstring="[hyper(333,a,18846,a(flip),b,21002,a),flip(a)].">
      <j1 rule="hyper" parents="333 18846 21002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21004">
    <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(20998(a,1),20999(a,1,2,2))].">
      <j1 rule="para" parents="20998 20999"/>
    </justification>
  </clause>

  <clause id="21005">
    <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(63,a,19150,a(flip),b,21004,a)].">
      <j1 rule="hyper" parents="63 19150 21004"/>
    </justification>
  </clause>

  <clause id="21007">
    <literal><![CDATA[
      T((K(x \ K(y,z),L(x,u,w)) * K(x,x \ K(y,z))) * L(K(x,x \ K(y,z)),u,w),K(K(z,y) * x,x \ 1)) = K(K(z,y) * x,x \ 1)
    ]]></literal>
    <justification jstring="[para(10898(a,1),20960(a,1,1,1,1))].">
      <j1 rule="para" parents="10898 20960"/>
    </justification>
  </clause>

  <clause id="21008">
    <literal><![CDATA[
      T(a(x \ K(y,z),u,K(w,x)) * L(K(x,x \ K(y,z)),u,w),K(K(z,y) * x,x \ 1)) = K(K(z,y) * x,x \ 1)
    ]]></literal>
    <justification jstring="[para(13750(a,1),21007(a,1,1,1))].">
      <j1 rule="para" parents="13750 21007"/>
    </justification>
  </clause>

  <clause id="21009">
    <literal><![CDATA[
      T(a(K(x,y),z,K(u,w)) * L(K(w,w \ K(x,y)),z,u),K(K(y,x) * w,w \ 1)) = K(K(y,x) * w,w \ 1)
    ]]></literal>
    <justification jstring="[para(13800(a,1),21008(a,1,1,1))].">
      <j1 rule="para" parents="13800 21008"/>
    </justification>
  </clause>

  <clause id="21010">
    <literal><![CDATA[
      T(1 * L(K(x,x \ K(y,z)),u,w),K(K(z,y) * x,x \ 1)) = K(K(z,y) * x,x \ 1)
    ]]></literal>
    <justification jstring="[para(17526(a,1),21009(a,1,1,1))].">
      <j1 rule="para" parents="17526 21009"/>
    </justification>
  </clause>

  <clause id="21011">
    <literal><![CDATA[
      T(1 * K(x,L(x \ K(y,z),u,w)),K(K(z,y) * x,x \ 1)) = K(K(z,y) * x,x \ 1)
    ]]></literal>
    <justification jstring="[para(9457(a,1),21010(a,1,1,2))].">
      <j1 rule="para" parents="9457 21010"/>
    </justification>
  </clause>

  <clause id="21013">
    <literal><![CDATA[
      T(K(x,L(x \ K(y,z),u,w)),K(K(z,y) * x,x \ 1)) = K(K(z,y) * x,x \ 1)
    ]]></literal>
    <justification jstring="[para(7(a,1),21011(a,1,1))].">
      <j1 rule="para" parents="7 21011"/>
    </justification>
  </clause>

  <clause id="21014">
    <literal><![CDATA[
      K(x,L(x \ K(y,z),u,w)) = K(K(z,y) * x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(15512,a,21013,a)].">
      <j1 rule="hyper" parents="15512 21013"/>
    </justification>
  </clause>

  <clause id="21015">
    <literal><![CDATA[
      K(x,L(x \ K(y,z),u,w)) = K(x,x \ K(y,z))
    ]]></literal>
    <justification jstring="[hyper(333,a,15496,a(flip),b,21014,a),flip(a)].">
      <j1 rule="hyper" parents="333 15496 21014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21017">
    <literal><![CDATA[
      K(x,L(y \ K(z,u),w,v5) * (K(y,y \ K(z,u)) * v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,T(L(y \ K(z,u),w,v5),y) * v6) = v7
    ]]></literal>
    <justification jstring="[para(21015(a,1),18828(a,1,2,2,1))].">
      <j1 rule="para" parents="21015 18828"/>
    </justification>
  </clause>

  <clause id="21018">
    <literal><![CDATA[
      K(x,L(y \ K(z,u),w,v5) * (K(y,K(z,u)) * v6)) = K(x,T(L(y \ K(z,u),w,v5),y) * v6)
    ]]></literal>
    <justification jstring="[hyper(21017,a,12798,a),flip(a)].">
      <j1 rule="hyper" parents="21017 12798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21019">
    <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(16489,a,21018,a),flip(a)].">
      <j1 rule="hyper" parents="16489 21018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21021">
    <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(63,a,14978,a(flip),b,21019,a)].">
      <j1 rule="hyper" parents="63 14978 21019"/>
    </justification>
  </clause>

  <clause id="21022">
    <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(63,a,19230,a,b,21021,a)].">
      <j1 rule="hyper" parents="63 19230 21021"/>
    </justification>
  </clause>

  <clause id="21023">
    <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(333,a,20906,a(flip),b,21022,a),flip(a)].">
      <j1 rule="hyper" parents="333 20906 21022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21025">
    <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(18864(a,1),15836(a,1,1))].">
      <j1 rule="para" parents="18864 15836"/>
    </justification>
  </clause>

  <clause id="21026">
    <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(16333(a,1),18382(a,1,1))].">
      <j1 rule="para" parents="16333 18382"/>
    </justification>
  </clause>

  <clause id="21028">
    <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(18874(a,1),21026(a,1,1))].">
      <j1 rule="para" parents="18874 21026"/>
    </justification>
  </clause>

  <clause id="21029">
    <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(63,a,20562,a(flip),b,21028,a)].">
      <j1 rule="hyper" parents="63 20562 21028"/>
    </justification>
  </clause>

  <clause id="21030">
    <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(63,a,20304,a,b,21029,a)].">
      <j1 rule="hyper" parents="63 20304 21029"/>
    </justification>
  </clause>

  <clause id="21031">
    <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(15467,a,21030,a)].">
      <j1 rule="hyper" parents="15467 21030"/>
    </justification>
  </clause>

  <clause id="21032">
    <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(16569,a,21031,a),flip(a)].">
      <j1 rule="hyper" parents="16569 21031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21034">
    <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(333,a,15435,a(flip),b,21032,a),flip(a)].">
      <j1 rule="hyper" parents="333 15435 21032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21035">
    <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(18381(a,1),21034(a,1,2))].">
      <j1 rule="para" parents="18381 21034"/>
    </justification>
  </clause>

  <clause id="21036">
    <literal><![CDATA[
      K(x,y * T(z,T(u / w,v5))) = K(x,y * T(z,u * w))
    ]]></literal>
    <justification jstring="[hyper(13429,a,21035,a)].">
      <j1 rule="hyper" parents="13429 21035"/>
    </justification>
  </clause>

  <clause id="21037">
    <literal><![CDATA[
      K(x,y * T(z,u \ w)) = K(x,y * T(z,w * u))
    ]]></literal>
    <justification jstring="[para(113(a,1),21036(a,1,2,2,2))].">
      <j1 rule="para" parents="113 21036"/>
    </justification>
  </clause>

  <clause id="21038">
    <literal><![CDATA[
      K(x,y * T(z,u \ (w \ v5))) = K(x,y * T(z,v5 * (u * w)))
    ]]></literal>
    <justification jstring="[hyper(20612,a,21037,a)].">
      <j1 rule="hyper" parents="20612 21037"/>
    </justification>
  </clause>

  <clause id="21039">
    <literal><![CDATA[
      K(x,y * T(z,(u \ w) * v5)) = K(x,y * T(z,w * (v5 * u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,21037,a(flip),b,21038,a)].">
      <j1 rule="hyper" parents="63 21037 21038"/>
    </justification>
  </clause>

  <clause id="21040">
    <literal><![CDATA[
      K(T(x,y),(z \ u) * T(w,u * (x * z))) = K(T(x,y),w * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,18755,a(flip),b,21039,a),flip(a)].">
      <j1 rule="hyper" parents="63 18755 21039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21041">
    <literal><![CDATA[
      K(x,T((y \ z) * T(u,z * (x * y)),w)) = K(T(x,w),u * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(6695,a,21040,a)].">
      <j1 rule="hyper" parents="6695 21040"/>
    </justification>
  </clause>

  <clause id="21042">
    <literal><![CDATA[
      K(x,T(y,z * (x * u)) * (u \ z)) = K(T(x,z * u),y * (u \ z))
    ]]></literal>
    <justification jstring="[hyper(15414,a,21041,a)].">
      <j1 rule="hyper" parents="15414 21041"/>
    </justification>
  </clause>

  <clause id="21043">
    <literal><![CDATA[
      K(x,T(y,z * (x * u)) * (u \ z)) = K(x,T(y * (u \ z),z * u))
    ]]></literal>
    <justification jstring="[hyper(333,a,6370,a(flip),b,21042,a),flip(a)].">
      <j1 rule="hyper" parents="333 6370 21042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21044">
    <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(21043(a,2),15415(a,1))].">
      <j1 rule="para" parents="21043 15415"/>
    </justification>
  </clause>

  <clause id="21045">
    <literal><![CDATA[
      ((x * y) \ (K(z,(x * y) / (x * (u \ y))) * ((x * K(u,z)) * y))) / a(z,x * (K(u,z) * y),a(L(u,y,x),K(u,z),K(y,x))) = a(x,K(u,z),y)
    ]]></literal>
    <justification jstring="[para(13732(a,2),20925(a,1,2,3))].">
      <j1 rule="para" parents="13732 20925"/>
    </justification>
  </clause>

  <clause id="21046">
    <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(6691,a,21025,a)].">
      <j1 rule="hyper" parents="6691 21025"/>
    </justification>
  </clause>

  <clause id="21047">
    <literal><![CDATA[
      ((x * y) \ (K(z,(x * y) / (x * (u \ y))) * ((x * K(u,z)) * y))) / a(z,x * (K(u,z) * y),1) = a(x,K(u,z),y)
    ]]></literal>
    <justification jstring="[para(19291(a,1),21045(a,1,2,3))].">
      <j1 rule="para" parents="19291 21045"/>
    </justification>
  </clause>

  <clause id="21048">
    <literal><![CDATA[
      ((x * y) \ (K(z,(x * y) / (x * (u \ y))) * ((x * K(u,z)) * y))) / 1 = a(x,K(u,z),y)
    ]]></literal>
    <justification jstring="[para(380(a,1),21047(a,1,2))].">
      <j1 rule="para" parents="380 21047"/>
    </justification>
  </clause>

  <clause id="21050">
    <literal><![CDATA[
      L(a(x,K(y,z),u),x * (K(y,z) * u),K(z,L(y,u,x))) = a(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,20924,a,b,21048,a)].">
      <j1 rule="hyper" parents="63 20924 21048"/>
    </justification>
  </clause>

  <clause id="21052">
    <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(16572,a,21046,a)].">
      <j1 rule="hyper" parents="16572 21046"/>
    </justification>
  </clause>

  <clause id="21054">
    <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(9(a,1),21052(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 21052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21055">
    <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(333,a,16552,a(flip),b,21054,a),flip(a)].">
      <j1 rule="hyper" parents="333 16552 21054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21058">
    <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(333,a,20942,a(flip),b,21055,a),flip(a)].">
      <j1 rule="hyper" parents="333 20942 21055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21059">
    <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(15651(a,1),21058(a,1,2))].">
      <j1 rule="para" parents="15651 21058"/>
    </justification>
  </clause>

  <clause id="21060">
    <literal><![CDATA[
      K(x,y * ((z * K(u,w)) * v5)) = K(x,y * (K(u,w) * (z * v5)))
    ]]></literal>
    <justification jstring="[hyper(13429,a,21059,a)].">
      <j1 rule="hyper" parents="13429 21059"/>
    </justification>
  </clause>

  <clause id="21061">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (w * ((v5 \ w) / w)))) = K(x,y * (w / (K(u,z) * v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,19935,a(flip),b,21060,a),flip(a)].">
      <j1 rule="hyper" parents="63 19935 21060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21062">
    <literal><![CDATA[
      K(x,y * (K(z,u) * ((w * z) * v5))) = K(x,y * ((w * T(z,u)) * v5))
    ]]></literal>
    <justification jstring="[para(5984(a,1),21060(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5984 21060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21063">
    <literal><![CDATA[
      K(x,y * ((z * T(u,x)) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * ((z * u) * w)) = v5
    ]]></literal>
    <justification jstring="[para(21062(a,1),18830(a,1))].">
      <j1 rule="para" parents="21062 18830"/>
    </justification>
  </clause>

  <clause id="21064">
    <literal><![CDATA[
      K(x,K(y,z) * ((u * (u \ (w \ u))) * v5)) = K(x,(w \ (u * K(z,y))) * v5)
    ]]></literal>
    <justification jstring="[hyper(21063,a,19789,a)].">
      <j1 rule="hyper" parents="21063 19789"/>
    </justification>
  </clause>

  <clause id="21065">
    <literal><![CDATA[
      K(x,y * (K(z,u) * T(w \ v5,v5))) = K(x,y * (v5 / (K(u,z) * w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,18839,a(flip),b,21061,a)].">
      <j1 rule="hyper" parents="63 18839 21061"/>
    </justification>
  </clause>

  <clause id="21066">
    <literal><![CDATA[
      K(x,y * (z / (K(u,w) * v5))) = K(x,y * (K(w,u) * (z / v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,16864,a(flip),b,21065,a),flip(a)].">
      <j1 rule="hyper" parents="63 16864 21065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21067">
    <literal><![CDATA[
      K(x,y * ((K(z,u) * w) / v5)) = K(x,y * (K(z,u) * (w / v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,18738,a,b,21066,a)].">
      <j1 rule="hyper" parents="63 18738 21066"/>
    </justification>
  </clause>

  <clause id="21068">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (w / T(v5,w)))) = K(x,y * (v5 \ (K(z,u) * w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,19775,a(flip),b,21067,a),flip(a)].">
      <j1 rule="hyper" parents="63 19775 21067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21069">
    <literal><![CDATA[
      K(x,y * (z \ (K(u,w) * v5))) = K(x,y * (K(u,w) * (z \ v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,18362,a(flip),b,21068,a),flip(a)].">
      <j1 rule="hyper" parents="63 18362 21068"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21070">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (w \ (v5 \ 1)))) = K(x,y * (w \ (v5 \ K(z,u))))
    ]]></literal>
    <justification jstring="[hyper(16705,a,21069,a),flip(a)].">
      <j1 rule="hyper" parents="16705 21069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21071">
    <literal><![CDATA[
      K(x,y * (z \ (u * K(w,v5)))) = K(x,y * (K(w,v5) * (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(16704,a,21069,a)].">
      <j1 rule="hyper" parents="16704 21069"/>
    </justification>
  </clause>

  <clause id="21072">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (w \ (v5 \ 1)))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (w \ (v5 \ K(z,u)))) = v6
    ]]></literal>
    <justification jstring="[para(21069(a,1),16705(a,1))].">
      <j1 rule="para" parents="21069 16705"/>
    </justification>
  </clause>

  <clause id="21073">
    <literal><![CDATA[
      K(x,y * (z \ (u * (w * K(v5,v6))))) = K(x,y * (K(v5,v6) * (z \ (u * w))))
    ]]></literal>
    <justification jstring="[hyper(63,a,20011,a(flip),b,21071,a)].">
      <j1 rule="hyper" parents="63 20011 21071"/>
    </justification>
  </clause>

  <clause id="21074">
    <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(63,a,18570,a(flip),b,21071,a),flip(a)].">
      <j1 rule="hyper" parents="63 18570 21071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21075">
    <literal><![CDATA[
      K(x,y * (z \ (u \ K(w,w * v5)))) = K(x,y * (K(w,v5) * (z \ (u \ 1))))
    ]]></literal>
    <justification jstring="[hyper(63,a,12768,a(flip),b,21070,a),flip(a)].">
      <j1 rule="hyper" parents="63 12768 21070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21076">
    <literal><![CDATA[
      K(x,y * ((T(z,u) \ u) \ (w \ K(u,z)))) = K(x,y * ((z \ u) \ (w \ 1)))
    ]]></literal>
    <justification jstring="[para(12912(a,1),21070(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12912 21070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21077">
    <literal><![CDATA[
      K(x,(y \ (z * K(u,w))) * v5) = K(x,K(w,u) * ((y \ z) * v5))
    ]]></literal>
    <justification jstring="[para(10(a,1),21064(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10 21064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21078">
    <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(63,a,20188,a,b,21077,a),flip(a)].">
      <j1 rule="hyper" parents="63 20188 21077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21080">
    <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(63,a,20699,a,b,21073,a)].">
      <j1 rule="hyper" parents="63 20699 21073"/>
    </justification>
  </clause>

  <clause id="21081">
    <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(21076(a,1),19555(a,1))].">
      <j1 rule="para" parents="21076 19555"/>
    </justification>
  </clause>

  <clause id="21082">
    <literal><![CDATA[
      K(x,y * (z \ (u \ K(w,w * v5)))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z \ (u \ K(w,v5)))) = v6
    ]]></literal>
    <justification jstring="[para(21075(a,2),21072(a,1))].">
      <j1 rule="para" parents="21075 21072"/>
    </justification>
  </clause>

  <clause id="21083">
    <literal><![CDATA[
      K(x,y * (z \ (T(u,w) / (u / (w \ 1))))) = K(x,y * (z \ (T(w,u) \ K(u,w))))
    ]]></literal>
    <justification jstring="[hyper(21082,a,19561,a),flip(a)].">
      <j1 rule="hyper" parents="21082 19561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21084">
    <literal><![CDATA[
      K(x,y * (z \ (T(u,w) / (u / (w \ 1))))) = K(x,y * (z \ (w \ 1)))
    ]]></literal>
    <justification jstring="[hyper(333,a,20981,a(flip),b,21083,a),flip(a)].">
      <j1 rule="hyper" parents="333 20981 21083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21086">
    <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(19016(a,1),21074(a,1,2,2,2))].">
      <j1 rule="para" parents="19016 21074"/>
    </justification>
  </clause>

  <clause id="21087">
    <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(20392(a,1),21086(a,1,2,2))].">
      <j1 rule="para" parents="20392 21086"/>
    </justification>
  </clause>

  <clause id="21088">
    <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(18321,a,21087,a),flip(a)].">
      <j1 rule="hyper" parents="18321 21087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21089">
    <literal><![CDATA[
      K(x,y * L(z,K(u,w),v5)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(16396,a,21088,a),flip(a)].">
      <j1 rule="hyper" parents="16396 21088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21090">
    <literal><![CDATA[
      K(x,y * L(z,K(u,w),v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = v6
    ]]></literal>
    <justification jstring="[para(21088(a,1),16396(a,1))].">
      <j1 rule="para" parents="21088 16396"/>
    </justification>
  </clause>

  <clause id="21092">
    <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(577(a,1),21089(a,1,2,2))].">
      <j1 rule="para" parents="577 21089"/>
    </justification>
  </clause>

  <clause id="21093">
    <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(6036(a,1),21090(a,1,2))].">
      <j1 rule="para" parents="6036 21090"/>
    </justification>
  </clause>

  <clause id="21094">
    <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(4567(a,1),21092(a,2,2,2,1))].">
      <j1 rule="para" parents="4567 21092"/>
    </justification>
  </clause>

  <clause id="21095">
    <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(63,a,18496,a,b,21094,a)].">
      <j1 rule="hyper" parents="63 18496 21094"/>
    </justification>
  </clause>

  <clause id="21096">
    <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(4567(a,1),21095(a,1,2,2,1,1))].">
      <j1 rule="para" parents="4567 21095"/>
    </justification>
  </clause>

  <clause id="21097">
    <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(63,a,18771,a(flip),b,21096,a)].">
      <j1 rule="hyper" parents="63 18771 21096"/>
    </justification>
  </clause>

  <clause id="21098">
    <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(15607,a,21097,a),flip(a)].">
      <j1 rule="hyper" parents="15607 21097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21099">
    <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(9(a,1),21098(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="9 21098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21100">
    <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(20252(a,1),21080(a,1,2,2,2))].">
      <j1 rule="para" parents="20252 21080"/>
    </justification>
  </clause>

  <clause id="21101">
    <literal><![CDATA[
      K(x,y * (z \ (u * (K(w,v5) * v6)))) = K(x,y * (K(w,v5) * (z \ (u * v6))))
    ]]></literal>
    <justification jstring="[hyper(17874,a,21100,a)].">
      <j1 rule="hyper" parents="17874 21100"/>
    </justification>
  </clause>

  <clause id="21102">
    <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(63,a,21099,a(flip),b,21101,a),flip(a)].">
      <j1 rule="hyper" parents="63 21099 21101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21103">
    <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(18(a,2),21102(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="18 21102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21104">
    <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(21093,a,21103,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="21093 21103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21105">
    <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(17982,a,21104,a)].">
      <j1 rule="hyper" parents="17982 21104"/>
    </justification>
  </clause>

  <clause id="21106">
    <literal><![CDATA[
      K(x,y * L(y \ 1,z,u)) = a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,21023,a(flip),b,21105,a),flip(a)].">
      <j1 rule="hyper" parents="63 21023 21105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21107">
    <literal><![CDATA[
      K(x,y * L(((z * u) / z) \ z,w,v5)) = K(x,y * L(z / u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,19247,a(flip),b,21105,a)].">
      <j1 rule="hyper" parents="63 19247 21105"/>
    </justification>
  </clause>

  <clause id="21108">
    <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(63,a,20694,a(flip),b,21106,a)].">
      <j1 rule="hyper" parents="63 20694 21106"/>
    </justification>
  </clause>

  <clause id="21109">
    <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(15383,a,21107,a),flip(a)].">
      <j1 rule="hyper" parents="15383 21107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21111">
    <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(6370(a,1),21108(a,2,3))].">
      <j1 rule="para" parents="6370 21108"/>
    </justification>
  </clause>

  <clause id="21112">
    <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(4968(a,1),21111(a,2,3))].">
      <j1 rule="para" parents="4968 21111"/>
    </justification>
  </clause>

  <clause id="21113">
    <literal><![CDATA[
      K(x,L(y / ((y \ z) * y),u,w) / (z \ y)) = a(x,u,K(y \ z,w))
    ]]></literal>
    <justification jstring="[para(6431(a,1),21112(a,2,3))].">
      <j1 rule="para" parents="6431 21112"/>
    </justification>
  </clause>

  <clause id="21114">
    <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(63,a,18095,a(flip),b,21109,a)].">
      <j1 rule="hyper" parents="63 18095 21109"/>
    </justification>
  </clause>

  <clause id="21115">
    <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(63,a,18041,a(flip),b,21114,a)].">
      <j1 rule="hyper" parents="63 18041 21114"/>
    </justification>
  </clause>

  <clause id="21116">
    <literal><![CDATA[
      K(x,y * L(z / (y * z),u,w)) = K(x,y * L((z * y) \ z,u,w))
    ]]></literal>
    <justification jstring="[para(11(a,1),21115(a,1,2,1))].">
      <j1 rule="para" parents="11 21115"/>
    </justification>
  </clause>

  <clause id="21117">
    <literal><![CDATA[
      K(x,L(y / (z * y),u,w) * z) = K(x,z * L((y * z) \ y,u,w))
    ]]></literal>
    <justification jstring="[hyper(14226,a,21116,a)].">
      <j1 rule="hyper" parents="14226 21116"/>
    </justification>
  </clause>

  <clause id="21118">
    <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(63,a,17981,a(flip),b,21078,a),flip(a)].">
      <j1 rule="hyper" parents="63 17981 21078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21119">
    <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(63,a,19104,a(flip),b,21118,a)].">
      <j1 rule="hyper" parents="63 19104 21118"/>
    </justification>
  </clause>

  <clause id="21120">
    <literal><![CDATA[
      K(x,(y \ T(z,K(u,w) * v5)) * v6) = K(x,(y \ ((v5 * z) / v5)) * v6)
    ]]></literal>
    <justification jstring="[para(4558(a,1),21119(a,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4558 21119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21121">
    <literal><![CDATA[
      K(x,(y \ T(z,K(u,w) * v5)) * v6) = K(x,(y \ T(z,v5)) * v6)
    ]]></literal>
    <justification jstring="[hyper(333,a,18095,a(flip),b,21120,a),flip(a)].">
      <j1 rule="hyper" parents="333 18095 21120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21122">
    <literal><![CDATA[
      K(x,(y \ T(z,u * K(w,v5))) * v6) = K(x,(y \ T(z,u)) * v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,16301,a(flip),b,21121,a)].">
      <j1 rule="hyper" parents="63 16301 21121"/>
    </justification>
  </clause>

  <clause id="21124">
    <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(13247(a,1),18947(a,1,1,1))].">
      <j1 rule="para" parents="13247 18947"/>
    </justification>
  </clause>

  <clause id="21125">
    <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(13141(a,1),21124(a,1,1,2,3))].">
      <j1 rule="para" parents="13141 21124"/>
    </justification>
  </clause>

  <clause id="21126">
    <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(19729(a,1),21125(a,1,1,2))].">
      <j1 rule="para" parents="19729 21125"/>
    </justification>
  </clause>

  <clause id="21127">
    <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(63,a,19831,a(flip),b,21126,a)].">
      <j1 rule="hyper" parents="63 19831 21126"/>
    </justification>
  </clause>

  <clause id="21128">
    <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(333,a,18946,a(flip),b,21127,a),flip(a)].">
      <j1 rule="hyper" parents="333 18946 21127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21130">
    <literal><![CDATA[
      (x * y) \ (((x * K(z,u)) * y) * K(u,T((x * y) / (x * (z \ y)),(x * K(z,u)) * y))) = a(x,K(z,u),y)
    ]]></literal>
    <justification jstring="[hyper(333,a,21050,a(flip),b,20926,a),flip(a)].">
      <j1 rule="hyper" parents="333 21050 20926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21131">
    <literal><![CDATA[
      (x * y) \ (((x * K(z,u)) * y) * K(u,T((x * y) / (x * (z \ y)),x * y))) = a(x,K(z,u),y)
    ]]></literal>
    <justification jstring="[para(8135(a,1),21130(a,1,2,2))].">
      <j1 rule="para" parents="8135 21130"/>
    </justification>
  </clause>

  <clause id="21132">
    <literal><![CDATA[
      (x * y) \ (((x * K(z,u)) * y) * K(u,(x * (z \ y)) \ (x * y))) = a(x,K(z,u),y)
    ]]></literal>
    <justification jstring="[para(6368(a,1),21131(a,1,2,2))].">
      <j1 rule="para" parents="6368 21131"/>
    </justification>
  </clause>

  <clause id="21135">
    <literal><![CDATA[
      (x * y) \ (((x * K(z,u)) * y) * K(L(u,y,x),T(z,y))) = a(x,K(z,u),y)
    ]]></literal>
    <justification jstring="[para(10895(a,1),21132(a,1,2,2))].">
      <j1 rule="para" parents="10895 21132"/>
    </justification>
  </clause>

  <clause id="21136">
    <literal><![CDATA[
      (x * y) \ (((K(z,u) * x) * y) * K(L(T(u,x),y,x),T(z,y))) = a(x,K(z,T(u,x)),y)
    ]]></literal>
    <justification jstring="[para(6390(a,1),21135(a,1,2,1,1))].">
      <j1 rule="para" parents="6390 21135"/>
    </justification>
  </clause>

  <clause id="21137">
    <literal><![CDATA[
      (x * y) \ (((K(z,u) * x) * y) * K(L(u,y,x),T(T(z,y),x))) = a(x,K(z,T(u,x)),y)
    ]]></literal>
    <justification jstring="[para(6429(a,1),21136(a,1,2,2))].">
      <j1 rule="para" parents="6429 21136"/>
    </justification>
  </clause>

  <clause id="21138">
    <literal><![CDATA[
      (x * y) \ (((K(z,u) * x) * y) * K(L(u,y,x),T(T(z,y),x))) = a(x,K(z,u),y)
    ]]></literal>
    <justification jstring="[hyper(333,a,20132,a(flip),b,21137,a),flip(a)].">
      <j1 rule="hyper" parents="333 20132 21137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21140">
    <literal><![CDATA[
      (x * y) \ (((K(z,u) * x) * y) * K(u,L(T(T(z,y),x),y,x))) = a(x,K(z,u),y)
    ]]></literal>
    <justification jstring="[para(10898(a,1),21138(a,1,2,2))].">
      <j1 rule="para" parents="10898 21138"/>
    </justification>
  </clause>

  <clause id="21141">
    <literal><![CDATA[
      (x * y) \ ((K(z,u) * x) * (y * K(u,T(T(z,y),x)))) = a(x,K(z,u),y)
    ]]></literal>
    <justification jstring="[para(19574(a,1),21140(a,1,2))].">
      <j1 rule="para" parents="19574 21140"/>
    </justification>
  </clause>

  <clause id="21142">
    <literal><![CDATA[
      (x * y) \ ((K(z,u) * x) * (K(u,T(z,x)) * y)) = a(x,K(z,u),y)
    ]]></literal>
    <justification jstring="[para(6494(a,1),21141(a,1,2,2))].">
      <j1 rule="para" parents="6494 21141"/>
    </justification>
  </clause>

  <clause id="21143">
    <literal><![CDATA[
      (x * y) \ ((x * K(z,u)) * (K(u,z) * y)) = a(x,K(z,u),y)
    ]]></literal>
    <justification jstring="[para(10018(a,1),21142(a,1,2))].">
      <j1 rule="para" parents="10018 21142"/>
    </justification>
  </clause>

  <clause id="21144">
    <literal><![CDATA[
      a(x,K(y,z),K(z,y) * u) = a(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(4583,a,21143,a)].">
      <j1 rule="hyper" parents="4583 21143"/>
    </justification>
  </clause>

  <clause id="21145">
    <literal><![CDATA[
      ((K(x,y) * (K(y,x) * z)) * u) \ (R(u,K(x,y),K(y,x) * z) * T(K(x,y) * (K(y,x) * z),u)) = a(u,K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,9128,a(flip),b,21144,a)].">
      <j1 rule="hyper" parents="63 9128 21144"/>
    </justification>
  </clause>

  <clause id="21146">
    <literal><![CDATA[
      (x * y) \ (R(y,K(z,u),K(u,z) * x) * T(K(z,u) * (K(u,z) * x),y)) = a(y,K(z,u),x)
    ]]></literal>
    <justification jstring="[para(4558(a,1),21145(a,1,1,1))].">
      <j1 rule="para" parents="4558 21145"/>
    </justification>
  </clause>

  <clause id="21147">
    <literal><![CDATA[
      (x * y) \ (L(y,K(z,u),K(u,z) * x) * T(K(z,u) * (K(u,z) * x),y)) = a(y,K(z,u),x)
    ]]></literal>
    <justification jstring="[para(20213(a,1),21146(a,1,2,1))].">
      <j1 rule="para" parents="20213 21146"/>
    </justification>
  </clause>

  <clause id="21148">
    <literal><![CDATA[
      (x * y) \ (L(y,K(z,u),K(u,z) * x) * T(x,y)) = a(y,K(z,u),x)
    ]]></literal>
    <justification jstring="[para(4558(a,1),21147(a,1,2,2,1))].">
      <j1 rule="para" parents="4558 21147"/>
    </justification>
  </clause>

  <clause id="21149">
    <literal><![CDATA[
      (x * y) \ (x * L(y,K(z,u),K(u,z) * x)) = a(y,K(z,u),x)
    ]]></literal>
    <justification jstring="[para(19310(a,1),21148(a,1,2))].">
      <j1 rule="para" parents="19310 21148"/>
    </justification>
  </clause>

  <clause id="21150">
    <literal><![CDATA[
      (x * y) \ ((x * K(z,u)) * (K(u,z) * y)) = a(y,K(u,z),x)
    ]]></literal>
    <justification jstring="[para(17681(a,1),21149(a,1,2))].">
      <j1 rule="para" parents="17681 21149"/>
    </justification>
  </clause>

  <clause id="21151">
    <literal><![CDATA[
      a(x,K(y,z),u) = a(u,K(z,y),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,21143,a(flip),b,21150,a)].">
      <j1 rule="hyper" parents="63 21143 21150"/>
    </justification>
  </clause>

  <clause id="21152">
    <literal><![CDATA[
      a(T(x,y),K(z,u),w) = a(w,K(u,z),x)
    ]]></literal>
    <justification jstring="[hyper(333,a,20316,a(flip),b,21151,a),flip(a)].">
      <j1 rule="hyper" parents="333 20316 21151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21153">
    <literal><![CDATA[
      a(x,K(y,z),u) / (w \ T(a(u,K(z,y),x),w)) = T(w,a(u,K(z,y),x))
    ]]></literal>
    <justification jstring="[hyper(123,a,21151,a,b,3650,a)].">
      <j1 rule="hyper" parents="123 21151 3650"/>
    </justification>
  </clause>

  <clause id="21154">
    <literal><![CDATA[
      T(a(x,K(y,z),u),w) = a(u,K(z,y),x)
    ]]></literal>
    <justification jstring="[hyper(37,a,19312,a(flip),b,21153,a)].">
      <j1 rule="hyper" parents="37 19312 21153"/>
    </justification>
  </clause>

  <clause id="21155">
    <literal><![CDATA[
      L(a(x,K(y,z),u),w,K(v5,v6)) = a(u,K(z,y),x)
    ]]></literal>
    <justification jstring="[hyper(15937,a,21154,a)].">
      <j1 rule="hyper" parents="15937 21154"/>
    </justification>
  </clause>

  <clause id="21156">
    <literal><![CDATA[
      a(x,K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      a(u,K(z,y),x) = w
    ]]></literal>
    <justification jstring="[para(21154(a,1),181(a,1)),flip(b)].">
      <j1 rule="para" parents="21154 181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21158">
    <literal><![CDATA[
      L(a(x,K(y,z),u),w,K(v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,K(y,z),u) = v7
    ]]></literal>
    <justification jstring="[para(21155(a,2),21156(a,1))].">
      <j1 rule="para" parents="21155 21156"/>
    </justification>
  </clause>

  <clause id="21159">
    <literal><![CDATA[
      L(a(x,K(y,z),u),w,K(v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      a(u,K(z,y),x) = v7
    ]]></literal>
    <justification jstring="[para(21151(a,1),21158(a,1,1))].">
      <j1 rule="para" parents="21151 21158"/>
    </justification>
  </clause>

  <clause id="21160">
    <literal><![CDATA[
      K(x,(y * K(z,K(u,w))) / (T(K(z,K(u,w)) \ v5,v6) * K(z,K(u,w)))) = K(x,y / T(v5 * K(z,K(u,w)),v6))
    ]]></literal>
    <justification jstring="[hyper(17640,a,17410,a),flip(a)].">
      <j1 rule="hyper" parents="17640 17410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21162">
    <literal><![CDATA[
      K(x,(y * K(z,K(u,w))) / (T(K(z,K(u,w)) * v5,v6) * K(z,K(u,w)))) = K(x,y / T(v5 * K(z,K(u,w)),v6))
    ]]></literal>
    <justification jstring="[para(6829(a,1),21160(a,1,2,2,1,1))].">
      <j1 rule="para" parents="6829 21160"/>
    </justification>
  </clause>

  <clause id="21163">
    <literal><![CDATA[
      K(x,(y * K(z,K(u,w))) / T((K(z,K(u,w)) * v5) * K(z,K(u,w)),v6)) = K(x,y / T(v5 * K(z,K(u,w)),v6))
    ]]></literal>
    <justification jstring="[para(15831(a,2),21162(a,1,2,2))].">
      <j1 rule="para" parents="15831 21162"/>
    </justification>
  </clause>

  <clause id="21164">
    <literal><![CDATA[
      K(x,(y * K(z,K(u,w))) / T(v5,v6)) = K(x,y / T(v5 * K(z,K(u,w)),v6))
    ]]></literal>
    <justification jstring="[para(15630(a,1),21163(a,1,2,2,1))].">
      <j1 rule="para" parents="15630 21163"/>
    </justification>
  </clause>

  <clause id="21165">
    <literal><![CDATA[
      K(x,y / T(z * K(u,K(w,v5)),v6)) = K(x,(y / T(z,v6)) * K(u,K(w,v5)))
    ]]></literal>
    <justification jstring="[para(17782(a,1),21164(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17782 21164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21166">
    <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(21165(a,2),16380(a,1))].">
      <j1 rule="para" parents="21165 16380"/>
    </justification>
  </clause>

  <clause id="21167">
    <literal><![CDATA[
      K(x,y / T(z,K(u,w) * v5)) = K(x,y / T(z,v5))
    ]]></literal>
    <justification jstring="[hyper(21166,a,19468,a),flip(a)].">
      <j1 rule="hyper" parents="21166 19468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21169">
    <literal><![CDATA[
      K(x,y / T((K(z,u) * w) \ v5,w)) = K(x,y / (v5 / (K(z,u) * w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,15165,a(flip),b,21167,a),flip(a)].">
      <j1 rule="hyper" parents="63 15165 21167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21170">
    <literal><![CDATA[
      K(x,(((K(y,z) * u) \ w) / v5) \ K((K(y,z) * u) \ w,u)) = K(x,v5 / (w / (K(y,z) * u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,19406,a,b,21169,a)].">
      <j1 rule="hyper" parents="63 19406 21169"/>
    </justification>
  </clause>

  <clause id="21171">
    <literal><![CDATA[
      K(x,y / ((K(z,u) \ w) / v5)) = K(x,y / (w / (K(z,u) * v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,18732,a(flip),b,21169,a)].">
      <j1 rule="hyper" parents="63 18732 21169"/>
    </justification>
  </clause>

  <clause id="21172">
    <literal><![CDATA[
      K(x,y / ((K(z,u) * w) / v5)) = K(x,y / (w / (K(u,z) * v5)))
    ]]></literal>
    <justification jstring="[para(4567(a,1),21171(a,1,2,2,1))].">
      <j1 rule="para" parents="4567 21171"/>
    </justification>
  </clause>

  <clause id="21173">
    <literal><![CDATA[
      K(x,(((K(y,z) * u) \ w) / v5) \ K(u \ (K(z,y) * w),u)) = K(x,v5 / (w / (K(y,z) * u)))
    ]]></literal>
    <justification jstring="[para(17543(a,1),21170(a,1,2,2))].">
      <j1 rule="para" parents="17543 21170"/>
    </justification>
  </clause>

  <clause id="21174">
    <literal><![CDATA[
      K(x,(((K(y,z) * u) \ w) / v5) \ K(K(z,y) * (u \ w),u)) = K(x,v5 / (w / (K(y,z) * u)))
    ]]></literal>
    <justification jstring="[para(10836(a,1),21173(a,1,2,2))].">
      <j1 rule="para" parents="10836 21173"/>
    </justification>
  </clause>

  <clause id="21175">
    <literal><![CDATA[
      K(x,(((K(y,z) * u) \ w) / v5) \ K(w * K(z,y),u)) = K(x,v5 / (w / (K(y,z) * u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,16708,a(flip),b,21174,a)].">
      <j1 rule="hyper" parents="63 16708 21174"/>
    </justification>
  </clause>

  <clause id="21176">
    <literal><![CDATA[
      K(x,(((K(y,z) * u) \ w) / v5) \ K(u,w)) = K(x,v5 / (w / (K(y,z) * u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,18510,a(flip),b,21175,a)].">
      <j1 rule="hyper" parents="63 18510 21175"/>
    </justification>
  </clause>

  <clause id="21177">
    <literal><![CDATA[
      K(x,K(y,z) * (u / ((K(w,v5) * y) \ z))) = K(x,u / (z / (K(w,v5) * y)))
    ]]></literal>
    <justification jstring="[hyper(19450,a,21176,a)].">
      <j1 rule="hyper" parents="19450 21176"/>
    </justification>
  </clause>

  <clause id="21179">
    <literal><![CDATA[
      K(x,y / ((K(z,u) * w) \ T(v5,w))) = K(x,y / (v5 / (K(z,u) * w)))
    ]]></literal>
    <justification jstring="[hyper(19387,a,21177,a)].">
      <j1 rule="hyper" parents="19387 21177"/>
    </justification>
  </clause>

  <clause id="21180">
    <literal><![CDATA[
      K(x,y / (z \ (K(u,w) * T(v5,z)))) = K(x,y / (v5 / (K(w,u) * z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,18572,a(flip),b,21179,a)].">
      <j1 rule="hyper" parents="63 18572 21179"/>
    </justification>
  </clause>

  <clause id="21181">
    <literal><![CDATA[
      K(x,y * ((z \ T(u,z)) \ K(w,v5))) = K(x,y / (u / (K(w,v5) * z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,20644,a(flip),b,21180,a)].">
      <j1 rule="hyper" parents="63 20644 21180"/>
    </justification>
  </clause>

  <clause id="21182">
    <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(21181(a,1),19554(a,1))].">
      <j1 rule="para" parents="21181 19554"/>
    </justification>
  </clause>

  <clause id="21183">
    <literal><![CDATA[
      K(x,T(y,z) * (((T(y,z) / u) / w) \ K(z,y))) = K(x,((y * w) * u) / T(y,z))
    ]]></literal>
    <justification jstring="[hyper(21182,a,20420,a)].">
      <j1 rule="hyper" parents="21182 20420"/>
    </justification>
  </clause>

  <clause id="21184">
    <literal><![CDATA[
      K(x,y / ((K(z,u) * w) / v5)) = K(x,y * ((w / v5) \ K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(21182,a,21172,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="21182 21172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21185">
    <literal><![CDATA[
      K(x,y / ((K(z,u) * w) / v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * ((w / v5) \ K(u,z))) = v6
    ]]></literal>
    <justification jstring="[para(21172(a,2),21182(a,1))].">
      <j1 rule="para" parents="21172 21182"/>
    </justification>
  </clause>

  <clause id="21186">
    <literal><![CDATA[
      K(x,y * (((z \ u) / w) \ K(z,v5))) = K(x,y / ((T(z,v5) \ u) / w))
    ]]></literal>
    <justification jstring="[para(4555(a,1),21184(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4555 21184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21187">
    <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(63,a,20728,a,b,21186,a)].">
      <j1 rule="hyper" parents="63 20728 21186"/>
    </justification>
  </clause>

  <clause id="21188">
    <literal><![CDATA[
      K(x,T(T(y,z),z) / ((T(y,z) / u) / w)) = K(x,((y * w) * u) / T(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,17814,a(flip),b,21183,a)].">
      <j1 rule="hyper" parents="63 17814 21183"/>
    </justification>
  </clause>

  <clause id="21189">
    <literal><![CDATA[
      K(x,((y * z) * u) / T(y,w)) = K(x,y / ((T(y,w) / u) / z))
    ]]></literal>
    <justification jstring="[hyper(63,a,15045,a(flip),b,21188,a),flip(a)].">
      <j1 rule="hyper" parents="63 15045 21188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21191">
    <literal><![CDATA[
      K(x,y / ((K(z,y) * (y / u)) / w)) = K(x,y / ((T(y,z) / u) / w))
    ]]></literal>
    <justification jstring="[hyper(63,a,20423,a,b,21189,a)].">
      <j1 rule="hyper" parents="63 20423 21189"/>
    </justification>
  </clause>

  <clause id="21192">
    <literal><![CDATA[
      K(x,y * (((y / z) / u) \ K(y,w))) = K(x,y / ((T(y,w) / z) / u))
    ]]></literal>
    <justification jstring="[hyper(21185,a,21191,a)].">
      <j1 rule="hyper" parents="21185 21191"/>
    </justification>
  </clause>

  <clause id="21193">
    <literal><![CDATA[
      K(x,T(y,z) / ((y / u) / w)) = K(x,y / ((T(y,z) / u) / w))
    ]]></literal>
    <justification jstring="[hyper(63,a,16482,a(flip),b,21192,a)].">
      <j1 rule="hyper" parents="63 16482 21192"/>
    </justification>
  </clause>

  <clause id="21194">
    <literal><![CDATA[
      K(x,y / ((T(y,z * u) / z) / u)) = K(x,y \ ((y * u) * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,19861,a(flip),b,21193,a),flip(a)].">
      <j1 rule="hyper" parents="63 19861 21193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21195">
    <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(333,a,18816,a(flip),b,21187,a),flip(a)].">
      <j1 rule="hyper" parents="333 18816 21187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21196">
    <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(18131(a,1),13455(a,1,1))].">
      <j1 rule="para" parents="18131 13455"/>
    </justification>
  </clause>

  <clause id="21197">
    <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(63,a,20562,a(flip),b,21196,a)].">
      <j1 rule="hyper" parents="63 20562 21196"/>
    </justification>
  </clause>

  <clause id="21198">
    <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(16920,a,21197,a)].">
      <j1 rule="hyper" parents="16920 21197"/>
    </justification>
  </clause>

  <clause id="21199">
    <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(63,a,18297,a(flip),b,21198,a)].">
      <j1 rule="hyper" parents="63 18297 21198"/>
    </justification>
  </clause>

  <clause id="21200">
    <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(16576,a,21199,a),flip(a)].">
      <j1 rule="hyper" parents="16576 21199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21202">
    <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(333,a,12229,a(flip),b,21200,a),flip(a)].">
      <j1 rule="hyper" parents="333 12229 21200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21203">
    <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(5003(a,1),21202(a,1,2))].">
      <j1 rule="para" parents="5003 21202"/>
    </justification>
  </clause>

  <clause id="21204">
    <literal><![CDATA[
      K(x,y * K(z \ (u * (w \ 1)),v5)) = K(x,y * K(v5,w * (u \ z)))
    ]]></literal>
    <justification jstring="[hyper(13429,a,21203,a)].">
      <j1 rule="hyper" parents="13429 21203"/>
    </justification>
  </clause>

  <clause id="21205">
    <literal><![CDATA[
      K(x,y \ T(z,u \ (w * (1 / v5)))) = K(x,(y \ z) * K(z,v5 * (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(15885,a,21204,a)].">
      <j1 rule="hyper" parents="15885 21204"/>
    </justification>
  </clause>

  <clause id="21206">
    <literal><![CDATA[
      K(x,y \ T(z,u \ (w * (1 / v5)))) = K(x,y \ T(z,v5 * (w \ u)))
    ]]></literal>
    <justification jstring="[para(13255(a,1),21205(a,2,2))].">
      <j1 rule="para" parents="13255 21205"/>
    </justification>
  </clause>

  <clause id="21207">
    <literal><![CDATA[
      K(x,y \ T(z,u \ (w * (v5 \ 1)))) = K(x,y \ T(z,v5 * (w \ u)))
    ]]></literal>
    <justification jstring="[para(5140(a,1),21206(a,1,2,2))].">
      <j1 rule="para" parents="5140 21206"/>
    </justification>
  </clause>

  <clause id="21208">
    <literal><![CDATA[
      K(x,y \ T(z,u * (w * (v5 \ 1)))) = K(x,y \ T(z,v5 * (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(16196,a,21207,a)].">
      <j1 rule="hyper" parents="16196 21207"/>
    </justification>
  </clause>

  <clause id="21209">
    <literal><![CDATA[
      K(x,y \ T(z,u * (w * (v5 \ 1)))) = K(x,y \ T(z,v5 * (w * u)))
    ]]></literal>
    <justification jstring="[hyper(333,a,20344,a(flip),b,21208,a),flip(a)].">
      <j1 rule="hyper" parents="333 20344 21208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21210">
    <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(63,a,21005,a(flip),b,21209,a),flip(a)].">
      <j1 rule="hyper" parents="63 21005 21209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21211">
    <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(6695,a,21210,a)].">
      <j1 rule="hyper" parents="6695 21210"/>
    </justification>
  </clause>

  <clause id="21212">
    <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(15797,a,21211,a)].">
      <j1 rule="hyper" parents="15797 21211"/>
    </justification>
  </clause>

  <clause id="21213">
    <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(15416,a,21212,a)].">
      <j1 rule="hyper" parents="15416 21212"/>
    </justification>
  </clause>

  <clause id="21214">
    <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(333,a,6370,a(flip),b,21213,a),flip(a)].">
      <j1 rule="hyper" parents="333 6370 21213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21215">
    <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(16987(a,1),21214(a,2,2))].">
      <j1 rule="para" parents="16987 21214"/>
    </justification>
  </clause>

  <clause id="21216">
    <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(21215(a,2),15516(a,1))].">
      <j1 rule="para" parents="21215 15516"/>
    </justification>
  </clause>

  <clause id="21225">
    <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(1686(a,1),14775(a,2,1))].">
      <j1 rule="para" parents="1686 14775"/>
    </justification>
  </clause>

  <clause id="21226">
    <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(333,a,12592,a(flip),b,21225,a),flip(a)].">
      <j1 rule="hyper" parents="333 12592 21225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21228">
    <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(9319(a,1),21226(a,1,1))].">
      <j1 rule="para" parents="9319 21226"/>
    </justification>
  </clause>

  <clause id="21229">
    <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(10130,a,21228,a)].">
      <j1 rule="hyper" parents="10130 21228"/>
    </justification>
  </clause>

  <clause id="21230">
    <literal><![CDATA[
      T(x,a(y,z,u) \ x) = x * a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,14424,a(flip),b,21229,a),flip(a)].">
      <j1 rule="hyper" parents="63 14424 21229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21231">
    <literal><![CDATA[
      T(x,a(y,z,u) \ x) = x * a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(333,a,13742,a(flip),b,21230,a),flip(a)].">
      <j1 rule="hyper" parents="333 13742 21230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21232">
    <literal><![CDATA[
      K(x,a(y,z,u) \ x) = a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(4305,a,21231,a)].">
      <j1 rule="hyper" parents="4305 21231"/>
    </justification>
  </clause>

  <clause id="21233">
    <literal><![CDATA[
      a(x,y,K(z,a(x,y,z) \ u)) = a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,14393,a(flip),b,21232,a)].">
      <j1 rule="hyper" parents="63 14393 21232"/>
    </justification>
  </clause>

  <clause id="21234">
    <literal><![CDATA[
      K(x,y) * a(y,z,a(x,u,K(w,v5))) = K(x,L(y,z,a(w,u,v5) \ x))
    ]]></literal>
    <justification jstring="[para(21232(a,1),13765(a,1,2,3))].">
      <j1 rule="para" parents="21232 13765"/>
    </justification>
  </clause>

  <clause id="21235">
    <literal><![CDATA[
      a(x,y,K(z,u)) * x = a(z,y,u) * (x / a(z,y,u))
    ]]></literal>
    <justification jstring="[para(21233(a,1),13541(a,1,1))].">
      <j1 rule="para" parents="21233 13541"/>
    </justification>
  </clause>

  <clause id="21236">
    <literal><![CDATA[
      a(x,y,z) \ L(u,y,K(x,z)) = u / a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(121,a,14479,a(flip),b,21235,a(flip))].">
      <j1 rule="hyper" parents="121 14479 21235"/>
    </justification>
  </clause>

  <clause id="21237">
    <literal><![CDATA[
      x / a(y,z,x) = a(y,z,x) \ x
    ]]></literal>
    <justification jstring="[para(6597(a,1),21236(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6597 21236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21238">
    <literal><![CDATA[
      a(x,y,z) \ L(u,y,K(z,x)) = u / a(x,y,z)
    ]]></literal>
    <justification jstring="[para(15927(a,1),21236(a,1,2))].">
      <j1 rule="para" parents="15927 21236"/>
    </justification>
  </clause>

  <clause id="21239">
    <literal><![CDATA[
      (K(x,y) * z) / a(u,w,z) = a(u,w,z) \ (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(17896(a,1),21236(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17896 21236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21240">
    <literal><![CDATA[
      a(x,y,z) \ L(u * (1 / a(x,y,z)),y,K(z,x)) = u * ((1 / a(x,y,z)) / a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(333,a,6277,a(flip),b,21238,a),flip(a)].">
      <j1 rule="hyper" parents="333 6277 21238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21241">
    <literal><![CDATA[
      a(x,y,z) \ (K(u,w) * z) = K(u,w) * (z / a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,19544,a(flip),b,21239,a),flip(a)].">
      <j1 rule="hyper" parents="63 19544 21239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21242">
    <literal><![CDATA[
      a(x,y,z) \ (K(u,w) * z) = K(u,w) * (a(x,y,z) \ z)
    ]]></literal>
    <justification jstring="[para(21237(a,1),21241(a,2,2))].">
      <j1 rule="para" parents="21237 21241"/>
    </justification>
  </clause>

  <clause id="21243">
    <literal><![CDATA[
      K(x,y) * (a(z \ 1,z,u) \ u) = L(K(x,y) * u,z,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,20067,a(flip),b,21242,a),flip(a)].">
      <j1 rule="hyper" parents="63 20067 21242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21244">
    <literal><![CDATA[
      L(K(x,y) * z,u,u \ 1) = K(x,y) * L(z,u,u \ 1)
    ]]></literal>
    <justification jstring="[para(3207(a,1),21243(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3207 21243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21245">
    <literal><![CDATA[
      x * L(K(y,x) * (x \ z),u,u \ 1) = T(x,y) \ L(x * z,u,u \ 1)
    ]]></literal>
    <justification jstring="[para(21244(a,2),5278(a,1,2))].">
      <j1 rule="para" parents="21244 5278"/>
    </justification>
  </clause>

  <clause id="21246">
    <literal><![CDATA[
      K(x,L(y,z,a(u,w,v5) \ x)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,a(v5,w,u))) = v6
    ]]></literal>
    <justification jstring="[para(21234(a,1),14058(a,1))].">
      <j1 rule="para" parents="21234 14058"/>
    </justification>
  </clause>

  <clause id="21247">
    <literal><![CDATA[
      K(x,L(y,z,a(u,w,v5) \ 1)) = K(x,L(y,z,a(v5,w,u)))
    ]]></literal>
    <justification jstring="[hyper(21246,a,14127,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="21246 14127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21249">
    <literal><![CDATA[
      K(x,L(y,z,a(u \ 1,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(14106,a,21247,a),flip(a)].">
      <j1 rule="hyper" parents="14106 21247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21250">
    <literal><![CDATA[
      K(x,y) * a(x,z,a(y,u,K(w,v5))) = K(x,L(y,z,a(w,u,v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,13989,a,b,21247,a)].">
      <j1 rule="hyper" parents="63 13989 21247"/>
    </justification>
  </clause>

  <clause id="21251">
    <literal><![CDATA[
      K(x,(a(y \ 1,y,z) \ u) \ w) = K(x,u \ (a(y \ 1,y,z) * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,14010,a(flip),b,21249,a),flip(a)].">
      <j1 rule="hyper" parents="63 14010 21249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21252">
    <literal><![CDATA[
      K(x,L(y,z,(L(u,w,v5) \ u) \ y)) = K(x,L(y,z,a(u,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(14113,a,21250,a)].">
      <j1 rule="hyper" parents="14113 21250"/>
    </justification>
  </clause>

  <clause id="21253">
    <literal><![CDATA[
      K(x,L(y,z,u \ L(u,w,v5))) = K(x,L(y,z,a(u,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(14130,a,21252,a)].">
      <j1 rule="hyper" parents="14130 21252"/>
    </justification>
  </clause>

  <clause id="21254">
    <literal><![CDATA[
      K(x,L(T(y,z),u,w) / (v5 * (y \ L(T(y,z),u,w)))) = K(x,L(y / v5,L(T(y,z),u,w),a(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,19777,a(flip),b,21253,a)].">
      <j1 rule="hyper" parents="63 19777 21253"/>
    </justification>
  </clause>

  <clause id="21255">
    <literal><![CDATA[
      K(x,L(y,L(z,u,w),a(z,u,w))) = K(x,L(y,z,z \ L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,14012,a(flip),b,21253,a),flip(a)].">
      <j1 rule="hyper" parents="63 14012 21253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21256">
    <literal><![CDATA[
      K(x,L(y,L(z,u,w),a(z,u,w))) = K(x,L(y,z,a(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(333,a,21253,a(flip),b,21255,a),flip(a)].">
      <j1 rule="hyper" parents="333 21253 21255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21257">
    <literal><![CDATA[
      K(x,L(y,L(z,u,w),a(z,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,19537,a(flip),b,21256,a),flip(a)].">
      <j1 rule="hyper" parents="333 19537 21256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21258">
    <literal><![CDATA[
      K(x,L(y,L(z,u,w),a(z,u,w))) = K(x,L(y,v5,a(v5,v6,v7)))
    ]]></literal>
    <justification jstring="[hyper(333,a,19537,a,b,21257,a),flip(a)].">
      <j1 rule="hyper" parents="333 19537 21257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21260">
    <literal><![CDATA[
      K(x,L(y,L(z,u,w),a(z,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(21258(a,2),9476(a,1))].">
      <j1 rule="para" parents="21258 9476"/>
    </justification>
  </clause>

  <clause id="21261">
    <literal><![CDATA[
      T(x,y) \ L(x * z,u,u \ 1) = x * L(T(x,y) \ z,u,u \ 1)
    ]]></literal>
    <justification jstring="[para(4555(a,1),21245(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4555 21245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21262">
    <literal><![CDATA[
      K(x,y) * (x * L(T(x,y) \ z,u,u \ 1)) = x \ L(x * z,u,u \ 1)
    ]]></literal>
    <justification jstring="[hyper(126,a,21261,a(flip),b,4511,a)].">
      <j1 rule="hyper" parents="126 21261 4511"/>
    </justification>
  </clause>

  <clause id="21263">
    <literal><![CDATA[
      T(x,y) * L(T(x,y) \ z,u,u \ 1) = x \ L(x * z,u,u \ 1)
    ]]></literal>
    <justification jstring="[hyper(4539,a,21262,a)].">
      <j1 rule="hyper" parents="4539 21262"/>
    </justification>
  </clause>

  <clause id="21264">
    <literal><![CDATA[
      T(x,y) * L(T(x,y) \ z,u,u \ 1) = x * L(x \ z,u,u \ 1)
    ]]></literal>
    <justification jstring="[hyper(333,a,2576,a(flip),b,21263,a),flip(a)].">
      <j1 rule="hyper" parents="333 2576 21263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21265">
    <literal><![CDATA[
      x \ T(x * L(x \ y,z,z \ 1),u) = L(x \ T(y,u),z,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(1966,a,21264,a)].">
      <j1 rule="hyper" parents="1966 21264"/>
    </justification>
  </clause>

  <clause id="21266">
    <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(21265(a,1),13456(a,1,2))].">
      <j1 rule="para" parents="21265 13456"/>
    </justification>
  </clause>

  <clause id="21267">
    <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(21265(a,2),20001(a,2,2,2))].">
      <j1 rule="para" parents="21265 20001"/>
    </justification>
  </clause>

  <clause id="21268">
    <literal><![CDATA[
      a(x,y,z) \ L(u * (a(x,y,z) \ 1),y,K(z,x)) = u * ((1 / a(x,y,z)) / a(x,y,z))
    ]]></literal>
    <justification jstring="[para(12442(a,1),21240(a,1,2,1,2))].">
      <j1 rule="para" parents="12442 21240"/>
    </justification>
  </clause>

  <clause id="21269">
    <literal><![CDATA[
      a(x,y,z) \ ((a(x,y,z) \ 1) * u) = u * ((1 / a(x,y,z)) / a(x,y,z))
    ]]></literal>
    <justification jstring="[para(14859(a,1),21268(a,1,2))].">
      <j1 rule="para" parents="14859 21268"/>
    </justification>
  </clause>

  <clause id="21270">
    <literal><![CDATA[
      x * ((1 / a(y,z,u)) / a(y,z,u)) = (a(y,z,u) * a(y,z,u)) \ x
    ]]></literal>
    <justification jstring="[hyper(721,a,21269,a),flip(a)].">
      <j1 rule="hyper" parents="721 21269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21271">
    <literal><![CDATA[
      x * ((a(y,z,u) \ 1) / a(y,z,u)) = (a(y,z,u) * a(y,z,u)) \ x
    ]]></literal>
    <justification jstring="[para(12442(a,1),21270(a,1,2,1))].">
      <j1 rule="para" parents="12442 21270"/>
    </justification>
  </clause>

  <clause id="21272">
    <literal><![CDATA[
      x * (a(y,z,u) \ (1 / a(y,z,u))) = (a(y,z,u) * a(y,z,u)) \ x
    ]]></literal>
    <justification jstring="[para(985(a,1),21271(a,1,2))].">
      <j1 rule="para" parents="985 21271"/>
    </justification>
  </clause>

  <clause id="21273">
    <literal><![CDATA[
      (a(x,y,z) * a(x,y,z)) * ((a(x,y,z) * a(x,y,z)) \ u) = T(u,a(x,y,z) \ (a(x,y,z) \ 1))
    ]]></literal>
    <justification jstring="[para(21272(a,1),12445(a,1,2))].">
      <j1 rule="para" parents="21272 12445"/>
    </justification>
  </clause>

  <clause id="21274">
    <literal><![CDATA[
      T(x,a(y,z,u) \ (a(y,z,u) \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(274,a,21273,a),flip(a)].">
      <j1 rule="hyper" parents="274 21273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21275">
    <literal><![CDATA[
      T(x,a(y,z,u) \ (a(y,z,u) \ w)) = T(x,w)
    ]]></literal>
    <justification jstring="[hyper(15960,a,21274,a)].">
      <j1 rule="hyper" parents="15960 21274"/>
    </justification>
  </clause>

  <clause id="21277">
    <literal><![CDATA[
      T(x,a(y,z,u) \ w) = T(x,a(y,z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(40,a,15989,a,b,21275,a),flip(a)].">
      <j1 rule="hyper" parents="40 15989 21275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21278">
    <literal><![CDATA[
      T(x,a(y,y,z) * u) = T(x,u * a(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,17902,a(flip),b,21277,a),flip(a)].">
      <j1 rule="hyper" parents="63 17902 21277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21279">
    <literal><![CDATA[
      x / T(x,a(y,z,u) * w) = K(a(y,z,u) \ w,x)
    ]]></literal>
    <justification jstring="[hyper(197,a,21277,a(flip),b,4233,a(flip))].">
      <j1 rule="hyper" parents="197 21277 4233"/>
    </justification>
  </clause>

  <clause id="21280">
    <literal><![CDATA[
      x \ T(x,a(y,z,u) * w) = K(x,a(y,z,u) \ w)
    ]]></literal>
    <justification jstring="[hyper(121,a,21277,a(flip),b,4222,a(flip))].">
      <j1 rule="hyper" parents="121 21277 4222"/>
    </justification>
  </clause>

  <clause id="21281">
    <literal><![CDATA[
      T(x,y * a(z,u,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y * a(u,u,z)) = w
    ]]></literal>
    <justification jstring="[para(21278(a,1),17601(a,1))].">
      <j1 rule="para" parents="21278 17601"/>
    </justification>
  </clause>

  <clause id="21282">
    <literal><![CDATA[
      K(a(x,y,z) \ u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(a(x,y,z) * u,w) = v5
    ]]></literal>
    <justification jstring="[para(21279(a,1),4313(a,1))].">
      <j1 rule="para" parents="21279 4313"/>
    </justification>
  </clause>

  <clause id="21283">
    <literal><![CDATA[
      K(x,a(y,z,u) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,a(y,z,u) * w) = v5
    ]]></literal>
    <justification jstring="[para(21280(a,1),4306(a,1))].">
      <j1 rule="para" parents="21280 4306"/>
    </justification>
  </clause>

  <clause id="21284">
    <literal><![CDATA[
      K(x,a(y,y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,a(z,y,y) * u) = w
    ]]></literal>
    <justification jstring="[para(16253(a,1),21283(a,1))].">
      <j1 rule="para" parents="16253 21283"/>
    </justification>
  </clause>

  <clause id="21285">
    <literal><![CDATA[
      K(x,L(T(y,z),u,w) / (v5 * (y \ L(T(y,z),u,w)))) = K(x,L(y / v5,L(y,u,w),a(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(333,a,19628,a(flip),b,21254,a),flip(a)].">
      <j1 rule="hyper" parents="333 19628 21254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21287">
    <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(21285(a,2),21260(a,1))].">
      <j1 rule="para" parents="21285 21260"/>
    </justification>
  </clause>

  <clause id="21288">
    <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(21287,a,20772,a),flip(a)].">
      <j1 rule="hyper" parents="21287 20772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21289">
    <literal><![CDATA[
      K(x,y * ((z \ L(y,u,w)) / L(y,u,w))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(1242(a,1),21288(a,1,2,2,1,2,1))].">
      <j1 rule="para" parents="1242 21288"/>
    </justification>
  </clause>

  <clause id="21290">
    <literal><![CDATA[
      K(x,y * (L(y,z,u) \ (L(y,z,u) / w))) = K(x,y / w)
    ]]></literal>
    <justification jstring="[hyper(63,a,15236,a(flip),b,21289,a)].">
      <j1 rule="hyper" parents="63 15236 21289"/>
    </justification>
  </clause>

  <clause id="21291">
    <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(9(a,1),21266(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 21266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21292">
    <literal><![CDATA[
      K(x,T(y * L(y \ z,u,u \ 1),y)) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(20070,a,21291,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="20070 21291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21294">
    <literal><![CDATA[
      K(x,y * L(z / y,u,u \ 1)) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(12282,a,21292,a)].">
      <j1 rule="hyper" parents="12282 21292"/>
    </justification>
  </clause>

  <clause id="21295">
    <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(63,a,21294,a(flip),b,21267,a)].">
      <j1 rule="hyper" parents="63 21294 21267"/>
    </justification>
  </clause>

  <clause id="21297">
    <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(63,a,13630,a(flip),b,21295,a)].">
      <j1 rule="hyper" parents="63 13630 21295"/>
    </justification>
  </clause>

  <clause id="21298">
    <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(12281,a,21297,a),flip(a)].">
      <j1 rule="hyper" parents="12281 21297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21299">
    <literal><![CDATA[
      K(x,y * L(z \ T(u,w),v5,v5 \ 1)) = K(x,y * (z \ T(u,w)))
    ]]></literal>
    <justification jstring="[para(21265(a,1),21298(a,1,2,2))].">
      <j1 rule="para" parents="21265 21298"/>
    </justification>
  </clause>

  <clause id="21300">
    <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(63,a,20959,a(flip),b,21299,a)].">
      <j1 rule="hyper" parents="63 20959 21299"/>
    </justification>
  </clause>

  <clause id="21301">
    <literal><![CDATA[
      K(x,y * ((z \ T(u,w)) \ L(z \ T(u,w),v5,v5 \ 1))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(12(a,1),21300(a,2,2))].">
      <j1 rule="para" parents="12 21300"/>
    </justification>
  </clause>

  <clause id="21302">
    <literal><![CDATA[
      K(x,y * a(z \ T(u,w),v5,v5 \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(15355,a,21301,a)].">
      <j1 rule="hyper" parents="15355 21301"/>
    </justification>
  </clause>

  <clause id="21305">
    <literal><![CDATA[
      K(x,y * a(z,u,u \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(79(a,1),21302(a,1,2,2,1))].">
      <j1 rule="para" parents="79 21302"/>
    </justification>
  </clause>

  <clause id="21306">
    <literal><![CDATA[
      K(x,a(y \ 1,y,z) \ u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,18312,a,b,21305,a)].">
      <j1 rule="hyper" parents="63 18312 21305"/>
    </justification>
  </clause>

  <clause id="21307">
    <literal><![CDATA[
      K(x,y * L(z,u,u \ 1)) = K(x,(y \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,20074,a(flip),b,21305,a)].">
      <j1 rule="hyper" parents="63 20074 21305"/>
    </justification>
  </clause>

  <clause id="21309">
    <literal><![CDATA[
      K(x,a(y \ 1,y,z) * u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(21283,a,21306,a)].">
      <j1 rule="hyper" parents="21283 21306"/>
    </justification>
  </clause>

  <clause id="21310">
    <literal><![CDATA[
      K(x,y / a(z \ 1,z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(17569,a,21306,a)].">
      <j1 rule="hyper" parents="17569 21306"/>
    </justification>
  </clause>

  <clause id="21312">
    <literal><![CDATA[
      K(x,y * (L(y,z,z \ 1) \ u)) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,14455,a,b,21309,a)].">
      <j1 rule="hyper" parents="63 14455 21309"/>
    </justification>
  </clause>

  <clause id="21313">
    <literal><![CDATA[
      K(x,a(y,y,z) * u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,16254,a(flip),b,21309,a)].">
      <j1 rule="hyper" parents="63 16254 21309"/>
    </justification>
  </clause>

  <clause id="21314">
    <literal><![CDATA[
      K(x,a(y,z,z) * u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(21284,a,21313,a)].">
      <j1 rule="hyper" parents="21284 21313"/>
    </justification>
  </clause>

  <clause id="21316">
    <literal><![CDATA[
      T(x,a(y,y,z) * u) = T(x,u)
    ]]></literal>
    <justification jstring="[hyper(124,a,21313,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 21313 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21317">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * (a(u,w,w) \ z)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,(a(u,w,w) \ z) * y) = v5
    ]]></literal>
    <justification jstring="[para(21314(a,1),15816(a,1,1,2))].">
      <j1 rule="para" parents="21314 15816"/>
    </justification>
  </clause>

  <clause id="21318">
    <literal><![CDATA[
      K(x,y * (a(z \ 1,z,u) \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(13442,a,21310,a)].">
      <j1 rule="hyper" parents="13442 21310"/>
    </justification>
  </clause>

  <clause id="21320">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1) / u) = K(x,y / u)
    ]]></literal>
    <justification jstring="[hyper(63,a,21290,a(flip),b,21312,a),flip(a)].">
      <j1 rule="hyper" parents="63 21290 21312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21321">
    <literal><![CDATA[
      K(x,a(y,z,z \ 1) \ u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,16241,a(flip),b,21312,a)].">
      <j1 rule="hyper" parents="63 16241 21312"/>
    </justification>
  </clause>

  <clause id="21323">
    <literal><![CDATA[
      K(x,a(y,z,z \ 1) \ u) = K(x,w * (L(w,v5,v5 \ 1) \ u))
    ]]></literal>
    <justification jstring="[hyper(333,a,21312,a,b,21321,a),flip(a)].">
      <j1 rule="hyper" parents="333 21312 21321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21325">
    <literal><![CDATA[
      (x * (a(y \ 1,y,z) \ 1)) / T(x * (a(y \ 1,y,z) \ 1),u) = K(u,x)
    ]]></literal>
    <justification jstring="[hyper(4234,a,21318,a)].">
      <j1 rule="hyper" parents="4234 21318"/>
    </justification>
  </clause>

  <clause id="21328">
    <literal><![CDATA[
      K(x,y * L(z,u,u \ 1)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = w
    ]]></literal>
    <justification jstring="[para(21307(a,2),13421(a,1))].">
      <j1 rule="para" parents="21307 13421"/>
    </justification>
  </clause>

  <clause id="21330">
    <literal><![CDATA[
      K(x,y * (z * (u \ 1))) = K(x,y * (z / u))
    ]]></literal>
    <justification jstring="[hyper(21328,a,16046,a),flip(a)].">
      <j1 rule="hyper" parents="21328 16046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21331">
    <literal><![CDATA[
      K(x,y * (z * (u \ 1))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z / u)) = w
    ]]></literal>
    <justification jstring="[para(16046(a,1),21328(a,1))].">
      <j1 rule="para" parents="16046 21328"/>
    </justification>
  </clause>

  <clause id="21332">
    <literal><![CDATA[
      T(x,y * (z * (u \ 1))) = T(x,y * (z / u))
    ]]></literal>
    <justification jstring="[hyper(124,a,21330,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 21330 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21333">
    <literal><![CDATA[
      K(x,y * (z / (u \ 1))) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,5018,a(flip),b,21330,a),flip(a)].">
      <j1 rule="hyper" parents="63 5018 21330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21334">
    <literal><![CDATA[
      T(T(x,K(y,z * (z * u))),y / (z \ (z / (u \ 1)))) = T(x,L(u,u,z) \ y)
    ]]></literal>
    <justification jstring="[para(21333(a,1),15956(a,1,1,2))].">
      <j1 rule="para" parents="21333 15956"/>
    </justification>
  </clause>

  <clause id="21335">
    <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(18865(a,2),21331(a,1))].">
      <j1 rule="para" parents="18865 21331"/>
    </justification>
  </clause>

  <clause id="21336">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1) \ (y * u)) = K(x,a(w,v5,v5 \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(1258(a,2),21323(a,2,2)),flip(a)].">
      <j1 rule="para" parents="1258 21323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21337">
    <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(63,a,19862,a,b,21336,a),flip(a)].">
      <j1 rule="hyper" parents="63 19862 21336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21341">
    <literal><![CDATA[
      T(x * (a(y \ 1,y,z) \ 1),u) = T(x,u) * (a(y \ 1,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(36,a,4607,a,b,21325,a),flip(a)].">
      <j1 rule="hyper" parents="36 4607 21325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21342">
    <literal><![CDATA[
      T(x * (a(y \ 1,y,z) \ 1),u) / (x * (a(y \ 1,y,z) \ 1)) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(123,a,21341,a,b,4273,a)].">
      <j1 rule="hyper" parents="123 21341 4273"/>
    </justification>
  </clause>

  <clause id="21343">
    <literal><![CDATA[
      K(x * (a(y \ 1,y,z) \ 1),u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(4345,a,21342,a)].">
      <j1 rule="hyper" parents="4345 21342"/>
    </justification>
  </clause>

  <clause id="21344">
    <literal><![CDATA[
      K(x / a(y \ 1,y,z),u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(13493,a,21343,a)].">
      <j1 rule="hyper" parents="13493 21343"/>
    </justification>
  </clause>

  <clause id="21345">
    <literal><![CDATA[
      K(a(x \ 1,x,y) \ z,u) = K(z,u)
    ]]></literal>
    <justification jstring="[para(13813(a,1),21344(a,1,1))].">
      <j1 rule="para" parents="13813 21344"/>
    </justification>
  </clause>

  <clause id="21346">
    <literal><![CDATA[
      K(a(x \ 1,x,y) * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(z,u) = w
    ]]></literal>
    <justification jstring="[para(21345(a,1),4614(a,1))].">
      <j1 rule="para" parents="21345 4614"/>
    </justification>
  </clause>

  <clause id="21347">
    <literal><![CDATA[
      K(a(x,x,y) * z,u) = K(z,u)
    ]]></literal>
    <justification jstring="[hyper(21346,a,16259,a),flip(a)].">
      <j1 rule="hyper" parents="21346 16259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21348">
    <literal><![CDATA[
      (a(x,x,y) * z) * K(z,u) = T(a(x,x,y) * z,u)
    ]]></literal>
    <justification jstring="[hyper(126,a,21347,a(flip),b,4215,a(flip))].">
      <j1 rule="hyper" parents="126 21347 4215"/>
    </justification>
  </clause>

  <clause id="21349">
    <literal><![CDATA[
      T(a(x,x,y) * z,u) = a(x,x,y) * T(z,u)
    ]]></literal>
    <justification jstring="[hyper(6089,a,21348,a),flip(a)].">
      <j1 rule="hyper" parents="6089 21348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21350">
    <literal><![CDATA[
      T(T(x,K(y,z)),y / (u \ (u / (z \ 1)))) = T(x,L(z,z,u) \ y)
    ]]></literal>
    <justification jstring="[para(15813(a,1),21334(a,1,1))].">
      <j1 rule="para" parents="15813 21334"/>
    </justification>
  </clause>

  <clause id="21353">
    <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(3996(a,1),21337(a,2,2,1,2))].">
      <j1 rule="para" parents="3996 21337"/>
    </justification>
  </clause>

  <clause id="21354">
    <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(13813(a,1),21353(a,2,2,1))].">
      <j1 rule="para" parents="13813 21353"/>
    </justification>
  </clause>

  <clause id="21355">
    <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(333,a,21251,a(flip),b,21354,a),flip(a)].">
      <j1 rule="hyper" parents="333 21251 21354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21356">
    <literal><![CDATA[
      K(x,a(y,z,z \ 1) \ (u \ L(w,v5,v5 \ 1))) = K(x,u \ w)
    ]]></literal>
    <justification jstring="[para(3205(a,1),21355(a,2,2,2))].">
      <j1 rule="para" parents="3205 21355"/>
    </justification>
  </clause>

  <clause id="21357">
    <literal><![CDATA[
      K(x,y \ L(z,u,u \ 1)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,21321,a(flip),b,21356,a)].">
      <j1 rule="hyper" parents="63 21321 21356"/>
    </justification>
  </clause>

  <clause id="21359">
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ u) = K(x,(y \ z) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,15357,a(flip),b,21357,a),flip(a)].">
      <j1 rule="hyper" parents="63 15357 21357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21360">
    <literal><![CDATA[
      K(x,y \ (z * (u \ 1))) = K(x,y \ (z / u))
    ]]></literal>
    <justification jstring="[hyper(63,a,15352,a(flip),b,21357,a)].">
      <j1 rule="hyper" parents="63 15352 21357"/>
    </justification>
  </clause>

  <clause id="21361">
    <literal><![CDATA[
      K(x,(y * (z \ 1)) \ u) = K(x,(y / z) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,14760,a(flip),b,21357,a),flip(a)].">
      <j1 rule="hyper" parents="63 14760 21357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21368">
    <literal><![CDATA[
      T(x,(y * (z \ 1)) \ u) = T(x,(y / z) \ u)
    ]]></literal>
    <justification jstring="[hyper(124,a,21361,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 21361 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21369">
    <literal><![CDATA[
      K(x,((y * z) / y) \ ((z * y) * u)) = K(x,z \ (((y \ 1) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,20516,a(flip),b,21361,a),flip(a)].">
      <j1 rule="hyper" parents="63 20516 21361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21370">
    <literal><![CDATA[
      K(x,y \ (((z \ 1) \ y) * u)) = K(x,y \ ((T(y,z) * z) * u))
    ]]></literal>
    <justification jstring="[para(10167(a,1),21369(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10167 21369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21371">
    <literal><![CDATA[
      K(x,y \ (((z \ 1) \ y) * u)) = K(x,y \ ((z * y) * u))
    ]]></literal>
    <justification jstring="[hyper(333,a,19197,a(flip),b,21370,a),flip(a)].">
      <j1 rule="hyper" parents="333 19197 21370"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21372">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,z,y * z)) = K(x,z \ ((y * z) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,20046,a,b,21371,a)].">
      <j1 rule="hyper" parents="63 20046 21371"/>
    </justification>
  </clause>

  <clause id="21373">
    <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(5012(a,1),7115(a,1,1))].">
      <j1 rule="para" parents="5012 7115"/>
    </justification>
  </clause>

  <clause id="21374">
    <literal><![CDATA[
      (x * L(K(K(y,z),x) * u,x,K(y,z))) \ (L(x,K(y,z),L(u,x,K(y,z))) * L(K(K(y,z),x) * u,x,K(y,z))) = a(x,K(y,z),K(z,y) * L(K(x,K(y,z)) * u,x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(6799(a,1),20376(a,2,3,2,1,1))].">
      <j1 rule="para" parents="6799 20376"/>
    </justification>
  </clause>

  <clause id="21375">
    <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(385(a,1),21373(a,1,1,2,2))].">
      <j1 rule="para" parents="385 21373"/>
    </justification>
  </clause>

  <clause id="21376">
    <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(18518(a,1),21375(a,1,2,2))].">
      <j1 rule="para" parents="18518 21375"/>
    </justification>
  </clause>

  <clause id="21377">
    <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(16496,a,21376,a)].">
      <j1 rule="hyper" parents="16496 21376"/>
    </justification>
  </clause>

  <clause id="21378">
    <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(17930,a,21377,a)].">
      <j1 rule="hyper" parents="17930 21377"/>
    </justification>
  </clause>

  <clause id="21379">
    <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(63,a,13194,a(flip),b,21378,a)].">
      <j1 rule="hyper" parents="63 13194 21378"/>
    </justification>
  </clause>

  <clause id="21380">
    <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(20255,a,21379,a)].">
      <j1 rule="hyper" parents="20255 21379"/>
    </justification>
  </clause>

  <clause id="21381">
    <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(16573,a,21380,a),flip(a)].">
      <j1 rule="hyper" parents="16573 21380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21382">
    <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(333,a,17624,a(flip),b,21381,a),flip(a)].">
      <j1 rule="hyper" parents="333 17624 21381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21383">
    <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(18518(a,1),21382(a,1,1,2))].">
      <j1 rule="para" parents="18518 21382"/>
    </justification>
  </clause>

  <clause id="21384">
    <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(2259(a,1),21383(a,1,2))].">
      <j1 rule="para" parents="2259 21383"/>
    </justification>
  </clause>

  <clause id="21385">
    <literal><![CDATA[
      K(x,R(y,z,z \ 1) / u) = K(x,L(y,z,z \ 1) / u)
    ]]></literal>
    <justification jstring="[hyper(6024,a,21384,a),flip(a)].">
      <j1 rule="hyper" parents="6024 21384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21387">
    <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(63,a,18419,a,b,21385,a)].">
      <j1 rule="hyper" parents="63 18419 21385"/>
    </justification>
  </clause>

  <clause id="21388">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1) / (u * (z \ 1))) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[hyper(63,a,18486,a(flip),b,21387,a),flip(a)].">
      <j1 rule="hyper" parents="63 18486 21387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21389">
    <literal><![CDATA[
      K(x,y / (z * (u \ 1))) = K(x,y / (z / u))
    ]]></literal>
    <justification jstring="[hyper(63,a,21320,a(flip),b,21388,a)].">
      <j1 rule="hyper" parents="63 21320 21388"/>
    </justification>
  </clause>

  <clause id="21390">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1) / ((z \ 1) * u)) = K(x,y / (T(u,z) / z))
    ]]></literal>
    <justification jstring="[hyper(63,a,20799,a(flip),b,21388,a)].">
      <j1 rule="hyper" parents="63 20799 21388"/>
    </justification>
  </clause>

  <clause id="21392">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1) / ((z \ 1) * u)) = K(x,y / (z \ u))
    ]]></literal>
    <justification jstring="[hyper(333,a,18796,a(flip),b,21390,a),flip(a)].">
      <j1 rule="hyper" parents="333 18796 21390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21393">
    <literal><![CDATA[
      K(x,y / ((z \ 1) * u)) = K(x,y / (z \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,21320,a(flip),b,21392,a)].">
      <j1 rule="hyper" parents="63 21320 21392"/>
    </justification>
  </clause>

  <clause id="21395">
    <literal><![CDATA[
      K(x,y / (z \ T(u,z))) = K(x,y / (u * (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(63,a,19463,a(flip),b,21393,a),flip(a)].">
      <j1 rule="hyper" parents="63 19463 21393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21397">
    <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(21393(a,1),19081(a,1,2))].">
      <j1 rule="para" parents="21393 19081"/>
    </justification>
  </clause>

  <clause id="21398">
    <literal><![CDATA[
      K(x,y / ((T(z,u) / (z / (u \ 1))) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (u * w)) = v5
    ]]></literal>
    <justification jstring="[para(21393(a,1),20811(a,1))].">
      <j1 rule="para" parents="21393 20811"/>
    </justification>
  </clause>

  <clause id="21399">
    <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(21393(a,1),21216(a,1))].">
      <j1 rule="para" parents="21393 21216"/>
    </justification>
  </clause>

  <clause id="21400">
    <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(19866(a,1),21397(a,1,2))].">
      <j1 rule="para" parents="19866 21397"/>
    </justification>
  </clause>

  <clause id="21401">
    <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(19872(a,1),21400(a,1,2))].">
      <j1 rule="para" parents="19872 21400"/>
    </justification>
  </clause>

  <clause id="21402">
    <literal><![CDATA[
      K(x,y / (z / T(u,z))) = K(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,18215,a(flip),b,21401,a)].">
      <j1 rule="hyper" parents="63 18215 21401"/>
    </justification>
  </clause>

  <clause id="21403">
    <literal><![CDATA[
      K(x,y / (z \ u)) = K(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[hyper(63,a,18795,a(flip),b,21402,a)].">
      <j1 rule="hyper" parents="63 18795 21402"/>
    </justification>
  </clause>

  <clause id="21404">
    <literal><![CDATA[
      K(x,T(y,z * (x * u)) * (u \ z)) = K(x,((z \ 1) * u) \ y)
    ]]></literal>
    <justification jstring="[hyper(21399,a,21403,a),flip(a)].">
      <j1 rule="hyper" parents="21399 21403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21405">
    <literal><![CDATA[
      K(x,y * (z \ (T(u,w) / (u / (w \ 1))))) = K(x,y / (w * z))
    ]]></literal>
    <justification jstring="[hyper(21398,a,21403,a),flip(a)].">
      <j1 rule="hyper" parents="21398 21403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21406">
    <literal><![CDATA[
      T(x,y / (z \ u)) = T(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[hyper(124,a,21403,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 21403 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21407">
    <literal><![CDATA[
      K(x,y / (z * (u \ 1))) = K(x,y * (T(z,u) \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,21395,a(flip),b,21403,a)].">
      <j1 rule="hyper" parents="63 21395 21403"/>
    </justification>
  </clause>

  <clause id="21408">
    <literal><![CDATA[
      K(x,L(y / ((y \ z) * y),u,w) * (y \ z)) = a(x,u,K(y \ z,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,21113,a(flip),b,21403,a),flip(a)].">
      <j1 rule="hyper" parents="63 21113 21403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21409">
    <literal><![CDATA[
      K(x,y * ((T(z,u) * y) \ u)) = K(x,y \ ((y * u) / z))
    ]]></literal>
    <justification jstring="[hyper(63,a,19986,a(flip),b,21403,a),flip(a)].">
      <j1 rule="hyper" parents="63 19986 21403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21410">
    <literal><![CDATA[
      K(x,y \ ((y * (z * u)) / z)) = K(x,y * ((z * y) \ (u * z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,19985,a(flip),b,21403,a)].">
      <j1 rule="hyper" parents="63 19985 21403"/>
    </justification>
  </clause>

  <clause id="21411">
    <literal><![CDATA[
      x * K(y,x * ((z * x) \ (u * z))) = (x * z) / (z * K(u,y))
    ]]></literal>
    <justification jstring="[hyper(126,a,21403,a(flip),b,20250,a(flip))].">
      <j1 rule="hyper" parents="126 21403 20250"/>
    </justification>
  </clause>

  <clause id="21412">
    <literal><![CDATA[
      K(x,y * (z \ u)) * x = T(x,y / (u \ z))
    ]]></literal>
    <justification jstring="[hyper(125,a,21403,a(flip),b,4261,a(flip))].">
      <j1 rule="hyper" parents="125 21403 4261"/>
    </justification>
  </clause>

  <clause id="21414">
    <literal><![CDATA[
      T(x,y / (z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y * (u \ z)) = w
    ]]></literal>
    <justification jstring="[para(21412(a,1),4335(a,1))].">
      <j1 rule="para" parents="21412 4335"/>
    </justification>
  </clause>

  <clause id="21415">
    <literal><![CDATA[
      K(x,y / (z * (u \ 1))) = K(x,y * (u / z))
    ]]></literal>
    <justification jstring="[hyper(333,a,18150,a(flip),b,21407,a),flip(a)].">
      <j1 rule="hyper" parents="333 18150 21407"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21416">
    <literal><![CDATA[
      K(x,y / (z / u)) = K(x,y * (u / z))
    ]]></literal>
    <justification jstring="[hyper(63,a,21389,a(flip),b,21415,a)].">
      <j1 rule="hyper" parents="63 21389 21415"/>
    </justification>
  </clause>

  <clause id="21417">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,y,z \ 1)) = K(x,(z \ y) * (z / (u \ 1)))
    ]]></literal>
    <justification jstring="[hyper(63,a,20805,a,b,21416,a)].">
      <j1 rule="hyper" parents="63 20805 21416"/>
    </justification>
  </clause>

  <clause id="21419">
    <literal><![CDATA[
      K(x,y \ ((y * z) / u)) = K(x,(z / (y * u)) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,19462,a(flip),b,21409,a),flip(a)].">
      <j1 rule="hyper" parents="63 19462 21409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21420">
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ u) = K(x,(z \ y) * u)
    ]]></literal>
    <justification jstring="[hyper(21044,a,21404,a),flip(a)].">
      <j1 rule="hyper" parents="21044 21404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21421">
    <literal><![CDATA[
      K(x,(y \ z) \ u) = K(x,(z \ y) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,21359,a(flip),b,21420,a)].">
      <j1 rule="hyper" parents="63 21359 21420"/>
    </justification>
  </clause>

  <clause id="21422">
    <literal><![CDATA[
      T(x,(y \ z) \ u) = T(x,(z \ y) * u)
    ]]></literal>
    <justification jstring="[hyper(124,a,21421,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 21421 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21423">
    <literal><![CDATA[
      K(x,(T(y,z) \ u) * (u \ (y * z))) = K(x,L(T(z,y),y,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,20744,a(flip),b,21421,a),flip(a)].">
      <j1 rule="hyper" parents="63 20744 21421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21424">
    <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(21421(a,1),21195(a,1,1,3))].">
      <j1 rule="para" parents="21421 21195"/>
    </justification>
  </clause>

  <clause id="21425">
    <literal><![CDATA[
      T(x,(y \ (y / z)) * u) = T(x,z \ u)
    ]]></literal>
    <justification jstring="[para(79(a,1),21422(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="79 21422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21426">
    <literal><![CDATA[
      T(x,(y \ (y / z)) \ u) = T(x,z * u)
    ]]></literal>
    <justification jstring="[para(79(a,1),21422(a,2,2,1))].">
      <j1 rule="para" parents="79 21422"/>
    </justification>
  </clause>

  <clause id="21427">
    <literal><![CDATA[
      T(x,(y \ (y / z)) \ (u \ w)) = T(x,z / (w \ u))
    ]]></literal>
    <justification jstring="[hyper(333,a,21406,a,b,21426,a),flip(a)].">
      <j1 rule="hyper" parents="333 21406 21426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21428">
    <literal><![CDATA[
      T(x,(y \ (y / z)) \ (z \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(333,a,202,a(flip),b,21426,a),flip(a)].">
      <j1 rule="hyper" parents="333 202 21426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21429">
    <literal><![CDATA[
      T(x,((y \ z) / z) \ u) = T(x,y * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,18907,a,b,21426,a)].">
      <j1 rule="hyper" parents="63 18907 21426"/>
    </justification>
  </clause>

  <clause id="21430">
    <literal><![CDATA[
      T(T(x,(y \ (y / z)) * (z \ 1)),u / (y \ (y / z))) = T(x,u * (y \ (y / z)))
    ]]></literal>
    <justification jstring="[para(21428(a,1),15992(a,1,1)),flip(a)].">
      <j1 rule="para" parents="21428 15992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21432">
    <literal><![CDATA[
      T(x,(y / z) \ u) = T(x,(z / y) * u)
    ]]></literal>
    <justification jstring="[para(79(a,1),21429(a,1,2,1,1))].">
      <j1 rule="para" parents="79 21429"/>
    </justification>
  </clause>

  <clause id="21433">
    <literal><![CDATA[
      T(x,(y * (z \ 1)) \ u) = T(x,(z / y) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,21368,a,b,21432,a)].">
      <j1 rule="hyper" parents="63 21368 21432"/>
    </justification>
  </clause>

  <clause id="21434">
    <literal><![CDATA[
      T(x,((y \ 1) / z) * u) = T(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,3188,a(flip),b,21433,a),flip(a)].">
      <j1 rule="hyper" parents="63 3188 21433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21435">
    <literal><![CDATA[
      T(x,(y \ (y / z)) \ u) = T(x,z / (w \ (w / u)))
    ]]></literal>
    <justification jstring="[para(79(a,1),21427(a,1,2,2))].">
      <j1 rule="para" parents="79 21427"/>
    </justification>
  </clause>

  <clause id="21436">
    <literal><![CDATA[
      T(T(x,K(y,z)),(u \ (u / y)) \ (z \ 1)) = T(x,L(z,z,w) \ y)
    ]]></literal>
    <justification jstring="[hyper(333,a,21350,a(flip),b,21435,a),flip(a)].">
      <j1 rule="hyper" parents="333 21350 21435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21437">
    <literal><![CDATA[
      K(x,y * (z \ (u \ 1))) = K(x,y / (u * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,21084,a(flip),b,21405,a)].">
      <j1 rule="hyper" parents="63 21084 21405"/>
    </justification>
  </clause>

  <clause id="21438">
    <literal><![CDATA[
      K(x,y * ((z / u) \ (w \ K(z,u)))) = K(x,y / (w * (u \ z)))
    ]]></literal>
    <justification jstring="[hyper(21081,a,21437,a)].">
      <j1 rule="hyper" parents="21081 21437"/>
    </justification>
  </clause>

  <clause id="21439">
    <literal><![CDATA[
      K(x,((y * z) / (u * y)) * u) = K(x,u * ((y * u) \ (z * y)))
    ]]></literal>
    <justification jstring="[hyper(63,a,21419,a(flip),b,21410,a)].">
      <j1 rule="hyper" parents="63 21419 21410"/>
    </justification>
  </clause>

  <clause id="21440">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,y,z \ 1)) = K(x,(z \ y) * (z * u))
    ]]></literal>
    <justification jstring="[hyper(333,a,21333,a(flip),b,21417,a),flip(a)].">
      <j1 rule="hyper" parents="333 21333 21417"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21441">
    <literal><![CDATA[
      K(x,(y \ z) * (z \ (u * y))) = K(x,L(T(u,y),y,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,18085,a(flip),b,21423,a)].">
      <j1 rule="hyper" parents="63 18085 21423"/>
    </justification>
  </clause>

  <clause id="21442">
    <literal><![CDATA[
      K(x,((y * z) / u) * (u / y)) = K(x,L(T(z,y),y,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,19243,a,b,21441,a)].">
      <j1 rule="hyper" parents="63 19243 21441"/>
    </justification>
  </clause>

  <clause id="21444">
    <literal><![CDATA[
      K(x,(y \ z) * L((y * (y \ z)) \ y,u,w)) = a(x,u,K(y \ z,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,21117,a(flip),b,21408,a)].">
      <j1 rule="hyper" parents="63 21117 21408"/>
    </justification>
  </clause>

  <clause id="21445">
    <literal><![CDATA[
      K(x,(y \ z) * L(z \ y,u,w)) = a(x,u,K(y \ z,w))
    ]]></literal>
    <justification jstring="[para(10(a,1),21444(a,1,2,2,1,1))].">
      <j1 rule="para" parents="10 21444"/>
    </justification>
  </clause>

  <clause id="21446">
    <literal><![CDATA[
      K(x,L(y / z,u,w) * (z / y)) = a(x,u,K(y \ z,w))
    ]]></literal>
    <justification jstring="[hyper(18774,a,21445,a)].">
      <j1 rule="hyper" parents="18774 21445"/>
    </justification>
  </clause>

  <clause id="21448">
    <literal><![CDATA[
      T(T(x,y \ (y \ 1)),z / (u \ (u / y))) = T(x,z * (u \ (u / y)))
    ]]></literal>
    <justification jstring="[para(21425(a,1),21430(a,1,1))].">
      <j1 rule="para" parents="21425 21430"/>
    </justification>
  </clause>

  <clause id="21449">
    <literal><![CDATA[
      T(T(x,y \ (y \ 1)),(z \ (z / u)) \ y) = T(x,u * (w \ (w / y)))
    ]]></literal>
    <justification jstring="[hyper(63,a,21435,a,b,21448,a)].">
      <j1 rule="hyper" parents="63 21435 21448"/>
    </justification>
  </clause>

  <clause id="21451">
    <literal><![CDATA[
      T(x,y \ (y \ ((z \ (z / u)) \ y))) = T(x,u * (w \ (w / y)))
    ]]></literal>
    <justification jstring="[hyper(15962,a,21449,a)].">
      <j1 rule="hyper" parents="15962 21449"/>
    </justification>
  </clause>

  <clause id="21453">
    <literal><![CDATA[
      T(x,(y \ (y / z)) \ (u \ 1)) = T(x,z * (w \ (w / u)))
    ]]></literal>
    <justification jstring="[hyper(13706,a,21451,a)].">
      <j1 rule="hyper" parents="13706 21451"/>
    </justification>
  </clause>

  <clause id="21454">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * (u \ (u / z))) = T(x,L(z,z,w) \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,21436,a(flip),b,21453,a),flip(a)].">
      <j1 rule="hyper" parents="63 21436 21453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21455">
    <literal><![CDATA[
      T(x,L(y,y,z) \ u) = T(x,(w \ (w / y)) * u)
    ]]></literal>
    <justification jstring="[hyper(16061,a,21454,a),flip(a)].">
      <j1 rule="hyper" parents="16061 21454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21456">
    <literal><![CDATA[
      T(x,L(y / (y / z),y / (y / z),u) \ w) = T(x,(y \ ((z * (y / z)) / z)) * w)
    ]]></literal>
    <justification jstring="[para(3719(a,2),21455(a,2,2,1,2))].">
      <j1 rule="para" parents="3719 21455"/>
    </justification>
  </clause>

  <clause id="21457">
    <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(21416(a,1),21424(a,1,2))].">
      <j1 rule="para" parents="21416 21424"/>
    </justification>
  </clause>

  <clause id="21458">
    <literal><![CDATA[
      T(x,L(y / (y / z),(y / z) \ y,y) \ u) = T(x,(y \ ((z * (y / z)) / z)) * u)
    ]]></literal>
    <justification jstring="[para(14708(a,1),21456(a,1,2,1))].">
      <j1 rule="para" parents="14708 21456"/>
    </justification>
  </clause>

  <clause id="21459">
    <literal><![CDATA[
      K(x,y / (((z / u) \ 1) / w)) = K(x,y / ((u / z) / w))
    ]]></literal>
    <justification jstring="[hyper(63,a,21128,a(flip),b,21457,a)].">
      <j1 rule="hyper" parents="63 21128 21457"/>
    </justification>
  </clause>

  <clause id="21460">
    <literal><![CDATA[
      K(x,y * (z / ((u / w) \ 1))) = K(x,y / ((w / u) / z))
    ]]></literal>
    <justification jstring="[hyper(63,a,21416,a(flip),b,21459,a)].">
      <j1 rule="hyper" parents="63 21416 21459"/>
    </justification>
  </clause>

  <clause id="21461">
    <literal><![CDATA[
      K(x,y / ((z / u) / w)) = K(x,y * (w * (u / z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,21333,a(flip),b,21460,a),flip(a)].">
      <j1 rule="hyper" parents="63 21333 21460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21462">
    <literal><![CDATA[
      K(x,y * (z / (u / w))) = K(x,y * (z * (w / u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,21416,a(flip),b,21461,a)].">
      <j1 rule="hyper" parents="63 21416 21461"/>
    </justification>
  </clause>

  <clause id="21463">
    <literal><![CDATA[
      K(x,y * (z * (u / T(y,u * z)))) = K(x,y \ ((y * z) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,21194,a(flip),b,21461,a),flip(a)].">
      <j1 rule="hyper" parents="63 21194 21461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21464">
    <literal><![CDATA[
      K(x,y * (T(z,u * w) * (u / w))) = K(x,y * ((w / u) \ z))
    ]]></literal>
    <justification jstring="[hyper(18493,a,21462,a),flip(a)].">
      <j1 rule="hyper" parents="18493 21462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21465">
    <literal><![CDATA[
      K(x,y \ ((y * z) * u)) = K(x,(z * (u / y)) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,18694,a(flip),b,21463,a),flip(a)].">
      <j1 rule="hyper" parents="63 18694 21463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21466">
    <literal><![CDATA[
      K(x,y \ ((T(z,y * K(u,w)) * y) * v5)) = K(x,(z * (v5 / y)) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,19189,a,b,21465,a)].">
      <j1 rule="hyper" parents="63 19189 21465"/>
    </justification>
  </clause>

  <clause id="21467">
    <literal><![CDATA[
      K(x,(y * ((z \ 1) / u)) * u) = K(x,u \ ((u * y) / z))
    ]]></literal>
    <justification jstring="[hyper(63,a,21360,a(flip),b,21465,a),flip(a)].">
      <j1 rule="hyper" parents="63 21360 21465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21468">
    <literal><![CDATA[
      K(x,(y * ((z \ 1) / u)) * u) = K(x,(y / (u * z)) * u)
    ]]></literal>
    <justification jstring="[hyper(333,a,21419,a(flip),b,21467,a),flip(a)].">
      <j1 rule="hyper" parents="333 21419 21467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21469">
    <literal><![CDATA[
      K(x,y * ((z / u) \ w)) = K(x,y * ((u / z) * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,21003,a(flip),b,21464,a),flip(a)].">
      <j1 rule="hyper" parents="63 21003 21464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21470">
    <literal><![CDATA[
      T(x,y * ((z / u) \ w)) = T(x,y * ((u / z) * w))
    ]]></literal>
    <justification jstring="[hyper(124,a,21469,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 21469 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21471">
    <literal><![CDATA[
      K(x,y * ((z / u) * (w \ K(u,z)))) = K(x,y / (w * (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,21438,a(flip),b,21469,a),flip(a)].">
      <j1 rule="hyper" parents="63 21438 21469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21473">
    <literal><![CDATA[
      K(x,y / (z * (u \ w))) = K(x,y * ((w \ u) / z))
    ]]></literal>
    <justification jstring="[hyper(21335,a,21471,a),flip(a)].">
      <j1 rule="hyper" parents="21335 21471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21474">
    <literal><![CDATA[
      K(x,L(y / (z \ u),z \ u,z) * ((z \ u) / y)) = a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,20738,a(flip),b,21473,a),flip(a)].">
      <j1 rule="hyper" parents="63 20738 21473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21475">
    <literal><![CDATA[
      a(x,y \ z,K(u \ (y \ z),y)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,21446,a(flip),b,21474,a)].">
      <j1 rule="hyper" parents="63 21446 21474"/>
    </justification>
  </clause>

  <clause id="21476">
    <literal><![CDATA[
      a(x,y \ z,K(u \ z,y)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(13956,a,21475,a)].">
      <j1 rule="hyper" parents="13956 21475"/>
    </justification>
  </clause>

  <clause id="21477">
    <literal><![CDATA[
      a(x,y,K(z \ y,u)) = a(x,u,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,14082,a(flip),b,21476,a)].">
      <j1 rule="hyper" parents="63 14082 21476"/>
    </justification>
  </clause>

  <clause id="21478">
    <literal><![CDATA[
      a(x,y,K(z,y \ u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,21475,a(flip),b,21477,a),flip(a)].">
      <j1 rule="hyper" parents="63 21475 21477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21479">
    <literal><![CDATA[
      x * L(x \ y,x,K(z,u)) = y * a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(21477(a,1),19958(a,2,2))].">
      <j1 rule="para" parents="21477 19958"/>
    </justification>
  </clause>

  <clause id="21480">
    <literal><![CDATA[
      ((x / y) * (y * K(z,u))) * K(u,z) = x * a(z,u,K(y,x))
    ]]></literal>
    <justification jstring="[para(21477(a,1),20369(a,2,2))].">
      <j1 rule="para" parents="21477 20369"/>
    </justification>
  </clause>

  <clause id="21481">
    <literal><![CDATA[
      x * L(x \ y,x,K(z,u)) = L(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(333,a,14480,a(flip),b,21479,a),flip(a)].">
      <j1 rule="hyper" parents="333 14480 21479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21482">
    <literal><![CDATA[
      x * a(y,x,K(z,x \ u)) = L(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,19956,a(flip),b,21481,a)].">
      <j1 rule="hyper" parents="63 19956 21481"/>
    </justification>
  </clause>

  <clause id="21483">
    <literal><![CDATA[
      x * a(y,x,K(z,u)) = L(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[para(21478(a,1),21482(a,1,2))].">
      <j1 rule="para" parents="21478 21482"/>
    </justification>
  </clause>

  <clause id="21484">
    <literal><![CDATA[
      a(x,y,K(z,u)) = a(x,u,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(34,a,14480,a,b,21483,a)].">
      <j1 rule="hyper" parents="34 14480 21483"/>
    </justification>
  </clause>

  <clause id="21485">
    <literal><![CDATA[
      a(x,y,K(z,u)) = a(z,x,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(34,a,14466,a,b,21483,a)].">
      <j1 rule="hyper" parents="34 14466 21483"/>
    </justification>
  </clause>

  <clause id="21486">
    <literal><![CDATA[
      a(x,y,K(z,u)) = a(u,x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(333,a,13731,a,b,21484,a)].">
      <j1 rule="hyper" parents="333 13731 21484"/>
    </justification>
  </clause>

  <clause id="21487">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (a(x,u,K(z,y)) * w) = w
    ]]></literal>
    <justification jstring="[hyper(125,a,21484,a,b,9792,a)].">
      <j1 rule="hyper" parents="125 21484 9792"/>
    </justification>
  </clause>

  <clause id="21488">
    <literal><![CDATA[
      a(x,y,K(z,u)) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,16010,a,b,21484,a),flip(a)].">
      <j1 rule="hyper" parents="63 16010 21484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21489">
    <literal><![CDATA[
      K(x,y) * a(x,y,K(z,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(21484(a,1),13764(a,1,2))].">
      <j1 rule="para" parents="21484 13764"/>
    </justification>
  </clause>

  <clause id="21490">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(y,u)) = K(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[para(21484(a,2),13764(a,1,2))].">
      <j1 rule="para" parents="21484 13764"/>
    </justification>
  </clause>

  <clause id="21491">
    <literal><![CDATA[
      K(x,y) * a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(21484(a,1),13770(a,1,2))].">
      <j1 rule="para" parents="21484 13770"/>
    </justification>
  </clause>

  <clause id="21492">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,u,z)) = w
    ]]></literal>
    <justification jstring="[para(21484(a,2),13770(a,1,2))].">
      <j1 rule="para" parents="21484 13770"/>
    </justification>
  </clause>

  <clause id="21495">
    <literal><![CDATA[
      x * a(y,z,K(u,x)) = L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[para(21485(a,2),14480(a,1,2))].">
      <j1 rule="para" parents="21485 14480"/>
    </justification>
  </clause>

  <clause id="21496">
    <literal><![CDATA[
      x * a(x,y,K(z,u)) = L(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(126,a,21488,a,b,14491,a)].">
      <j1 rule="hyper" parents="126 21488 14491"/>
    </justification>
  </clause>

  <clause id="21497">
    <literal><![CDATA[
      L(x,y,K(z,u)) = L(x,u,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(14527,a,21495,a),flip(a)].">
      <j1 rule="hyper" parents="14527 21495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21499">
    <literal><![CDATA[
      L(x,T(y,z),K(u,w)) = L(x,u,K(w,y))
    ]]></literal>
    <justification jstring="[hyper(17725,a,21497,a),flip(a)].">
      <j1 rule="hyper" parents="17725 21497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21500">
    <literal><![CDATA[
      L(T(x,y),z,K(y,u)) = T(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(333,a,14486,a(flip),b,21497,a),flip(a)].">
      <j1 rule="hyper" parents="333 14486 21497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21501">
    <literal><![CDATA[
      L(x,y * z,K(y,u)) = L(x,u,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(333,a,11825,a(flip),b,21497,a),flip(a)].">
      <j1 rule="hyper" parents="333 11825 21497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21504">
    <literal><![CDATA[
      L(x,y,K(x * z,u)) = L(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,14553,a(flip),b,21497,a),flip(a)].">
      <j1 rule="hyper" parents="63 14553 21497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21505">
    <literal><![CDATA[
      (K(x,y) * z) * L(u,y,K(z,x)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * (z * u) = w
    ]]></literal>
    <justification jstring="[para(21497(a,1),306(a,1,2))].">
      <j1 rule="para" parents="21497 306"/>
    </justification>
  </clause>

  <clause id="21506">
    <literal><![CDATA[
      L(x,y,K(z,u \ 1)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,u,K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(21497(a,2),2631(a,1))].">
      <j1 rule="para" parents="21497 2631"/>
    </justification>
  </clause>

  <clause id="21507">
    <literal><![CDATA[
      L(x,T(y,z),K((u \ 1) \ w,v5)) = L(x,u \ w,K(v5,y))
    ]]></literal>
    <justification jstring="[hyper(333,a,2956,a(flip),b,21499,a),flip(a)].">
      <j1 rule="hyper" parents="333 2956 21499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21508">
    <literal><![CDATA[
      T(x,L(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,L(y,u,z)) = w
    ]]></literal>
    <justification jstring="[para(21500(a,1),15931(a,1))].">
      <j1 rule="para" parents="21500 15931"/>
    </justification>
  </clause>

  <clause id="21509">
    <literal><![CDATA[
      L(x,y * z,K(z,u)) = L(x,u,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(19713,a,21501,a)].">
      <j1 rule="hyper" parents="19713 21501"/>
    </justification>
  </clause>

  <clause id="21510">
    <literal><![CDATA[
      ((x * y) * K(z,u)) / (z * (y * K(z,u))) = L(R(x / z,z,y),u,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,14469,a(flip),b,21501,a)].">
      <j1 rule="hyper" parents="63 14469 21501"/>
    </justification>
  </clause>

  <clause id="21511">
    <literal><![CDATA[
      L(R(x,y,z),u,K(y,z)) = R(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(14475,a,21509,a),flip(a)].">
      <j1 rule="hyper" parents="14475 21509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21512">
    <literal><![CDATA[
      L(R(x,y,z),u,K(z,y)) = R(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(15930,a,21511,a)].">
      <j1 rule="hyper" parents="15930 21511"/>
    </justification>
  </clause>

  <clause id="21513">
    <literal><![CDATA[
      R(x,x,T(y,z)) = R(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,6570,a(flip),b,21511,a),flip(a)].">
      <j1 rule="hyper" parents="63 6570 21511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21515">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (L(w,v5,a(x,u,K(z,y))) * (a(x,u,K(z,y)) * v5)) = v5 * T(w,a(x,u,K(z,y)) * v5)
    ]]></literal>
    <justification jstring="[hyper(34,a,664,a,b,21487,a),flip(a)].">
      <j1 rule="hyper" parents="34 664 21487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21516">
    <literal><![CDATA[
      K(x,L(y,z,u * z)) = K(x,y) * a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(11159(a,1),21489(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11159 21489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21517">
    <literal><![CDATA[
      K(x,L(y,z,u)) = K(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(16013,a,21490,a)].">
      <j1 rule="hyper" parents="16013 21490"/>
    </justification>
  </clause>

  <clause id="21518">
    <literal><![CDATA[
      K(x,L(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,u,z)) = w
    ]]></literal>
    <justification jstring="[para(21490(a,1),16013(a,1))].">
      <j1 rule="para" parents="21490 16013"/>
    </justification>
  </clause>

  <clause id="21519">
    <literal><![CDATA[
      K(x,L(y,z,(u \ 1) * w)) = K(x,L(y,u \ w,z))
    ]]></literal>
    <justification jstring="[hyper(20036,a,21517,a)].">
      <j1 rule="hyper" parents="20036 21517"/>
    </justification>
  </clause>

  <clause id="21523">
    <literal><![CDATA[
      K((x \ y) \ z,L(u,x,y)) = K(y \ (x * z),u)
    ]]></literal>
    <justification jstring="[hyper(333,a,14007,a(flip),b,21517,a),flip(a)].">
      <j1 rule="hyper" parents="333 14007 21517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21524">
    <literal><![CDATA[
      (x * y) * K(z,L(u,x,y)) != w * v5
    ]]></literal>
    <literal><![CDATA[
      w \ (x * (y * K(z,u))) = v5
    ]]></literal>
    <justification jstring="[para(21517(a,1),10878(a,1,2))].">
      <j1 rule="para" parents="21517 10878"/>
    </justification>
  </clause>

  <clause id="21526">
    <literal><![CDATA[
      K(x,L(y,z,u * z)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(333,a,21489,a(flip),b,21516,a),flip(a)].">
      <j1 rule="hyper" parents="333 21489 21516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21527">
    <literal><![CDATA[
      K((x \ (y * x)) \ z,L(u,x,y)) = K((y * x) \ (x * z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,21523,a(flip),b,21526,a),flip(a)].">
      <j1 rule="hyper" parents="63 21523 21526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21528">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,z,y)) = K(x,z \ ((y * z) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,21372,a(flip),b,21526,a),flip(a)].">
      <j1 rule="hyper" parents="63 21372 21526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21529">
    <literal><![CDATA[
      K(x,L(y,z,u / z)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(12(a,1),21526(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="12 21526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21530">
    <literal><![CDATA[
      (x / (1 / y)) * (K(z,u) / y) = x * K(z,L(T(u,y),x,y))
    ]]></literal>
    <justification jstring="[para(21526(a,1),20271(a,1,2)),flip(a)].">
      <j1 rule="para" parents="21526 20271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21531">
    <literal><![CDATA[
      K(x,L(y \ z,y,u)) = K(x,u \ ((u / y) * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,9561,a(flip),b,21529,a),flip(a)].">
      <j1 rule="hyper" parents="63 9561 21529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21532">
    <literal><![CDATA[
      K(x,(y * z) \ (y * u)) = K(x,y \ ((y / z) * u))
    ]]></literal>
    <justification jstring="[hyper(9766,a,21531,a)].">
      <j1 rule="hyper" parents="9766 21531"/>
    </justification>
  </clause>

  <clause id="21533">
    <literal><![CDATA[
      K(x,L(y,(z \ 1) * u,w)) = K(x,L(y,z \ u,w))
    ]]></literal>
    <justification jstring="[hyper(21518,a,21519,a)].">
      <j1 rule="hyper" parents="21518 21519"/>
    </justification>
  </clause>

  <clause id="21534">
    <literal><![CDATA[
      K(x,L(y,z \ u,w)) = K(x,L(y,z * u,w))
    ]]></literal>
    <justification jstring="[para(2955(a,1),21533(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2955 21533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21535">
    <literal><![CDATA[
      K(x,L(y,z,u * z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(21516(a,2),21491(a,1))].">
      <j1 rule="para" parents="21516 21491"/>
    </justification>
  </clause>

  <clause id="21536">
    <literal><![CDATA[
      K(x,y) * a(x,z,a(y,u,K(w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,a(v5,u,w),z)) = v6
    ]]></literal>
    <justification jstring="[para(13732(a,2),21492(a,1,2,3))].">
      <j1 rule="para" parents="13732 21492"/>
    </justification>
  </clause>

  <clause id="21537">
    <literal><![CDATA[
      K(x,L(y,z,u \ 1)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,u,z)) = w
    ]]></literal>
    <justification jstring="[para(13797(a,1),21492(a,1))].">
      <j1 rule="para" parents="13797 21492"/>
    </justification>
  </clause>

  <clause id="21538">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,z,y)) = K(x,(z \ y) * (z * u))
    ]]></literal>
    <justification jstring="[hyper(21537,a,21440,a)].">
      <j1 rule="hyper" parents="21537 21440"/>
    </justification>
  </clause>

  <clause id="21539">
    <literal><![CDATA[
      K(x,L((y * z) \ u,y,z)) = K(x,z \ (y \ u))
    ]]></literal>
    <justification jstring="[hyper(21537,a,14182,a)].">
      <j1 rule="hyper" parents="21537 14182"/>
    </justification>
  </clause>

  <clause id="21540">
    <literal><![CDATA[
      K(x,L(L(y,z,u),u,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(21537,a,14180,a)].">
      <j1 rule="hyper" parents="21537 14180"/>
    </justification>
  </clause>

  <clause id="21541">
    <literal><![CDATA[
      K(x,((y * z) / u) * (u / y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(T(z,y),u,y)) = w
    ]]></literal>
    <justification jstring="[para(21442(a,2),21537(a,1))].">
      <j1 rule="para" parents="21442 21537"/>
    </justification>
  </clause>

  <clause id="21542">
    <literal><![CDATA[
      K(x,L(L(y,z,u),z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(21518,a,21540,a)].">
      <j1 rule="hyper" parents="21518 21540"/>
    </justification>
  </clause>

  <clause id="21546">
    <literal><![CDATA[
      K(x \ (y * z),L(u,x,y)) = K((y \ x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,21523,a(flip),b,21540,a)].">
      <j1 rule="hyper" parents="63 21523 21540"/>
    </justification>
  </clause>

  <clause id="21547">
    <literal><![CDATA[
      K(x / (y * z),L(u,z,y)) = K((x / z) / y,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,13902,a(flip),b,21540,a)].">
      <j1 rule="hyper" parents="63 13902 21540"/>
    </justification>
  </clause>

  <clause id="21548">
    <literal><![CDATA[
      K((x * y) \ z,L(u,y,x)) = K(y \ (x \ z),u)
    ]]></literal>
    <justification jstring="[hyper(11017,a,21542,a)].">
      <j1 rule="hyper" parents="11017 21542"/>
    </justification>
  </clause>

  <clause id="21549">
    <literal><![CDATA[
      K(x,L((y * z) \ u,z,y)) = K(x,z \ (y \ u))
    ]]></literal>
    <justification jstring="[para(311(a,1),21542(a,1,2,1))].">
      <j1 rule="para" parents="311 21542"/>
    </justification>
  </clause>

  <clause id="21550">
    <literal><![CDATA[
      K(x,L((y * ((y * z) / y)) \ u,T(y,z),z)) = K(x,z \ (T(y,z) \ u))
    ]]></literal>
    <justification jstring="[para(3311(a,1),21539(a,1,2,1,1))].">
      <j1 rule="para" parents="3311 21539"/>
    </justification>
  </clause>

  <clause id="21551">
    <literal><![CDATA[
      K((x \ y) \ (z * u),L(w,x * y,z)) = K((z \ (x \ y)) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,21534,a(flip),b,21546,a)].">
      <j1 rule="hyper" parents="63 21534 21546"/>
    </justification>
  </clause>

  <clause id="21552">
    <literal><![CDATA[
      K(L(x,y,z),y \ (z * u)) = (w * K((z \ y) \ u,x)) \ w
    ]]></literal>
    <justification jstring="[para(21546(a,1),5990(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="21546 5990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21553">
    <literal><![CDATA[
      K((((x * y) * z) / (y * z)) / x,u) = K(a(x,y,z),L(u,y * z,x))
    ]]></literal>
    <justification jstring="[para(13588(a,2),21547(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13588 21547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21554">
    <literal><![CDATA[
      K((x * y) \ T(z,u * w),L(v5,y,x)) = K(y \ (x \ T(z,u \ w)),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,16158,a(flip),b,21548,a)].">
      <j1 rule="hyper" parents="63 16158 21548"/>
    </justification>
  </clause>

  <clause id="21555">
    <literal><![CDATA[
      K((x * y) \ ((z \ 1) \ u),L(w,y,x)) = K(y \ (x \ ((1 / z) \ u)),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,5005,a(flip),b,21548,a)].">
      <j1 rule="hyper" parents="63 5005 21548"/>
    </justification>
  </clause>

  <clause id="21556">
    <literal><![CDATA[
      K(x,y \ ((z * y) * u)) = K(x,(y \ z) * (y * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,21528,a(flip),b,21538,a)].">
      <j1 rule="hyper" parents="63 21528 21538"/>
    </justification>
  </clause>

  <clause id="21557">
    <literal><![CDATA[
      K(x,(y \ T(z,y * K(u,w))) * (y * v5)) = K(x,(z * (v5 / y)) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,21466,a(flip),b,21556,a),flip(a)].">
      <j1 rule="hyper" parents="63 21466 21556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21559">
    <literal><![CDATA[
      L(x,T(y,z),K(u * w,v5)) = L(x,u \ w,K(v5,y))
    ]]></literal>
    <justification jstring="[para(13142(a,1),21507(a,1,3))].">
      <j1 rule="para" parents="13142 21507"/>
    </justification>
  </clause>

  <clause id="21560">
    <literal><![CDATA[
      L(x,y \ z,K(u,w)) = L(x,y * z,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,21499,a(flip),b,21559,a),flip(a)].">
      <j1 rule="hyper" parents="63 21499 21559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21561">
    <literal><![CDATA[
      L(x,y * z,K(u,w \ 1)) = L(x,w,K(y \ z,u))
    ]]></literal>
    <justification jstring="[hyper(21506,a,21560,a),flip(a)].">
      <j1 rule="hyper" parents="21506 21560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21562">
    <literal><![CDATA[
      L(x,y,K(z \ u,w)) = L(x,y,K(z * u,w))
    ]]></literal>
    <justification jstring="[hyper(21506,a,21561,a),flip(a)].">
      <j1 rule="hyper" parents="21506 21561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21563">
    <literal><![CDATA[
      x \ L(x,y,K(z * u,w)) = a(x,y,K(z \ u,w))
    ]]></literal>
    <justification jstring="[hyper(121,a,21562,a(flip),b,14466,a)].">
      <j1 rule="hyper" parents="121 21562 14466"/>
    </justification>
  </clause>

  <clause id="21564">
    <literal><![CDATA[
      a(x,y,K(z \ u,w)) = a(x,y,K(z * u,w))
    ]]></literal>
    <justification jstring="[hyper(14503,a,21563,a),flip(a)].">
      <j1 rule="hyper" parents="14503 21563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21565">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(u * w,y)) = K(x,L(y,z,w / u))
    ]]></literal>
    <justification jstring="[para(21564(a,1),17689(a,1,2))].">
      <j1 rule="para" parents="21564 17689"/>
    </justification>
  </clause>

  <clause id="21566">
    <literal><![CDATA[
      K(x,L(y,z,u / w)) = K(x,L(y,z,w * u))
    ]]></literal>
    <justification jstring="[hyper(13770,a,21565,a),flip(a)].">
      <j1 rule="hyper" parents="13770 21565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21567">
    <literal><![CDATA[
      K(x,L(y,z,u \ w)) = K(x,L(y,z,u * w))
    ]]></literal>
    <justification jstring="[hyper(17863,a,21566,a)].">
      <j1 rule="hyper" parents="17863 21566"/>
    </justification>
  </clause>

  <clause id="21568">
    <literal><![CDATA[
      K(T(x,y) \ z,L(u,y,x * y)) = K(y \ ((x \ y) * z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,14030,a(flip),b,21567,a),flip(a)].">
      <j1 rule="hyper" parents="63 14030 21567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21569">
    <literal><![CDATA[
      x * K(x,L(y,z,u * w)) = T(x,L(y,z,u \ w))
    ]]></literal>
    <justification jstring="[hyper(126,a,21567,a(flip),b,4215,a(flip))].">
      <j1 rule="hyper" parents="126 21567 4215"/>
    </justification>
  </clause>

  <clause id="21570">
    <literal><![CDATA[
      T(x,L(y,z,u \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,L(y,z,u * w)) = v5
    ]]></literal>
    <justification jstring="[para(21569(a,1),4285(a,1))].">
      <j1 rule="para" parents="21569 4285"/>
    </justification>
  </clause>

  <clause id="21571">
    <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(21480(a,2),14527(a,1))].">
      <j1 rule="para" parents="21480 14527"/>
    </justification>
  </clause>

  <clause id="21572">
    <literal><![CDATA[
      K(T(x,y) \ z,L(u,y,x)) = K((x * y) \ (y * z),u)
    ]]></literal>
    <justification jstring="[para(22(a,2),21527(a,1,1,1))].">
      <j1 rule="para" parents="22 21527"/>
    </justification>
  </clause>

  <clause id="21573">
    <literal><![CDATA[
      K(L(x,y,z),y \ (z * u)) = K(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[hyper(333,a,5990,a(flip),b,21552,a),flip(a)].">
      <j1 rule="hyper" parents="333 5990 21552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21574">
    <literal><![CDATA[
      K(x,L(y \ (z * u),y,z)) = K(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[hyper(10963,a,21573,a)].">
      <j1 rule="hyper" parents="10963 21573"/>
    </justification>
  </clause>

  <clause id="21575">
    <literal><![CDATA[
      T(x,L(y \ (z * u),y,z)) = T(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[hyper(124,a,21574,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 21574 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21576">
    <literal><![CDATA[
      K(x,L(y \ T(z * u,z \ 1),y,z)) = K(x,(z \ y) \ (((z \ 1) \ u) * (z \ 1)))
    ]]></literal>
    <justification jstring="[para(962(a,1),21574(a,1,2,1,2))].">
      <j1 rule="para" parents="962 21574"/>
    </justification>
  </clause>

  <clause id="21577">
    <literal><![CDATA[
      T(x,(y \ (y \ z)) \ u) = T(x,z \ (y * (y * u)))
    ]]></literal>
    <justification jstring="[para(515(a,1),21575(a,1,2)),flip(a)].">
      <j1 rule="para" parents="515 21575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21578">
    <literal><![CDATA[
      T(x,L((y \ z) \ ((y \ 1) * u),y \ z,y \ 1)) = T(x,((y \ z) / T(y \ 1,z)) \ u)
    ]]></literal>
    <justification jstring="[para(3936(a,2),21575(a,2,2,1))].">
      <j1 rule="para" parents="3936 21575"/>
    </justification>
  </clause>

  <clause id="21579">
    <literal><![CDATA[
      K(T(x,y) \ z,L(u,y,x)) = K(y \ ((x \ y) * z),u)
    ]]></literal>
    <justification jstring="[hyper(21535,a,21568,a)].">
      <j1 rule="hyper" parents="21535 21568"/>
    </justification>
  </clause>

  <clause id="21580">
    <literal><![CDATA[
      K((x * y) \ (y * z),u) = K(y \ ((x \ y) * z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,21572,a(flip),b,21579,a)].">
      <j1 rule="hyper" parents="63 21572 21579"/>
    </justification>
  </clause>

  <clause id="21581">
    <literal><![CDATA[
      K((x \ y) \ (y * z),L(u,x,y)) = K((y \ (x \ y)) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,17642,a(flip),b,21551,a)].">
      <j1 rule="hyper" parents="63 17642 21551"/>
    </justification>
  </clause>

  <clause id="21582">
    <literal><![CDATA[
      K((x \ (y \ x)) \ z,u) = K(x \ (y * (x * z)),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,21523,a(flip),b,21581,a),flip(a)].">
      <j1 rule="hyper" parents="63 21523 21581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21584">
    <literal><![CDATA[
      x \ (y * (x * K(z,u))) = T(y,x) * K(z,u)
    ]]></literal>
    <justification jstring="[hyper(21524,a,10873,a)].">
      <j1 rule="hyper" parents="21524 10873"/>
    </justification>
  </clause>

  <clause id="21585">
    <literal><![CDATA[
      x * (T(y,x) * K(z,u)) = y * (x * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(142,a,21584,a)].">
      <j1 rule="hyper" parents="142 21584"/>
    </justification>
  </clause>

  <clause id="21587">
    <literal><![CDATA[
      L((T(x,y) * K(z,T(u,w))) / K(z,T(u,w)),K(z,T(u,w)),y) = T((K(z,T(u,w)) * x) / K(z,T(u,w)),K(u,z) * y)
    ]]></literal>
    <justification jstring="[para(21584(a,1),16501(a,1,1,1))].">
      <j1 rule="para" parents="21584 16501"/>
    </justification>
  </clause>

  <clause id="21589">
    <literal><![CDATA[
      T((K(x,y) * z) * u,K(x,y)) = z * (u * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,18167,a,b,21585,a)].">
      <j1 rule="hyper" parents="63 18167 21585"/>
    </justification>
  </clause>

  <clause id="21590">
    <literal><![CDATA[
      x * (T(y,x) * a(z,u,K(w,v5))) = y * (x * K(a(z,u,w),v5))
    ]]></literal>
    <justification jstring="[para(13539(a,2),21585(a,1,2,2))].">
      <j1 rule="para" parents="13539 21585"/>
    </justification>
  </clause>

  <clause id="21591">
    <literal><![CDATA[
      T((x / y) * z,K(y,y \ x)) = (y \ x) * (z * K(y,y \ x))
    ]]></literal>
    <justification jstring="[para(4352(a,1),21589(a,1,1,1))].">
      <j1 rule="para" parents="4352 21589"/>
    </justification>
  </clause>

  <clause id="21593">
    <literal><![CDATA[
      x * T(y * a(z,u,K(w,v5)),x) = y * (x * K(a(z,u,w),v5))
    ]]></literal>
    <justification jstring="[para(18125(a,2),21590(a,1,2))].">
      <j1 rule="para" parents="18125 21590"/>
    </justification>
  </clause>

  <clause id="21594">
    <literal><![CDATA[
      (x \ y) * (z * K(x,x \ y)) = T((y / x) * z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(7215,a,21591,a),flip(a)].">
      <j1 rule="hyper" parents="7215 21591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21595">
    <literal><![CDATA[
      T((x / y) * z,K(y,x)) * y = ((y \ x) * z) * T(y,y \ x)
    ]]></literal>
    <justification jstring="[para(21594(a,1),6217(a,1,1))].">
      <j1 rule="para" parents="21594 6217"/>
    </justification>
  </clause>

  <clause id="21596">
    <literal><![CDATA[
      (x * a(y,z,K(u,w))) * v5 = x * (v5 * K(a(y,z,u),w))
    ]]></literal>
    <justification jstring="[hyper(300,a,21593,a)].">
      <j1 rule="hyper" parents="300 21593"/>
    </justification>
  </clause>

  <clause id="21597">
    <literal><![CDATA[
      (x * a(y,z,K(u,w))) * v5 = x * (v5 * a(y,z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(13539(a,2),21596(a,2,2,2))].">
      <j1 rule="para" parents="13539 21596"/>
    </justification>
  </clause>

  <clause id="21598">
    <literal><![CDATA[
      L(x,a(y,z,K(u,w)),v5) = x
    ]]></literal>
    <justification jstring="[hyper(19256,a,21597,a)].">
      <j1 rule="hyper" parents="19256 21597"/>
    </justification>
  </clause>

  <clause id="21600">
    <literal><![CDATA[
      ((x \ y) * z) * T(x,x \ y) != u
    ]]></literal>
    <literal><![CDATA[
      T(((y / x) * z) * x,K(x,y)) = u
    ]]></literal>
    <justification jstring="[para(21595(a,1),6187(a,1))].">
      <j1 rule="para" parents="21595 6187"/>
    </justification>
  </clause>

  <clause id="21601">
    <literal><![CDATA[
      K((((x * y) * z) / (y * z)) / x,u) = a(x,y,K(z,L(u,y * z,x)))
    ]]></literal>
    <justification jstring="[hyper(333,a,13539,a,b,21553,a),flip(a)].">
      <j1 rule="hyper" parents="333 13539 21553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21602">
    <literal><![CDATA[
      K(x,(y \ T(z,y)) * (y * u)) = K(x,(z * (u / y)) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,21122,a(flip),b,21557,a)].">
      <j1 rule="hyper" parents="63 21122 21557"/>
    </justification>
  </clause>

  <clause id="21603">
    <literal><![CDATA[
      K(x,(y * (z / u)) * u) = K(x,(y / u) * (u * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,18041,a(flip),b,21602,a),flip(a)].">
      <j1 rule="hyper" parents="63 18041 21602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21604">
    <literal><![CDATA[
      K(x,(y / z) * (z * (u \ 1))) = K(x,(y / (z * u)) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,21468,a(flip),b,21603,a),flip(a)].">
      <j1 rule="hyper" parents="63 21468 21603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21605">
    <literal><![CDATA[
      K(x,(y / (z * u)) * z) = K(x,(y / z) * (z / u))
    ]]></literal>
    <justification jstring="[hyper(21331,a,21604,a),flip(a)].">
      <j1 rule="hyper" parents="21331 21604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21606">
    <literal><![CDATA[
      K(x,((y * z) / u) * (u / y)) = K(x,u * ((y * u) \ (z * y)))
    ]]></literal>
    <justification jstring="[hyper(63,a,21439,a(flip),b,21605,a),flip(a)].">
      <j1 rule="hyper" parents="63 21439 21605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21607">
    <literal><![CDATA[
      K(x,y * ((z * y) \ (u * z))) = K(x,L(T(u,z),y,z))
    ]]></literal>
    <justification jstring="[hyper(21541,a,21606,a),flip(a)].">
      <j1 rule="hyper" parents="21541 21606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21608">
    <literal><![CDATA[
      x * K(y,L(T(z,u),x,u)) = (x * u) / (u * K(z,y))
    ]]></literal>
    <justification jstring="[para(21607(a,1),21411(a,1,2))].">
      <j1 rule="para" parents="21607 21411"/>
    </justification>
  </clause>

  <clause id="21609">
    <literal><![CDATA[
      (x / (1 / y)) * (K(z,u) / y) = (x * y) / (y * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,21530,a,b,21608,a)].">
      <j1 rule="hyper" parents="63 21530 21608"/>
    </justification>
  </clause>

  <clause id="21610">
    <literal><![CDATA[
      (x * y) / (y * K(T(z,y),u)) = (x / (y \ 1)) * (y \ K(u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,19838,a(flip),b,21609,a),flip(a)].">
      <j1 rule="hyper" parents="63 19838 21609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21611">
    <literal><![CDATA[
      (x / (y \ 1)) * (y \ K(z,u)) = (x * y) / (K(u,z) * y)
    ]]></literal>
    <justification jstring="[para(6357(a,1),21610(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6357 21610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21612">
    <literal><![CDATA[
      (x * (y / z)) / (K(u,y) * (y / z)) = (x / z) * (z * K(y,u))
    ]]></literal>
    <justification jstring="[hyper(20269,a,21611,a),flip(a)].">
      <j1 rule="hyper" parents="20269 21611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21613">
    <literal><![CDATA[
      (x * (T(y,z) / u)) / (y / u) = (x / u) * (u * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,20706,a(flip),b,21612,a)].">
      <j1 rule="hyper" parents="63 20706 21612"/>
    </justification>
  </clause>

  <clause id="21614">
    <literal><![CDATA[
      ((x / y) * (y * K(z,u))) * K(u,z) = L(x,K(u,z),y \ z)
    ]]></literal>
    <justification jstring="[para(21613(a,1),20720(a,1,1))].">
      <j1 rule="para" parents="21613 20720"/>
    </justification>
  </clause>

  <clause id="21615">
    <literal><![CDATA[
      L(x,K(y,z),u \ z) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(21571,a,21614,a),flip(a)].">
      <j1 rule="hyper" parents="21571 21614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21616">
    <literal><![CDATA[
      L(x,y,K(z,u \ z)) = L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,19338,a(flip),b,21615,a),flip(a)].">
      <j1 rule="hyper" parents="63 19338 21615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21617">
    <literal><![CDATA[
      L(x,K(y,z),u) = L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(11895,a,21616,a),flip(a)].">
      <j1 rule="hyper" parents="11895 21616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21620">
    <literal><![CDATA[
      L(x,K(y,z),u) = L(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(4391,a,21617,a)].">
      <j1 rule="hyper" parents="4391 21617"/>
    </justification>
  </clause>

  <clause id="21621">
    <literal><![CDATA[
      L(x,K(y,z),u) = L(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(333,a,21497,a(flip),b,21617,a),flip(a)].">
      <j1 rule="hyper" parents="333 21497 21617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21622">
    <literal><![CDATA[
      R(x,K(y,z),u) = L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,20213,a,b,21617,a)].">
      <j1 rule="hyper" parents="63 20213 21617"/>
    </justification>
  </clause>

  <clause id="21623">
    <literal><![CDATA[
      T(x,L(L(K(y,z) * u,z,K(w,y)),w * K(z,y),v5)) = T(x,K(y,z) * ((v5 * w) \ (v5 * (w * u))))
    ]]></literal>
    <justification jstring="[para(21617(a,1),20678(a,1,2,1))].">
      <j1 rule="para" parents="21617 20678"/>
    </justification>
  </clause>

  <clause id="21624">
    <literal><![CDATA[
      (K(x,y) * z) * L(u,y,K(z,x)) = z * (T(K(x,y),z) * u)
    ]]></literal>
    <justification jstring="[hyper(126,a,21620,a(flip),b,10082,a(flip))].">
      <j1 rule="hyper" parents="126 21620 10082"/>
    </justification>
  </clause>

  <clause id="21625">
    <literal><![CDATA[
      L(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,K(y,u),z) = w
    ]]></literal>
    <justification jstring="[para(21620(a,1),4391(a,1))].">
      <j1 rule="para" parents="21620 4391"/>
    </justification>
  </clause>

  <clause id="21626">
    <literal><![CDATA[
      x * a(x,y,K(z,u)) = R(x,K(z,u),y)
    ]]></literal>
    <justification jstring="[hyper(333,a,21496,a,b,21622,a)].">
      <j1 rule="hyper" parents="333 21496 21622"/>
    </justification>
  </clause>

  <clause id="21629">
    <literal><![CDATA[
      x * a(x,T(y,K(z,u)),K(w,v5)) = R(x,K(w,v5),y)
    ]]></literal>
    <justification jstring="[hyper(333,a,17587,a(flip),b,21626,a),flip(a)].">
      <j1 rule="hyper" parents="333 17587 21626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21630">
    <literal><![CDATA[
      ((x * K(y,z)) * u) / (K(y,z) * u) = x * a(x,T(u,K(w,v5)),K(y,z))
    ]]></literal>
    <justification jstring="[hyper(333,a,20,a(flip),b,21629,a)].">
      <j1 rule="hyper" parents="333 20 21629"/>
    </justification>
  </clause>

  <clause id="21631">
    <literal><![CDATA[
      x * (T(K(y,z),x) * u) = K(y,z) * (x * u)
    ]]></literal>
    <justification jstring="[hyper(21505,a,21624,a),flip(a)].">
      <j1 rule="hyper" parents="21505 21624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21632">
    <literal><![CDATA[
      x * (K(y,T(z,x)) * u) = K(y,z) * (x * u)
    ]]></literal>
    <justification jstring="[para(6365(a,2),21631(a,1,2,1))].">
      <j1 rule="para" parents="6365 21631"/>
    </justification>
  </clause>

  <clause id="21633">
    <literal><![CDATA[
      K(x,T(y,z)) * (z * u) = z * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[para(6896(a,1),21631(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6896 21631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21634">
    <literal><![CDATA[
      K(x,y * z) * (y * u) = y * (K(x,z * y) * u)
    ]]></literal>
    <justification jstring="[para(12230(a,1),21631(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12230 21631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21635">
    <literal><![CDATA[
      T(x,K(y,z) * (u * w)) = T(x,u * (K(y,z) * w))
    ]]></literal>
    <justification jstring="[para(21631(a,1),16402(a,1,2))].">
      <j1 rule="para" parents="21631 16402"/>
    </justification>
  </clause>

  <clause id="21636">
    <literal><![CDATA[
      x * (K(y,T(z,x)) * ((x \ 1) * u)) = K(y,z) * L(u,x,x)
    ]]></literal>
    <justification jstring="[para(2599(a,1),21632(a,2,2))].">
      <j1 rule="para" parents="2599 21632"/>
    </justification>
  </clause>

  <clause id="21638">
    <literal><![CDATA[
      K(x,T(y,z)) * ((z \ 1) * u) = (z \ 1) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[para(7261(a,1),21633(a,1,1))].">
      <j1 rule="para" parents="7261 21633"/>
    </justification>
  </clause>

  <clause id="21639">
    <literal><![CDATA[
      T(x,y * (K(z,z \ u) * w)) = T(x,K(z,u) * (y * w))
    ]]></literal>
    <justification jstring="[hyper(15795,a,21635,a),flip(a)].">
      <j1 rule="hyper" parents="15795 21635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21640">
    <literal><![CDATA[
      T(x,K(y,z) * (u * (z * w))) = T(x,u * (z * (K(y,z) * w)))
    ]]></literal>
    <justification jstring="[para(4712(a,1),21635(a,2,2,2))].">
      <j1 rule="para" parents="4712 21635"/>
    </justification>
  </clause>

  <clause id="21641">
    <literal><![CDATA[
      x * ((x \ 1) * (K(y,z) * u)) = K(y,z) * L(u,x,x)
    ]]></literal>
    <justification jstring="[para(21638(a,1),21636(a,1,2))].">
      <j1 rule="para" parents="21638 21636"/>
    </justification>
  </clause>

  <clause id="21642">
    <literal><![CDATA[
      L(K(x,y) * z,u,u) = K(x,y) * L(z,u,u)
    ]]></literal>
    <justification jstring="[hyper(2633,a,21641,a)].">
      <j1 rule="hyper" parents="2633 21641"/>
    </justification>
  </clause>

  <clause id="21643">
    <literal><![CDATA[
      L(K(x,y) * (K(y,x) * z),u,u) \ z = a(u,u,K(y,x) * z)
    ]]></literal>
    <justification jstring="[para(21642(a,2),14749(a,1,1))].">
      <j1 rule="para" parents="21642 14749"/>
    </justification>
  </clause>

  <clause id="21644">
    <literal><![CDATA[
      T(x,K(y,z) * (u * (z * w))) = T(x,u * (T(z,y) * w))
    ]]></literal>
    <justification jstring="[hyper(333,a,18844,a(flip),b,21640,a),flip(a)].">
      <j1 rule="hyper" parents="333 18844 21640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21645">
    <literal><![CDATA[
      T(x,y * (K(z,z \ u) * (u * w))) = T(x,y * (T(u,z) * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,21639,a,b,21644,a)].">
      <j1 rule="hyper" parents="63 21639 21644"/>
    </justification>
  </clause>

  <clause id="21646">
    <literal><![CDATA[
      a(x,x,K(y,z) * u) = L(u,x,x) \ u
    ]]></literal>
    <justification jstring="[para(4558(a,1),21643(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4558 21643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21647">
    <literal><![CDATA[
      a(x,x,K(y,z) * u) = a(x,x,u)
    ]]></literal>
    <justification jstring="[hyper(333,a,14335,a(flip),b,21646,a),flip(a)].">
      <j1 rule="hyper" parents="333 14335 21646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21648">
    <literal><![CDATA[
      a(x,x,T(y * (z \ u),K(z,u))) = a(x,x,y * (u / z))
    ]]></literal>
    <justification jstring="[para(7772(a,1),21647(a,1,3))].">
      <j1 rule="para" parents="7772 21647"/>
    </justification>
  </clause>

  <clause id="21649">
    <literal><![CDATA[
      a(x,x,y * (z / u)) = a(x,x,y * (u \ z))
    ]]></literal>
    <justification jstring="[hyper(20330,a,21648,a),flip(a)].">
      <j1 rule="hyper" parents="20330 21648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21651">
    <literal><![CDATA[
      T(x,y * ((z * (u / z)) * w)) = T(x,y * (T(u,z) * w))
    ]]></literal>
    <justification jstring="[para(10075(a,1),21645(a,1,2,2))].">
      <j1 rule="para" parents="10075 21645"/>
    </justification>
  </clause>

  <clause id="21652">
    <literal><![CDATA[
      T(x,y * (((z \ 1) * K(u \ 1,(1 / z) * u)) * w)) = T(x,y * (T(1 / z,u \ 1) * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,8561,a,b,21651,a)].">
      <j1 rule="hyper" parents="63 8561 21651"/>
    </justification>
  </clause>

  <clause id="21653">
    <literal><![CDATA[
      T(x,y * (T(z / (u \ 1),z) * w)) = T(x,y * ((T(z,u) / (u \ 1)) * w))
    ]]></literal>
    <justification jstring="[para(3095(a,2),21651(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="3095 21651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21654">
    <literal><![CDATA[
      K((((x * y) * z) / (y * z)) / x,u) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(333,a,13838,a(flip),b,21601,a),flip(a)].">
      <j1 rule="hyper" parents="333 13838 21601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21656">
    <literal><![CDATA[
      K(R(x,y,z) / x,u) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(20(a,2),21654(a,1,1,1))].">
      <j1 rule="para" parents="20 21654"/>
    </justification>
  </clause>

  <clause id="21657">
    <literal><![CDATA[
      K(x \ R(x,y,z),u) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(3022(a,1),21656(a,1,1))].">
      <j1 rule="para" parents="3022 21656"/>
    </justification>
  </clause>

  <clause id="21658">
    <literal><![CDATA[
      (x \ R(x,y,z)) * a(x,y,K(z,u)) = T(x \ R(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(126,a,21657,a(flip),b,4215,a(flip))].">
      <j1 rule="hyper" parents="126 21657 4215"/>
    </justification>
  </clause>

  <clause id="21659">
    <literal><![CDATA[
      L(x,y,K(z,u)) \ R(x,y,u) = T(x \ R(x,y,u),z)
    ]]></literal>
    <justification jstring="[hyper(17892,a,21658,a)].">
      <j1 rule="hyper" parents="17892 21658"/>
    </justification>
  </clause>

  <clause id="21660">
    <literal><![CDATA[
      R(L(x,y,K(x * z,u)) \ R(x,y,u),x,z) = T((x * z) \ (R(x,y,u) * z),x)
    ]]></literal>
    <justification jstring="[para(21659(a,2),1041(a,1,1))].">
      <j1 rule="para" parents="21659 1041"/>
    </justification>
  </clause>

  <clause id="21661">
    <literal><![CDATA[
      T(x \ R(x,x,y),z) = x \ R(x,x,y)
    ]]></literal>
    <justification jstring="[para(13305(a,1),21659(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13305 21659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21662">
    <literal><![CDATA[
      L(x,y,K(z,u)) \ R(x,y,z) = T(x \ R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(15927(a,1),21659(a,1,1))].">
      <j1 rule="para" parents="15927 21659"/>
    </justification>
  </clause>

  <clause id="21663">
    <literal><![CDATA[
      L(x,y,K(z,u)) \ R(x,u,z) = T(x \ R(x,u,z),y)
    ]]></literal>
    <justification jstring="[para(21497(a,2),21659(a,1,1))].">
      <j1 rule="para" parents="21497 21659"/>
    </justification>
  </clause>

  <clause id="21664">
    <literal><![CDATA[
      (x * (y \ R(y,z,u))) / x = T(y \ R(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,17789,a(flip),b,21662,a)].">
      <j1 rule="hyper" parents="63 17789 21662"/>
    </justification>
  </clause>

  <clause id="21665">
    <literal><![CDATA[
      T(x \ R(x,y,z),K(u,w)) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(17577(a,1),21662(a,1,1)),flip(a)].">
      <j1 rule="para" parents="17577 21662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21666">
    <literal><![CDATA[
      T(x \ R(x,y,z),K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      x \ R(x,y,z) = v5
    ]]></literal>
    <justification jstring="[para(21665(a,1),5305(a,1,1)),flip(b)].">
      <j1 rule="para" parents="21665 5305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21667">
    <literal><![CDATA[
      (a(x,y,x) * R(x,z,u)) / R(x,y,x) = T(x \ R(x,z,u),R(x,y,x))
    ]]></literal>
    <justification jstring="[para(9329(a,1),21664(a,1,1))].">
      <j1 rule="para" parents="9329 21664"/>
    </justification>
  </clause>

  <clause id="21668">
    <literal><![CDATA[
      K(x,L((y * ((y * z) / y)) \ u,y,z)) = K(x,z \ (T(y,z) \ u))
    ]]></literal>
    <justification jstring="[hyper(17658,a,21550,a)].">
      <j1 rule="hyper" parents="17658 21550"/>
    </justification>
  </clause>

  <clause id="21669">
    <literal><![CDATA[
      K(x,L(T(y * z,y) \ u,y,z)) = K(x,z \ (T(y,z) \ u))
    ]]></literal>
    <justification jstring="[hyper(15192,a,21668,a)].">
      <j1 rule="hyper" parents="15192 21668"/>
    </justification>
  </clause>

  <clause id="21671">
    <literal><![CDATA[
      K(x,L((y * z) \ u,z,y)) = K(x,y \ (T(z,y) \ u))
    ]]></literal>
    <justification jstring="[hyper(12902,a,21669,a)].">
      <j1 rule="hyper" parents="12902 21669"/>
    </justification>
  </clause>

  <clause id="21672">
    <literal><![CDATA[
      K(x,y \ (T(z,y) \ u)) = K(x,z \ (y \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,21549,a(flip),b,21671,a),flip(a)].">
      <j1 rule="hyper" parents="63 21549 21671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21673">
    <literal><![CDATA[
      T(x,y \ (T(z,y) \ u)) = x * K(x,z \ (y \ u))
    ]]></literal>
    <justification jstring="[hyper(126,a,21672,a(flip),b,4215,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="126 21672 4215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21674">
    <literal><![CDATA[
      K(x \ (T(y,x) \ z),u) = (w * K(u,y \ (x \ z))) \ w
    ]]></literal>
    <justification jstring="[para(21672(a,1),5990(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="21672 5990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21675">
    <literal><![CDATA[
      T(x,y \ (T(z,y) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ (y \ u)) = w
    ]]></literal>
    <justification jstring="[para(21673(a,2),4285(a,1))].">
      <j1 rule="para" parents="21673 4285"/>
    </justification>
  </clause>

  <clause id="21676">
    <literal><![CDATA[
      T(x,(y / z) \ (T(u,T(z \ y,z)) \ w)) = T(x,u \ (T(z \ y,z) \ w))
    ]]></literal>
    <justification jstring="[hyper(21675,a,14944,a),flip(a)].">
      <j1 rule="hyper" parents="21675 14944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21677">
    <literal><![CDATA[
      T(x,T(y,z) \ (z \ u)) = T(x,z \ (y \ u))
    ]]></literal>
    <justification jstring="[hyper(21675,a,14945,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="21675 14945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21678">
    <literal><![CDATA[
      T(x,((y \ 1) * z) \ (y \ u)) = T(x,y \ ((z * (y \ 1)) \ u))
    ]]></literal>
    <justification jstring="[hyper(17263,a,21677,a)].">
      <j1 rule="hyper" parents="17263 21677"/>
    </justification>
  </clause>

  <clause id="21679">
    <literal><![CDATA[
      T(x,y \ ((z \ 1) \ u)) = T(x,T(z,y) * (y \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,18191,a(flip),b,21677,a),flip(a)].">
      <j1 rule="hyper" parents="63 18191 21677"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21680">
    <literal><![CDATA[
      T(x,T(T(y,z) \ (z \ u),w)) = K(x,w) * T(x * K(w,x),z \ (y \ u))
    ]]></literal>
    <justification jstring="[hyper(126,a,21677,a(flip),b,8027,a),flip(a)].">
      <j1 rule="hyper" parents="126 21677 8027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21681">
    <literal><![CDATA[
      T(x,T(y,a(z,u,w)) * (a(z,u,w) \ v5)) = T(x,a(z,u,w) * ((y \ 1) \ v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,21277,a(flip),b,21679,a),flip(a)].">
      <j1 rule="hyper" parents="63 21277 21679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21684">
    <literal><![CDATA[
      K(x \ (T(y,x) \ z),u) = K(y \ (x \ z),u)
    ]]></literal>
    <justification jstring="[hyper(333,a,5990,a(flip),b,21674,a),flip(a)].">
      <j1 rule="hyper" parents="333 5990 21674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21685">
    <literal><![CDATA[
      K(T(x,y) \ (y \ z),u) = K(y \ (x \ z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,15761,a,b,21684,a)].">
      <j1 rule="hyper" parents="63 15761 21684"/>
    </justification>
  </clause>

  <clause id="21686">
    <literal><![CDATA[
      K(L(x,y,K(z,u)) \ (a(u,y,z) \ w),v5) = K(a(u,y,z) \ (x \ w),v5)
    ]]></literal>
    <justification jstring="[para(14461(a,2),21685(a,1,1,1))].">
      <j1 rule="para" parents="14461 21685"/>
    </justification>
  </clause>

  <clause id="21688">
    <literal><![CDATA[
      T(x,((y \ 1) * z) \ (y \ u)) = T(x,y * ((z * y) \ u))
    ]]></literal>
    <justification jstring="[hyper(333,a,13383,a(flip),b,21678,a),flip(a)].">
      <j1 rule="hyper" parents="333 13383 21678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21689">
    <literal><![CDATA[
      K(x \ (y \ T(z,u \ w)),v5) = K(x \ (y \ T(z,u * w)),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,21548,a(flip),b,21554,a),flip(a)].">
      <j1 rule="hyper" parents="63 21548 21554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21690">
    <literal><![CDATA[
      K((x \ 1) \ (y \ T(z,u * w)),v5) = K(x * (y \ T(z,u \ w)),v5)
    ]]></literal>
    <justification jstring="[hyper(13425,a,21689,a),flip(a)].">
      <j1 rule="hyper" parents="13425 21689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21691">
    <literal><![CDATA[
      (x * K(y \ (z \ T(u,w * v5)),v6)) \ (x * v6) = T(v6,y \ (z \ T(u,w \ v5)))
    ]]></literal>
    <justification jstring="[para(21689(a,1),5447(a,1,1,2))].">
      <j1 rule="para" parents="21689 5447"/>
    </justification>
  </clause>

  <clause id="21692">
    <literal><![CDATA[
      K((x \ K(x * (y \ T(z,u \ w)),x \ 1)) \ (y \ T(z,u * w)),v5) = K((y \ T(z,u \ w)) / (x \ 1),v5)
    ]]></literal>
    <justification jstring="[para(8677(a,1),21689(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8677 21689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21693">
    <literal><![CDATA[
      K(x * (y \ T(z,u \ w)),v5) = K(x * (y \ T(z,u * w)),v5)
    ]]></literal>
    <justification jstring="[hyper(13425,a,21690,a),flip(a)].">
      <j1 rule="hyper" parents="13425 21690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21694">
    <literal><![CDATA[
      K(x \ (y \ ((1 / z) \ u)),w) = K(x \ (y \ ((z \ 1) \ u)),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,21548,a(flip),b,21555,a),flip(a)].">
      <j1 rule="hyper" parents="63 21548 21555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21695">
    <literal><![CDATA[
      (x * K(y \ (z \ ((u \ 1) \ w)),v5)) \ (x * v5) = T(v5,y \ (z \ ((1 / u) \ w)))
    ]]></literal>
    <justification jstring="[para(21694(a,1),5447(a,1,1,2))].">
      <j1 rule="para" parents="21694 5447"/>
    </justification>
  </clause>

  <clause id="21696">
    <literal><![CDATA[
      T(((1 / x) * R(x,x,x \ y)) * x,K(x,1)) = R(x,x,T(x * y,x \ 1))
    ]]></literal>
    <justification jstring="[hyper(21600,a,14654,a)].">
      <j1 rule="hyper" parents="21600 14654"/>
    </justification>
  </clause>

  <clause id="21697">
    <literal><![CDATA[
      ((x * K(y,z)) * u) / L(K(y,z) * u,w,a(w,v5,K(v6,v7))) = x * a(x,T(u,K(v8,v9)),K(y,z))
    ]]></literal>
    <justification jstring="[para(13772(a,2),21630(a,1,2))].">
      <j1 rule="para" parents="13772 21630"/>
    </justification>
  </clause>

  <clause id="21698">
    <literal><![CDATA[
      R(a(x,y,x) * x,z,u) / R(x,y,x) = T(x \ R(x,z,u),R(x,y,x))
    ]]></literal>
    <justification jstring="[para(11924(a,2),21667(a,1,1))].">
      <j1 rule="para" parents="11924 21667"/>
    </justification>
  </clause>

  <clause id="21699">
    <literal><![CDATA[
      K(a(x,y,z) \ (u \ w),v5) = K(u \ (a(x,y,z) \ w),v5)
    ]]></literal>
    <justification jstring="[hyper(17929,a,21686,a),flip(a)].">
      <j1 rule="hyper" parents="17929 21686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21700">
    <literal><![CDATA[
      K(x \ (a(y,z,u) \ w),v5) = K(a(y,z,u) * (x \ w),v5)
    ]]></literal>
    <justification jstring="[hyper(21282,a,21699,a),flip(a)].">
      <j1 rule="hyper" parents="21282 21699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21702">
    <literal><![CDATA[
      R(R(x,y,x),z,u) / R(x,y,x) = T(x \ R(x,z,u),R(x,y,x))
    ]]></literal>
    <justification jstring="[para(8222(a,1),21698(a,1,1,1))].">
      <j1 rule="para" parents="8222 21698"/>
    </justification>
  </clause>

  <clause id="21703">
    <literal><![CDATA[
      R(x,y,x) \ R(R(x,y,x),z,u) = T(x \ R(x,z,u),R(x,y,x))
    ]]></literal>
    <justification jstring="[hyper(3024,a,21702,a)].">
      <j1 rule="hyper" parents="3024 21702"/>
    </justification>
  </clause>

  <clause id="21704">
    <literal><![CDATA[
      R(x,y,x) \ R(R(x,y,x),z,u) = x \ R(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(3035,a,21703,a(flip))].">
      <j1 rule="hyper" parents="3035 21703"/>
    </justification>
  </clause>

  <clause id="21705">
    <literal><![CDATA[
      ((x * y) * K(z,u)) / (z * (y * K(z,u))) = R(x / z,z,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(333,a,21512,a(flip),b,21510,a),flip(a)].">
      <j1 rule="hyper" parents="333 21512 21510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21706">
    <literal><![CDATA[
      T(x,y * ((T(z,u) / (u \ 1)) * w)) = T(x,y * (((u \ 1) \ z) * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,16724,a(flip),b,21653,a),flip(a)].">
      <j1 rule="hyper" parents="63 16724 21653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21707">
    <literal><![CDATA[
      T(x,(y / z) \ (T(u,y / z) \ w)) = T(x,u \ (T(z \ y,z) \ w))
    ]]></literal>
    <justification jstring="[para(6946(a,1),21676(a,1,2,2,1))].">
      <j1 rule="para" parents="6946 21676"/>
    </justification>
  </clause>

  <clause id="21708">
    <literal><![CDATA[
      T(x,y \ (T(z \ u,z) \ w)) = T(x,y \ ((u / z) \ w))
    ]]></literal>
    <justification jstring="[hyper(21675,a,21707,a),flip(a)].">
      <j1 rule="hyper" parents="21675 21707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21709">
    <literal><![CDATA[
      T(x,y \ (T(z \ u,z) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ ((u / z) \ w)) = v5
    ]]></literal>
    <justification jstring="[para(21707(a,1),21675(a,1))].">
      <j1 rule="para" parents="21707 21675"/>
    </justification>
  </clause>

  <clause id="21710">
    <literal><![CDATA[
      T(x,T(T(y,z) \ (z \ u),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,T(z \ (y \ u),w)) = v5
    ]]></literal>
    <justification jstring="[para(21680(a,2),8028(a,1))].">
      <j1 rule="para" parents="21680 8028"/>
    </justification>
  </clause>

  <clause id="21711">
    <literal><![CDATA[
      R(x,x,T(x * y,x \ 1)) = T(R(x,x,x \ y),K(x,1))
    ]]></literal>
    <justification jstring="[para(1579(a,1),21696(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1579 21696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21712">
    <literal><![CDATA[
      R(x,x,T(x * y,x \ 1)) = R(x,x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(333,a,3341,a(flip),b,21711,a),flip(a)].">
      <j1 rule="hyper" parents="333 3341 21711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21714">
    <literal><![CDATA[
      R(x,x,x \ y) = R(x,x,x * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,21513,a(flip),b,21712,a),flip(a)].">
      <j1 rule="hyper" parents="63 21513 21712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21716">
    <literal><![CDATA[
      R(x,x,x * y) * y = (x \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(125,a,21714,a(flip),b,762,a(flip))].">
      <j1 rule="hyper" parents="125 21714 762"/>
    </justification>
  </clause>

  <clause id="21717">
    <literal><![CDATA[
      x * R(y,y,y * x) = (y \ 1) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(21714(a,1),3114(a,1,2))].">
      <j1 rule="para" parents="21714 3114"/>
    </justification>
  </clause>

  <clause id="21718">
    <literal><![CDATA[
      (x / y) * R(y,y,T(x,y)) = (y \ 1) \ T(x / y,y)
    ]]></literal>
    <justification jstring="[para(14406(a,1),21717(a,1,2))].">
      <j1 rule="para" parents="14406 21717"/>
    </justification>
  </clause>

  <clause id="21719">
    <literal><![CDATA[
      (x \ 1) \ T(y / x,x) = (y / x) * R(x,x,y)
    ]]></literal>
    <justification jstring="[para(10340(a,1),21718(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10340 21718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21720">
    <literal><![CDATA[
      (x / y) * R(y,y,x) = (y \ 1) \ (y \ x)
    ]]></literal>
    <justification jstring="[para(113(a,1),21719(a,1,2)),flip(a)].">
      <j1 rule="para" parents="113 21719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21722">
    <literal><![CDATA[
      (x * y) \ (x \ ((x * x) * y)) = y \ ((x \ 1) \ (x \ y))
    ]]></literal>
    <justification jstring="[para(21720(a,1),14111(a,2,2))].">
      <j1 rule="para" parents="21720 14111"/>
    </justification>
  </clause>

  <clause id="21723">
    <literal><![CDATA[
      (x * y) \ (x \ ((x * x) * y)) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,17123,a(flip),b,21722,a),flip(a)].">
      <j1 rule="hyper" parents="333 17123 21722"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21725">
    <literal><![CDATA[
      T(x,a(y,z,u) * ((w \ 1) \ v5)) = T(x,w * (a(y,z,u) \ v5))
    ]]></literal>
    <justification jstring="[hyper(17925,a,21681,a),flip(a)].">
      <j1 rule="hyper" parents="17925 21681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21726">
    <literal><![CDATA[
      T(x,((y \ 1) \ z) * a(u,w,v5)) = T(x,y * (a(u,w,v5) \ z))
    ]]></literal>
    <justification jstring="[hyper(17601,a,21725,a)].">
      <j1 rule="hyper" parents="17601 21725"/>
    </justification>
  </clause>

  <clause id="21727">
    <literal><![CDATA[
      T(x,((y \ 1) \ z) * a(u,u,w)) = T(x,y * (a(w,u,u) \ z))
    ]]></literal>
    <justification jstring="[hyper(21281,a,21726,a)].">
      <j1 rule="hyper" parents="21281 21726"/>
    </justification>
  </clause>

  <clause id="21728">
    <literal><![CDATA[
      T(x,y * (a(z,u,u) \ w)) = T(x,y * (a(u,u,z) \ w))
    ]]></literal>
    <justification jstring="[hyper(63,a,21726,a(flip),b,21727,a),flip(a)].">
      <j1 rule="hyper" parents="63 21726 21727"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21733">
    <literal><![CDATA[
      R(L(x,y,K(z,u)) \ R(x,u,z),x,y) = T((x * y) \ (R(x,u,z) * y),x)
    ]]></literal>
    <justification jstring="[para(21504(a,1),21660(a,1,1,1))].">
      <j1 rule="para" parents="21504 21660"/>
    </justification>
  </clause>

  <clause id="21734">
    <literal><![CDATA[
      T((x * y) \ (R(x,z,u) * y),x) = R(T(x \ R(x,z,u),y),x,y)
    ]]></literal>
    <justification jstring="[para(21663(a,1),21733(a,1,1)),flip(a)].">
      <j1 rule="para" parents="21663 21733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21735">
    <literal><![CDATA[
      R(T(x \ R(x,y,z),u),x,u) = (x * u) \ (R(x,y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(3048,a,21734,a),flip(a)].">
      <j1 rule="hyper" parents="3048 21734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21736">
    <literal><![CDATA[
      T(x \ R(x,y,z),x * u) = T(x \ R(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(1045,a,21734,a)].">
      <j1 rule="hyper" parents="1045 21734"/>
    </justification>
  </clause>

  <clause id="21737">
    <literal><![CDATA[
      R(T(x \ R(x,y,z),u),x,u) != w
    ]]></literal>
    <literal><![CDATA[
      (x * u) \ (R(x,y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(21734(a,1),3048(a,1))].">
      <j1 rule="para" parents="21734 3048"/>
    </justification>
  </clause>

  <clause id="21738">
    <literal><![CDATA[
      T((1 / x) \ R(1 / x,y,z),x \ u) = T((1 / x) \ R(1 / x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(13609,a,21736,a)].">
      <j1 rule="hyper" parents="13609 21736"/>
    </justification>
  </clause>

  <clause id="21739">
    <literal><![CDATA[
      x \ (y \ ((L(y \ R(y,z,u),x,y) * y) * x)) = R(T(y \ R(y,z,u),x),y,x)
    ]]></literal>
    <justification jstring="[para(21736(a,1),1139(a,2,1))].">
      <j1 rule="para" parents="21736 1139"/>
    </justification>
  </clause>

  <clause id="21740">
    <literal><![CDATA[
      R(T(x \ R(x,x,y),y),x,y) = (x * y) \ (x \ ((x * x) * y))
    ]]></literal>
    <justification jstring="[para(1511(a,2),21735(a,2,2))].">
      <j1 rule="para" parents="1511 21735"/>
    </justification>
  </clause>

  <clause id="21741">
    <literal><![CDATA[
      (x * y) \ (x \ ((x * x) * y)) = R(x \ R(x,x,y),x,y)
    ]]></literal>
    <justification jstring="[para(21661(a,1),21740(a,1,1)),flip(a)].">
      <j1 rule="para" parents="21661 21740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21742">
    <literal><![CDATA[
      R(x \ R(x,x,y),x,y) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,21723,a(flip),b,21741,a),flip(a)].">
      <j1 rule="hyper" parents="63 21723 21741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21744">
    <literal><![CDATA[
      R(x * ((x \ y) / y),x,y) = a(x,x,y)
    ]]></literal>
    <justification jstring="[para(14600(a,1),21742(a,1,1))].">
      <j1 rule="para" parents="14600 21742"/>
    </justification>
  </clause>

  <clause id="21745">
    <literal><![CDATA[
      ((x \ 1) * y) \ (x \ y) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,17129,a(flip),b,21744,a)].">
      <j1 rule="hyper" parents="63 17129 21744"/>
    </justification>
  </clause>

  <clause id="21746">
    <literal><![CDATA[
      a(x,x,y) * ((x \ 1) * y) = x \ y
    ]]></literal>
    <justification jstring="[hyper(125,a,21744,a(flip),b,2194,a(flip))].">
      <j1 rule="hyper" parents="125 21744 2194"/>
    </justification>
  </clause>

  <clause id="21747">
    <literal><![CDATA[
      K(x \ 1,y) * a(x,x,y) = (y * (x \ 1)) \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(126,a,21745,a(flip),b,10010,a)].">
      <j1 rule="hyper" parents="126 21745 10010"/>
    </justification>
  </clause>

  <clause id="21748">
    <literal><![CDATA[
      a(x,x,y) * (y \ ((x \ 1) * y)) = y \ (x \ y)
    ]]></literal>
    <justification jstring="[para(21746(a,1),14663(a,1,2)),flip(a)].">
      <j1 rule="para" parents="21746 14663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21749">
    <literal><![CDATA[
      a(x,x,y) * T(x \ 1,y) = y \ (x \ y)
    ]]></literal>
    <justification jstring="[para(22(a,2),21748(a,1,2))].">
      <j1 rule="para" parents="22 21748"/>
    </justification>
  </clause>

  <clause id="21750">
    <literal><![CDATA[
      T(a(x,x,y) * (x \ 1),y) = y \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,21349,a,b,21749,a)].">
      <j1 rule="hyper" parents="63 21349 21749"/>
    </justification>
  </clause>

  <clause id="21751">
    <literal><![CDATA[
      T(x \ a(x,x,y),y) = y \ (x \ y)
    ]]></literal>
    <justification jstring="[para(15948(a,1),21750(a,1,1))].">
      <j1 rule="para" parents="15948 21750"/>
    </justification>
  </clause>

  <clause id="21752">
    <literal><![CDATA[
      x \ a(x,x,y) = (x \ y) / y
    ]]></literal>
    <justification jstring="[hyper(262,a,21751,a),flip(a)].">
      <j1 rule="hyper" parents="262 21751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21753">
    <literal><![CDATA[
      (x \ a(x,x,y)) * y = x \ y
    ]]></literal>
    <justification jstring="[hyper(143,a,21751,a)].">
      <j1 rule="hyper" parents="143 21751"/>
    </justification>
  </clause>

  <clause id="21754">
    <literal><![CDATA[
      T(x,T(y \ a(y,y,z \ 1),z \ 1) * u) = T(x,((1 / z) \ (y \ (z \ 1))) * u)
    ]]></literal>
    <justification jstring="[para(21751(a,2),14229(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="21751 14229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21755">
    <literal><![CDATA[
      x \ R(x,x,y) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(14601,a,21752,a)].">
      <j1 rule="hyper" parents="14601 21752"/>
    </justification>
  </clause>

  <clause id="21756">
    <literal><![CDATA[
      T(x,(y * ((z \ a(z,z,y)) * (y \ 1))) * u) = T(x,((y \ 1) * (z \ y)) * u)
    ]]></literal>
    <justification jstring="[para(21752(a,2),18446(a,1,2,1,2,1))].">
      <j1 rule="para" parents="21752 18446"/>
    </justification>
  </clause>

  <clause id="21757">
    <literal><![CDATA[
      a(x,x,x * y) = x * (y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(63,a,14602,a(flip),b,21755,a),flip(a)].">
      <j1 rule="hyper" parents="63 14602 21755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21758">
    <literal><![CDATA[
      (x \ a(x,x,y)) * (y \ 1) = x \ (y \ 1)
    ]]></literal>
    <justification jstring="[para(14323(a,1),21753(a,1,1,2))].">
      <j1 rule="para" parents="14323 21753"/>
    </justification>
  </clause>

  <clause id="21759">
    <literal><![CDATA[
      ((x \ 1) \ (x \ (x * y))) / (x * y) = x * (y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(63,a,17122,a,b,21757,a)].">
      <j1 rule="hyper" parents="63 17122 21757"/>
    </justification>
  </clause>

  <clause id="21761">
    <literal><![CDATA[
      K(x \ 1,(x \ 1) \ y) * a(x,x,(x \ 1) \ y) = K(x \ 1,(x \ 1) \ y) * (y \ (x \ ((x \ 1) \ y)))
    ]]></literal>
    <justification jstring="[hyper(333,a,10025,a,b,21747,a),flip(a)].">
      <j1 rule="hyper" parents="333 10025 21747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21762">
    <literal><![CDATA[
      K(x \ 1,x * (y / x)) * a(x,x,x * (y / x)) = ((x * (y * (x \ 1))) / x) \ (x \ (x * (y / x)))
    ]]></literal>
    <justification jstring="[para(989(a,2),21747(a,2,1))].">
      <j1 rule="para" parents="989 21747"/>
    </justification>
  </clause>

  <clause id="21763">
    <literal><![CDATA[
      ((x \ 1) \ y) / (x * y) = x * (y / (x * y))
    ]]></literal>
    <justification jstring="[para(9(a,1),21759(a,1,1,2))].">
      <j1 rule="para" parents="9 21759"/>
    </justification>
  </clause>

  <clause id="21764">
    <literal><![CDATA[
      (x * y) \ ((x \ 1) \ y) = x * (y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(63,a,2965,a(flip),b,21763,a)].">
      <j1 rule="hyper" parents="63 2965 21763"/>
    </justification>
  </clause>

  <clause id="21765">
    <literal><![CDATA[
      T((1 / x) \ R(1 / x,y,z),u) = T(x * R(x \ 1,y,z),x \ u)
    ]]></literal>
    <justification jstring="[para(1321(a,1),21738(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1321 21738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21766">
    <literal><![CDATA[
      T(x * R(x \ 1,y,z),x \ u) = T(x * R(x \ 1,y,z),u)
    ]]></literal>
    <justification jstring="[para(1321(a,1),21765(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1321 21765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21767">
    <literal><![CDATA[
      (x \ y) \ (y * R(y \ (x \ y),z,u)) = T(x * R(x \ 1,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,10744,a(flip),b,21766,a)].">
      <j1 rule="hyper" parents="63 10744 21766"/>
    </justification>
  </clause>

  <clause id="21768">
    <literal><![CDATA[
      T(x \ 1,x * y) * R((((x \ 1) \ y) \ y) \ 1,z,u) = T((x \ 1) * R((x \ 1) \ 1,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3938,a(flip),b,21767,a)].">
      <j1 rule="hyper" parents="63 3938 21767"/>
    </justification>
  </clause>

  <clause id="21769">
    <literal><![CDATA[
      T(x,((y \ 1) * (z \ y)) * u) = T(x,(y * (z \ (y \ 1))) * u)
    ]]></literal>
    <justification jstring="[para(21758(a,1),21756(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="21758 21756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21770">
    <literal><![CDATA[
      T(x,y \ (z \ T(u,w \ v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ (z \ T(u,w * v5))) = v6
    ]]></literal>
    <justification jstring="[para(21691(a,1),5458(a,1))].">
      <j1 rule="para" parents="21691 5458"/>
    </justification>
  </clause>

  <clause id="21771">
    <literal><![CDATA[
      T(x,y \ (z \ ((1 / u) \ w))) = T(x,y \ (z \ ((u \ 1) \ w)))
    ]]></literal>
    <justification jstring="[hyper(5458,a,21695,a),flip(a)].">
      <j1 rule="hyper" parents="5458 21695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21772">
    <literal><![CDATA[
      T(x,(y \ 1) \ (z \ ((u \ 1) \ w))) = T(x,y * (z \ ((1 / u) \ w)))
    ]]></literal>
    <justification jstring="[hyper(13423,a,21771,a),flip(a)].">
      <j1 rule="hyper" parents="13423 21771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21773">
    <literal><![CDATA[
      T(x,y * (z \ ((1 / u) \ w))) = T(x,y * (z \ ((u \ 1) \ w)))
    ]]></literal>
    <justification jstring="[hyper(13423,a,21772,a),flip(a)].">
      <j1 rule="hyper" parents="13423 21772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21774">
    <literal><![CDATA[
      T(x,y * ((z \ 1) \ (((1 / z) \ 1) \ u))) = T(x,y * (u * a(z,z,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,17132,a(flip),b,21773,a),flip(a)].">
      <j1 rule="hyper" parents="63 17132 21773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21775">
    <literal><![CDATA[
      T(x,y * ((z \ 1) \ (z \ u))) = T(x,y * (u * a(z,z,u)))
    ]]></literal>
    <justification jstring="[para(79(a,1),21774(a,1,2,2,2,1))].">
      <j1 rule="para" parents="79 21774"/>
    </justification>
  </clause>

  <clause id="21776">
    <literal><![CDATA[
      T(x,L(y / (y / z),z,y) \ u) = T(x,(y \ ((z * (y / z)) / z)) * u)
    ]]></literal>
    <justification jstring="[para(79(a,1),21458(a,1,2,1,2))].">
      <j1 rule="para" parents="79 21458"/>
    </justification>
  </clause>

  <clause id="21777">
    <literal><![CDATA[
      T(x,(y \ ((z * (y / z)) / z)) * u) = T(x,(y / (y * (1 / z))) \ u)
    ]]></literal>
    <justification jstring="[para(11078(a,1),21776(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11078 21776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21778">
    <literal><![CDATA[
      K(x,L(y \ T(z * u,z),y,z)) = K(x,(z \ y) \ (((z \ 1) \ u) * (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(17078,a,21576,a)].">
      <j1 rule="hyper" parents="17078 21576"/>
    </justification>
  </clause>

  <clause id="21779">
    <literal><![CDATA[
      K(x,(y \ z) \ (((y \ 1) \ u) * (y \ 1))) = K(x,(y * z) \ ((y * u) * y))
    ]]></literal>
    <justification jstring="[para(468(a,1),21778(a,1,2)),flip(a)].">
      <j1 rule="para" parents="468 21778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21780">
    <literal><![CDATA[
      K(x,(y \ z) \ (((y \ 1) \ u) * (y \ 1))) = K(x,(y * z) \ (y * (u * y)))
    ]]></literal>
    <justification jstring="[hyper(333,a,12750,a(flip),b,21779,a),flip(a)].">
      <j1 rule="hyper" parents="333 12750 21779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21781">
    <literal><![CDATA[
      K(x,(y \ z) \ (((y \ 1) \ u) * (y \ 1))) = K(x,y \ ((y / z) * (u * y)))
    ]]></literal>
    <justification jstring="[hyper(333,a,21532,a(flip),b,21780,a),flip(a)].">
      <j1 rule="hyper" parents="333 21532 21780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21782">
    <literal><![CDATA[
      K(x,(y \ z) \ T(u,y \ 1)) = K(x,y \ ((y / z) * (u * y)))
    ]]></literal>
    <justification jstring="[hyper(63,a,12726,a(flip),b,21781,a)].">
      <j1 rule="hyper" parents="63 12726 21781"/>
    </justification>
  </clause>

  <clause id="21783">
    <literal><![CDATA[
      K(x,y \ ((y / z) * (u * y))) = K(x,(y \ z) \ T(u,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,15343,a(flip),b,21782,a),flip(a)].">
      <j1 rule="hyper" parents="63 15343 21782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21784">
    <literal><![CDATA[
      K(x,(y \ z) \ T(u,y)) = K(x,(u \ z) \ y)
    ]]></literal>
    <justification jstring="[hyper(19855,a,21783,a),flip(a)].">
      <j1 rule="hyper" parents="19855 21783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21785">
    <literal><![CDATA[
      T(x,(y \ z) \ T(u,y)) = T(x,(u \ z) \ y)
    ]]></literal>
    <justification jstring="[hyper(124,a,21784,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 21784 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21786">
    <literal><![CDATA[
      T(x,T(y \ a(y,y,z \ 1),z \ 1) * u) = T(x,((z \ 1) \ (y \ (z \ 1))) * u)
    ]]></literal>
    <justification jstring="[hyper(333,a,14229,a(flip),b,21754,a),flip(a)].">
      <j1 rule="hyper" parents="333 14229 21754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21787">
    <literal><![CDATA[
      T(x,T(y \ a(y,y,z),z \ 1) * u) = T(x,((z \ 1) \ (y \ (z \ 1))) * u)
    ]]></literal>
    <justification jstring="[para(14323(a,1),21786(a,1,2,1,1,2))].">
      <j1 rule="para" parents="14323 21786"/>
    </justification>
  </clause>

  <clause id="21788">
    <literal><![CDATA[
      T(x,T(y \ a(y,y,z),z) * u) = T(x,((z \ 1) \ (y \ (z \ 1))) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,16137,a(flip),b,21787,a)].">
      <j1 rule="hyper" parents="63 16137 21787"/>
    </justification>
  </clause>

  <clause id="21789">
    <literal><![CDATA[
      T(x,((y \ 1) \ (z \ (y \ 1))) * u) = T(x,(y \ (z \ y)) * u)
    ]]></literal>
    <justification jstring="[para(21751(a,1),21788(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="21751 21788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21792">
    <literal><![CDATA[
      T(x,L((y \ z) \ ((y \ 1) * u),y \ z,y * 1)) = T(x,((y \ z) / T(y \ 1,z)) \ u)
    ]]></literal>
    <justification jstring="[hyper(21570,a,21578,a)].">
      <j1 rule="hyper" parents="21570 21578"/>
    </justification>
  </clause>

  <clause id="21794">
    <literal><![CDATA[
      T(x,L((y \ z) \ ((y \ 1) * u),y \ z,y)) = T(x,((y \ z) / T(y \ 1,z)) \ u)
    ]]></literal>
    <justification jstring="[para(8(a,1),21792(a,1,2,3))].">
      <j1 rule="para" parents="8 21792"/>
    </justification>
  </clause>

  <clause id="21795">
    <literal><![CDATA[
      T(x,((y \ z) / T(y \ 1,z)) \ u) = T(x,z \ (y * ((y \ 1) * u)))
    ]]></literal>
    <justification jstring="[para(515(a,1),21794(a,1,2)),flip(a)].">
      <j1 rule="para" parents="515 21794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21796">
    <literal><![CDATA[
      T(x,((y \ z) / T(y \ 1,z)) \ u) = T(x,z \ L(u,y,y))
    ]]></literal>
    <justification jstring="[para(2599(a,1),21795(a,2,2,2))].">
      <j1 rule="para" parents="2599 21795"/>
    </justification>
  </clause>

  <clause id="21797">
    <literal><![CDATA[
      T(x,((y \ 1) \ (y \ z)) \ u) = T(x,z \ L(u,y,y))
    ]]></literal>
    <justification jstring="[para(3936(a,1),21796(a,1,2,1))].">
      <j1 rule="para" parents="3936 21796"/>
    </justification>
  </clause>

  <clause id="21798">
    <literal><![CDATA[
      T(x,(y * z) \ L(u,y,y)) = T(x,((y \ 1) \ z) \ u)
    ]]></literal>
    <justification jstring="[para(9(a,1),21797(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="9 21797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21799">
    <literal><![CDATA[
      T(x,(y * a(z,z,y)) \ u) = T(x,y \ L(u,z,z))
    ]]></literal>
    <justification jstring="[para(17120(a,1),21797(a,1,2,1))].">
      <j1 rule="para" parents="17120 21797"/>
    </justification>
  </clause>

  <clause id="21800">
    <literal><![CDATA[
      T(x,L(y \ 1,z,z) * u) = T(x,y \ L(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(14346,a,21799,a)].">
      <j1 rule="hyper" parents="14346 21799"/>
    </justification>
  </clause>

  <clause id="21801">
    <literal><![CDATA[
      T(x,(y \ 1) \ L(z,u,u)) = T(x,L(y,u,u) * z)
    ]]></literal>
    <justification jstring="[hyper(13585,a,21800,a),flip(a)].">
      <j1 rule="hyper" parents="13585 21800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21802">
    <literal><![CDATA[
      T(x,L(y,z,z) * u) = T(x,y * L(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(13423,a,21801,a),flip(a)].">
      <j1 rule="hyper" parents="13423 21801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21803">
    <literal><![CDATA[
      T(x,(y \ z) * L(u,y,y)) = T(x,((y \ 1) * z) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,19102,a(flip),b,21802,a),flip(a)].">
      <j1 rule="hyper" parents="63 19102 21802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21804">
    <literal><![CDATA[
      T(x,y * L((z * z) * u,z,z)) = T(x,(z * (z * y)) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,18933,a(flip),b,21802,a),flip(a)].">
      <j1 rule="hyper" parents="63 18933 21802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21805">
    <literal><![CDATA[
      T(x,T((y \ 1) * z,y) * L(u,y,y)) = T(x,(((y \ 1) * ((1 / (y \ 1)) * z)) * (y \ 1)) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,17250,a(flip),b,21802,a),flip(a)].">
      <j1 rule="hyper" parents="63 17250 21802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21806">
    <literal><![CDATA[
      T(x,(y * (y * z)) * u) = T(x,z * (y * (y * u)))
    ]]></literal>
    <justification jstring="[para(2577(a,1),21804(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2577 21804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21807">
    <literal><![CDATA[
      T(x,(K(y,z) * (K(y,z) * u)) * ((z * y) * w)) = T(x,u * (K(y,z) * ((y * z) * w)))
    ]]></literal>
    <justification jstring="[para(10080(a,1),21806(a,2,2,2,2))].">
      <j1 rule="para" parents="10080 21806"/>
    </justification>
  </clause>

  <clause id="21808">
    <literal><![CDATA[
      T(x,(y * (T(T(y,z),z) \ u)) * ((y * z) * w)) = T(x,u * (K(z,y) * ((z * y) * w)))
    ]]></literal>
    <justification jstring="[para(5205(a,1),21807(a,1,2,1))].">
      <j1 rule="para" parents="5205 21807"/>
    </justification>
  </clause>

  <clause id="21809">
    <literal><![CDATA[
      T(x,y * (z * (T(T(z,u),u) \ ((z * u) * w)))) = T(x,y * (K(u,z) * ((u * z) * w)))
    ]]></literal>
    <justification jstring="[para(16758(a,1),21808(a,1,2))].">
      <j1 rule="para" parents="16758 21808"/>
    </justification>
  </clause>

  <clause id="21810">
    <literal><![CDATA[
      T(x,y * (K(z,u) * ((z * u) * w))) = T(x,y * ((u * z) * w))
    ]]></literal>
    <justification jstring="[hyper(18934,a,21809,a),flip(a)].">
      <j1 rule="hyper" parents="18934 21809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21811">
    <literal><![CDATA[
      T(x,y * ((T(z,u) * u) * w)) = T(x,y * ((u * z) * w))
    ]]></literal>
    <justification jstring="[para(10166(a,1),21810(a,1,2,2))].">
      <j1 rule="para" parents="10166 21810"/>
    </justification>
  </clause>

  <clause id="21812">
    <literal><![CDATA[
      T(x,y * (((z \ 1) * K(u \ 1,(1 / z) * u)) * w)) = T(x,y * (T(1 / z,u * 1) * w))
    ]]></literal>
    <justification jstring="[hyper(333,a,16938,a(flip),b,21652,a),flip(a)].">
      <j1 rule="hyper" parents="333 16938 21652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21813">
    <literal><![CDATA[
      T(x,y * (((z \ 1) * K(u \ 1,(1 / z) * u)) * w)) = T(x,y * (T(1 / z,u) * w))
    ]]></literal>
    <justification jstring="[para(8(a,1),21812(a,2,2,2,1,2))].">
      <j1 rule="para" parents="8 21812"/>
    </justification>
  </clause>

  <clause id="21814">
    <literal><![CDATA[
      T(x,y * (((z \ 1) * K(u \ 1,(1 / z) * u)) * w)) = T(x,y * (T(z \ 1,u) * w))
    ]]></literal>
    <justification jstring="[hyper(333,a,5613,a(flip),b,21813,a),flip(a)].">
      <j1 rule="hyper" parents="333 5613 21813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21815">
    <literal><![CDATA[
      T(x,y * (((z \ 1) * K(u \ 1,z \ u)) * w)) = T(x,y * (T(z \ 1,u) * w))
    ]]></literal>
    <justification jstring="[para(13161(a,1),21814(a,1,2,2,1,2))].">
      <j1 rule="para" parents="13161 21814"/>
    </justification>
  </clause>

  <clause id="21816">
    <literal><![CDATA[
      T(x,y * ((z \ K(u \ 1,z \ u)) * w)) = T(x,y * (T(z \ 1,u) * w))
    ]]></literal>
    <justification jstring="[para(13126(a,1),21815(a,1,2,2,1))].">
      <j1 rule="para" parents="13126 21815"/>
    </justification>
  </clause>

  <clause id="21817">
    <literal><![CDATA[
      ((x * K(y,z)) * u) / L(T(u,K(z,y)) * K(y,z),w,a(w,v5,K(v6,v7))) = x * a(x,T(u,K(v8,v9)),K(y,z))
    ]]></literal>
    <justification jstring="[para(5304(a,2),21697(a,1,2,1))].">
      <j1 rule="para" parents="5304 21697"/>
    </justification>
  </clause>

  <clause id="21818">
    <literal><![CDATA[
      T(x,(((y \ 1) * ((1 / (y \ 1)) * z)) * (y \ 1)) * u) = T(x,(z * (y \ 1)) * L(u,y,y))
    ]]></literal>
    <justification jstring="[hyper(16141,a,21805,a),flip(a)].">
      <j1 rule="hyper" parents="16141 21805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21820">
    <literal><![CDATA[
      T(x,(((y \ 1) * (y * z)) * (y \ 1)) * u) = T(x,(z * (y \ 1)) * L(u,y,y))
    ]]></literal>
    <justification jstring="[para(76(a,1),21818(a,1,2,1,1,2,1))].">
      <j1 rule="para" parents="76 21818"/>
    </justification>
  </clause>

  <clause id="21822">
    <literal><![CDATA[
      T(x,L(L(K(y,z) * u,z,K(w,y)),w,v5)) = T(x,K(y,z) * ((v5 * w) \ (v5 * (w * u))))
    ]]></literal>
    <justification jstring="[hyper(63,a,19703,a(flip),b,21623,a)].">
      <j1 rule="hyper" parents="63 19703 21623"/>
    </justification>
  </clause>

  <clause id="21824">
    <literal><![CDATA[
      T(x \ 1,x * y) * R((((x \ 1) \ y) \ y) \ 1,z,u) = T(x \ R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(1313(a,1),21768(a,2,1))].">
      <j1 rule="para" parents="1313 21768"/>
    </justification>
  </clause>

  <clause id="21825">
    <literal><![CDATA[
      T(R(x,y,x) \ 1,R(x * K(z,x),y,x)) * R((((R(x,y,x) \ 1) \ K(z,x)) \ K(z,x)) \ 1,u,w) = T(R(x,y,x) \ R(R(x,y,x),u,w),K(z,x))
    ]]></literal>
    <justification jstring="[para(6340(a,2),21824(a,1,1,2))].">
      <j1 rule="para" parents="6340 21824"/>
    </justification>
  </clause>

  <clause id="21826">
    <literal><![CDATA[
      ((x * (y * (x \ 1))) / x) \ (x \ (x * (y / x))) = K(x \ 1,T(y,x)) * a(x,x,x * (y / x))
    ]]></literal>
    <justification jstring="[para(12249(a,1),21762(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12249 21762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21827">
    <literal><![CDATA[
      ((x * (y * (x \ 1))) / x) \ (x \ (x * (y / x))) = K(x \ 1,y) * a(x,x,x * (y / x))
    ]]></literal>
    <justification jstring="[para(6387(a,1),21826(a,2,1))].">
      <j1 rule="para" parents="6387 21826"/>
    </justification>
  </clause>

  <clause id="21828">
    <literal><![CDATA[
      ((x * (y * (x \ 1))) / x) \ (x \ (x * (y / x))) = K(x \ 1,y) * a(x,x,x * (x \ y))
    ]]></literal>
    <justification jstring="[para(21649(a,1),21827(a,2,2))].">
      <j1 rule="para" parents="21649 21827"/>
    </justification>
  </clause>

  <clause id="21829">
    <literal><![CDATA[
      ((x * (y * (x \ 1))) / x) \ (x \ (x * (y / x))) = K(x \ 1,y) * a(x,x,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),21828(a,2,2,3))].">
      <j1 rule="para" parents="10 21828"/>
    </justification>
  </clause>

  <clause id="21830">
    <literal><![CDATA[
      ((x * (y * (x \ 1))) / x) \ (x \ (x * (y / x))) = (y * (x \ 1)) \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(333,a,21747,a(flip),b,21829,a),flip(a)].">
      <j1 rule="hyper" parents="333 21747 21829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21831">
    <literal><![CDATA[
      ((x * (y / x)) * (x \ 1)) \ (x \ (x * (y / x))) = (y * (x \ 1)) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(989(a,1),21830(a,1,1))].">
      <j1 rule="para" parents="989 21830"/>
    </justification>
  </clause>

  <clause id="21832">
    <literal><![CDATA[
      ((x * (y / x)) * (x \ 1)) \ (y / x) = (y * (x \ 1)) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(9(a,1),21831(a,1,2))].">
      <j1 rule="para" parents="9 21831"/>
    </justification>
  </clause>

  <clause id="21834">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (L(w,v5,a(x,u,K(z,y))) * (a(x,u,K(z,y)) * v5)) = v5 * T(w,v5)
    ]]></literal>
    <justification jstring="[para(17908(a,1),21515(a,2,2))].">
      <j1 rule="para" parents="17908 21515"/>
    </justification>
  </clause>

  <clause id="21835">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (L(w,v5,a(x,u,K(z,y))) * (a(x,u,K(z,y)) * v5)) = w * v5
    ]]></literal>
    <justification jstring="[hyper(333,a,111,a(flip),b,21834,a),flip(a)].">
      <j1 rule="hyper" parents="333 111 21834"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21837">
    <literal><![CDATA[
      K(x \ 1,(x \ 1) \ y) * (y \ (x \ ((x \ 1) \ y))) = K(x \ 1,x * y) * a(x,x,(x \ 1) \ y)
    ]]></literal>
    <justification jstring="[para(6258(a,1),21761(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6258 21761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21838">
    <literal><![CDATA[
      K(x \ 1,(x \ 1) \ y) * (y \ (x \ ((x \ 1) \ y))) = K(x \ 1,x * y) * a(x,x,x * y)
    ]]></literal>
    <justification jstring="[para(16100(a,1),21837(a,2,2))].">
      <j1 rule="para" parents="16100 21837"/>
    </justification>
  </clause>

  <clause id="21839">
    <literal><![CDATA[
      K(x \ 1,(x \ 1) \ y) * (y \ (x \ ((x \ 1) \ y))) = ((x * y) * (x \ 1)) \ (x \ (x * y))
    ]]></literal>
    <justification jstring="[hyper(333,a,21747,a(flip),b,21838,a),flip(a)].">
      <j1 rule="hyper" parents="333 21747 21838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21840">
    <literal><![CDATA[
      K(x \ 1,(x \ 1) \ y) * (y \ (x \ ((x \ 1) \ y))) = ((x * y) * (x \ 1)) \ y
    ]]></literal>
    <justification jstring="[para(9(a,1),21839(a,2,2))].">
      <j1 rule="para" parents="9 21839"/>
    </justification>
  </clause>

  <clause id="21841">
    <literal><![CDATA[
      K(x \ 1,x * y) * (y \ (x \ ((x \ 1) \ y))) = ((x * y) * (x \ 1)) \ y
    ]]></literal>
    <justification jstring="[para(6258(a,1),21840(a,1,1))].">
      <j1 rule="para" parents="6258 21840"/>
    </justification>
  </clause>

  <clause id="21842">
    <literal><![CDATA[
      (x * T(y,K(z,u))) * K(u,z) = (x * K(u,z)) * y
    ]]></literal>
    <justification jstring="[hyper(14360,a,21817,a)].">
      <j1 rule="hyper" parents="14360 21817"/>
    </justification>
  </clause>

  <clause id="21843">
    <literal><![CDATA[
      (x * K(y,z)) * T(u,K(y,z)) = (x * u) * K(y,z)
    ]]></literal>
    <justification jstring="[para(5303(a,1),21842(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5303 21842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21844">
    <literal><![CDATA[
      T((x * T(y,K(z,u))) \ ((x * y) * K(z,u)),x) = R(T(K(z,u),x * T(y,K(z,u))),x,T(y,K(z,u)))
    ]]></literal>
    <justification jstring="[para(21843(a,1),1044(a,1,1,2))].">
      <j1 rule="para" parents="21843 1044"/>
    </justification>
  </clause>

  <clause id="21845">
    <literal><![CDATA[
      (x * T(y,z)) * T(u,K(y,z)) = ((x * y) * u) * K(y,z)
    ]]></literal>
    <justification jstring="[para(5984(a,1),21843(a,1,1))].">
      <j1 rule="para" parents="5984 21843"/>
    </justification>
  </clause>

  <clause id="21846">
    <literal><![CDATA[
      (((x * y) * z) * K(y,u)) / (T(y,u) * T(z,K(y,u))) = R(x,T(y,u),T(z,K(y,u)))
    ]]></literal>
    <justification jstring="[hyper(123,a,21845,a(flip),b,107,a)].">
      <j1 rule="hyper" parents="123 21845 107"/>
    </justification>
  </clause>

  <clause id="21847">
    <literal><![CDATA[
      (((x * y) * z) * K(y,u)) / (y * (z * K(y,u))) = R(x,T(y,u),T(z,K(y,u)))
    ]]></literal>
    <justification jstring="[para(4512(a,1),21846(a,1,2))].">
      <j1 rule="para" parents="4512 21846"/>
    </justification>
  </clause>

  <clause id="21848">
    <literal><![CDATA[
      R((x * y) / y,y,T(z,u)) = R(x,T(y,u),T(z,K(y,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,21705,a(flip),b,21847,a)].">
      <j1 rule="hyper" parents="63 21705 21847"/>
    </justification>
  </clause>

  <clause id="21849">
    <literal><![CDATA[
      R(x,T(y,z),T(u,K(y,z))) = R(x,y,T(u,z))
    ]]></literal>
    <justification jstring="[para(11(a,1),21848(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 21848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21850">
    <literal><![CDATA[
      R(x,T(y,z),u) = R(x,y,T(u,z))
    ]]></literal>
    <justification jstring="[hyper(17610,a,21849,a)].">
      <j1 rule="hyper" parents="17610 21849"/>
    </justification>
  </clause>

  <clause id="21851">
    <literal><![CDATA[
      R(x \ 1,T(x,y),z) = R(x \ 1,x,z)
    ]]></literal>
    <justification jstring="[hyper(333,a,20278,a(flip),b,21850,a),flip(a)].">
      <j1 rule="hyper" parents="333 20278 21850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21853">
    <literal><![CDATA[
      T(x * R(x \ 1,x,y),z) = (y / (T(x,z) * y)) * T(x,z)
    ]]></literal>
    <justification jstring="[para(21851(a,1),1797(a,1,1,2))].">
      <j1 rule="para" parents="21851 1797"/>
    </justification>
  </clause>

  <clause id="21854">
    <literal><![CDATA[
      (x / (T(y,z) * x)) * T(y,z) = y * R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,18888,a(flip),b,21853,a),flip(a)].">
      <j1 rule="hyper" parents="63 18888 21853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21857">
    <literal><![CDATA[
      (x / (T(y,z) * x)) * T(y,z) = (x / (y * x)) * y
    ]]></literal>
    <justification jstring="[hyper(333,a,692,a,b,21854,a),flip(a)].">
      <j1 rule="hyper" parents="333 692 21854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21858">
    <literal><![CDATA[
      (x / (y * x)) * K(z,y) = x / (T(y,z) * x)
    ]]></literal>
    <justification jstring="[hyper(5456,a,21857,a)].">
      <j1 rule="hyper" parents="5456 21857"/>
    </justification>
  </clause>

  <clause id="21859">
    <literal><![CDATA[
      K(x,y) * ((z / (x * z)) \ u) = (z / (T(x,y) * z)) \ u
    ]]></literal>
    <justification jstring="[para(21858(a,1),5237(a,1,1)),flip(a)].">
      <j1 rule="para" parents="21858 5237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21860">
    <literal><![CDATA[
      K((x / (T(y,z) * x)) \ u,w) = K(T(x / (y * x),z) \ u,w)
    ]]></literal>
    <justification jstring="[para(21859(a,1),16270(a,1,1))].">
      <j1 rule="para" parents="21859 16270"/>
    </justification>
  </clause>

  <clause id="21861">
    <literal><![CDATA[
      K(T(x / (y * x),z) \ u,w) = K((x \ (x / T(y,z))) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(18159,a,21860,a),flip(a)].">
      <j1 rule="hyper" parents="18159 21860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21862">
    <literal><![CDATA[
      K(T(x / (y * x),x * y) \ z,u) = K((x / T(y * x,y)) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(333,a,18813,a(flip),b,21861,a),flip(a)].">
      <j1 rule="hyper" parents="333 18813 21861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21863">
    <literal><![CDATA[
      K(T((x * y) \ y,K(y,x)) \ z,u) = K((y / T(x * y,x)) \ z,u)
    ]]></literal>
    <justification jstring="[para(12261(a,1),21862(a,1,1,1))].">
      <j1 rule="para" parents="12261 21862"/>
    </justification>
  </clause>

  <clause id="21864">
    <literal><![CDATA[
      K((x / T(y * x,y)) \ z,u) = K(((y * x) \ x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(16391,a,21863,a),flip(a)].">
      <j1 rule="hyper" parents="16391 21863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21866">
    <literal><![CDATA[
      R(T(K(x,y),z * T(u,K(x,y))),z,T(u,K(x,y))) = T(T(K(x,y),u),z)
    ]]></literal>
    <justification jstring="[para(6086(a,1),21844(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6086 21844"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21868">
    <literal><![CDATA[
      R(T(K(x,y),z * T(u,K(x,y))),z,T(u,K(x,y))) = T(K(x,T(y,u)),z)
    ]]></literal>
    <justification jstring="[para(6365(a,2),21866(a,2,1))].">
      <j1 rule="para" parents="6365 21866"/>
    </justification>
  </clause>

  <clause id="21869">
    <literal><![CDATA[
      R(T(K(x,y),z * T(u,K(x,y))),z,T(u,K(x,y))) = K(x,T(T(y,u),z))
    ]]></literal>
    <justification jstring="[hyper(333,a,6365,a,b,21868,a),flip(a)].">
      <j1 rule="hyper" parents="333 6365 21868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21870">
    <literal><![CDATA[
      R(T(K(x,y),z * u),z,T(u,K(x,y))) = K(x,T(T(y,u),z))
    ]]></literal>
    <justification jstring="[para(7359(a,1),21869(a,1,1))].">
      <j1 rule="para" parents="7359 21869"/>
    </justification>
  </clause>

  <clause id="21871">
    <literal><![CDATA[
      R(K(x,T(y,z * u)),z,T(u,K(x,y))) = K(x,T(T(y,u),z))
    ]]></literal>
    <justification jstring="[para(6365(a,2),21870(a,1,1))].">
      <j1 rule="para" parents="6365 21870"/>
    </justification>
  </clause>

  <clause id="21873">
    <literal><![CDATA[
      R(K(x,T(y,z * u)),z,u) = K(x,T(T(y,u),z))
    ]]></literal>
    <justification jstring="[hyper(17610,a,21871,a)].">
      <j1 rule="hyper" parents="17610 21871"/>
    </justification>
  </clause>

  <clause id="21874">
    <literal><![CDATA[
      K(x,L(T(y,z * u),z,u)) = K(x,T(T(y,u),z))
    ]]></literal>
    <justification jstring="[hyper(13899,a,21873,a)].">
      <j1 rule="hyper" parents="13899 21873"/>
    </justification>
  </clause>

  <clause id="21876">
    <literal><![CDATA[
      K((x * y) \ (z * y),u) = K(z / x,T(T(u,y),x))
    ]]></literal>
    <justification jstring="[hyper(13904,a,21874,a)].">
      <j1 rule="hyper" parents="13904 21874"/>
    </justification>
  </clause>

  <clause id="21877">
    <literal><![CDATA[
      K((x * y) \ (z * y),u) = K(x \ z,T(u,y))
    ]]></literal>
    <justification jstring="[hyper(333,a,6431,a(flip),b,21876,a),flip(a)].">
      <j1 rule="hyper" parents="333 6431 21876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21878">
    <literal><![CDATA[
      K((x * y) \ (z * x),u) = K(T(y,x) \ z,T(u,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,16179,a(flip),b,21877,a)].">
      <j1 rule="hyper" parents="63 16179 21877"/>
    </justification>
  </clause>

  <clause id="21879">
    <literal><![CDATA[
      K((x * y) \ (y * z),u) = K(x \ T(z,y),T(u,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,16169,a(flip),b,21877,a)].">
      <j1 rule="hyper" parents="63 16169 21877"/>
    </justification>
  </clause>

  <clause id="21880">
    <literal><![CDATA[
      K((x / y) \ z,T(u,y)) = K(x \ (z * y),u)
    ]]></literal>
    <justification jstring="[para(12(a,1),21877(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="12 21877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21881">
    <literal><![CDATA[
      K(T(x,y) / (z \ y),u) = K(y \ (x * z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,16186,a(flip),b,21880,a)].">
      <j1 rule="hyper" parents="63 16186 21880"/>
    </justification>
  </clause>

  <clause id="21882">
    <literal><![CDATA[
      K(x \ (y * z),T(u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K((x / z) \ y,u) = w
    ]]></literal>
    <justification jstring="[para(21880(a,1),7064(a,1))].">
      <j1 rule="para" parents="21880 7064"/>
    </justification>
  </clause>

  <clause id="21883">
    <literal><![CDATA[
      K(x \ (T(y,x) * z),u) = K(y / (z \ x),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,15133,a(flip),b,21881,a),flip(a)].">
      <j1 rule="hyper" parents="63 15133 21881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21884">
    <literal><![CDATA[
      K(x \ (T(y,x) * z),u) = (w * K(u,y / (z \ x))) \ w
    ]]></literal>
    <justification jstring="[hyper(333,a,5990,a,b,21883,a),flip(a)].">
      <j1 rule="hyper" parents="333 5990 21883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21885">
    <literal><![CDATA[
      (x * K(T(y,z) \ u,T(w,z))) \ x = K(w,(z * y) \ (u * z))
    ]]></literal>
    <justification jstring="[para(21878(a,1),5990(a,1,1,2))].">
      <j1 rule="para" parents="21878 5990"/>
    </justification>
  </clause>

  <clause id="21886">
    <literal><![CDATA[
      K(x \ ((y \ x) * z),u) = K(y \ T(z,x),T(u,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,21580,a(flip),b,21879,a)].">
      <j1 rule="hyper" parents="63 21580 21879"/>
    </justification>
  </clause>

  <clause id="21887">
    <literal><![CDATA[
      (x * K(y \ T(z,u),T(w,u))) \ (x * w) = T(w,u \ ((y \ u) * z))
    ]]></literal>
    <justification jstring="[para(21886(a,1),5447(a,1,1,2))].">
      <j1 rule="para" parents="21886 5447"/>
    </justification>
  </clause>

  <clause id="21888">
    <literal><![CDATA[
      K(x \ (y * T(z * u,z)),T(w,u * z)) != v5
    ]]></literal>
    <literal><![CDATA[
      K((x / T(z * u,z)) \ y,w) = v5
    ]]></literal>
    <justification jstring="[para(12225(a,1),21882(a,1,2))].">
      <j1 rule="para" parents="12225 21882"/>
    </justification>
  </clause>

  <clause id="21889">
    <literal><![CDATA[
      T(x,y \ (T(z,y) * u)) = x * K(x,z / (u \ y))
    ]]></literal>
    <justification jstring="[hyper(4209,a,21884,a)].">
      <j1 rule="hyper" parents="4209 21884"/>
    </justification>
  </clause>

  <clause id="21890">
    <literal><![CDATA[
      T(x,y \ (T(z,y) * u)) = T(x,z / (u \ y))
    ]]></literal>
    <justification jstring="[hyper(4307,a,21889,a),flip(a)].">
      <j1 rule="hyper" parents="4307 21889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21891">
    <literal><![CDATA[
      T(x,y \ (T(z,y) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,z * (y \ u)) = w
    ]]></literal>
    <justification jstring="[para(21890(a,2),21414(a,1))].">
      <j1 rule="para" parents="21890 21414"/>
    </justification>
  </clause>

  <clause id="21892">
    <literal><![CDATA[
      T(x,T(y,z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,z * (y \ (z \ u))) = w
    ]]></literal>
    <justification jstring="[para(4705(a,1),21891(a,1,2))].">
      <j1 rule="para" parents="4705 21891"/>
    </justification>
  </clause>

  <clause id="21893">
    <literal><![CDATA[
      T(x,y * (z \ (y \ u))) = T(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(21892,a,xx)].">
      <j1 rule="hyper" parents="21892"/>
    </justification>
  </clause>

  <clause id="21894">
    <literal><![CDATA[
      K(x,T(T(y,z) \ u,z)) = K(x,(z * y) \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(6456,a,21885,a)].">
      <j1 rule="hyper" parents="6456 21885"/>
    </justification>
  </clause>

  <clause id="21895">
    <literal><![CDATA[
      T(x,T(T(y,z) \ u,z)) = T(x,(z * y) \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(124,a,21894,a,b,4837,a),flip(a)].">
      <j1 rule="hyper" parents="124 21894 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21896">
    <literal><![CDATA[
      T(x,T(T(y,z \ 1) \ ((z \ 1) \ u),z \ 1)) = T(x,((z \ 1) * y) \ (z \ T(z * u,z \ 1)))
    ]]></literal>
    <justification jstring="[para(963(a,2),21895(a,2,2,2))].">
      <j1 rule="para" parents="963 21895"/>
    </justification>
  </clause>

  <clause id="21897">
    <literal><![CDATA[
      T(x,y \ ((z \ y) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T(z \ T(u,y),y)) = w
    ]]></literal>
    <justification jstring="[para(21887(a,1),6450(a,1))].">
      <j1 rule="para" parents="21887 6450"/>
    </justification>
  </clause>

  <clause id="21898">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),T(u \ T(z,y),y)) = T(x,((y \ u) \ z) / y)
    ]]></literal>
    <justification jstring="[hyper(21897,a,19224,a)].">
      <j1 rule="hyper" parents="21897 19224"/>
    </justification>
  </clause>

  <clause id="21899">
    <literal><![CDATA[
      T(x,((y \ z) \ u) / y) = T(x,z \ T(u,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,16755,a(flip),b,21898,a),flip(a)].">
      <j1 rule="hyper" parents="63 16755 21898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21901">
    <literal><![CDATA[
      T(x,y \ (K(z * z,u) * (z \ (z \ u)))) = T(x,(((z \ 1) \ y) \ ((z \ u) / z)) / (z \ 1))
    ]]></literal>
    <justification jstring="[para(16110(a,2),21899(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="16110 21899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21902">
    <literal><![CDATA[
      K(x \ (y * (z * u)),T(w,z * u)) = K((x / T(u * z,u)) \ y,w)
    ]]></literal>
    <justification jstring="[hyper(21888,a,12973,a),flip(a)].">
      <j1 rule="hyper" parents="21888 12973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21903">
    <literal><![CDATA[
      K((x / T(y * z,y)) \ u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K((x / (z * y)) \ u,w) = v5
    ]]></literal>
    <justification jstring="[para(21902(a,1),21882(a,1))].">
      <j1 rule="para" parents="21902 21882"/>
    </justification>
  </clause>

  <clause id="21904">
    <literal><![CDATA[
      T(x,y \ (K(z * z,u) * (z \ (z \ u)))) = T(x,(((z \ 1) \ y) \ ((z \ u) / z)) * z)
    ]]></literal>
    <justification jstring="[hyper(333,a,13325,a(flip),b,21901,a),flip(a)].">
      <j1 rule="hyper" parents="333 13325 21901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21905">
    <literal><![CDATA[
      T(x,T(T(y,z \ 1) \ ((z \ 1) \ u),z \ 1)) = T(x,((z \ 1) * y) \ (z \ T(z * u,z * 1)))
    ]]></literal>
    <justification jstring="[hyper(21770,a,21896,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="21770 21896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21906">
    <literal><![CDATA[
      T(x,T(T(y,z \ 1) \ ((z \ 1) \ u),z \ 1)) = T(x,((z \ 1) * y) \ (z \ T(z * u,z)))
    ]]></literal>
    <justification jstring="[para(8(a,1),21905(a,2,2,2,2,2))].">
      <j1 rule="para" parents="8 21905"/>
    </justification>
  </clause>

  <clause id="21907">
    <literal><![CDATA[
      T(x,T(T(y,z \ 1) \ ((z \ 1) \ u),z \ 1)) = T(x,((z \ 1) * y) \ ((z * u) / z))
    ]]></literal>
    <justification jstring="[hyper(333,a,18162,a(flip),b,21906,a),flip(a)].">
      <j1 rule="hyper" parents="333 18162 21906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21908">
    <literal><![CDATA[
      T(x,T(T(y,z \ 1) \ ((z \ 1) \ u),z \ 1)) = T(x,((z \ 1) * y) \ T(u,z))
    ]]></literal>
    <justification jstring="[hyper(333,a,15011,a(flip),b,21907,a),flip(a)].">
      <j1 rule="hyper" parents="333 15011 21907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21909">
    <literal><![CDATA[
      T(x,T(T(y,z \ 1) \ ((z \ 1) \ u),z)) = T(x,((z \ 1) * y) \ T(u,z))
    ]]></literal>
    <justification jstring="[hyper(7273,a,21908,a)].">
      <j1 rule="hyper" parents="7273 21908"/>
    </justification>
  </clause>

  <clause id="21910">
    <literal><![CDATA[
      T(x,T((y \ 1) \ (z \ u),y)) = T(x,((y \ 1) * z) \ T(u,y))
    ]]></literal>
    <justification jstring="[hyper(21710,a,21909,a)].">
      <j1 rule="hyper" parents="21710 21909"/>
    </justification>
  </clause>

  <clause id="21911">
    <literal><![CDATA[
      T(x,((y \ 1) * z) \ T(u,y)) = T(x,T(y * (z \ u),y))
    ]]></literal>
    <justification jstring="[hyper(63,a,13520,a(flip),b,21910,a),flip(a)].">
      <j1 rule="hyper" parents="63 13520 21910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21912">
    <literal><![CDATA[
      T(x,((y \ 1) * z) \ T(u,y)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(z \ u) * y) = w
    ]]></literal>
    <justification jstring="[para(21911(a,2),12232(a,1))].">
      <j1 rule="para" parents="21911 12232"/>
    </justification>
  </clause>

  <clause id="21913">
    <literal><![CDATA[
      T(x,((y \ 1) * z) \ T(T(u,w),y)) = T(x,(z \ ((w * u) / w)) * y)
    ]]></literal>
    <justification jstring="[hyper(21912,a,15130,a),flip(a)].">
      <j1 rule="hyper" parents="21912 15130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21914">
    <literal><![CDATA[
      T(x,((y \ 1) * z) \ (y \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(z \ (u / y)) * y) = w
    ]]></literal>
    <justification jstring="[para(113(a,1),21912(a,1,2,2))].">
      <j1 rule="para" parents="113 21912"/>
    </justification>
  </clause>

  <clause id="21915">
    <literal><![CDATA[
      T(x,(y \ (z / u)) * u) = T(x,u * ((y * u) \ z))
    ]]></literal>
    <justification jstring="[hyper(21914,a,21688,a)].">
      <j1 rule="hyper" parents="21914 21688"/>
    </justification>
  </clause>

  <clause id="21916">
    <literal><![CDATA[
      T(x,y \ (K(z * z,u) * (z \ (z \ u)))) = T(x,z * ((((z \ 1) \ y) * z) \ (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,21904,a,b,21915,a)].">
      <j1 rule="hyper" parents="63 21904 21915"/>
    </justification>
  </clause>

  <clause id="21917">
    <literal><![CDATA[
      T(x,(y \ ((z * u) / z)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,(y \ T(u,z)) * w) = v5
    ]]></literal>
    <justification jstring="[para(21913(a,1),21912(a,1))].">
      <j1 rule="para" parents="21913 21912"/>
    </justification>
  </clause>

  <clause id="21918">
    <literal><![CDATA[
      K((x \ K(x * (y \ T(z,u \ w)),x \ 1)) \ (y \ T(z,u * w)),v5) = K((y \ T(z,u \ w)) * x,v5)
    ]]></literal>
    <justification jstring="[hyper(333,a,13275,a(flip),b,21692,a),flip(a)].">
      <j1 rule="hyper" parents="333 13275 21692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21919">
    <literal><![CDATA[
      K((x \ K(x * (y \ T(z,u * w)),x \ 1)) \ (y \ T(z,u * w)),v5) = K((y \ T(z,u \ w)) * x,v5)
    ]]></literal>
    <justification jstring="[para(21693(a,1),21918(a,1,1,1,2))].">
      <j1 rule="para" parents="21693 21918"/>
    </justification>
  </clause>

  <clause id="21920">
    <literal><![CDATA[
      K((x \ T(y,z * u)) / (w \ 1),v5) = K((x \ T(y,z \ u)) * w,v5)
    ]]></literal>
    <justification jstring="[para(8677(a,1),21919(a,1,1))].">
      <j1 rule="para" parents="8677 21919"/>
    </justification>
  </clause>

  <clause id="21921">
    <literal><![CDATA[
      K((x \ T(y,z \ u)) * w,v5) = K((x \ T(y,z * u)) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(13424,a,21920,a),flip(a)].">
      <j1 rule="hyper" parents="13424 21920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21922">
    <literal><![CDATA[
      K((x \ T(y,y * z)) * u,w) = K((x \ ((y \ z) \ z)) * u,w)
    ]]></literal>
    <justification jstring="[para(112(a,1),21921(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="112 21921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21923">
    <literal><![CDATA[
      K((T(x,x \ ((y \ z) \ z)) \ T(y,y * z)) * u,w) = K(T(x \ ((y \ z) \ z),x) * u,w)
    ]]></literal>
    <justification jstring="[para(3648(a,1),21922(a,2,1,1))].">
      <j1 rule="para" parents="3648 21922"/>
    </justification>
  </clause>

  <clause id="21924">
    <literal><![CDATA[
      K((T(x,x \ T(y,z)) \ T(y,y * z)) * u,w) = K(T(x \ ((y \ z) \ z),x) * u,w)
    ]]></literal>
    <justification jstring="[para(15083(a,1),21923(a,1,1,1,1))].">
      <j1 rule="para" parents="15083 21923"/>
    </justification>
  </clause>

  <clause id="21925">
    <literal><![CDATA[
      K((T(x,T(x \ y,z)) \ T(y,y * z)) * u,w) = K(T(x \ ((y \ z) \ z),x) * u,w)
    ]]></literal>
    <justification jstring="[para(11344(a,2),21924(a,1,1,1,1))].">
      <j1 rule="para" parents="11344 21924"/>
    </justification>
  </clause>

  <clause id="21926">
    <literal><![CDATA[
      K(T(x \ ((y \ z) \ z),x) * u,w) = K((T(x,x \ y) \ T(y,y * z)) * u,w)
    ]]></literal>
    <justification jstring="[hyper(18481,a,21925,a),flip(a)].">
      <j1 rule="hyper" parents="18481 21925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21927">
    <literal><![CDATA[
      K(T(x \ ((y \ z) \ z),x) * u,w) = K((T(x \ y,x) * K(y,y * z)) * u,w)
    ]]></literal>
    <justification jstring="[para(13367(a,1),21926(a,2,1,1))].">
      <j1 rule="para" parents="13367 21926"/>
    </justification>
  </clause>

  <clause id="21928">
    <literal><![CDATA[
      K(T(x \ ((y \ z) \ z),x) * u,w) = K(T(x \ y,x) * (K(y,y * z) * u),w)
    ]]></literal>
    <justification jstring="[hyper(333,a,17880,a(flip),b,21927,a),flip(a)].">
      <j1 rule="hyper" parents="333 17880 21927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21929">
    <literal><![CDATA[
      K(T(x \ ((y \ z) \ z),x) * u,w) = K(T(x \ y,x) * (K(y,z) * u),w)
    ]]></literal>
    <justification jstring="[hyper(333,a,14223,a(flip),b,21928,a),flip(a)].">
      <j1 rule="hyper" parents="333 14223 21928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21930">
    <literal><![CDATA[
      K(T(x \ ((y \ z) \ z),x) * u,w) = K((y / x) * (K(y,z) * u),w)
    ]]></literal>
    <justification jstring="[hyper(333,a,15124,a(flip),b,21929,a),flip(a)].">
      <j1 rule="hyper" parents="333 15124 21929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21931">
    <literal><![CDATA[
      K(T(x \ ((y \ z) \ z),x) * u,w) = K((T(y,z) / x) * u,w)
    ]]></literal>
    <justification jstring="[hyper(333,a,17883,a(flip),b,21930,a),flip(a)].">
      <j1 rule="hyper" parents="333 17883 21930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21932">
    <literal><![CDATA[
      K((((x \ y) \ y) / z) * u,w) = K((T(x,y) / z) * u,w)
    ]]></literal>
    <justification jstring="[hyper(15125,a,21931,a)].">
      <j1 rule="hyper" parents="15125 21931"/>
    </justification>
  </clause>

  <clause id="21933">
    <literal><![CDATA[
      K((((T(x,y) \ z) \ z) / y) * u,w) = K((y \ T(x,z)) * u,w)
    ]]></literal>
    <justification jstring="[hyper(333,a,18274,a(flip),b,21932,a),flip(a)].">
      <j1 rule="hyper" parents="333 18274 21932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21934">
    <literal><![CDATA[
      K((T((x \ y) \ y,z) / z) * u,w) = K((z \ T(x,y)) * u,w)
    ]]></literal>
    <justification jstring="[para(6668(a,2),21933(a,1,1,1,1))].">
      <j1 rule="para" parents="6668 21933"/>
    </justification>
  </clause>

  <clause id="21935">
    <literal><![CDATA[
      K((x \ ((y \ z) \ z)) * u,w) = K((x \ T(y,z)) * u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,18273,a(flip),b,21934,a)].">
      <j1 rule="hyper" parents="63 18273 21934"/>
    </justification>
  </clause>

  <clause id="21936">
    <literal><![CDATA[
      K((((x \ (y \ x)) * ((y \ x) \ x)) \ T(y,x)) * z,u) = K(((x \ (y \ x)) \ 1) * z,u)
    ]]></literal>
    <justification jstring="[para(1477(a,1),21935(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="1477 21935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21937">
    <literal><![CDATA[
      K((((x \ (y \ x)) * ((y \ x) \ x)) \ T(y,x)) * z,u) = K((x \ (y \ x)) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(333,a,13215,a(flip),b,21936,a),flip(a)].">
      <j1 rule="hyper" parents="333 13215 21936"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21938">
    <literal><![CDATA[
      K((((x \ (y \ x)) * ((y \ x) \ x)) \ T(y,x)) * z,u) = K(x \ (y * (x * z)),u)
    ]]></literal>
    <justification jstring="[hyper(333,a,21582,a(flip),b,21937,a),flip(a)].">
      <j1 rule="hyper" parents="333 21582 21937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21939">
    <literal><![CDATA[
      K((((x \ (x / y)) * y) \ T(y,x)) * z,u) = K(x \ (y * (x * z)),u)
    ]]></literal>
    <justification jstring="[para(13563(a,1),21938(a,1,1,1,1))].">
      <j1 rule="para" parents="13563 21938"/>
    </justification>
  </clause>

  <clause id="21940">
    <literal><![CDATA[
      K(((x * ((y * x) \ y)) \ T(x,y)) * z,u) = K(y \ (x * (y * z)),u)
    ]]></literal>
    <justification jstring="[para(2885(a,1),21939(a,1,1,1,1))].">
      <j1 rule="para" parents="2885 21939"/>
    </justification>
  </clause>

  <clause id="21941">
    <literal><![CDATA[
      K((1 / ((x * y) \ y)) * z,u) = K(y \ (x * (y * z)),u)
    ]]></literal>
    <justification jstring="[para(8408(a,1),21940(a,1,1,1))].">
      <j1 rule="para" parents="8408 21940"/>
    </justification>
  </clause>

  <clause id="21942">
    <literal><![CDATA[
      K(((x * y) \ y) \ z,u) = K(y \ (x * (y * z)),u)
    ]]></literal>
    <justification jstring="[hyper(13491,a,21941,a)].">
      <j1 rule="hyper" parents="13491 21941"/>
    </justification>
  </clause>

  <clause id="21943">
    <literal><![CDATA[
      K((x / T(y * x,y)) \ z,u) = K(x \ (y * (x * z)),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,21864,a,b,21942,a)].">
      <j1 rule="hyper" parents="63 21864 21942"/>
    </justification>
  </clause>

  <clause id="21944">
    <literal><![CDATA[
      K((x / (x * y)) \ z,u) = K(x \ (y * (x * z)),u)
    ]]></literal>
    <justification jstring="[hyper(21903,a,21943,a)].">
      <j1 rule="hyper" parents="21903 21943"/>
    </justification>
  </clause>

  <clause id="21945">
    <literal><![CDATA[
      (x * K(y \ (z * (y * u)),w)) \ (x * w) = T(w,(y / (y * z)) \ u)
    ]]></literal>
    <justification jstring="[para(21944(a,1),5447(a,1,1,2))].">
      <j1 rule="para" parents="21944 5447"/>
    </justification>
  </clause>

  <clause id="21946">
    <literal><![CDATA[
      T(x,(y / (y * z)) \ u) = T(x,y \ (z * (y * u)))
    ]]></literal>
    <justification jstring="[hyper(5458,a,21945,a),flip(a)].">
      <j1 rule="hyper" parents="5458 21945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21947">
    <literal><![CDATA[
      T(x,(y \ ((z * (y / z)) / z)) * u) = T(x,y \ ((1 / z) * (y * u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,21777,a,b,21946,a)].">
      <j1 rule="hyper" parents="63 21777 21946"/>
    </justification>
  </clause>

  <clause id="21948">
    <literal><![CDATA[
      T(x,(y \ ((z * (y / z)) / z)) * u) = T(x,y \ ((z \ 1) * (y * u)))
    ]]></literal>
    <justification jstring="[hyper(333,a,5141,a(flip),b,21947,a),flip(a)].">
      <j1 rule="hyper" parents="333 5141 21947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21949">
    <literal><![CDATA[
      T(x,y \ ((z \ 1) * (y * u))) = T(x,(y \ T(y / z,z)) * u)
    ]]></literal>
    <justification jstring="[hyper(21917,a,21948,a),flip(a)].">
      <j1 rule="hyper" parents="21917 21948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21950">
    <literal><![CDATA[
      T(x,y \ ((z \ 1) * (y * u))) = T(x,(y \ (z \ y)) * u)
    ]]></literal>
    <justification jstring="[para(113(a,1),21949(a,2,2,1,2))].">
      <j1 rule="para" parents="113 21949"/>
    </justification>
  </clause>

  <clause id="21951">
    <literal><![CDATA[
      T(x,((y \ 1) \ (z \ (y \ 1))) * (u * a(y,y,u))) = T(x,(y \ 1) \ ((z \ 1) * (y \ u)))
    ]]></literal>
    <justification jstring="[para(17121(a,1),21950(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="17121 21950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21952">
    <literal><![CDATA[
      T(x,((y \ 1) \ (z \ (y \ 1))) * (u * a(y,y,u))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y * ((z \ 1) * (y \ u))) = w
    ]]></literal>
    <justification jstring="[para(21951(a,2),13423(a,1))].">
      <j1 rule="para" parents="21951 13423"/>
    </justification>
  </clause>

  <clause id="21953">
    <literal><![CDATA[
      T((K(x,T(y,z)) * u) / K(x,T(y,z)),K(y,x) * w) = L(T(u,w),K(x,T(y,z)),w)
    ]]></literal>
    <justification jstring="[para(11(a,1),21587(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 21587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21954">
    <literal><![CDATA[
      T((K(x,T(y,z)) * u) / K(x,T(y,z)),K(y,x) * w) = L(T(u,w),K(y,x),w)
    ]]></literal>
    <justification jstring="[hyper(333,a,20212,a(flip),b,21953,a),flip(a)].">
      <j1 rule="hyper" parents="333 20212 21953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21957">
    <literal><![CDATA[
      T((K(x,T(y,z)) * u) * K(y,T(x,z)),K(y,x) * w) = L(T(u,w),K(y,x),w)
    ]]></literal>
    <justification jstring="[para(6424(a,1),21954(a,1,1))].">
      <j1 rule="para" parents="6424 21954"/>
    </justification>
  </clause>

  <clause id="21958">
    <literal><![CDATA[
      T(K(x,T(y,z)) * (u * K(y,T(x,z))),K(y,x) * w) = L(T(u,w),K(y,x),w)
    ]]></literal>
    <justification jstring="[para(9504(a,1),21957(a,1,1))].">
      <j1 rule="para" parents="9504 21957"/>
    </justification>
  </clause>

  <clause id="21959">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,y) * u) = L(T(x,u),K(z,y),u)
    ]]></literal>
    <justification jstring="[para(15586(a,1),21958(a,1,1))].">
      <j1 rule="para" parents="15586 21958"/>
    </justification>
  </clause>

  <clause id="21960">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,y) * u) = L(T(x,u),y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(333,a,21621,a(flip),b,21959,a),flip(a)].">
      <j1 rule="hyper" parents="333 21621 21959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21961">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,y) * u) = T(x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(333,a,14486,a(flip),b,21960,a),flip(a)].">
      <j1 rule="hyper" parents="333 14486 21960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21962">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,y) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,L(u,z,y)) = w
    ]]></literal>
    <justification jstring="[para(21961(a,2),21508(a,1))].">
      <j1 rule="para" parents="21961 21508"/>
    </justification>
  </clause>

  <clause id="21963">
    <literal><![CDATA[
      T(L(x \ 1,y,x),R(x * K(z,x),y,x)) * R((((R(x,y,x) \ 1) \ K(z,x)) \ K(z,x)) \ 1,u,w) = T(R(x,y,x) \ R(R(x,y,x),u,w),K(z,x))
    ]]></literal>
    <justification jstring="[para(8003(a,2),21825(a,1,1,1))].">
      <j1 rule="para" parents="8003 21825"/>
    </justification>
  </clause>

  <clause id="21964">
    <literal><![CDATA[
      T(L(x \ 1,y,x),L(x * K(z,x),y,x)) * R((((R(x,y,x) \ 1) \ K(z,x)) \ K(z,x)) \ 1,u,w) = T(R(x,y,x) \ R(R(x,y,x),u,w),K(z,x))
    ]]></literal>
    <justification jstring="[para(13879(a,1),21963(a,1,1))].">
      <j1 rule="para" parents="13879 21963"/>
    </justification>
  </clause>

  <clause id="21965">
    <literal><![CDATA[
      T(L(x \ 1,y,x),L(T(x,z),y,x)) * R((((R(x,y,x) \ 1) \ K(z,x)) \ K(z,x)) \ 1,u,w) = T(R(x,y,x) \ R(R(x,y,x),u,w),K(z,x))
    ]]></literal>
    <justification jstring="[para(7558(a,1),21964(a,1,1))].">
      <j1 rule="para" parents="7558 21964"/>
    </justification>
  </clause>

  <clause id="21966">
    <literal><![CDATA[
      T(L(x \ 1,y,x),T(x,z)) * R((((R(x,y,x) \ 1) \ K(z,x)) \ K(z,x)) \ 1,u,w) = T(R(x,y,x) \ R(R(x,y,x),u,w),K(z,x))
    ]]></literal>
    <justification jstring="[para(9487(a,1),21965(a,1,1))].">
      <j1 rule="para" parents="9487 21965"/>
    </justification>
  </clause>

  <clause id="21967">
    <literal><![CDATA[
      L(T(x \ 1,T(x,y)),z,x) * R((((R(x,z,x) \ 1) \ K(y,x)) \ K(y,x)) \ 1,u,w) = T(R(x,z,x) \ R(R(x,z,x),u,w),K(y,x))
    ]]></literal>
    <justification jstring="[para(25(a,2),21966(a,1,1))].">
      <j1 rule="para" parents="25 21966"/>
    </justification>
  </clause>

  <clause id="21969">
    <literal><![CDATA[
      L(T(x \ 1,x),y,x) * R((((R(x,y,x) \ 1) \ K(z,x)) \ K(z,x)) \ 1,u,w) = T(R(x,y,x) \ R(R(x,y,x),u,w),K(z,x))
    ]]></literal>
    <justification jstring="[para(3374(a,1),21967(a,1,1,1))].">
      <j1 rule="para" parents="3374 21967"/>
    </justification>
  </clause>

  <clause id="21971">
    <literal><![CDATA[
      L(T(x \ 1,x),y,x) * R(((L(x \ 1,y,x) \ K(z,x)) \ K(z,x)) \ 1,u,w) = T(R(x,y,x) \ R(R(x,y,x),u,w),K(z,x))
    ]]></literal>
    <justification jstring="[para(8003(a,2),21969(a,1,2,1,1,1,1))].">
      <j1 rule="para" parents="8003 21969"/>
    </justification>
  </clause>

  <clause id="21972">
    <literal><![CDATA[
      L(T(x \ 1,x),y,x) * R(L(((x \ 1) \ K(z,x)) \ K(z,x),y,x) \ 1,u,w) = T(R(x,y,x) \ R(R(x,y,x),u,w),K(z,x))
    ]]></literal>
    <justification jstring="[para(11071(a,2),21971(a,1,2,1,1))].">
      <j1 rule="para" parents="11071 21971"/>
    </justification>
  </clause>

  <clause id="21973">
    <literal><![CDATA[
      T(R(x,y,x) \ R(R(x,y,x),z,u),K(w,x)) = L(T(x \ 1,x),y,x) * R(L(T(x \ 1,x),y,x) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(7559(a,1),21972(a,1,2,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7559 21972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21974">
    <literal><![CDATA[
      T(R(x,y,x) \ R(R(x,y,x),z,u),K(w,x)) = L(T(x \ 1,x) * R(T(x \ 1,x) \ 1,z,u),y,x)
    ]]></literal>
    <justification jstring="[hyper(333,a,4014,a(flip),b,21973,a),flip(a)].">
      <j1 rule="hyper" parents="333 4014 21973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21976">
    <literal><![CDATA[
      T(R(x,y,x) \ R(R(x,y,x),z,u),K(w,x)) = L(T((x \ 1) * R((x \ 1) \ 1,z,u),x),y,x)
    ]]></literal>
    <justification jstring="[para(1795(a,1),21974(a,2,1))].">
      <j1 rule="para" parents="1795 21974"/>
    </justification>
  </clause>

  <clause id="21977">
    <literal><![CDATA[
      T(R(x,y,x) \ R(R(x,y,x),z,u),K(w,x)) = L(T(x \ R(x,z,u),x),y,x)
    ]]></literal>
    <justification jstring="[para(1313(a,1),21976(a,2,1,1))].">
      <j1 rule="para" parents="1313 21976"/>
    </justification>
  </clause>

  <clause id="21978">
    <literal><![CDATA[
      T(R(x,y,x) \ R(R(x,y,x),z,u),K(w,x)) = L(x \ R(x,z,u),y,x)
    ]]></literal>
    <justification jstring="[para(3020(a,1),21977(a,2,1))].">
      <j1 rule="para" parents="3020 21977"/>
    </justification>
  </clause>

  <clause id="21979">
    <literal><![CDATA[
      T(x \ R(x,y,z),K(u,x)) = L(x \ R(x,y,z),w,x)
    ]]></literal>
    <justification jstring="[para(21704(a,1),21978(a,1,1))].">
      <j1 rule="para" parents="21704 21978"/>
    </justification>
  </clause>

  <clause id="21980">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,x) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(21666,a,21979,a),flip(a)].">
      <j1 rule="hyper" parents="21666 21979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21983">
    <literal><![CDATA[
      x \ (y \ (((y \ R(y,z,u)) * y) * x)) = R(T(y \ R(y,z,u),x),y,x)
    ]]></literal>
    <justification jstring="[para(21980(a,1),21739(a,1,2,2,1,1))].">
      <j1 rule="para" parents="21980 21739"/>
    </justification>
  </clause>

  <clause id="21984">
    <literal><![CDATA[
      R(T(x \ R(x,y,z),u),x,u) = u \ (x \ (R(x,y,z) * u))
    ]]></literal>
    <justification jstring="[para(3016(a,1),21983(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="3016 21983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21986">
    <literal><![CDATA[
      R(T(x \ R(x,y,z),u),x,u) = u \ (R(x,y,z) * (x \ u))
    ]]></literal>
    <justification jstring="[para(1510(a,1),21984(a,2,2))].">
      <j1 rule="para" parents="1510 21984"/>
    </justification>
  </clause>

  <clause id="21987">
    <literal><![CDATA[
      (x * y) \ (R(x,z,u) * y) = y \ (R(x,z,u) * (x \ y))
    ]]></literal>
    <justification jstring="[hyper(21737,a,21986,a)].">
      <j1 rule="hyper" parents="21737 21986"/>
    </justification>
  </clause>

  <clause id="21988">
    <literal><![CDATA[
      (x * y) \ (R(x,z,z \ y) * y) = y \ (x \ ((x * z) * (z \ y)))
    ]]></literal>
    <justification jstring="[para(1521(a,1),21987(a,2,2))].">
      <j1 rule="para" parents="1521 21987"/>
    </justification>
  </clause>

  <clause id="21989">
    <literal><![CDATA[
      (x * y) \ (R(x,x,x * y) * y) = y \ (x \ ((x * x) * (x \ y)))
    ]]></literal>
    <justification jstring="[para(21714(a,1),21988(a,1,2,1))].">
      <j1 rule="para" parents="21714 21988"/>
    </justification>
  </clause>

  <clause id="21990">
    <literal><![CDATA[
      x \ (y \ ((y * y) * (y \ x))) = (y * x) \ ((y \ 1) \ x)
    ]]></literal>
    <justification jstring="[para(21716(a,1),21989(a,1,2)),flip(a)].">
      <j1 rule="para" parents="21716 21989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21991">
    <literal><![CDATA[
      x \ (y \ ((y * y) * (y \ x))) = y * (x / (y * x))
    ]]></literal>
    <justification jstring="[hyper(333,a,21764,a(flip),b,21990,a),flip(a)].">
      <j1 rule="hyper" parents="333 21764 21990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21992">
    <literal><![CDATA[
      x \ (y \ ((y \ 1) \ x)) = y * (x / (y * x))
    ]]></literal>
    <justification jstring="[para(708(a,1),21991(a,1,2,2))].">
      <j1 rule="para" parents="708 21991"/>
    </justification>
  </clause>

  <clause id="21993">
    <literal><![CDATA[
      K(x \ 1,x * y) * (x * (y / (x * y))) = ((x * y) * (x \ 1)) \ y
    ]]></literal>
    <justification jstring="[para(21992(a,1),21841(a,1,2))].">
      <j1 rule="para" parents="21992 21841"/>
    </justification>
  </clause>

  <clause id="21994">
    <literal><![CDATA[
      x * (K(x \ 1,y * x) * (y / (x * y))) = ((x * y) * (x \ 1)) \ y
    ]]></literal>
    <justification jstring="[hyper(63,a,21634,a(flip),b,21993,a)].">
      <j1 rule="hyper" parents="63 21634 21993"/>
    </justification>
  </clause>

  <clause id="21995">
    <literal><![CDATA[
      x * T(y / (x * y),y * x) = ((x * y) * (x \ 1)) \ y
    ]]></literal>
    <justification jstring="[para(4975(a,1),21994(a,1,2))].">
      <j1 rule="para" parents="4975 21994"/>
    </justification>
  </clause>

  <clause id="21996">
    <literal><![CDATA[
      x * T((x * y) \ y,K(y,x)) = ((x * y) * (x \ 1)) \ y
    ]]></literal>
    <justification jstring="[para(12261(a,1),21995(a,1,2))].">
      <j1 rule="para" parents="12261 21995"/>
    </justification>
  </clause>

  <clause id="21997">
    <literal><![CDATA[
      ((x * y) * (x \ 1)) \ y = x * ((x * y) \ y)
    ]]></literal>
    <justification jstring="[para(6881(a,1),21996(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6881 21996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21998">
    <literal><![CDATA[
      x * ((x * (y / x)) \ (y / x)) = (y * (x \ 1)) \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,21832,a(flip),b,21997,a),flip(a)].">
      <j1 rule="hyper" parents="63 21832 21997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22000">
    <literal><![CDATA[
      (x * (y \ 1)) \ (y \ x) = y * (x \ (y \ x))
    ]]></literal>
    <justification jstring="[para(5079(a,1),21998(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5079 21998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22001">
    <literal><![CDATA[
      ((1 / (x \ 1)) \ (x \ 1)) * (x * (y \ (x \ y))) = (y * (1 / (x \ 1))) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(22000(a,1),1115(a,1,2))].">
      <j1 rule="para" parents="22000 1115"/>
    </justification>
  </clause>

  <clause id="22002">
    <literal><![CDATA[
      (x \ (x \ 1)) * (x * (y \ (x \ y))) = (y * (1 / (x \ 1))) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(76(a,1),22001(a,1,1,1))].">
      <j1 rule="para" parents="76 22001"/>
    </justification>
  </clause>

  <clause id="22005">
    <literal><![CDATA[
      (x * (1 / (y \ 1))) \ (y \ x) = (y * y) \ (y * (x \ (y \ x)))
    ]]></literal>
    <justification jstring="[hyper(735,a,22002,a),flip(a)].">
      <j1 rule="hyper" parents="735 22002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22007">
    <literal><![CDATA[
      L(x \ (y \ (x \ y)),x,x) = (y * (1 / (x \ 1))) \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(333,a,99,a,b,22005,a)].">
      <j1 rule="hyper" parents="333 99 22005"/>
    </justification>
  </clause>

  <clause id="22009">
    <literal><![CDATA[
      (x * (1 / (y \ 1))) \ (y \ x) = y \ (x \ (y \ x))
    ]]></literal>
    <justification jstring="[hyper(63,a,8810,a(flip),b,22007,a),flip(a)].">
      <j1 rule="hyper" parents="63 8810 22007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22011">
    <literal><![CDATA[
      (x * y) \ (y \ x) = y \ (x \ (y \ x))
    ]]></literal>
    <justification jstring="[para(76(a,1),22009(a,1,1,2))].">
      <j1 rule="para" parents="76 22009"/>
    </justification>
  </clause>

  <clause id="22014">
    <literal><![CDATA[
      (x / y) \ (x \ ((x / y) \ x)) = (x * (x / y)) \ y
    ]]></literal>
    <justification jstring="[para(79(a,1),22011(a,1,2)),flip(a)].">
      <j1 rule="para" parents="79 22011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22015">
    <literal><![CDATA[
      (x * (x / y)) \ y = (x / y) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(79(a,1),22014(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="79 22014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22016">
    <literal><![CDATA[
      (x * L(K(K(y,z),x) * u,x,K(y,z))) \ (L(x,K(y,z),L(u,x,K(y,z))) * L(K(K(y,z),x) * u,x,K(y,z))) = a(x,K(y,z),L(K(z,y) * (K(x,K(y,z)) * u),x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(19882(a,2),21374(a,2,3))].">
      <j1 rule="para" parents="19882 21374"/>
    </justification>
  </clause>

  <clause id="22017">
    <literal><![CDATA[
      (x * L(K(K(y,z),x) * u,x,K(y,z))) \ (L(x,K(y,z),L(u,x,K(y,z))) * L(K(K(y,z),x) * u,x,K(y,z))) = a(x,K(y,z),L(y * (T(T(y,K(x,z)),z) \ u),x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(15584(a,1),22016(a,2,3,1))].">
      <j1 rule="para" parents="15584 22016"/>
    </justification>
  </clause>

  <clause id="22018">
    <literal><![CDATA[
      (x * L(K(K(y,z),x) * u,x,K(y,z))) \ (L(x,K(y,z),L(u,x,K(y,z))) * L(K(K(y,z),x) * u,x,K(y,z))) = a(x,K(y,z),L(y * (T(y,T(z,x)) \ u),x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(6859(a,1),22017(a,2,3,1,2,1))].">
      <j1 rule="para" parents="6859 22017"/>
    </justification>
  </clause>

  <clause id="22019">
    <literal><![CDATA[
      (x * L(K(K(y,z),x) * u,x,K(y,z))) \ (L(x,K(y,z),L(u,x,K(y,z))) * L(K(K(y,z),x) * u,x,K(y,z))) = a(x,K(y,z),L(K(T(z,x),y) * u,x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(4556(a,1),22018(a,2,3,1))].">
      <j1 rule="para" parents="4556 22018"/>
    </justification>
  </clause>

  <clause id="22020">
    <literal><![CDATA[
      (x * L(K(K(y,z),x) * u,x,K(y,z))) \ (L(x,K(y,z),L(u,x,K(y,z))) * L(K(K(y,z),x) * u,x,K(y,z))) = a(x,K(y,z),L(K(z,T(y,x)) * u,x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(6370(a,1),22019(a,2,3,1,1))].">
      <j1 rule="para" parents="6370 22019"/>
    </justification>
  </clause>

  <clause id="22021">
    <literal><![CDATA[
      (x * L(K(K(y,z),x) * u,x,K(y,z))) \ (L(x,K(y,z),L(u,x,K(y,z))) * L(K(K(y,z),x) * u,x,K(y,z))) = a(x,K(y,z),L(u * K(z,y),x,K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(333,a,20384,a(flip),b,22020,a),flip(a)].">
      <j1 rule="hyper" parents="333 20384 22020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22023">
    <literal><![CDATA[
      (x * L(K(K(y,z),x) * u,x,K(y,z))) \ (L(x,K(y,z),L(u,x,K(y,z))) * L(K(K(y,z),x) * u,x,K(y,z))) = a(x,K(y,z),u * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(333,a,20317,a(flip),b,22021,a),flip(a)].">
      <j1 rule="hyper" parents="333 20317 22021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22025">
    <literal><![CDATA[
      (x * L(K(x,K(y,z)) * u,x,K(y,z))) \ (L(x,K(y,z),L(u,x,K(y,z))) * L(K(K(y,z),x) * u,x,K(y,z))) = a(x,K(y,z),u * K(z,y))
    ]]></literal>
    <justification jstring="[para(6799(a,1),22023(a,1,1,2,1,1))].">
      <j1 rule="para" parents="6799 22023"/>
    </justification>
  </clause>

  <clause id="22026">
    <literal><![CDATA[
      (T(x,K(y,z)) * L(u,x,K(y,z))) \ (L(x,K(y,z),L(u,x,K(y,z))) * L(K(K(y,z),x) * u,x,K(y,z))) = a(x,K(y,z),u * K(z,y))
    ]]></literal>
    <justification jstring="[para(10148(a,1),22025(a,1,1))].">
      <j1 rule="para" parents="10148 22025"/>
    </justification>
  </clause>

  <clause id="22027">
    <literal><![CDATA[
      (K(x,y) * ((z * K(y,x)) * u)) \ (L(z,K(x,y),L(u,z,K(x,y))) * L(K(K(x,y),z) * u,z,K(x,y))) = a(z,K(x,y),u * K(y,x))
    ]]></literal>
    <justification jstring="[para(19734(a,1),22026(a,1,1))].">
      <j1 rule="para" parents="19734 22026"/>
    </justification>
  </clause>

  <clause id="22028">
    <literal><![CDATA[
      (K(x,y) * ((z * K(y,x)) * u)) \ (L(z,K(x,y),u) * L(K(K(x,y),z) * u,z,K(x,y))) = a(z,K(x,y),u * K(y,x))
    ]]></literal>
    <justification jstring="[para(14811(a,1),22027(a,1,2,1))].">
      <j1 rule="para" parents="14811 22027"/>
    </justification>
  </clause>

  <clause id="22029">
    <literal><![CDATA[
      (K(x,y) * ((z * K(y,x)) * u)) \ (L(z,K(x,y),u) * L(K(z,K(x,y)) * u,z,K(x,y))) = a(z,K(x,y),u * K(y,x))
    ]]></literal>
    <justification jstring="[para(6799(a,1),22028(a,1,2,2,1,1))].">
      <j1 rule="para" parents="6799 22028"/>
    </justification>
  </clause>

  <clause id="22031">
    <literal><![CDATA[
      (K(x,y) * ((z * K(y,x)) * u)) \ (L(T(z,K(x,y)),K(x,y),u) * L(u,z,K(x,y))) = a(z,K(x,y),u * K(y,x))
    ]]></literal>
    <justification jstring="[para(10418(a,1),22029(a,1,2))].">
      <j1 rule="para" parents="10418 22029"/>
    </justification>
  </clause>

  <clause id="22032">
    <literal><![CDATA[
      (K(x,y) * ((z * K(y,x)) * u)) \ (K(x,y) * (z * (K(y,x) * u))) = a(z,K(x,y),u * K(y,x))
    ]]></literal>
    <justification jstring="[para(20784(a,1),22031(a,1,2))].">
      <j1 rule="para" parents="20784 22031"/>
    </justification>
  </clause>

  <clause id="22033">
    <literal><![CDATA[
      L(a(x,K(y,z),u),(u * K(y,z)) * x,K(z,y)) = a(u,K(z,y),x * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,20495,a(flip),b,22032,a)].">
      <j1 rule="hyper" parents="63 20495 22032"/>
    </justification>
  </clause>

  <clause id="22034">
    <literal><![CDATA[
      a(x,K(y,z),u * K(z,y)) = a(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(21159,a,22033,a),flip(a)].">
      <j1 rule="hyper" parents="21159 22033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22035">
    <literal><![CDATA[
      L(x \ L(x,K(y,z),u),T(x,w),T(u,v5)) = a(T(x,w),K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(20916,a,22034,a)].">
      <j1 rule="hyper" parents="20916 22034"/>
    </justification>
  </clause>

  <clause id="22037">
    <literal><![CDATA[
      L(x \ L(x,K(y,z),u),T(x,w),T(u,v5)) = a(u,K(z,y),x)
    ]]></literal>
    <justification jstring="[hyper(333,a,21152,a(flip),b,22035,a),flip(a)].">
      <j1 rule="hyper" parents="333 21152 22035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22039">
    <literal><![CDATA[
      L(x \ L(x,y,K(z,u)),T(x,w),T(z,v5)) = a(z,K(u,y),x)
    ]]></literal>
    <justification jstring="[para(21617(a,1),22037(a,1,1,2))].">
      <j1 rule="para" parents="21617 22037"/>
    </justification>
  </clause>

  <clause id="22040">
    <literal><![CDATA[
      L(a(x,y,K(z,u)),T(z,w),T(u,v5)) = a(u,K(x,y),z)
    ]]></literal>
    <justification jstring="[para(14491(a,1),22039(a,1,1))].">
      <j1 rule="para" parents="14491 22039"/>
    </justification>
  </clause>

  <clause id="22041">
    <literal><![CDATA[
      a(x,y,K(z,L(u,T(z,w),T(u,v5)))) = a(u,K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,13644,a,b,22040,a)].">
      <j1 rule="hyper" parents="63 13644 22040"/>
    </justification>
  </clause>

  <clause id="22042">
    <literal><![CDATA[
      a(x,K(y,z),u) = a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[para(9473(a,1),22041(a,1,3)),flip(a)].">
      <j1 rule="para" parents="9473 22041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22043">
    <literal><![CDATA[
      a(x,K(y,z),u) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(333,a,21486,a(flip),b,22042,a),flip(a)].">
      <j1 rule="hyper" parents="333 21486 22042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22046">
    <literal><![CDATA[
      a(x,a(y,z,K(u,w)),v5) = a(x,a(y,z,u),K(v5,w))
    ]]></literal>
    <justification jstring="[para(13539(a,2),22043(a,1,2))].">
      <j1 rule="para" parents="13539 22043"/>
    </justification>
  </clause>

  <clause id="22047">
    <literal><![CDATA[
      a(x,a(y,z,K(u,w)),v5) = a(x,y,K(v5,a(w,z,u)))
    ]]></literal>
    <justification jstring="[para(13732(a,2),22043(a,1,2))].">
      <j1 rule="para" parents="13732 22043"/>
    </justification>
  </clause>

  <clause id="22048">
    <literal><![CDATA[
      a(x,a(y,z,u),K(w,v5)) = a(x,y,K(w,a(v5,z,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,22046,a(flip),b,22047,a)].">
      <j1 rule="hyper" parents="63 22046 22047"/>
    </justification>
  </clause>

  <clause id="22049">
    <literal><![CDATA[
      a(x,a(y,z,u),K(w,v5)) = a(x,y,a(w,z,K(u,v5)))
    ]]></literal>
    <justification jstring="[para(13732(a,2),22048(a,2,3))].">
      <j1 rule="para" parents="13732 22048"/>
    </justification>
  </clause>

  <clause id="22050">
    <literal><![CDATA[
      K(x,y) * a(x,z,a(y,u,K(w,v5))) = K(x,L(y,v5,a(z,u,w)))
    ]]></literal>
    <justification jstring="[para(22049(a,1),21490(a,1,2))].">
      <j1 rule="para" parents="22049 21490"/>
    </justification>
  </clause>

  <clause id="22051">
    <literal><![CDATA[
      K(x,L(y,a(z,u,w),v5)) = K(x,L(y,z,a(v5,u,w)))
    ]]></literal>
    <justification jstring="[hyper(21536,a,22050,a)].">
      <j1 rule="hyper" parents="21536 22050"/>
    </justification>
  </clause>

  <clause id="22052">
    <literal><![CDATA[
      T(x * K(y,L(x,z,a(u,w,v5))),y) = L(x,a(z,w,v5),K(u,y))
    ]]></literal>
    <justification jstring="[para(22051(a,1),14550(a,1,1,2))].">
      <j1 rule="para" parents="22051 14550"/>
    </justification>
  </clause>

  <clause id="22053">
    <literal><![CDATA[
      L(x,a(y,z,u),K(w,v5)) = L(x,y,K(a(w,z,u),v5))
    ]]></literal>
    <justification jstring="[hyper(15938,a,22052,a),flip(a)].">
      <j1 rule="hyper" parents="15938 22052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22054">
    <literal><![CDATA[
      L(x,a(y,z,u),K(w,v5)) = L(x,y,a(w,z,K(u,v5)))
    ]]></literal>
    <justification jstring="[para(13539(a,2),22053(a,2,3))].">
      <j1 rule="para" parents="13539 22053"/>
    </justification>
  </clause>

  <clause id="22055">
    <literal><![CDATA[
      L(x,K(a(y,z,u),w),v5) = L(x,y,a(v5,z,K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(21625,a,22054,a)].">
      <j1 rule="hyper" parents="21625 22054"/>
    </justification>
  </clause>

  <clause id="22056">
    <literal><![CDATA[
      L(x,a(y,z,K(u,w)),v5) = L(x,y,a(v5,z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(13539(a,2),22055(a,1,2))].">
      <j1 rule="para" parents="13539 22055"/>
    </justification>
  </clause>

  <clause id="22057">
    <literal><![CDATA[
      L(x,y,a(z,u,K(w,v5))) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,21598,a(flip),b,22056,a),flip(a)].">
      <j1 rule="hyper" parents="63 21598 22056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22061">
    <literal><![CDATA[
      L(x,a(y,z,u),K(w,v5)) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,22054,a,b,22057,a)].">
      <j1 rule="hyper" parents="63 22054 22057"/>
    </justification>
  </clause>

  <clause id="22062">
    <literal><![CDATA[
      (a(x,y,K(z,u)) * w) / v5 = a(x,y,K(z,u)) * (w / v5)
    ]]></literal>
    <justification jstring="[hyper(197,a,22057,a(flip),b,10409,a(flip))].">
      <j1 rule="hyper" parents="197 22057 10409"/>
    </justification>
  </clause>

  <clause id="22066">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (w * (a(x,u,K(z,y)) * v5)) = w * v5
    ]]></literal>
    <justification jstring="[para(22057(a,1),21835(a,1,2,1))].">
      <j1 rule="para" parents="22057 21835"/>
    </justification>
  </clause>

  <clause id="22069">
    <literal><![CDATA[
      a(a(x,y,z),u,K(w,v5)) = 1
    ]]></literal>
    <justification jstring="[hyper(120,a,22061,a(flip),b,21495,a),flip(a)].">
      <j1 rule="hyper" parents="120 22061 21495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22070">
    <literal><![CDATA[
      a(a(x,y,z),u,K(w,v5)) = v6 \ v6
    ]]></literal>
    <justification jstring="[hyper(333,a,66,a,b,22069,a),flip(a)].">
      <j1 rule="hyper" parents="333 66 22069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22072">
    <literal><![CDATA[
      (a(x,y,z) * u) * K(w,v5) = a(x,y,z) * (u * K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(145,a,22070,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 22070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22074">
    <literal><![CDATA[
      a(x,y,K(z,u)) * ((w * T(v5,a(x,y,K(z,u)) * w)) / v6) = (L(v5,w,a(x,y,K(z,u))) * (a(x,y,K(z,u)) * w)) / v6
    ]]></literal>
    <justification jstring="[para(664(a,1),22062(a,1,1)),flip(a)].">
      <j1 rule="para" parents="664 22062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22075">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (w * v5) = w * (a(x,z,K(u,y)) * v5)
    ]]></literal>
    <justification jstring="[hyper(9794,a,22066,a)].">
      <j1 rule="hyper" parents="9794 22066"/>
    </justification>
  </clause>

  <clause id="22076">
    <literal><![CDATA[
      K(x,L(y,z,a(u,w,v5))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(10967,a,22072,a)].">
      <j1 rule="hyper" parents="10967 22072"/>
    </justification>
  </clause>

  <clause id="22080">
    <literal><![CDATA[
      K((a(x,y,z) * u) \ w,v5) = K(u \ (a(x,y,z) \ w),v5)
    ]]></literal>
    <justification jstring="[hyper(14014,a,22076,a)].">
      <j1 rule="hyper" parents="14014 22076"/>
    </justification>
  </clause>

  <clause id="22086">
    <literal><![CDATA[
      (x * (a(y,z,K(u,w)) * (v5 * v6))) / T(x * v5,a(y,u,K(w,z)) * v6) = L(a(y,u,K(w,z)) * v6,v5,x)
    ]]></literal>
    <justification jstring="[para(22075(a,2),13403(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="22075 13403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22087">
    <literal><![CDATA[
      K((a(x,y,z) * u) \ w,v5) = K(a(x,y,z) * (u \ w),v5)
    ]]></literal>
    <justification jstring="[hyper(333,a,21700,a(flip),b,22080,a),flip(a)].">
      <j1 rule="hyper" parents="333 21700 22080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22088">
    <literal><![CDATA[
      (x * K(a(y,z,u) * (w \ v5),v6)) \ (x * v6) = T(v6,(a(y,z,u) * w) \ v5)
    ]]></literal>
    <justification jstring="[para(22087(a,1),5447(a,1,1,2))].">
      <j1 rule="para" parents="22087 5447"/>
    </justification>
  </clause>

  <clause id="22089">
    <literal><![CDATA[
      T(x,(a(y,z,u) * w) \ v5) = T(x,a(y,z,u) * (w \ v5))
    ]]></literal>
    <justification jstring="[hyper(5458,a,22088,a),flip(a)].">
      <j1 rule="hyper" parents="5458 22088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22090">
    <literal><![CDATA[
      T(x,(y * a(z,u,w)) \ v5) = T(x,a(z,u,w) * (y \ v5))
    ]]></literal>
    <justification jstring="[hyper(17926,a,22089,a)].">
      <j1 rule="hyper" parents="17926 22089"/>
    </justification>
  </clause>

  <clause id="22091">
    <literal><![CDATA[
      T(x,T(y * (z * (a(u,w,v5) \ 1)),a(u,w,v5) * a(u,w,v5))) = T(x,a(u,w,v5) * (a(u,w,v5) \ (y * (z * a(u,w,v5)))))
    ]]></literal>
    <justification jstring="[para(14160(a,2),22089(a,1,2))].">
      <j1 rule="para" parents="14160 22089"/>
    </justification>
  </clause>

  <clause id="22092">
    <literal><![CDATA[
      T(x,a(y,y,z) * (z \ u)) = T(x,z \ L(u,y,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,21799,a(flip),b,22090,a),flip(a)].">
      <j1 rule="hyper" parents="63 21799 22090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22093">
    <literal><![CDATA[
      T(x,y \ L(z,u,u)) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,21316,a(flip),b,22092,a),flip(a)].">
      <j1 rule="hyper" parents="63 21316 22092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22094">
    <literal><![CDATA[
      T(x,T(y,z) \ L(u,w,w)) = T(x,z * (y \ (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(333,a,21893,a,b,22093,a),flip(a)].">
      <j1 rule="hyper" parents="333 21893 22093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22096">
    <literal><![CDATA[
      T(x,y \ ((z \ 1) \ u)) = T(x,y \ (z * u))
    ]]></literal>
    <justification jstring="[para(2601(a,1),22093(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2601 22093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22097">
    <literal><![CDATA[
      T(x,(y \ 1) \ (z * u)) = T(x,y * ((z \ 1) \ u))
    ]]></literal>
    <justification jstring="[hyper(13423,a,22096,a),flip(a)].">
      <j1 rule="hyper" parents="13423 22096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22098">
    <literal><![CDATA[
      T(x,y * ((z \ 1) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y * (z * u)) = w
    ]]></literal>
    <justification jstring="[para(22097(a,1),13423(a,1))].">
      <j1 rule="para" parents="22097 13423"/>
    </justification>
  </clause>

  <clause id="22099">
    <literal><![CDATA[
      T(x,(y * z) \ L(u,w,w)) = T(x,y * ((z * y) \ (y \ u)))
    ]]></literal>
    <justification jstring="[hyper(15107,a,22094,a)].">
      <j1 rule="hyper" parents="15107 22094"/>
    </justification>
  </clause>

  <clause id="22100">
    <literal><![CDATA[
      T(x,T(y,z) * L(u,w,w)) = T(x,z * ((y \ 1) \ (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,18191,a(flip),b,22094,a)].">
      <j1 rule="hyper" parents="63 18191 22094"/>
    </justification>
  </clause>

  <clause id="22101">
    <literal><![CDATA[
      T(x,a(y,z,u) * (w * v5)) = T(x,w * (a(y,z,u) \ v5))
    ]]></literal>
    <justification jstring="[hyper(22098,a,21725,a)].">
      <j1 rule="hyper" parents="22098 21725"/>
    </justification>
  </clause>

  <clause id="22102">
    <literal><![CDATA[
      T(x,y * (a(z,z,u) \ w)) = T(x,y * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,21316,a(flip),b,22101,a),flip(a)].">
      <j1 rule="hyper" parents="63 21316 22101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22103">
    <literal><![CDATA[
      T(x,y * ((z * y) \ (y \ u))) = T(x,((y \ 1) \ z) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,21798,a(flip),b,22099,a),flip(a)].">
      <j1 rule="hyper" parents="63 21798 22099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22105">
    <literal><![CDATA[
      T(x,y \ (K(z * z,u) * (z \ (z \ u)))) = T(x,((z \ 1) \ ((z \ 1) \ y)) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,21916,a,b,22103,a)].">
      <j1 rule="hyper" parents="63 21916 22103"/>
    </justification>
  </clause>

  <clause id="22106">
    <literal><![CDATA[
      T(x,T(y,z) * L(u,w,w)) = T(x,z * (y * (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(22098,a,22100,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="22098 22100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22107">
    <literal><![CDATA[
      T(x,y * (z * (y \ u))) = T(x,T(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,17913,a(flip),b,22106,a),flip(a)].">
      <j1 rule="hyper" parents="63 17913 22106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22108">
    <literal><![CDATA[
      T(x,T(y,z) * (z * u)) = T(x,z * (y * u))
    ]]></literal>
    <justification jstring="[para(9(a,1),22107(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="9 22107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22109">
    <literal><![CDATA[
      T(x,y * (T(z,y) * u)) = T(x,z * (y * u))
    ]]></literal>
    <justification jstring="[hyper(16685,a,22108,a),flip(a)].">
      <j1 rule="hyper" parents="16685 22108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22110">
    <literal><![CDATA[
      T(x,y * (T(z,y) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,z * (y * u)) = w
    ]]></literal>
    <justification jstring="[para(22108(a,1),16685(a,1))].">
      <j1 rule="para" parents="22108 16685"/>
    </justification>
  </clause>

  <clause id="22111">
    <literal><![CDATA[
      T(x,((y \ 1) / z) * (T(u,y \ (z \ 1)) * w)) = T(x,u * (((y \ 1) / z) * w))
    ]]></literal>
    <justification jstring="[para(13379(a,1),22109(a,1,2,2,1))].">
      <j1 rule="para" parents="13379 22109"/>
    </justification>
  </clause>

  <clause id="22112">
    <literal><![CDATA[
      T(x,(y / (z \ 1)) * (T(u,y * z) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,u * ((y / (z \ 1)) * w)) = v5
    ]]></literal>
    <justification jstring="[para(13325(a,1),22110(a,1,2,2,1))].">
      <j1 rule="para" parents="13325 22110"/>
    </justification>
  </clause>

  <clause id="22113">
    <literal><![CDATA[
      T(x,y \ (K(z * z,u) * (z \ (z \ u)))) = T(x,y \ ((z \ 1) * ((z \ 1) * u)))
    ]]></literal>
    <justification jstring="[hyper(333,a,21577,a(flip),b,22105,a),flip(a)].">
      <j1 rule="hyper" parents="333 21577 22105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22114">
    <literal><![CDATA[
      T(x,((y \ 1) / z) * (T(u,y * (z \ 1)) * w)) = T(x,u * (((y \ 1) / z) * w))
    ]]></literal>
    <justification jstring="[hyper(16940,a,22111,a)].">
      <j1 rule="hyper" parents="16940 22111"/>
    </justification>
  </clause>

  <clause id="22115">
    <literal><![CDATA[
      T(x,y \ T((z \ u) / z,z \ 1)) = T(x,y \ ((z \ 1) * ((z \ 1) * u)))
    ]]></literal>
    <justification jstring="[para(16110(a,1),22113(a,1,2,2))].">
      <j1 rule="para" parents="16110 22113"/>
    </justification>
  </clause>

  <clause id="22116">
    <literal><![CDATA[
      T(x,y \ T((z \ u) / z,z)) = T(x,y \ ((z \ 1) * ((z \ 1) * u)))
    ]]></literal>
    <justification jstring="[hyper(15231,a,22115,a)].">
      <j1 rule="hyper" parents="15231 22115"/>
    </justification>
  </clause>

  <clause id="22117">
    <literal><![CDATA[
      T(x,y \ ((z \ 1) * ((z \ 1) * u))) = T(x,y \ (z \ (z \ u)))
    ]]></literal>
    <justification jstring="[para(113(a,1),22116(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="113 22116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22118">
    <literal><![CDATA[
      T(x,(y \ K(y,(z \ 1) * ((z \ 1) * u))) \ (z \ (z \ u))) = T(x,(y \ 1) \ T((z \ 1) * ((z \ 1) * u),y))
    ]]></literal>
    <justification jstring="[para(8518(a,1),22117(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8518 22117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22119">
    <literal><![CDATA[
      T(x,((y \ 1) / z) * (T(u,y / z) * w)) = T(x,u * (((y \ 1) / z) * w))
    ]]></literal>
    <justification jstring="[para(13244(a,1),22114(a,1,2,2,1))].">
      <j1 rule="para" parents="13244 22114"/>
    </justification>
  </clause>

  <clause id="22120">
    <literal><![CDATA[
      T(x,((y \ 1) / z) * (T(u,z * y) * w)) = T(x,u * (((y \ 1) / z) * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,19087,a(flip),b,22119,a)].">
      <j1 rule="hyper" parents="63 19087 22119"/>
    </justification>
  </clause>

  <clause id="22121">
    <literal><![CDATA[
      T(x,(y * z) \ (T(u,y * z) * w)) = T(x,u * (((z \ 1) / y) * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,21434,a(flip),b,22120,a)].">
      <j1 rule="hyper" parents="63 21434 22120"/>
    </justification>
  </clause>

  <clause id="22122">
    <literal><![CDATA[
      T(x,y * (((z \ 1) / u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y * ((u * z) \ w)) = v5
    ]]></literal>
    <justification jstring="[para(22121(a,1),21891(a,1))].">
      <j1 rule="para" parents="22121 21891"/>
    </justification>
  </clause>

  <clause id="22123">
    <literal><![CDATA[
      (x * (a(y,z,K(u,w)) * (v5 * v6))) / T(x * v5,v6) = L(a(y,u,K(w,z)) * v6,v5,x)
    ]]></literal>
    <justification jstring="[para(17908(a,1),22086(a,1,2))].">
      <j1 rule="para" parents="17908 22086"/>
    </justification>
  </clause>

  <clause id="22125">
    <literal><![CDATA[
      T(x,(y \ K(y,(z \ 1) * ((z \ 1) * u))) \ (z \ (z \ u))) = T(x,(((z \ 1) * ((z \ 1) * u)) \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(333,a,21785,a(flip),b,22118,a),flip(a)].">
      <j1 rule="hyper" parents="333 21785 22118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22126">
    <literal><![CDATA[
      T(x,(y \ K(y,(z \ 1) * ((z \ 1) * u))) \ (z \ (z \ u))) = T(x,((z \ 1) * ((z \ 1) * u)) * y)
    ]]></literal>
    <justification jstring="[hyper(333,a,13206,a(flip),b,22125,a),flip(a)].">
      <j1 rule="hyper" parents="333 13206 22125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22127">
    <literal><![CDATA[
      T(x,(y \ K(y,(z \ 1) * ((z \ 1) * u))) \ (z \ (z \ u))) = T(x,u * ((z \ 1) * ((z \ 1) * y)))
    ]]></literal>
    <justification jstring="[hyper(333,a,21806,a(flip),b,22126,a),flip(a)].">
      <j1 rule="hyper" parents="333 21806 22126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22128">
    <literal><![CDATA[
      a(x,y,K(z,u)) * ((w * T(v5,a(x,y,K(z,u)) * w)) / v6) = (v5 * (a(x,y,K(z,u)) * w)) / v6
    ]]></literal>
    <justification jstring="[para(22057(a,1),22074(a,2,1,1))].">
      <j1 rule="para" parents="22057 22074"/>
    </justification>
  </clause>

  <clause id="22129">
    <literal><![CDATA[
      a(x,y,K(z,u)) * ((w * T(v5,w)) / v6) = (v5 * (a(x,y,K(z,u)) * w)) / v6
    ]]></literal>
    <justification jstring="[para(17908(a,1),22128(a,1,2,1,2))].">
      <j1 rule="para" parents="17908 22128"/>
    </justification>
  </clause>

  <clause id="22130">
    <literal><![CDATA[
      (x * (a(y,z,K(u,w)) * v5)) / v6 = a(y,z,K(u,w)) * ((x * v5) / v6)
    ]]></literal>
    <justification jstring="[para(111(a,1),22129(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="111 22129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22132">
    <literal><![CDATA[
      a(x,y,K(z,u)) * ((w * (v5 * v6)) / T(w * v5,v6)) = L(a(x,z,K(u,y)) * v6,v5,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,22123,a(flip),b,22130,a),flip(a)].">
      <j1 rule="hyper" parents="63 22123 22130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22133">
    <literal><![CDATA[
      L(a(x,y,K(z,u)) * w,v5,v6) = a(x,u,K(y,z)) * L(w,v5,v6)
    ]]></literal>
    <justification jstring="[para(13403(a,2),22132(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13403 22132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22134">
    <literal><![CDATA[
      T(x,T(L(a(y,z,K(u,w)) * (K(v5,v6) * u),v7,v8),L(z,w,y) \ z)) = T(x,L(u * K(v5,v6),v7,v8))
    ]]></literal>
    <justification jstring="[para(22133(a,2),19078(a,1,2,1))].">
      <j1 rule="para" parents="22133 19078"/>
    </justification>
  </clause>

  <clause id="22135">
    <literal><![CDATA[
      T(x,T(L(K(y,z) * L(u,w,K(v5,v6)),v7,v8),L(w,v6,v5) \ w)) = T(x,L(u * K(y,z),v7,v8))
    ]]></literal>
    <justification jstring="[para(17891(a,1),22134(a,1,2,1,1))].">
      <j1 rule="para" parents="17891 22134"/>
    </justification>
  </clause>

  <clause id="22136">
    <literal><![CDATA[
      T(x,T(L(L(K(y,z) * u,w,K(v5,v6)),v7,v8),L(w,v6,v5) \ w)) = T(x,L(u * K(y,z),v7,v8))
    ]]></literal>
    <justification jstring="[para(19882(a,2),22135(a,1,2,1,1))].">
      <j1 rule="para" parents="19882 22135"/>
    </justification>
  </clause>

  <clause id="22137">
    <literal><![CDATA[
      T(x,L(L(L(K(y,z) * u,w,K(v5,v6)),v7,v8),v6,K(w,v5))) = T(x,L(u * K(y,z),v7,v8))
    ]]></literal>
    <justification jstring="[para(14482(a,1),22136(a,1,2))].">
      <j1 rule="para" parents="14482 22136"/>
    </justification>
  </clause>

  <clause id="22138">
    <literal><![CDATA[
      T(x,L(L(K(y,z) * u,w,K(v5,v6)),v7,v8)) = T(x,L(u * K(y,z),v7,v8))
    ]]></literal>
    <justification jstring="[hyper(17650,a,22137,a)].">
      <j1 rule="hyper" parents="17650 22137"/>
    </justification>
  </clause>

  <clause id="22140">
    <literal><![CDATA[
      T(x,K(y,z) * ((u * w) \ (u * (w * v5)))) = T(x,L(v5 * K(y,z),w,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,21822,a(flip),b,22138,a)].">
      <j1 rule="hyper" parents="63 21822 22138"/>
    </justification>
  </clause>

  <clause id="22142">
    <literal><![CDATA[
      T(x,L(y * K(z,u),w,v5)) = T(x,K(z,u) * L(y,w,v5))
    ]]></literal>
    <justification jstring="[para(18(a,2),22140(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="18 22140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22144">
    <literal><![CDATA[
      T(x,a(y,z,u) * (a(y,z,u) \ (w * (v5 * a(y,z,u))))) = T(x,w * (v5 * (a(y,z,u) \ 1)))
    ]]></literal>
    <justification jstring="[hyper(15410,a,22091,a),flip(a)].">
      <j1 rule="hyper" parents="15410 22091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22146">
    <literal><![CDATA[
      T(x,y * (z * (a(u,w,v5) \ 1))) = T(x,y * (z * a(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(10(a,1),22144(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 22144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22147">
    <literal><![CDATA[
      T(x,y * (z / a(u,w,v5))) = T(x,y * (z * a(u,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,21332,a(flip),b,22146,a)].">
      <j1 rule="hyper" parents="63 21332 22146"/>
    </justification>
  </clause>

  <clause id="22149">
    <literal><![CDATA[
      T(x,y * (z * a(u,u,z))) = T(x,y * L(z,u,u))
    ]]></literal>
    <justification jstring="[para(14342(a,1),22146(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14342 22146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22150">
    <literal><![CDATA[
      T(x,((y \ 1) \ (z \ (y \ 1))) * L(u,y,y)) = T(x,y * ((z \ 1) * (y \ u)))
    ]]></literal>
    <justification jstring="[hyper(21952,a,22149,a),flip(a)].">
      <j1 rule="hyper" parents="21952 22149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22151">
    <literal><![CDATA[
      T(x,y * ((z \ 1) \ (z \ u))) = T(x,y * L(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,21775,a,b,22149,a)].">
      <j1 rule="hyper" parents="63 21775 22149"/>
    </justification>
  </clause>

  <clause id="22152">
    <literal><![CDATA[
      T(x,y * L(z * u,z,z)) = T(x,y * ((z \ 1) \ u))
    ]]></literal>
    <justification jstring="[para(16103(a,1),22149(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="16103 22149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22153">
    <literal><![CDATA[
      T(x,y * (z * (z \ u))) = T(x,y * L(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(22098,a,22151,a)].">
      <j1 rule="hyper" parents="22098 22151"/>
    </justification>
  </clause>

  <clause id="22154">
    <literal><![CDATA[
      T(x,y * L(z,u,u)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(10(a,1),22153(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 22153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22158">
    <literal><![CDATA[
      T(x,(y * z) * L(L(u,z,y),w,w)) = T(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(97(a,1),22154(a,2,2))].">
      <j1 rule="para" parents="97 22154"/>
    </justification>
  </clause>

  <clause id="22159">
    <literal><![CDATA[
      T(x,y * ((z * z) \ u)) = T(x,y * (z \ (z \ u)))
    ]]></literal>
    <justification jstring="[para(311(a,1),22154(a,1,2,2))].">
      <j1 rule="para" parents="311 22154"/>
    </justification>
  </clause>

  <clause id="22160">
    <literal><![CDATA[
      T(x,y * ((z * z) * u)) = T(x,y * (z * (z * u)))
    ]]></literal>
    <justification jstring="[para(2577(a,1),22154(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2577 22154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22161">
    <literal><![CDATA[
      T(T(x,y * (z \ (z \ u))),w) = T(T(x,y * u),z \ (z \ w))
    ]]></literal>
    <justification jstring="[para(22159(a,1),16882(a,1,1))].">
      <j1 rule="para" parents="22159 16882"/>
    </justification>
  </clause>

  <clause id="22162">
    <literal><![CDATA[
      T(x,y * L((1 / z) * u,1 / z,1 / z)) = T(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[para(79(a,1),22152(a,2,2,2,1))].">
      <j1 rule="para" parents="79 22152"/>
    </justification>
  </clause>

  <clause id="22163">
    <literal><![CDATA[
      T(x,y * (a(z,u,w) \ v5)) = T(x,y * (v5 * a(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,17922,a(flip),b,22147,a)].">
      <j1 rule="hyper" parents="63 17922 22147"/>
    </justification>
  </clause>

  <clause id="22164">
    <literal><![CDATA[
      T(x,y * (z * L(u,w,w))) = T(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(461(a,1),22158(a,1,2))].">
      <j1 rule="para" parents="461 22158"/>
    </justification>
  </clause>

  <clause id="22165">
    <literal><![CDATA[
      T(x,y * (z * ((u * u) \ w))) = T(x,y * (z * (u \ (u \ w))))
    ]]></literal>
    <justification jstring="[para(311(a,1),22164(a,1,2,2,2))].">
      <j1 rule="para" parents="311 22164"/>
    </justification>
  </clause>

  <clause id="22166">
    <literal><![CDATA[
      T(x,y * (a(z,z,u) \ w)) = T(x,y * (w * a(u,z,z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,21728,a(flip),b,22163,a)].">
      <j1 rule="hyper" parents="63 21728 22163"/>
    </justification>
  </clause>

  <clause id="22167">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * (z * a(u,w,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,(a(u,w,w) \ z) * y) = v5
    ]]></literal>
    <justification jstring="[para(22163(a,1),21317(a,1))].">
      <j1 rule="para" parents="22163 21317"/>
    </justification>
  </clause>

  <clause id="22168">
    <literal><![CDATA[
      T(x,y * (z * a(u,w,w))) = T(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,22102,a(flip),b,22166,a),flip(a)].">
      <j1 rule="hyper" parents="63 22102 22166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22171">
    <literal><![CDATA[
      T(T(x,y * ((z / u) * (u \ z))),(z / u) \ ((z / u) \ w)) = T(T(x,y * (u \ (z / T(z / u,z / u)))),w)
    ]]></literal>
    <justification jstring="[para(8191(a,1),22161(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8191 22161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22172">
    <literal><![CDATA[
      T(T(x,y * (z * (u \ (u \ w)))),v5) = T(T(x,y * (z * w)),u \ (u \ v5))
    ]]></literal>
    <justification jstring="[para(22165(a,1),16883(a,1,1))].">
      <j1 rule="para" parents="22165 16883"/>
    </justification>
  </clause>

  <clause id="22173">
    <literal><![CDATA[
      T(x,y * L((1 / z) * u,z,z)) = T(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(16840,a,22162,a)].">
      <j1 rule="hyper" parents="16840 22162"/>
    </justification>
  </clause>

  <clause id="22174">
    <literal><![CDATA[
      T(x,y * R(z * (1 / u),u,u)) = T(x,y * (u \ T(z,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,16869,a(flip),b,22173,a)].">
      <j1 rule="hyper" parents="63 16869 22173"/>
    </justification>
  </clause>

  <clause id="22175">
    <literal><![CDATA[
      T(x,y * R(z * (1 / u),u,u)) = T(x,y * (z / u))
    ]]></literal>
    <justification jstring="[hyper(333,a,18149,a(flip),b,22174,a),flip(a)].">
      <j1 rule="hyper" parents="333 18149 22174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22176">
    <literal><![CDATA[
      T(x,y * L(z * (1 / u),u,u)) = T(x,y * (z / u))
    ]]></literal>
    <justification jstring="[hyper(16838,a,22175,a)].">
      <j1 rule="hyper" parents="16838 22175"/>
    </justification>
  </clause>

  <clause id="22177">
    <literal><![CDATA[
      T(x,y * ((z \ 1) * (u * (z \ 1)))) = T(x,y * ((z \ u) / z))
    ]]></literal>
    <justification jstring="[hyper(19038,a,22176,a)].">
      <j1 rule="hyper" parents="19038 22176"/>
    </justification>
  </clause>

  <clause id="22178">
    <literal><![CDATA[
      T(x,y * ((z \ 1) * (u * (z \ 1)))) = T(x,y * (z \ (u / z)))
    ]]></literal>
    <justification jstring="[hyper(333,a,12759,a(flip),b,22177,a),flip(a)].">
      <j1 rule="hyper" parents="333 12759 22177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22179">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * (u \ (z / u))) = T(x,(((u \ 1) * z) * (u \ 1)) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,19244,a(flip),b,22178,a),flip(a)].">
      <j1 rule="hyper" parents="63 19244 22178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22180">
    <literal><![CDATA[
      T(x,(((y \ 1) * z) * (y \ 1)) * u) = T(x,(y \ (z / y)) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,16089,a(flip),b,22179,a),flip(a)].">
      <j1 rule="hyper" parents="63 16089 22179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22181">
    <literal><![CDATA[
      T(x,(y * (z \ 1)) * L(u,z,z)) = T(x,(z \ ((z * y) / z)) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,21820,a(flip),b,22180,a)].">
      <j1 rule="hyper" parents="63 21820 22180"/>
    </justification>
  </clause>

  <clause id="22182">
    <literal><![CDATA[
      T(x,(y * (z \ 1)) * L(u,z,z)) = T(x,(z \ T(y,z)) * u)
    ]]></literal>
    <justification jstring="[hyper(333,a,18103,a(flip),b,22181,a),flip(a)].">
      <j1 rule="hyper" parents="333 18103 22181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22183">
    <literal><![CDATA[
      T(x,(y * (z \ 1)) * L(u,z,z)) = T(x,(y / z) * u)
    ]]></literal>
    <justification jstring="[hyper(333,a,18043,a(flip),b,22182,a),flip(a)].">
      <j1 rule="hyper" parents="333 18043 22182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22184">
    <literal><![CDATA[
      T(x,(y * ((1 / z) \ 1)) * L(u,1 / z,1 / z)) = T(x,(y / (z \ 1)) * u)
    ]]></literal>
    <justification jstring="[hyper(333,a,3183,a(flip),b,22183,a),flip(a)].">
      <j1 rule="hyper" parents="333 3183 22183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22185">
    <literal><![CDATA[
      T(x,(y \ (z \ y)) * L(u,y,y)) = T(x,y * ((z \ 1) * (y \ u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,21789,a(flip),b,22150,a)].">
      <j1 rule="hyper" parents="63 21789 22150"/>
    </justification>
  </clause>

  <clause id="22186">
    <literal><![CDATA[
      T(x,((y \ 1) * (z \ y)) * u) = T(x,y * ((z \ 1) * (y \ u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,21803,a(flip),b,22185,a)].">
      <j1 rule="hyper" parents="63 21803 22185"/>
    </justification>
  </clause>

  <clause id="22187">
    <literal><![CDATA[
      T(x,(y * (z \ (y \ 1))) * u) = T(x,y * ((z \ 1) * (y \ u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,21769,a(flip),b,22186,a)].">
      <j1 rule="hyper" parents="63 21769 22186"/>
    </justification>
  </clause>

  <clause id="22188">
    <literal><![CDATA[
      T(x,y * (((z * y) \ 1) * (y \ u))) = T(x,(z \ (y \ 1)) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,14849,a(flip),b,22187,a),flip(a)].">
      <j1 rule="hyper" parents="63 14849 22187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22189">
    <literal><![CDATA[
      T(x,T((y * z) \ 1,z) * u) = T(x,(y \ (z \ 1)) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,22107,a(flip),b,22188,a)].">
      <j1 rule="hyper" parents="63 22107 22188"/>
    </justification>
  </clause>

  <clause id="22190">
    <literal><![CDATA[
      T(x,T(y * z,z) \ u) = T(x,(y \ (z \ 1)) * u)
    ]]></literal>
    <justification jstring="[hyper(18195,a,22189,a)].">
      <j1 rule="hyper" parents="18195 22189"/>
    </justification>
  </clause>

  <clause id="22191">
    <literal><![CDATA[
      T(x,(y \ (z \ 1)) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(z * y) \ u) = w
    ]]></literal>
    <justification jstring="[para(22190(a,1),15107(a,1))].">
      <j1 rule="para" parents="22190 15107"/>
    </justification>
  </clause>

  <clause id="22192">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * z) = T(x,(a(u,w,w) \ z) * y)
    ]]></literal>
    <justification jstring="[hyper(22167,a,22168,a),flip(a)].">
      <j1 rule="hyper" parents="22167 22168"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22193">
    <literal><![CDATA[
      T(x,(a(y,z,z) \ u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,u * w) = v5
    ]]></literal>
    <justification jstring="[para(22192(a,1),12297(a,1))].">
      <j1 rule="para" parents="22192 12297"/>
    </justification>
  </clause>

  <clause id="22194">
    <literal><![CDATA[
      T(x,(y * z) * L(u,1 / z,1 / z)) = T(x,(y / (z \ 1)) * u)
    ]]></literal>
    <justification jstring="[para(79(a,1),22184(a,1,2,1,2))].">
      <j1 rule="para" parents="79 22184"/>
    </justification>
  </clause>

  <clause id="22195">
    <literal><![CDATA[
      T(x,(y / (z \ 1)) * u) = T(x,(y * z) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,22154,a(flip),b,22194,a),flip(a)].">
      <j1 rule="hyper" parents="63 22154 22194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22196">
    <literal><![CDATA[
      T(x,(y * z) * (T(u,y * z) * w)) = T(x,u * ((y / (z \ 1)) * w))
    ]]></literal>
    <justification jstring="[hyper(22112,a,22195,a),flip(a)].">
      <j1 rule="hyper" parents="22112 22195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22198">
    <literal><![CDATA[
      T(x,y * ((z / (u \ 1)) * w)) = T(x,y * ((z * u) * w))
    ]]></literal>
    <justification jstring="[hyper(22110,a,22196,a),flip(a)].">
      <j1 rule="hyper" parents="22110 22196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22199">
    <literal><![CDATA[
      T(x,y * (((z \ 1) \ u) * w)) = T(x,y * ((T(u,z) * z) * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,21706,a(flip),b,22198,a)].">
      <j1 rule="hyper" parents="63 21706 22198"/>
    </justification>
  </clause>

  <clause id="22200">
    <literal><![CDATA[
      T(x,y * ((z * (u \ 1)) * w)) = T(x,y * ((z / u) * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,19048,a(flip),b,22198,a),flip(a)].">
      <j1 rule="hyper" parents="63 19048 22198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22201">
    <literal><![CDATA[
      T(x,y * (((z \ 1) * (u \ 1)) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y * ((u * z) \ w)) = v5
    ]]></literal>
    <justification jstring="[para(22200(a,2),22122(a,1))].">
      <j1 rule="para" parents="22200 22122"/>
    </justification>
  </clause>

  <clause id="22202">
    <literal><![CDATA[
      T(x,y * (((z \ 1) \ u) * w)) = T(x,y * ((z * u) * w))
    ]]></literal>
    <justification jstring="[hyper(333,a,21811,a(flip),b,22199,a),flip(a)].">
      <j1 rule="hyper" parents="333 21811 22199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22203">
    <literal><![CDATA[
      T(x,y * (((z \ 1) * u) * w)) = T(x,y * ((z \ u) * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,18896,a(flip),b,22202,a),flip(a)].">
      <j1 rule="hyper" parents="63 18896 22202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22204">
    <literal><![CDATA[
      T(x,a(y,y,z) * (((u \ 1) * w) * v5)) = T(x,(u \ w) * v5)
    ]]></literal>
    <justification jstring="[hyper(333,a,21316,a(flip),b,22203,a),flip(a)].">
      <j1 rule="hyper" parents="333 21316 22203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22205">
    <literal><![CDATA[
      T(x,y * (((z \ 1) / u) * w)) = T(x,y * ((z \ (u \ 1)) * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,22200,a(flip),b,22203,a)].">
      <j1 rule="hyper" parents="63 22200 22203"/>
    </justification>
  </clause>

  <clause id="22206">
    <literal><![CDATA[
      T(x,a(y,y,z) * ((u \ K(w \ 1,(w \ 1) \ (u \ 1))) * v5)) = T(x,(w \ ((u \ 1) / (w \ 1))) * v5)
    ]]></literal>
    <justification jstring="[para(10330(a,2),22204(a,1,2,2,1))].">
      <j1 rule="para" parents="10330 22204"/>
    </justification>
  </clause>

  <clause id="22207">
    <literal><![CDATA[
      T(x,y * ((z \ (u \ 1)) * w)) = T(x,y * ((u * z) \ w))
    ]]></literal>
    <justification jstring="[hyper(22122,a,22205,a),flip(a)].">
      <j1 rule="hyper" parents="22122 22205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22208">
    <literal><![CDATA[
      T(x,y * (((z / u) \ (z \ 1)) * u)) = T(x,y * ((z / u) \ (z \ u)))
    ]]></literal>
    <justification jstring="[para(22015(a,1),22207(a,2,2,2))].">
      <j1 rule="para" parents="22015 22207"/>
    </justification>
  </clause>

  <clause id="22209">
    <literal><![CDATA[
      T(x,y * ((z / u) \ (z \ u))) = T(x,y * ((u / (z * z)) * u))
    ]]></literal>
    <justification jstring="[para(908(a,1),22208(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="908 22208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22210">
    <literal><![CDATA[
      T(x,y * ((z / u) \ (z \ u))) = T(x,y * (u * ((z * z) \ u)))
    ]]></literal>
    <justification jstring="[para(707(a,1),22209(a,2,2,2))].">
      <j1 rule="para" parents="707 22209"/>
    </justification>
  </clause>

  <clause id="22211">
    <literal><![CDATA[
      T(x,y * ((z / u) \ (z \ u))) = T(x,y * (u * (z \ (z \ u))))
    ]]></literal>
    <justification jstring="[hyper(333,a,22165,a(flip),b,22210,a),flip(a)].">
      <j1 rule="hyper" parents="333 22165 22210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22212">
    <literal><![CDATA[
      T(x,y * ((z / u) * (u \ z))) = T(x,y * (z * (u \ (u \ z))))
    ]]></literal>
    <justification jstring="[hyper(63,a,21470,a(flip),b,22211,a)].">
      <j1 rule="hyper" parents="63 21470 22211"/>
    </justification>
  </clause>

  <clause id="22213">
    <literal><![CDATA[
      T(x,y * ((z \ 1) * ((z \ 1) * u))) = T(x,y * ((z * z) \ u))
    ]]></literal>
    <justification jstring="[hyper(22201,a,22160,a),flip(a)].">
      <j1 rule="hyper" parents="22201 22160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22214">
    <literal><![CDATA[
      T(x,y * ((z \ 1) * ((z \ 1) * u))) = T(x,y * (z \ (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(333,a,22159,a(flip),b,22213,a),flip(a)].">
      <j1 rule="hyper" parents="333 22159 22213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22215">
    <literal><![CDATA[
      T(x,(y \ K(y,(z \ 1) * ((z \ 1) * u))) \ (z \ (z \ u))) = T(x,u * (z \ (z \ y)))
    ]]></literal>
    <justification jstring="[hyper(63,a,22127,a,b,22214,a)].">
      <j1 rule="hyper" parents="63 22127 22214"/>
    </justification>
  </clause>

  <clause id="22216">
    <literal><![CDATA[
      T(x,(y \ K(y,z \ ((z \ 1) * u))) \ (z \ (z \ u))) = T(x,u * (z \ (z \ y)))
    ]]></literal>
    <justification jstring="[para(13212(a,1),22215(a,1,2,1,2))].">
      <j1 rule="para" parents="13212 22215"/>
    </justification>
  </clause>

  <clause id="22217">
    <literal><![CDATA[
      T(x,(y \ K(y,(z * z) \ u)) \ (z \ (z \ u))) = T(x,u * (z \ (z \ y)))
    ]]></literal>
    <justification jstring="[para(712(a,1),22216(a,1,2,1,2,2))].">
      <j1 rule="para" parents="712 22216"/>
    </justification>
  </clause>

  <clause id="22218">
    <literal><![CDATA[
      T(x,(y \ K(y,z \ (z \ u))) \ (z \ (z \ u))) = T(x,u * (z \ (z \ y)))
    ]]></literal>
    <justification jstring="[para(13124(a,1),22217(a,1,2,1,2))].">
      <j1 rule="para" parents="13124 22217"/>
    </justification>
  </clause>

  <clause id="22219">
    <literal><![CDATA[
      T(x,K(y \ (y \ z),u) * (u * (y \ (y \ z)))) = T(x,z * (y \ (y \ u)))
    ]]></literal>
    <justification jstring="[hyper(18006,a,22218,a)].">
      <j1 rule="hyper" parents="18006 22218"/>
    </justification>
  </clause>

  <clause id="22220">
    <literal><![CDATA[
      T(x,(y \ (y \ z)) * u) = T(x,z * (y \ (y \ u)))
    ]]></literal>
    <justification jstring="[para(4201(a,1),22219(a,1,2))].">
      <j1 rule="para" parents="4201 22219"/>
    </justification>
  </clause>

  <clause id="22221">
    <literal><![CDATA[
      T(x,a(y,y,z) * ((u \ K(w \ 1,w / u)) * v5)) = T(x,(w \ ((u \ 1) / (w \ 1))) * v5)
    ]]></literal>
    <justification jstring="[para(13245(a,1),22206(a,1,2,2,1,2))].">
      <j1 rule="para" parents="13245 22206"/>
    </justification>
  </clause>

  <clause id="22222">
    <literal><![CDATA[
      T(x,a(y,y,z) * ((u \ K(w \ 1,u \ w)) * v5)) = T(x,(w \ ((u \ 1) / (w \ 1))) * v5)
    ]]></literal>
    <justification jstring="[para(5816(a,1),22221(a,1,2,2,1,2))].">
      <j1 rule="para" parents="5816 22221"/>
    </justification>
  </clause>

  <clause id="22223">
    <literal><![CDATA[
      T(x,a(y,y,z) * (T(u \ 1,w) * v5)) = T(x,(w \ ((u \ 1) / (w \ 1))) * v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,21816,a(flip),b,22222,a)].">
      <j1 rule="hyper" parents="63 21816 22222"/>
    </justification>
  </clause>

  <clause id="22224">
    <literal><![CDATA[
      T(x,(y \ ((z \ 1) / (y \ 1))) * u) = T(x,T(z \ 1,y) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,21316,a(flip),b,22223,a),flip(a)].">
      <j1 rule="hyper" parents="63 21316 22223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22225">
    <literal><![CDATA[
      T(x,(y \ ((z \ 1) / (y \ 1))) * u) = T(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(333,a,18194,a(flip),b,22224,a),flip(a)].">
      <j1 rule="hyper" parents="333 18194 22224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22226">
    <literal><![CDATA[
      T(x,(a(y,z,z) \ ((a(y,z,z) \ 1) \ (u \ 1))) * w) = T(x,T(u,a(y,z,z)) \ w)
    ]]></literal>
    <justification jstring="[para(14328(a,1),22225(a,1,2,1,2))].">
      <j1 rule="para" parents="14328 22225"/>
    </justification>
  </clause>

  <clause id="22227">
    <literal><![CDATA[
      T(x,((a(y,z,z) \ 1) \ (u \ 1)) * w) = T(x,T(u,a(y,z,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(22193,a,22226,a)].">
      <j1 rule="hyper" parents="22193 22226"/>
    </justification>
  </clause>

  <clause id="22228">
    <literal><![CDATA[
      T(x,(y * (a(z,u,u) \ 1)) \ w) = T(x,T(y,a(z,u,u)) \ w)
    ]]></literal>
    <justification jstring="[hyper(22191,a,22227,a)].">
      <j1 rule="hyper" parents="22191 22227"/>
    </justification>
  </clause>

  <clause id="22229">
    <literal><![CDATA[
      T(x,T(y,a(z,u,u)) \ w) = T(x,(a(z,u,u) / y) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,21433,a(flip),b,22228,a),flip(a)].">
      <j1 rule="hyper" parents="63 21433 22228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22230">
    <literal><![CDATA[
      T(x,T(y,a(z,u,u)) \ w) = T(x,(y \ a(z,u,u)) * w)
    ]]></literal>
    <justification jstring="[hyper(333,a,17948,a(flip),b,22229,a),flip(a)].">
      <j1 rule="hyper" parents="333 17948 22229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22231">
    <literal><![CDATA[
      T(x,(y \ a(z,u,u)) * w) = T(x,y \ w)
    ]]></literal>
    <justification jstring="[hyper(17927,a,22230,a),flip(a)].">
      <j1 rule="hyper" parents="17927 22230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22232">
    <literal><![CDATA[
      T(x,y \ (T(z \ u,z) \ w)) = T(x,(y \ a(v5,v6,v6)) * ((u / z) \ w))
    ]]></literal>
    <justification jstring="[hyper(333,a,21708,a,b,22231,a)].">
      <j1 rule="hyper" parents="333 21708 22231"/>
    </justification>
  </clause>

  <clause id="22233">
    <literal><![CDATA[
      T(x,y \ (T(z \ u,z) \ w)) = T(x,(y \ a(v5,v6,v6)) * ((z / u) * w))
    ]]></literal>
    <justification jstring="[hyper(333,a,21470,a(flip),b,22232,a),flip(a)].">
      <j1 rule="hyper" parents="333 21470 22232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22234">
    <literal><![CDATA[
      T(x,y \ (T(z \ u,z) \ w)) = T(x,y \ ((z / u) * w))
    ]]></literal>
    <justification jstring="[hyper(333,a,22231,a(flip),b,22233,a),flip(a)].">
      <j1 rule="hyper" parents="333 22231 22233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22235">
    <literal><![CDATA[
      T(x,y \ ((z / u) \ w)) = T(x,y \ ((u / z) * w))
    ]]></literal>
    <justification jstring="[hyper(21709,a,22234,a)].">
      <j1 rule="hyper" parents="21709 22234"/>
    </justification>
  </clause>

  <clause id="22236">
    <literal><![CDATA[
      T(T(x,y * ((z / u) * (u \ z))),(z / u) \ ((z / u) \ w)) = T(T(x,y * (u \ (z / (z / u)))),w)
    ]]></literal>
    <justification jstring="[para(110(a,1),22171(a,2,1,2,2,2,2))].">
      <j1 rule="para" parents="110 22171"/>
    </justification>
  </clause>

  <clause id="22237">
    <literal><![CDATA[
      T(T(x,y * ((z / u) * (u \ z))),(z / u) \ ((z / u) \ w)) = T(T(x,y * K(u \ z,u)),w)
    ]]></literal>
    <justification jstring="[para(4175(a,1),22236(a,2,1,2,2))].">
      <j1 rule="para" parents="4175 22236"/>
    </justification>
  </clause>

  <clause id="22238">
    <literal><![CDATA[
      T(T(x,y * ((z / u) * (u \ z))),(z / u) \ ((z / u) \ w)) = T(T(x,K(z,u) * y),w)
    ]]></literal>
    <justification jstring="[para(15619(a,1),22237(a,2,1))].">
      <j1 rule="para" parents="15619 22237"/>
    </justification>
  </clause>

  <clause id="22239">
    <literal><![CDATA[
      T(T(x,y * (z * (u \ (u \ z)))),(z / u) \ ((z / u) \ w)) = T(T(x,K(z,u) * y),w)
    ]]></literal>
    <justification jstring="[para(22212(a,1),22238(a,1,1))].">
      <j1 rule="para" parents="22212 22238"/>
    </justification>
  </clause>

  <clause id="22240">
    <literal><![CDATA[
      T(T(x,y * (z * (u \ (u \ z)))),(z / u) \ ((u / z) * w)) = T(T(x,K(z,u) * y),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,22235,a(flip),b,22239,a)].">
      <j1 rule="hyper" parents="63 22235 22239"/>
    </justification>
  </clause>

  <clause id="22241">
    <literal><![CDATA[
      T(T(x,y * (z * (u \ (u \ z)))),(u / z) * ((u / z) * w)) = T(T(x,K(z,u) * y),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,21432,a(flip),b,22240,a)].">
      <j1 rule="hyper" parents="63 21432 22240"/>
    </justification>
  </clause>

  <clause id="22242">
    <literal><![CDATA[
      T(T(x,y * (z * z)),u \ (u \ ((u / z) * ((u / z) * w)))) = T(T(x,K(z,u) * y),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,22172,a(flip),b,22241,a)].">
      <j1 rule="hyper" parents="63 22172 22241"/>
    </justification>
  </clause>

  <clause id="22243">
    <literal><![CDATA[
      T(T(x,y),(z \ (z \ ((z / u) * ((z / u) * w)))) * (u * u)) = T(T(x,K(u,z) * y),w)
    ]]></literal>
    <justification jstring="[hyper(15791,a,22242,a)].">
      <j1 rule="hyper" parents="15791 22242"/>
    </justification>
  </clause>

  <clause id="22244">
    <literal><![CDATA[
      T(T(x,y),((z / u) * ((z / u) * w)) * (z \ (z \ (u * u)))) = T(T(x,K(u,z) * y),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,22220,a(flip),b,22243,a)].">
      <j1 rule="hyper" parents="63 22220 22243"/>
    </justification>
  </clause>

  <clause id="22245">
    <literal><![CDATA[
      T(T(x,y),z * ((u / w) * ((u / w) * (u \ (u \ (w * w)))))) = T(T(x,K(w,u) * y),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,21806,a(flip),b,22244,a)].">
      <j1 rule="hyper" parents="63 21806 22244"/>
    </justification>
  </clause>

  <clause id="22246">
    <literal><![CDATA[
      T(T(x,y),z * ((u \ w) * ((u \ w) * (w \ (w \ (u * u)))))) = T(T(x,K(u,w) * y),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,19044,a(flip),b,22245,a)].">
      <j1 rule="hyper" parents="63 19044 22245"/>
    </justification>
  </clause>

  <clause id="22247">
    <literal><![CDATA[
      T(T(T(x,y),z),T(T(x,y),u) * ((w \ v5) * ((w \ v5) * (v5 \ (v5 \ (w * w)))))) = T(T(T(x,K(w,v5) * y),T(x,y)),z)
    ]]></literal>
    <justification jstring="[para(22246(a,1),7402(a,2,1))].">
      <j1 rule="para" parents="22246 7402"/>
    </justification>
  </clause>

  <clause id="22248">
    <literal><![CDATA[
      T(T(x,L(K(y,z) \ K(u,w),v5,v6) * K(w,u)),v7 * ((y \ z) * ((y \ z) * (z \ (z \ (y * y)))))) = T(T(x,(K(w,u) / K(y,z)) * L(K(y,z) * K(u,w),v5,v6)),v7)
    ]]></literal>
    <justification jstring="[para(17231(a,2),22246(a,2,1,2))].">
      <j1 rule="para" parents="17231 22246"/>
    </justification>
  </clause>

  <clause id="22249">
    <literal><![CDATA[
      T(T(T(x,y),K(z,u) * w),T(T(x,y),v5)) = T(T(T(x,K(z,u) * y),T(x,y)),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,22246,a(flip),b,22247,a)].">
      <j1 rule="hyper" parents="63 22246 22247"/>
    </justification>
  </clause>

  <clause id="22250">
    <literal><![CDATA[
      T(T(x,K(y,z) * u),w) = T(T(x,u),K(y,z) * w)
    ]]></literal>
    <justification jstring="[hyper(40,a,3629,a,b,22249,a)].">
      <j1 rule="hyper" parents="40 3629 22249"/>
    </justification>
  </clause>

  <clause id="22253">
    <literal><![CDATA[
      T(T(x,L(K(y,z) * K(u,w),v5,v6) * K(w,u)),v7 * ((z \ y) * ((z \ y) * (y \ (y \ (z * z)))))) = T(T(x,(K(w,u) / K(z,y)) * L(K(z,y) * K(u,w),v5,v6)),v7)
    ]]></literal>
    <justification jstring="[para(4567(a,1),22248(a,1,1,2,1,1))].">
      <j1 rule="para" parents="4567 22248"/>
    </justification>
  </clause>

  <clause id="22254">
    <literal><![CDATA[
      T(T(x,K(y,z) * L(K(z,y) * K(u,w),v5,v6)),v7 * ((w \ u) * ((w \ u) * (u \ (u \ (w * w)))))) = T(T(x,(K(y,z) / K(w,u)) * L(K(w,u) * K(z,y),v5,v6)),v7)
    ]]></literal>
    <justification jstring="[para(6114(a,1),22253(a,1,1,2))].">
      <j1 rule="para" parents="6114 22253"/>
    </justification>
  </clause>

  <clause id="22255">
    <literal><![CDATA[
      T(T(x,L((K(y,z) * K(u,w)) * K(z,y),v5,v6)),v7 * ((w \ u) * ((w \ u) * (u \ (u \ (w * w)))))) = T(T(x,(K(z,y) / K(w,u)) * L(K(w,u) * K(y,z),v5,v6)),v7)
    ]]></literal>
    <justification jstring="[para(22142(a,2),22254(a,1,1))].">
      <j1 rule="para" parents="22142 22254"/>
    </justification>
  </clause>

  <clause id="22256">
    <literal><![CDATA[
      T(T(x,L(K(y,z),u,w)),v5 * ((z \ y) * ((z \ y) * (y \ (y \ (z * z)))))) = T(T(x,(K(v6,v7) / K(z,y)) * L(K(z,y) * K(v7,v6),u,w)),v5)
    ]]></literal>
    <justification jstring="[para(15491(a,1),22255(a,1,1,2,1))].">
      <j1 rule="para" parents="15491 22255"/>
    </justification>
  </clause>

  <clause id="22258">
    <literal><![CDATA[
      T(T(x,K(y,z)),u * ((z \ y) * ((z \ y) * (y \ (y \ (z * z)))))) = T(T(x,(K(w,v5) / K(z,y)) * L(K(z,y) * K(v5,w),v6,v7)),u)
    ]]></literal>
    <justification jstring="[para(17576(a,1),22256(a,1,1))].">
      <j1 rule="para" parents="17576 22256"/>
    </justification>
  </clause>

  <clause id="22259">
    <literal><![CDATA[
      T(T(x,K(y,z)),u * ((y \ z) * ((y \ z) * (z \ (z \ (y * y)))))) = T(T(x,(K(w,v5) / K(y,z)) * L(K(y,z) * K(v5,w),v6,v7)),u)
    ]]></literal>
    <justification jstring="[para(6840(a,1),22258(a,1,1))].">
      <j1 rule="para" parents="6840 22258"/>
    </justification>
  </clause>

  <clause id="22261">
    <literal><![CDATA[
      T(T(x,(K(y,z) / K(u,w)) * L(K(u,w) * K(z,y),v5,v6)),v7) = T(T(x,K(u,w) * K(u,w)),v7)
    ]]></literal>
    <justification jstring="[hyper(63,a,22246,a(flip),b,22259,a),flip(a)].">
      <j1 rule="hyper" parents="63 22246 22259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22262">
    <literal><![CDATA[
      T(T(x,(K(y,z) / K(u,w)) * L(K(u,w) * K(z,y),v5,v6)),v7) = T(x,v7)
    ]]></literal>
    <justification jstring="[para(15708(a,1),22261(a,2,1))].">
      <j1 rule="para" parents="15708 22261"/>
    </justification>
  </clause>

  <clause id="22263">
    <literal><![CDATA[
      T(T(x,(K(y,z) * K(u,w)) * L(K(w,u) * K(z,y),v5,v6)),v7) = T(x,v7)
    ]]></literal>
    <justification jstring="[para(5994(a,1),22262(a,1,1,2,1))].">
      <j1 rule="para" parents="5994 22262"/>
    </justification>
  </clause>

  <clause id="22264">
    <literal><![CDATA[
      T(T(x,K(y,z) * (K(u,w) * L(K(z,y) * K(w,u),v5,v6))),v7) = T(x,v7)
    ]]></literal>
    <justification jstring="[para(17979(a,1),22263(a,1,1))].">
      <j1 rule="para" parents="17979 22263"/>
    </justification>
  </clause>

  <clause id="22265">
    <literal><![CDATA[
      T(T(x,K(y,z) * L(K(u,w) * K(z,y),v5,v6)),K(w,u) * v7) = T(x,v7)
    ]]></literal>
    <justification jstring="[hyper(63,a,22250,a(flip),b,22264,a)].">
      <j1 rule="hyper" parents="63 22250 22264"/>
    </justification>
  </clause>

  <clause id="22266">
    <literal><![CDATA[
      T(T(x,L(K(y,z),u,w)),K(z,y) * v5) = T(x,v5)
    ]]></literal>
    <justification jstring="[para(2457(a,1),22265(a,1,1,2))].">
      <j1 rule="para" parents="2457 22265"/>
    </justification>
  </clause>

  <clause id="22267">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,y) * u) = T(x,u)
    ]]></literal>
    <justification jstring="[para(371(a,1),22266(a,1,1,2))].">
      <j1 rule="para" parents="371 22266"/>
    </justification>
  </clause>

  <clause id="22268">
    <literal><![CDATA[
      T(x,L(y,z,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(21962,a,22267,a)].">
      <j1 rule="hyper" parents="21962 22267"/>
    </justification>
  </clause>

  <clause id="22289">
    <literal><![CDATA[
      a(x,y,K(z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(122,a,22268,a(flip),b,13769,a),flip(a)].">
      <j1 rule="hyper" parents="122 22268 13769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22306">
    <literal><![CDATA[
      a(K(x,y),z,u) = 1
    ]]></literal>
    <justification jstring="[hyper(17710,a,22289,a)].">
      <j1 rule="hyper" parents="17710 22289"/>
    </justification>
  </clause>

  <clause id="22307">
    <literal><![CDATA[
      $F
    ]]></literal>
    <attribute><![CDATA[
      answer("aK1")
    ]]></attribute>
    <justification jstring="[resolve(22306,a,64,a)].">
      <j1 rule="resolve" parents="22306 64"/>
    </justification>
  </clause>

</proof>

</proofs>
